\hypertarget{group__PLASMA__Complex64__t}{\section{Simple Interface -\/ Double Complex}
\label{group__PLASMA__Complex64__t}\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}}
}
\subsection*{Functions/\-Subroutines}
\begin{DoxyCompactItemize}
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga6733ad2b79f186348ba47778e2e26fae_ga6733ad2b79f186348ba47778e2e26fae}{P\-L\-A\-S\-M\-A\-\_\-zcgels} (P\-L\-A\-S\-M\-A\-\_\-enum trans, int M, int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$X, int L\-D\-X, int $\ast$I\-T\-E\-R)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gab372ccb64517ddb8e0f7ea66088489a9_gab372ccb64517ddb8e0f7ea66088489a9}{P\-L\-A\-S\-M\-A\-\_\-zcgesv} (int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, int $\ast$I\-P\-I\-V, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$X, int L\-D\-X, int $\ast$I\-T\-E\-R)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga11ee4c71901e8675d5423cfceecaaf43_ga11ee4c71901e8675d5423cfceecaaf43}{P\-L\-A\-S\-M\-A\-\_\-zcposv} (P\-L\-A\-S\-M\-A\-\_\-enum uplo, int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$X, int L\-D\-X, int $\ast$I\-T\-E\-R)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gaba15b4f438d8d2fe41f2c38820d043ef_gaba15b4f438d8d2fe41f2c38820d043ef}{P\-L\-A\-S\-M\-A\-\_\-zcungesv} (P\-L\-A\-S\-M\-A\-\_\-enum trans, int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$X, int L\-D\-X, int $\ast$I\-T\-E\-R)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga9b52418f313c60c7f11f320fdfa262a7_ga9b52418f313c60c7f11f320fdfa262a7}{P\-L\-A\-S\-M\-A\-\_\-zgebrd} (int M, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, double $\ast$D, double $\ast$E, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T)
\item 
\hypertarget{group__PLASMA__Complex64__t_ga5fc5e88c0c1e0175b95415d2e4b20514_ga5fc5e88c0c1e0175b95415d2e4b20514}{int {\bfseries L\-A\-P\-A\-C\-K\-\_\-\-G\-L\-O\-B\-A\-L} (zlacn2, Z\-L\-A\-C\-N2)}\label{group__PLASMA__Complex64__t_ga5fc5e88c0c1e0175b95415d2e4b20514_ga5fc5e88c0c1e0175b95415d2e4b20514}

\item 
int \hyperlink{group__PLASMA__Complex64__t_ga8990facf0cb04df2a107c02e5dd5f3f7_ga8990facf0cb04df2a107c02e5dd5f3f7}{P\-L\-A\-S\-M\-A\-\_\-zgelqf} (int M, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga8e8b7d834eb0ad99766799bcfa48d4b1_ga8e8b7d834eb0ad99766799bcfa48d4b1}{P\-L\-A\-S\-M\-A\-\_\-zgelqs} (int M, int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga37e31dd7208585a1720db61e38e31a55_ga37e31dd7208585a1720db61e38e31a55}{P\-L\-A\-S\-M\-A\-\_\-zgels} (P\-L\-A\-S\-M\-A\-\_\-enum trans, int M, int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga1a0f8d759e535f9947ae11baa0af6fa3_ga1a0f8d759e535f9947ae11baa0af6fa3}{P\-L\-A\-S\-M\-A\-\_\-zgemm} (P\-L\-A\-S\-M\-A\-\_\-enum trans\-A, P\-L\-A\-S\-M\-A\-\_\-enum trans\-B, int M, int N, int K, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t alpha, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t beta, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$C, int L\-D\-C)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga9d4fae8697b364c384faa7480aea3118_ga9d4fae8697b364c384faa7480aea3118}{P\-L\-A\-S\-M\-A\-\_\-zgeqrf} (int M, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gaaded5cbc1a55a5d1cc6a231b8da07bf0_gaaded5cbc1a55a5d1cc6a231b8da07bf0}{P\-L\-A\-S\-M\-A\-\_\-zgeqrs} (int M, int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga94397d6fba523c946f1e56cfe9aa967d_ga94397d6fba523c946f1e56cfe9aa967d}{P\-L\-A\-S\-M\-A\-\_\-zgesv} (int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, int $\ast$I\-P\-I\-V, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga27916109c8ac4bed6d101fcb98b27fad_ga27916109c8ac4bed6d101fcb98b27fad}{P\-L\-A\-S\-M\-A\-\_\-zgesv\-\_\-incpiv} (int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-L, int $\ast$I\-P\-I\-V, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga36fc556f67632e00105090a60657dab2_ga36fc556f67632e00105090a60657dab2}{P\-L\-A\-S\-M\-A\-\_\-zgesvd} (P\-L\-A\-S\-M\-A\-\_\-enum jobu, P\-L\-A\-S\-M\-A\-\_\-enum jobvt, int M, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, double $\ast$S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$U, int L\-D\-U, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$V\-T, int L\-D\-V\-T, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga03449aa4e83b2f2223dad281d122697d_ga03449aa4e83b2f2223dad281d122697d}{P\-L\-A\-S\-M\-A\-\_\-zgetrf} (int M, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, int $\ast$I\-P\-I\-V)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga085b5e62180512c7c603e72a9092ad8d_ga085b5e62180512c7c603e72a9092ad8d}{P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv} (int M, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-L, int $\ast$I\-P\-I\-V)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga96b45d431296d17561924b09a770ce17_ga96b45d431296d17561924b09a770ce17}{P\-L\-A\-S\-M\-A\-\_\-zgetri} (int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, int $\ast$I\-P\-I\-V)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gad7b041e52be07ced12ad09ca2c51ddc6_gad7b041e52be07ced12ad09ca2c51ddc6}{P\-L\-A\-S\-M\-A\-\_\-zgetrs} (P\-L\-A\-S\-M\-A\-\_\-enum trans, int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, int $\ast$I\-P\-I\-V, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga421d402c25832837b8247720d1ce79d5_ga421d402c25832837b8247720d1ce79d5}{P\-L\-A\-S\-M\-A\-\_\-zgetrs\-\_\-incpiv} (P\-L\-A\-S\-M\-A\-\_\-enum trans, int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-L, int $\ast$I\-P\-I\-V, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gad148e141c13feede49709370caea9c2a_gad148e141c13feede49709370caea9c2a}{P\-L\-A\-S\-M\-A\-\_\-zheev} (P\-L\-A\-S\-M\-A\-\_\-enum jobz, P\-L\-A\-S\-M\-A\-\_\-enum uplo, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, double $\ast$W, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$Q, int L\-D\-Q)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gad7de537e69c66566cc4e8e0b9fbfdb87_gad7de537e69c66566cc4e8e0b9fbfdb87}{P\-L\-A\-S\-M\-A\-\_\-zheevd} (P\-L\-A\-S\-M\-A\-\_\-enum jobz, P\-L\-A\-S\-M\-A\-\_\-enum uplo, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, double $\ast$W, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$Q, int L\-D\-Q)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga387eb7a21f8b3d03aec26324255e7510_ga387eb7a21f8b3d03aec26324255e7510}{P\-L\-A\-S\-M\-A\-\_\-zhegst} (P\-L\-A\-S\-M\-A\-\_\-enum itype, P\-L\-A\-S\-M\-A\-\_\-enum uplo, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gaec004491cb00c99f63f9604c84ef8f43_gaec004491cb00c99f63f9604c84ef8f43}{P\-L\-A\-S\-M\-A\-\_\-zhegv} (P\-L\-A\-S\-M\-A\-\_\-enum itype, P\-L\-A\-S\-M\-A\-\_\-enum jobz, P\-L\-A\-S\-M\-A\-\_\-enum uplo, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B, double $\ast$W, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$Q, int L\-D\-Q)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga6ee549df75bf7738aa6066c564ff72a9_ga6ee549df75bf7738aa6066c564ff72a9}{P\-L\-A\-S\-M\-A\-\_\-zhegvd} (P\-L\-A\-S\-M\-A\-\_\-enum itype, P\-L\-A\-S\-M\-A\-\_\-enum jobz, P\-L\-A\-S\-M\-A\-\_\-enum uplo, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B, double $\ast$W, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$Q, int L\-D\-Q)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gad53a9ae69e0ff46c3859f19c16b97081_gad53a9ae69e0ff46c3859f19c16b97081}{P\-L\-A\-S\-M\-A\-\_\-zhemm} (P\-L\-A\-S\-M\-A\-\_\-enum side, P\-L\-A\-S\-M\-A\-\_\-enum uplo, int M, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t alpha, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t beta, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$C, int L\-D\-C)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga1086284f7bd6db0de2341eeaa3a3e655_ga1086284f7bd6db0de2341eeaa3a3e655}{P\-L\-A\-S\-M\-A\-\_\-zher2k} (P\-L\-A\-S\-M\-A\-\_\-enum uplo, P\-L\-A\-S\-M\-A\-\_\-enum trans, int N, int K, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t alpha, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B, double beta, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$C, int L\-D\-C)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga37897923ff4fb613bbd5a69a58b12fb8_ga37897923ff4fb613bbd5a69a58b12fb8}{P\-L\-A\-S\-M\-A\-\_\-zherk} (P\-L\-A\-S\-M\-A\-\_\-enum uplo, P\-L\-A\-S\-M\-A\-\_\-enum trans, int N, int K, double alpha, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, double beta, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$C, int L\-D\-C)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gadeaa16b417f2033a10685c130db081fb_gadeaa16b417f2033a10685c130db081fb}{P\-L\-A\-S\-M\-A\-\_\-zhetrd} (P\-L\-A\-S\-M\-A\-\_\-enum jobz, P\-L\-A\-S\-M\-A\-\_\-enum uplo, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, double $\ast$D, double $\ast$E, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$Q, int L\-D\-Q)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga8502c982b63153d2a7c11c05fe51cd39_ga8502c982b63153d2a7c11c05fe51cd39}{P\-L\-A\-S\-M\-A\-\_\-zlacpy} (P\-L\-A\-S\-M\-A\-\_\-enum uplo, int M, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B)
\item 
double \hyperlink{group__PLASMA__Complex64__t_ga89327462733d7b77d403e9612954474d_ga89327462733d7b77d403e9612954474d}{P\-L\-A\-S\-M\-A\-\_\-zlange} (P\-L\-A\-S\-M\-A\-\_\-enum norm, int M, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, double $\ast$work)
\item 
double \hyperlink{group__PLASMA__Complex64__t_ga3667b32ec418aa44fe1e28b78a670af6_ga3667b32ec418aa44fe1e28b78a670af6}{P\-L\-A\-S\-M\-A\-\_\-zlanhe} (P\-L\-A\-S\-M\-A\-\_\-enum norm, P\-L\-A\-S\-M\-A\-\_\-enum uplo, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, double $\ast$work)
\item 
double \hyperlink{group__PLASMA__Complex64__t_ga56ed091feed59f955ba15b8c6204e06a_ga56ed091feed59f955ba15b8c6204e06a}{P\-L\-A\-S\-M\-A\-\_\-zlansy} (P\-L\-A\-S\-M\-A\-\_\-enum norm, P\-L\-A\-S\-M\-A\-\_\-enum uplo, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, double $\ast$work)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gad41de0032d2290e448cfc67683dc01bb_gad41de0032d2290e448cfc67683dc01bb}{P\-L\-A\-S\-M\-A\-\_\-zlaset} (P\-L\-A\-S\-M\-A\-\_\-enum uplo, int M, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t alpha, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t beta, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga33f553c60d1f95a0d7da9e7e17e2a160_ga33f553c60d1f95a0d7da9e7e17e2a160}{P\-L\-A\-S\-M\-A\-\_\-zlaswp} (int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, int K1, int K2, int $\ast$I\-P\-I\-V, int I\-N\-C\-X)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gae7d7a89512a3d4c6e733de30a25dc5cc_gae7d7a89512a3d4c6e733de30a25dc5cc}{P\-L\-A\-S\-M\-A\-\_\-zlaswpc} (int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, int K1, int K2, int $\ast$I\-P\-I\-V, int I\-N\-C\-X)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga0e1f064db19e3855c590172274fbdf43_ga0e1f064db19e3855c590172274fbdf43}{P\-L\-A\-S\-M\-A\-\_\-zlauum} (P\-L\-A\-S\-M\-A\-\_\-enum uplo, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga3a50559a69450b4f13a23c4af092c60e_ga3a50559a69450b4f13a23c4af092c60e}{P\-L\-A\-S\-M\-A\-\_\-zplghe} (double bump, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, unsigned long long int seed)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga065c2bc2190fc079035e1de4d16e4e60_ga065c2bc2190fc079035e1de4d16e4e60}{P\-L\-A\-S\-M\-A\-\_\-zplgsy} (P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t bump, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, unsigned long long int seed)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gaed78cffc7c2835c485ef7c8e3761d127_gaed78cffc7c2835c485ef7c8e3761d127}{P\-L\-A\-S\-M\-A\-\_\-zplrnt} (int M, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, unsigned long long int seed)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gaed71622155778ea4372e34879184e742_gaed71622155778ea4372e34879184e742}{P\-L\-A\-S\-M\-A\-\_\-zposv} (P\-L\-A\-S\-M\-A\-\_\-enum uplo, int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga850a6c9da7c5632d160b28f211cdf2eb_ga850a6c9da7c5632d160b28f211cdf2eb}{P\-L\-A\-S\-M\-A\-\_\-zpotrf} (P\-L\-A\-S\-M\-A\-\_\-enum uplo, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga6dd563144dd8c7f29a58659f220f44a0_ga6dd563144dd8c7f29a58659f220f44a0}{P\-L\-A\-S\-M\-A\-\_\-zpotri} (P\-L\-A\-S\-M\-A\-\_\-enum uplo, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gafa3392d835a508f57674c601c46eb331_gafa3392d835a508f57674c601c46eb331}{P\-L\-A\-S\-M\-A\-\_\-zpotrs} (P\-L\-A\-S\-M\-A\-\_\-enum uplo, int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga78d0974b51b7d019e0606422b3292b46_ga78d0974b51b7d019e0606422b3292b46}{P\-L\-A\-S\-M\-A\-\_\-zsymm} (P\-L\-A\-S\-M\-A\-\_\-enum side, P\-L\-A\-S\-M\-A\-\_\-enum uplo, int M, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t alpha, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t beta, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$C, int L\-D\-C)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga575230c6f1629fabf7ba151a09e4c7a7_ga575230c6f1629fabf7ba151a09e4c7a7}{P\-L\-A\-S\-M\-A\-\_\-zsyr2k} (P\-L\-A\-S\-M\-A\-\_\-enum uplo, P\-L\-A\-S\-M\-A\-\_\-enum trans, int N, int K, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t alpha, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t beta, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$C, int L\-D\-C)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gaae2f934da463e7256c82500587c3042b_gaae2f934da463e7256c82500587c3042b}{P\-L\-A\-S\-M\-A\-\_\-zsyrk} (P\-L\-A\-S\-M\-A\-\_\-enum uplo, P\-L\-A\-S\-M\-A\-\_\-enum trans, int N, int K, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t alpha, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t beta, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$C, int L\-D\-C)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga9d25baa9dfdb84cd69270558338ce9b1_ga9d25baa9dfdb84cd69270558338ce9b1}{P\-L\-A\-S\-M\-A\-\_\-ztrmm} (P\-L\-A\-S\-M\-A\-\_\-enum side, P\-L\-A\-S\-M\-A\-\_\-enum uplo, P\-L\-A\-S\-M\-A\-\_\-enum trans\-A, P\-L\-A\-S\-M\-A\-\_\-enum diag, int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t alpha, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga36cf60d55716c7ab0c2fba7fb8833e2c_ga36cf60d55716c7ab0c2fba7fb8833e2c}{P\-L\-A\-S\-M\-A\-\_\-ztrsm} (P\-L\-A\-S\-M\-A\-\_\-enum side, P\-L\-A\-S\-M\-A\-\_\-enum uplo, P\-L\-A\-S\-M\-A\-\_\-enum trans\-A, P\-L\-A\-S\-M\-A\-\_\-enum diag, int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t alpha, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gac1801a329693ff71b7ee1bd772f76994_gac1801a329693ff71b7ee1bd772f76994}{P\-L\-A\-S\-M\-A\-\_\-ztrsmpl} (int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-L, int $\ast$I\-P\-I\-V, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gadc613ba744f045286d0869bbbf6765ac_gadc613ba744f045286d0869bbbf6765ac}{P\-L\-A\-S\-M\-A\-\_\-ztrsmrv} (P\-L\-A\-S\-M\-A\-\_\-enum side, P\-L\-A\-S\-M\-A\-\_\-enum uplo, P\-L\-A\-S\-M\-A\-\_\-enum trans\-A, P\-L\-A\-S\-M\-A\-\_\-enum diag, int N, int N\-R\-H\-S, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t alpha, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$B, int L\-D\-B)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gaf634d0dec7f2b59a571b5aafa19892d1_gaf634d0dec7f2b59a571b5aafa19892d1}{P\-L\-A\-S\-M\-A\-\_\-ztrtri} (P\-L\-A\-S\-M\-A\-\_\-enum uplo, P\-L\-A\-S\-M\-A\-\_\-enum diag, int N, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga8d2c7940bdd249a0a1e633b0ac6d107c_ga8d2c7940bdd249a0a1e633b0ac6d107c}{P\-L\-A\-S\-M\-A\-\_\-zunglq} (int M, int N, int K, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$Q, int L\-D\-Q)
\item 
int \hyperlink{group__PLASMA__Complex64__t_gafedf859d9373a2738b24e5780360ec5b_gafedf859d9373a2738b24e5780360ec5b}{P\-L\-A\-S\-M\-A\-\_\-zungqr} (int M, int N, int K, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$Q, int L\-D\-Q)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga2c015740671fa101298fb9841b25f5d2_ga2c015740671fa101298fb9841b25f5d2}{P\-L\-A\-S\-M\-A\-\_\-zunmlq} (P\-L\-A\-S\-M\-A\-\_\-enum side, P\-L\-A\-S\-M\-A\-\_\-enum trans, int M, int N, int K, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$C, int L\-D\-C)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga2a00379e9ae15c89c8a21d7dfa945e8f_ga2a00379e9ae15c89c8a21d7dfa945e8f}{P\-L\-A\-S\-M\-A\-\_\-zunmqr} (P\-L\-A\-S\-M\-A\-\_\-enum side, P\-L\-A\-S\-M\-A\-\_\-enum trans, int M, int N, int K, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$A, int L\-D\-A, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$desc\-T, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$C, int L\-D\-C)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga54817e0733e678bcdfdfeaa76ab486f6_ga54817e0733e678bcdfdfeaa76ab486f6}{P\-L\-A\-S\-M\-A\-\_\-z\-Lapack\-\_\-to\-\_\-\-Tile} (P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$Af77, int L\-D\-A, \hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$A)
\item 
int \hyperlink{group__PLASMA__Complex64__t_ga8df0b9fdc5537a648d7544b528c9e6e3_ga8df0b9fdc5537a648d7544b528c9e6e3}{P\-L\-A\-S\-M\-A\-\_\-z\-Tile\-\_\-to\-\_\-\-Lapack} (\hyperlink{structplasma__desc__t}{P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$A, P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$Af77, int L\-D\-A)
\end{DoxyCompactItemize}


\subsection{Detailed Description}
This is the group of double complex functions using the simple user interface. 

\subsection{Function/\-Subroutine Documentation}
\hypertarget{group__PLASMA__Complex64__t_ga6733ad2b79f186348ba47778e2e26fae_ga6733ad2b79f186348ba47778e2e26fae}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zcgels@{P\-L\-A\-S\-M\-A\-\_\-zcgels}}
\index{P\-L\-A\-S\-M\-A\-\_\-zcgels@{P\-L\-A\-S\-M\-A\-\_\-zcgels}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zcgels}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zcgels (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{X, }
\item[{int}]{L\-D\-X, }
\item[{int $\ast$}]{I\-T\-E\-R}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga6733ad2b79f186348ba47778e2e26fae_ga6733ad2b79f186348ba47778e2e26fae}
P\-L\-A\-S\-M\-A\-\_\-zcgels -\/ Solves overdetermined or underdetermined linear systems involving an M-\/by-\/\-N matrix A using the Q\-R or the L\-Q factorization of A. It is assumed that A has full rank. The following options are provided\-:

\subsection*{trans = Plasma\-No\-Trans and M $>$= N\-: find the least squares solution of an overdetermined}

system, i.\-e., solve the least squares problem\-: minimize $|$$|$ B -\/ A$\ast$\-X $|$$|$.

\subsection*{trans = Plasma\-No\-Trans and M $<$ N\-: find the minimum norm solution of an underdetermined}

system A $\ast$ X = B.

Several right hand side vectors B and solution vectors X can be handled in a single call; they are stored as the columns of the M-\/by-\/\-N\-R\-H\-S right hand side matrix B and the N-\/by-\/\-N\-R\-H\-S solution matrix X.

P\-L\-A\-S\-M\-A\-\_\-zcgels first attempts to factorize the matrix in C\-O\-M\-P\-L\-E\-X and use this factorization within an iterative refinement procedure to produce a solution with C\-O\-M\-P\-L\-E\-X$\ast$16 normwise backward error quality (see below). If the approach fails the method switches to a C\-O\-M\-P\-L\-E\-X$\ast$16 factorization and solve.

The iterative refinement is not going to be a winning strategy if the ratio C\-O\-M\-P\-L\-E\-X performance over C\-O\-M\-P\-L\-E\-X$\ast$16 performance is too small. A reasonable strategy should take the number of right-\/hand sides and the size of the matrix into account. This might be done with a call to I\-L\-A\-E\-N\-V in the future. Up to now, we always try iterative refinement.

The iterative refinement process is stopped if I\-T\-E\-R $>$ I\-T\-E\-R\-M\-A\-X or for all the R\-H\-S we have\-: R\-N\-R\-M $<$ N$\ast$\-X\-N\-R\-M$\ast$\-A\-N\-R\-M$\ast$\-E\-P\-S$\ast$\-B\-W\-D\-M\-A\-X where\-:


\begin{DoxyItemize}
\item I\-T\-E\-R is the number of the current iteration in the iterative refinement process
\item R\-N\-R\-M is the infinity-\/norm of the residual
\item X\-N\-R\-M is the infinity-\/norm of the solution
\item A\-N\-R\-M is the infinity-\/operator-\/norm of the matrix A
\item E\-P\-S is the machine epsilon returned by D\-L\-A\-M\-C\-H('Epsilon').
\end{DoxyItemize}

Actually, in its current state (P\-L\-A\-S\-M\-A 2.\-1.\-0), the test is slightly relaxed.

The values I\-T\-E\-R\-M\-A\-X and B\-W\-D\-M\-A\-X are fixed to 30 and 1.\-0\-D+00 respectively.

We follow Bjorck's algorithm proposed in \char`\"{}\-Iterative Refinement of Linear
 Least Squares solutions I\char`\"{}, B\-I\-T, 7\-:257-\/278, 1967.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em trans} & Intended usage\-: = Plasma\-No\-Trans\-: the linear system involves A; = Plasma\-Conj\-Trans\-: the linear system involves A$\ast$$\ast$\-H. Currently only Plasma\-No\-Trans is supported.\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of right hand sides, i.\-e., the number of columns of the matrices B and X. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The M-\/by-\/\-N matrix A. This matrix is not modified.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt in}  & {\em B} & The M-\/by-\/\-N\-R\-H\-S matrix B of right hand side vectors, stored columnwise. Not modified.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= M\-A\-X(1,\-M,\-N).\\
\hline
\mbox{\tt out}  & {\em X} & If return value = 0, the solution vectors, stored columnwise. if M $>$= N, rows 1 to N of X contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of the modulus of elements N+1 to M in that column; if M $<$ N, rows 1 to N of X contain the minimum norm solution vectors;\\
\hline
\mbox{\tt in}  & {\em L\-D\-X} & The leading dimension of the array X. L\-D\-X $>$= M\-A\-X(1,\-M,\-N).\\
\hline
\mbox{\tt out}  & {\em I\-T\-E\-R} & The number of the current iteration in the iterative refinement process\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga6bd738a1ffefcf9d561cd5d82a7e2f10_ga6bd738a1ffefcf9d561cd5d82a7e2f10}{P\-L\-A\-S\-M\-A\-\_\-zcgels\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga996b201266467b1742e9797eea79130d_ga996b201266467b1742e9797eea79130d}{P\-L\-A\-S\-M\-A\-\_\-zcgels\-\_\-\-Tile\-\_\-\-Async} 

P\-L\-A\-S\-M\-A\-\_\-dsgels 

\hyperlink{group__PLASMA__Complex64__t_ga37e31dd7208585a1720db61e38e31a55_ga37e31dd7208585a1720db61e38e31a55}{P\-L\-A\-S\-M\-A\-\_\-zgels} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gab372ccb64517ddb8e0f7ea66088489a9_gab372ccb64517ddb8e0f7ea66088489a9}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zcgesv@{P\-L\-A\-S\-M\-A\-\_\-zcgesv}}
\index{P\-L\-A\-S\-M\-A\-\_\-zcgesv@{P\-L\-A\-S\-M\-A\-\_\-zcgesv}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zcgesv}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zcgesv (
\begin{DoxyParamCaption}
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{int $\ast$}]{I\-P\-I\-V, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{X, }
\item[{int}]{L\-D\-X, }
\item[{int $\ast$}]{I\-T\-E\-R}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gab372ccb64517ddb8e0f7ea66088489a9_gab372ccb64517ddb8e0f7ea66088489a9}
P\-L\-A\-S\-M\-A\-\_\-zcgesv -\/ Computes the solution to a system of linear equations A $\ast$ X = B, where A is an N-\/by-\/\-N matrix and X and B are N-\/by-\/\-N\-R\-H\-S matrices.

P\-L\-A\-S\-M\-A\-\_\-zcgesv first attempts to factorize the matrix in C\-O\-M\-P\-L\-E\-X and use this factorization within an iterative refinement procedure to produce a solution with C\-O\-M\-P\-L\-E\-X$\ast$16 normwise backward error quality (see below). If the approach fails the method switches to a C\-O\-M\-P\-L\-E\-X$\ast$16 factorization and solve.

The iterative refinement is not going to be a winning strategy if the ratio C\-O\-M\-P\-L\-E\-X performance over C\-O\-M\-P\-L\-E\-X$\ast$16 performance is too small. A reasonable strategy should take the number of right-\/hand sides and the size of the matrix into account. This might be done with a call to I\-L\-A\-E\-N\-V in the future. Up to now, we always try iterative refinement.

The iterative refinement process is stopped if I\-T\-E\-R $>$ I\-T\-E\-R\-M\-A\-X or for all the R\-H\-S we have\-: R\-N\-R\-M $<$ N$\ast$\-X\-N\-R\-M$\ast$\-A\-N\-R\-M$\ast$\-E\-P\-S$\ast$\-B\-W\-D\-M\-A\-X where\-:


\begin{DoxyItemize}
\item I\-T\-E\-R is the number of the current iteration in the iterative refinement process
\item R\-N\-R\-M is the infinity-\/norm of the residual
\item X\-N\-R\-M is the infinity-\/norm of the solution
\item A\-N\-R\-M is the infinity-\/operator-\/norm of the matrix A
\item E\-P\-S is the machine epsilon returned by D\-L\-A\-M\-C\-H('Epsilon').
\end{DoxyItemize}

Actually, in its current state (P\-L\-A\-S\-M\-A 2.\-1.\-0), the test is slightly relaxed.

The values I\-T\-E\-R\-M\-A\-X and B\-W\-D\-M\-A\-X are fixed to 30 and 1.\-0\-D+00 respectively.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em N} & The number of linear equations, i.\-e., the order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of right hand sides, i.\-e., the number of columns of the matrix B. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The N-\/by-\/\-N coefficient matrix A. This matrix is not modified.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt out}  & {\em I\-P\-I\-V} & On exit, the pivot indices that define the permutations.\\
\hline
\mbox{\tt in}  & {\em B} & The N-\/by-\/\-N\-R\-H\-S matrix of right hand side matrix B.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-N).\\
\hline
\mbox{\tt out}  & {\em X} & If return value = 0, the N-\/by-\/\-N\-R\-H\-S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\-D\-X} & The leading dimension of the array B. L\-D\-X $>$= max(1,\-N).\\
\hline
\mbox{\tt out}  & {\em I\-T\-E\-R} & The number of the current iteration in the iterative refinement process\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga1323bdbc5973b2ee613e9c128a98d419_ga1323bdbc5973b2ee613e9c128a98d419}{P\-L\-A\-S\-M\-A\-\_\-zcgesv\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga951cf5fa265511341d92979d9ca86613_ga951cf5fa265511341d92979d9ca86613}{P\-L\-A\-S\-M\-A\-\_\-zcgesv\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__double_ga50fe4c984e8994fe22aac09c0f6c3422_ga50fe4c984e8994fe22aac09c0f6c3422}{P\-L\-A\-S\-M\-A\-\_\-dsgesv} 

\hyperlink{group__PLASMA__Complex64__t_ga94397d6fba523c946f1e56cfe9aa967d_ga94397d6fba523c946f1e56cfe9aa967d}{P\-L\-A\-S\-M\-A\-\_\-zgesv} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga11ee4c71901e8675d5423cfceecaaf43_ga11ee4c71901e8675d5423cfceecaaf43}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zcposv@{P\-L\-A\-S\-M\-A\-\_\-zcposv}}
\index{P\-L\-A\-S\-M\-A\-\_\-zcposv@{P\-L\-A\-S\-M\-A\-\_\-zcposv}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zcposv}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zcposv (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{X, }
\item[{int}]{L\-D\-X, }
\item[{int $\ast$}]{I\-T\-E\-R}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga11ee4c71901e8675d5423cfceecaaf43_ga11ee4c71901e8675d5423cfceecaaf43}
P\-L\-A\-S\-M\-A\-\_\-zcposv -\/ Computes the solution to a system of linear equations A $\ast$ X = B, where A is an N-\/by-\/\-N symmetric positive definite (or Hermitian positive definite in the complex case) matrix and X and B are N-\/by-\/\-N\-R\-H\-S matrices. The Cholesky decomposition is used to factor A as

A = U$\ast$$\ast$\-H $\ast$ U, if uplo = Plasma\-Upper, or A = L $\ast$ L$\ast$$\ast$\-H, if uplo = Plasma\-Lower,

where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A $\ast$ X = B.

P\-L\-A\-S\-M\-A\-\_\-zcposv first attempts to factorize the matrix in C\-O\-M\-P\-L\-E\-X and use this factorization within an iterative refinement procedure to produce a solution with C\-O\-M\-P\-L\-E\-X$\ast$16 normwise backward error quality (see below). If the approach fails the method switches to a C\-O\-M\-P\-L\-E\-X$\ast$16 factorization and solve.

The iterative refinement is not going to be a winning strategy if the ratio C\-O\-M\-P\-L\-E\-X performance over C\-O\-M\-P\-L\-E\-X$\ast$16 performance is too small. A reasonable strategy should take the number of right-\/hand sides and the size of the matrix into account. This might be done with a call to I\-L\-A\-E\-N\-V in the future. Up to now, we always try iterative refinement.

The iterative refinement process is stopped if I\-T\-E\-R $>$ I\-T\-E\-R\-M\-A\-X or for all the R\-H\-S we have\-: R\-N\-R\-M $<$ N$\ast$\-X\-N\-R\-M$\ast$\-A\-N\-R\-M$\ast$\-E\-P\-S$\ast$\-B\-W\-D\-M\-A\-X where\-:


\begin{DoxyItemize}
\item I\-T\-E\-R is the number of the current iteration in the iterative refinement process
\item R\-N\-R\-M is the infinity-\/norm of the residual
\item X\-N\-R\-M is the infinity-\/norm of the solution
\item A\-N\-R\-M is the infinity-\/operator-\/norm of the matrix A
\item E\-P\-S is the machine epsilon returned by D\-L\-A\-M\-C\-H('Epsilon').
\end{DoxyItemize}

Actually, in its current state (P\-L\-A\-S\-M\-A 2.\-1.\-0), the test is slightly relaxed.

The values I\-T\-E\-R\-M\-A\-X and B\-W\-D\-M\-A\-X are fixed to 30 and 1.\-0\-D+00 respectively.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\-: = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The number of linear equations, i.\-e., the order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of right hand sides, i.\-e., the number of columns of the matrix B. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The N-\/by-\/\-N symmetric positive definite (or Hermitian) coefficient matrix A. If uplo = Plasma\-Upper, the leading N-\/by-\/\-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If U\-P\-L\-O = 'L', the leading N-\/by-\/\-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. This matrix is not modified.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in}  & {\em B} & The N-\/by-\/\-N\-R\-H\-S matrix of right hand side matrix B.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-N).\\
\hline
\mbox{\tt out}  & {\em X} & If return value = 0, the N-\/by-\/\-N\-R\-H\-S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\-D\-X} & The leading dimension of the array B. L\-D\-X $>$= max(1,\-N).\\
\hline
\mbox{\tt out}  & {\em I\-T\-E\-R} & The number of the current iteration in the iterative refinement process\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga0be255f00d6a4cc70a544a715bdc6dd3_ga0be255f00d6a4cc70a544a715bdc6dd3}{P\-L\-A\-S\-M\-A\-\_\-zcposv\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gad582515d56a856b1d1477dbfac676a40_gad582515d56a856b1d1477dbfac676a40}{P\-L\-A\-S\-M\-A\-\_\-zcposv\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__double_gaf4c055accc54907abd1ea3a85555c9b4_gaf4c055accc54907abd1ea3a85555c9b4}{P\-L\-A\-S\-M\-A\-\_\-dsposv} 

\hyperlink{group__PLASMA__Complex64__t_gaed71622155778ea4372e34879184e742_gaed71622155778ea4372e34879184e742}{P\-L\-A\-S\-M\-A\-\_\-zposv} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gaba15b4f438d8d2fe41f2c38820d043ef_gaba15b4f438d8d2fe41f2c38820d043ef}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zcungesv@{P\-L\-A\-S\-M\-A\-\_\-zcungesv}}
\index{P\-L\-A\-S\-M\-A\-\_\-zcungesv@{P\-L\-A\-S\-M\-A\-\_\-zcungesv}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zcungesv}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zcungesv (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans, }
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{X, }
\item[{int}]{L\-D\-X, }
\item[{int $\ast$}]{I\-T\-E\-R}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gaba15b4f438d8d2fe41f2c38820d043ef_gaba15b4f438d8d2fe41f2c38820d043ef}
P\-L\-A\-S\-M\-A\-\_\-zcungesv -\/ Solves overdetermined or underdetermined linear systems involving an M-\/by-\/\-N matrix A using the Q\-R or the L\-Q factorization of A. It is assumed that A has full rank. The following options are provided\-:

\subsection*{trans = Plasma\-No\-Trans and M $>$= N\-: find the least squares solution of an overdetermined}

system, i.\-e., solve the least squares problem\-: minimize $|$$|$ B -\/ A$\ast$\-X $|$$|$.

\subsection*{trans = Plasma\-No\-Trans and M $<$ N\-: find the minimum norm solution of an underdetermined}

system A $\ast$ X = B.

Several right hand side vectors B and solution vectors X can be handled in a single call; they are stored as the columns of the M-\/by-\/\-N\-R\-H\-S right hand side matrix B and the N-\/by-\/\-N\-R\-H\-S solution matrix X.

P\-L\-A\-S\-M\-A\-\_\-zcungesv first attempts to factorize the matrix in C\-O\-M\-P\-L\-E\-X and use this factorization within an iterative refinement procedure to produce a solution with C\-O\-M\-P\-L\-E\-X$\ast$16 normwise backward error quality (see below). If the approach fails the method switches to a C\-O\-M\-P\-L\-E\-X$\ast$16 factorization and solve.

The iterative refinement is not going to be a winning strategy if the ratio C\-O\-M\-P\-L\-E\-X performance over C\-O\-M\-P\-L\-E\-X$\ast$16 performance is too small. A reasonable strategy should take the number of right-\/hand sides and the size of the matrix into account. This might be done with a call to I\-L\-A\-E\-N\-V in the future. Up to now, we always try iterative refinement.

The iterative refinement process is stopped if I\-T\-E\-R $>$ I\-T\-E\-R\-M\-A\-X or for all the R\-H\-S we have\-: R\-N\-R\-M $<$ N$\ast$\-X\-N\-R\-M$\ast$\-A\-N\-R\-M$\ast$\-E\-P\-S$\ast$\-B\-W\-D\-M\-A\-X where\-:


\begin{DoxyItemize}
\item I\-T\-E\-R is the number of the current iteration in the iterative refinement process
\item R\-N\-R\-M is the infinity-\/norm of the residual
\item X\-N\-R\-M is the infinity-\/norm of the solution
\item A\-N\-R\-M is the infinity-\/operator-\/norm of the matrix A
\item E\-P\-S is the machine epsilon returned by D\-L\-A\-M\-C\-H('Epsilon').
\end{DoxyItemize}

Actually, in its current state (P\-L\-A\-S\-M\-A 2.\-1.\-0), the test is slightly relaxed.

The values I\-T\-E\-R\-M\-A\-X and B\-W\-D\-M\-A\-X are fixed to 30 and 1.\-0\-D+00 respectively.

We follow Bjorck's algorithm proposed in \char`\"{}\-Iterative Refinement of Linear
 Least Squares solutions I\char`\"{}, B\-I\-T, 7\-:257-\/278, 1967.\-4


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em trans} & Intended usage\-: = Plasma\-No\-Trans\-: the linear system involves A; = Plasma\-Conj\-Trans\-: the linear system involves A$\ast$$\ast$\-H. Currently only Plasma\-No\-Trans is supported.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of right hand sides, i.\-e., the number of columns of the matrices B and X. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The M-\/by-\/\-N matrix A. This matrix is not modified.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt in}  & {\em B} & The M-\/by-\/\-N\-R\-H\-S matrix B of right hand side vectors, stored columnwise. Not modified.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= M\-A\-X(1,\-M,\-N).\\
\hline
\mbox{\tt out}  & {\em X} & If return value = 0, the solution vectors, stored columnwise. if M $>$= N, rows 1 to N of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of the modulus of elements N+1 to M in that column; if M $<$ N, rows 1 to N of B contain the minimum norm solution vectors;\\
\hline
\mbox{\tt in}  & {\em L\-D\-X} & The leading dimension of the array B. L\-D\-B $>$= M\-A\-X(1,\-M,\-N).\\
\hline
\mbox{\tt out}  & {\em I\-T\-E\-R} & The number of the current iteration in the iterative refinement process\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga5eecfe4fcf4814dd939f39c0629d2222_ga5eecfe4fcf4814dd939f39c0629d2222}{P\-L\-A\-S\-M\-A\-\_\-zcungesv\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga968e899d87b6805ffbd6975359e05efd_ga968e899d87b6805ffbd6975359e05efd}{P\-L\-A\-S\-M\-A\-\_\-zcungesv\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__double_ga5ad1a5e52e906d9add120b37fc4301fc_ga5ad1a5e52e906d9add120b37fc4301fc}{P\-L\-A\-S\-M\-A\-\_\-dsungesv} 

\hyperlink{group__PLASMA__Complex64__t_ga37e31dd7208585a1720db61e38e31a55_ga37e31dd7208585a1720db61e38e31a55}{P\-L\-A\-S\-M\-A\-\_\-zgels} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga9b52418f313c60c7f11f320fdfa262a7_ga9b52418f313c60c7f11f320fdfa262a7}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zgebrd@{P\-L\-A\-S\-M\-A\-\_\-zgebrd}}
\index{P\-L\-A\-S\-M\-A\-\_\-zgebrd@{P\-L\-A\-S\-M\-A\-\_\-zgebrd}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zgebrd}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zgebrd (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{double $\ast$}]{D, }
\item[{double $\ast$}]{E, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga9b52418f313c60c7f11f320fdfa262a7_ga9b52418f313c60c7f11f320fdfa262a7}
P\-L\-A\-S\-M\-A\-\_\-zgebrd -\/ reduces a general complex M-\/by-\/\-N matrix A to upper or lower bidiagonal form B using a two-\/stage approach First stage\-: reduction to band bidiagonal form (orthogonal matrices Q1 and P1); Second stage\-: reduction from band to bidiagonal form (orthogonal matrices Q2 and P2). Let Q = Q1 $\ast$ Q2 be the global left unitary transformation; Let P = P1 $\ast$ P2 be the global right unitary transformation; Q$\ast$$\ast$\-H $\ast$ A $\ast$ P = B. If M $>$= N, B is upper bidiagonal; if M $<$ N, B is lower bidiagonal. Not L\-A\-P\-A\-C\-K Compliant for now! Note\-: T is incomplete and contains only the block reflectors of the first stage. Therefore, Q and P can not be built completely.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\-N matrix A. On exit, if M $>$= N, the diagonal and the first superdiagonal are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array T, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the array T, represent the unitary matrix P as a product of elementary reflectors; if M $<$ N, the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array T, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the diagonal, with the array T, represent the unitary matrix P as a product of elementary reflectors.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt out}  & {\em D} & On exit, the diagonal elements of the bidiagonal matrix\-: D(i) = A(i,i). Dimension (min(\-M,\-N)).\\
\hline
\mbox{\tt out}  & {\em E} & On exit, the off-\/diagonal elements of the bidiagonal matrix\-: if M $>$= N, E(i) = A(i,i+1) for i = 1,2,...,N-\/1; if M $<$ N, E(i) = A(i+1,i) for i = 1,2,...,M-\/1. Dimension (min(\-M,\-N)-\/1).\\
\hline
\mbox{\tt out}  & {\em desc\-T} & On entry, descriptor as return by P\-L\-A\-S\-M\-A\-\_\-\-Alloc\-\_\-\-Workspace\-\_\-zgesvd On exit, contains auxiliary factorization data.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga8cdcb2d19227dd121f7dd95015e5b8ba_ga8cdcb2d19227dd121f7dd95015e5b8ba}{P\-L\-A\-S\-M\-A\-\_\-zgebrd\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga377b1d782ab2cfd071ac86ee8683263e_ga377b1d782ab2cfd071ac86ee8683263e}{P\-L\-A\-S\-M\-A\-\_\-zgebrd\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gabeb6f33d6e788ac66b06a9603701d43c_gabeb6f33d6e788ac66b06a9603701d43c}{P\-L\-A\-S\-M\-A\-\_\-cgebrd} 

\hyperlink{group__double_ga8d1eafa453f15e7db35e9f86b1efc599_ga8d1eafa453f15e7db35e9f86b1efc599}{P\-L\-A\-S\-M\-A\-\_\-dgebrd} 

\hyperlink{group__float_ga89adf36f43f20bcc2e6911cd9d9538d6_ga89adf36f43f20bcc2e6911cd9d9538d6}{P\-L\-A\-S\-M\-A\-\_\-sgebrd} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga8990facf0cb04df2a107c02e5dd5f3f7_ga8990facf0cb04df2a107c02e5dd5f3f7}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zgelqf@{P\-L\-A\-S\-M\-A\-\_\-zgelqf}}
\index{P\-L\-A\-S\-M\-A\-\_\-zgelqf@{P\-L\-A\-S\-M\-A\-\_\-zgelqf}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zgelqf}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zgelqf (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga8990facf0cb04df2a107c02e5dd5f3f7_ga8990facf0cb04df2a107c02e5dd5f3f7}
P\-L\-A\-S\-M\-A\-\_\-zgelqf -\/ Computes the tile L\-Q factorization of a complex M-\/by-\/\-N matrix A\-: A = L $\ast$ Q.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\-N matrix A. On exit, the elements on and below the diagonal of the array contain the m-\/by-\/min(M,N) lower trapezoidal matrix L (L is lower triangular if M $<$= N); the elements above the diagonal represent the unitary matrix Q as a product of elementary reflectors, stored by tiles.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt out}  & {\em desc\-T} & On exit, auxiliary factorization data, required by P\-L\-A\-S\-M\-A\-\_\-zgelqs to solve the system of equations.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga67a829a6a8c8fa6f0fbdfee5ea61ce12_ga67a829a6a8c8fa6f0fbdfee5ea61ce12}{P\-L\-A\-S\-M\-A\-\_\-zgelqf\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga045cbdfc84b025ffbf9aa8af9877a2a4_ga045cbdfc84b025ffbf9aa8af9877a2a4}{P\-L\-A\-S\-M\-A\-\_\-zgelqf\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gadab1e78967134c5e784bb80d03760b25_gadab1e78967134c5e784bb80d03760b25}{P\-L\-A\-S\-M\-A\-\_\-cgelqf} 

\hyperlink{group__double_ga60fffe07485af5c38c0447efccf8ccfe_ga60fffe07485af5c38c0447efccf8ccfe}{P\-L\-A\-S\-M\-A\-\_\-dgelqf} 

\hyperlink{group__float_gaecbccf81ab27bc4a0a5913baedf3b7ef_gaecbccf81ab27bc4a0a5913baedf3b7ef}{P\-L\-A\-S\-M\-A\-\_\-sgelqf} 

\hyperlink{group__PLASMA__Complex64__t_ga8e8b7d834eb0ad99766799bcfa48d4b1_ga8e8b7d834eb0ad99766799bcfa48d4b1}{P\-L\-A\-S\-M\-A\-\_\-zgelqs} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga8e8b7d834eb0ad99766799bcfa48d4b1_ga8e8b7d834eb0ad99766799bcfa48d4b1}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zgelqs@{P\-L\-A\-S\-M\-A\-\_\-zgelqs}}
\index{P\-L\-A\-S\-M\-A\-\_\-zgelqs@{P\-L\-A\-S\-M\-A\-\_\-zgelqs}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zgelqs}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zgelqs (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga8e8b7d834eb0ad99766799bcfa48d4b1_ga8e8b7d834eb0ad99766799bcfa48d4b1}
P\-L\-A\-S\-M\-A\-\_\-zgelqs -\/ Compute a minimum-\/norm solution min $|$$|$ A$\ast$\-X -\/ B $|$$|$ using the L\-Q factorization A = L$\ast$\-Q computed by P\-L\-A\-S\-M\-A\-\_\-zgelqf.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of columns of B. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & Details of the L\-Q factorization of the original matrix A as returned by P\-L\-A\-S\-M\-A\-\_\-zgelqf.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= M.\\
\hline
\mbox{\tt in}  & {\em desc\-T} & Auxiliary factorization data, computed by P\-L\-A\-S\-M\-A\-\_\-zgelqf.\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the M-\/by-\/\-N\-R\-H\-S right hand side matrix B. On exit, the N-\/by-\/\-N\-R\-H\-S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= N.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gaa6c2e67e567c4f9a4e3f3a84e4b54b8c_gaa6c2e67e567c4f9a4e3f3a84e4b54b8c}{P\-L\-A\-S\-M\-A\-\_\-zgelqs\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gaea984817531da99d1188623a0822e5f6_gaea984817531da99d1188623a0822e5f6}{P\-L\-A\-S\-M\-A\-\_\-zgelqs\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gab6c2a5892b81e8ee9740268d06adf9b1_gab6c2a5892b81e8ee9740268d06adf9b1}{P\-L\-A\-S\-M\-A\-\_\-cgelqs} 

\hyperlink{group__double_ga092545f106c9fae67b82eb65f11ca4ab_ga092545f106c9fae67b82eb65f11ca4ab}{P\-L\-A\-S\-M\-A\-\_\-dgelqs} 

\hyperlink{group__float_ga4bde040498b35dcbc88268de59de7d12_ga4bde040498b35dcbc88268de59de7d12}{P\-L\-A\-S\-M\-A\-\_\-sgelqs} 

\hyperlink{group__PLASMA__Complex64__t_ga8990facf0cb04df2a107c02e5dd5f3f7_ga8990facf0cb04df2a107c02e5dd5f3f7}{P\-L\-A\-S\-M\-A\-\_\-zgelqf} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga37e31dd7208585a1720db61e38e31a55_ga37e31dd7208585a1720db61e38e31a55}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zgels@{P\-L\-A\-S\-M\-A\-\_\-zgels}}
\index{P\-L\-A\-S\-M\-A\-\_\-zgels@{P\-L\-A\-S\-M\-A\-\_\-zgels}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zgels}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zgels (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga37e31dd7208585a1720db61e38e31a55_ga37e31dd7208585a1720db61e38e31a55}
P\-L\-A\-S\-M\-A\-\_\-zgels -\/ solves overdetermined or underdetermined linear systems involving an M-\/by-\/\-N matrix A using the Q\-R or the L\-Q factorization of A. It is assumed that A has full rank. The following options are provided\-:

\subsection*{trans = Plasma\-No\-Trans and M $>$= N\-: find the least squares solution of an overdetermined}

system, i.\-e., solve the least squares problem\-: minimize $|$$|$ B -\/ A$\ast$\-X $|$$|$.

\subsection*{trans = Plasma\-No\-Trans and M $<$ N\-: find the minimum norm solution of an underdetermined}

system A $\ast$ X = B.

Several right hand side vectors B and solution vectors X can be handled in a single call; they are stored as the columns of the M-\/by-\/\-N\-R\-H\-S right hand side matrix B and the N-\/by-\/\-N\-R\-H\-S solution matrix X.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em trans} & Intended usage\-: = Plasma\-No\-Trans\-: the linear system involves A; = Plasma\-Conj\-Trans\-: the linear system involves A$\ast$$\ast$\-H. Currently only Plasma\-No\-Trans is supported.\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of right hand sides, i.\-e., the number of columns of the matrices B and X. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\-N matrix A. On exit, if M $>$= N, A is overwritten by details of its Q\-R factorization as returned by P\-L\-A\-S\-M\-A\-\_\-zgeqrf; if M $<$ N, A is overwritten by details of its L\-Q factorization as returned by P\-L\-A\-S\-M\-A\-\_\-zgelqf.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt out}  & {\em desc\-T} & On exit, auxiliary factorization data.\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the M-\/by-\/\-N\-R\-H\-S matrix B of right hand side vectors, stored columnwise; On exit, if return value = 0, B is overwritten by the solution vectors, stored columnwise\-: if M $>$= N, rows 1 to N of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of the modulus of elements N+1 to M in that column; if M $<$ N, rows 1 to N of B contain the minimum norm solution vectors;\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= M\-A\-X(1,\-M,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga2bb601838348c183a781a1ec00023065_ga2bb601838348c183a781a1ec00023065}{P\-L\-A\-S\-M\-A\-\_\-zgels\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gaef149ecf3716aec86c4da1b4ab4974f9_gaef149ecf3716aec86c4da1b4ab4974f9}{P\-L\-A\-S\-M\-A\-\_\-zgels\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga047c51e0c630ac15b2679b8352013f7b_ga047c51e0c630ac15b2679b8352013f7b}{P\-L\-A\-S\-M\-A\-\_\-cgels} 

\hyperlink{group__double_ga4bfc0cdaf567c26828f484e54d457d92_ga4bfc0cdaf567c26828f484e54d457d92}{P\-L\-A\-S\-M\-A\-\_\-dgels} 

\hyperlink{group__float_ga2bbab59e86acca698a73c5bc8023e5c3_ga2bbab59e86acca698a73c5bc8023e5c3}{P\-L\-A\-S\-M\-A\-\_\-sgels} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga1a0f8d759e535f9947ae11baa0af6fa3_ga1a0f8d759e535f9947ae11baa0af6fa3}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zgemm@{P\-L\-A\-S\-M\-A\-\_\-zgemm}}
\index{P\-L\-A\-S\-M\-A\-\_\-zgemm@{P\-L\-A\-S\-M\-A\-\_\-zgemm}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zgemm}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zgemm (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans\-B, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{alpha, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{beta, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{C, }
\item[{int}]{L\-D\-C}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga1a0f8d759e535f9947ae11baa0af6fa3_ga1a0f8d759e535f9947ae11baa0af6fa3}
P\-L\-A\-S\-M\-A\-\_\-zgemm -\/ Performs one of the matrix-\/matrix operations

\[ C = \alpha [op( A )\times op( B )] + \beta C \],

where op( X ) is one of

op( X ) = X or op( X ) = X' or op( X ) = conjg( X' )

alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em trans\-A} & Specifies whether the matrix A is transposed, not transposed or conjugate transposed\-: = Plasma\-No\-Trans\-: A is not transposed; = Plasma\-Trans\-: A is transposed; = Plasma\-Conj\-Trans\-: A is conjugate transposed.\\
\hline
\mbox{\tt in}  & {\em trans\-B} & Specifies whether the matrix B is transposed, not transposed or conjugate transposed\-: = Plasma\-No\-Trans\-: B is not transposed; = Plasma\-Trans\-: B is transposed; = Plasma\-Conj\-Trans\-: B is conjugate transposed.\\
\hline
\mbox{\tt in}  & {\em M} & M specifies the number of rows of the matrix op( A ) and of the matrix C. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & N specifies the number of columns of the matrix op( B ) and of the matrix C. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em K} & K specifies the number of columns of the matrix op( A ) and the number of rows of the matrix op( B ). K $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha\\
\hline
\mbox{\tt in}  & {\em A} & A is a L\-D\-A-\/by-\/ka matrix, where ka is K when trans\-A = Plasma\-No\-Trans, and is M otherwise.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt in}  & {\em B} & B is a L\-D\-B-\/by-\/kb matrix, where kb is N when trans\-B = Plasma\-No\-Trans, and is K otherwise.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-N).\\
\hline
\mbox{\tt in}  & {\em beta} & beta specifies the scalar beta\\
\hline
\mbox{\tt in,out}  & {\em C} & C is a L\-D\-C-\/by-\/\-N matrix. On exit, the array is overwritten by the M by N matrix ( alpha$\ast$op( A )$\ast$op( B ) + beta$\ast$\-C )\\
\hline
\mbox{\tt in}  & {\em L\-D\-C} & The leading dimension of the array C. L\-D\-C $>$= max(1,\-M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga988b90795ec2367dc11590bc5dd05ada_ga988b90795ec2367dc11590bc5dd05ada}{P\-L\-A\-S\-M\-A\-\_\-zgemm\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex32__t_ga5505cdf8794ea00c9160d656d2a00ec9_ga5505cdf8794ea00c9160d656d2a00ec9}{P\-L\-A\-S\-M\-A\-\_\-cgemm} 

\hyperlink{group__double_ga5c560bea8139857be91339582ba830ef_ga5c560bea8139857be91339582ba830ef}{P\-L\-A\-S\-M\-A\-\_\-dgemm} 

\hyperlink{group__float_gace4e6452ba3ffb8cef11be1987091382_gace4e6452ba3ffb8cef11be1987091382}{P\-L\-A\-S\-M\-A\-\_\-sgemm} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga9d4fae8697b364c384faa7480aea3118_ga9d4fae8697b364c384faa7480aea3118}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zgeqrf@{P\-L\-A\-S\-M\-A\-\_\-zgeqrf}}
\index{P\-L\-A\-S\-M\-A\-\_\-zgeqrf@{P\-L\-A\-S\-M\-A\-\_\-zgeqrf}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zgeqrf}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zgeqrf (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga9d4fae8697b364c384faa7480aea3118_ga9d4fae8697b364c384faa7480aea3118}
P\-L\-A\-S\-M\-A\-\_\-zgeqrf -\/ Computes the tile Q\-R factorization of a complex M-\/by-\/\-N matrix A\-: A = Q $\ast$ R.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(\-M,\-N)-\/by-\/\-N upper trapezoidal matrix R (R is upper triangular if M $>$= N); the elements below the diagonal represent the unitary matrix Q as a product of elementary reflectors stored by tiles.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt out}  & {\em desc\-T} & On exit, auxiliary factorization data, required by P\-L\-A\-S\-M\-A\-\_\-zgeqrs to solve the system of equations.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gabc10a21174d94b348a2493d6e885be57_gabc10a21174d94b348a2493d6e885be57}{P\-L\-A\-S\-M\-A\-\_\-zgeqrf\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga82e726155a07c9f4bb8e9c3a0298c1c4_ga82e726155a07c9f4bb8e9c3a0298c1c4}{P\-L\-A\-S\-M\-A\-\_\-zgeqrf\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gae8490d9c587725716adbb347d85537b2_gae8490d9c587725716adbb347d85537b2}{P\-L\-A\-S\-M\-A\-\_\-cgeqrf} 

\hyperlink{group__double_gaad8136b3520b4bda7261d3f921c8a740_gaad8136b3520b4bda7261d3f921c8a740}{P\-L\-A\-S\-M\-A\-\_\-dgeqrf} 

\hyperlink{group__float_gad2dff40bb75ba6ee7a91306e0a3e889e_gad2dff40bb75ba6ee7a91306e0a3e889e}{P\-L\-A\-S\-M\-A\-\_\-sgeqrf} 

\hyperlink{group__PLASMA__Complex64__t_gaaded5cbc1a55a5d1cc6a231b8da07bf0_gaaded5cbc1a55a5d1cc6a231b8da07bf0}{P\-L\-A\-S\-M\-A\-\_\-zgeqrs} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gaaded5cbc1a55a5d1cc6a231b8da07bf0_gaaded5cbc1a55a5d1cc6a231b8da07bf0}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zgeqrs@{P\-L\-A\-S\-M\-A\-\_\-zgeqrs}}
\index{P\-L\-A\-S\-M\-A\-\_\-zgeqrs@{P\-L\-A\-S\-M\-A\-\_\-zgeqrs}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zgeqrs}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zgeqrs (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gaaded5cbc1a55a5d1cc6a231b8da07bf0_gaaded5cbc1a55a5d1cc6a231b8da07bf0}
P\-L\-A\-S\-M\-A\-\_\-zgeqrs -\/ Compute a minimum-\/norm solution min $|$$|$ A$\ast$\-X -\/ B $|$$|$ using the R\-Q factorization A = R$\ast$\-Q computed by P\-L\-A\-S\-M\-A\-\_\-zgeqrf.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of columns of B. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & Details of the Q\-R factorization of the original matrix A as returned by P\-L\-A\-S\-M\-A\-\_\-zgeqrf.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= M.\\
\hline
\mbox{\tt in}  & {\em desc\-T} & Auxiliary factorization data, computed by P\-L\-A\-S\-M\-A\-\_\-zgeqrf.\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the m-\/by-\/nrhs right hand side matrix B. On exit, the n-\/by-\/nrhs solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gac9063541a51dbee5a3e51ea774d30de9_gac9063541a51dbee5a3e51ea774d30de9}{P\-L\-A\-S\-M\-A\-\_\-zgeqrs\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga2e3360f39f4b262354718a6aaefe649c_ga2e3360f39f4b262354718a6aaefe649c}{P\-L\-A\-S\-M\-A\-\_\-zgeqrs\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga961a4dfc433c5086670b813e5fa53bbf_ga961a4dfc433c5086670b813e5fa53bbf}{P\-L\-A\-S\-M\-A\-\_\-cgeqrs} 

\hyperlink{group__double_gaa133b69ef592ef01466fd93b6ac7689d_gaa133b69ef592ef01466fd93b6ac7689d}{P\-L\-A\-S\-M\-A\-\_\-dgeqrs} 

\hyperlink{group__float_ga15cad3c163c8d1137d13d66594652b7d_ga15cad3c163c8d1137d13d66594652b7d}{P\-L\-A\-S\-M\-A\-\_\-sgeqrs} 

\hyperlink{group__PLASMA__Complex64__t_ga9d4fae8697b364c384faa7480aea3118_ga9d4fae8697b364c384faa7480aea3118}{P\-L\-A\-S\-M\-A\-\_\-zgeqrf} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga94397d6fba523c946f1e56cfe9aa967d_ga94397d6fba523c946f1e56cfe9aa967d}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zgesv@{P\-L\-A\-S\-M\-A\-\_\-zgesv}}
\index{P\-L\-A\-S\-M\-A\-\_\-zgesv@{P\-L\-A\-S\-M\-A\-\_\-zgesv}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zgesv}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zgesv (
\begin{DoxyParamCaption}
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{int $\ast$}]{I\-P\-I\-V, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga94397d6fba523c946f1e56cfe9aa967d_ga94397d6fba523c946f1e56cfe9aa967d}
P\-L\-A\-S\-M\-A\-\_\-zgesv -\/ Computes the solution to a system of linear equations A $\ast$ X = B, where A is an N-\/by-\/\-N matrix and X and B are N-\/by-\/\-N\-R\-H\-S matrices. The tile L\-U decomposition with partial tile pivoting and row interchanges is used to factor A. The factored form of A is then used to solve the system of equations A $\ast$ X = B.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em N} & The number of linear equations, i.\-e., the order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of right hand sides, i.\-e., the number of columns of the matrix B. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the N-\/by-\/\-N coefficient matrix A. On exit, the tile L and U factors from the factorization.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt out}  & {\em I\-P\-I\-V} & On exit, the pivot indices that define the permutations.\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\-N\-R\-H\-S matrix of right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\-N\-R\-H\-S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gae332d3896516a34f413881d7383506d4_gae332d3896516a34f413881d7383506d4}{P\-L\-A\-S\-M\-A\-\_\-zgesv\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga34f307dbc6cd1dc5adab0970fe559a30_ga34f307dbc6cd1dc5adab0970fe559a30}{P\-L\-A\-S\-M\-A\-\_\-zgesv\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga5ec3217862ee4b820b9cd9d4b343bfae_ga5ec3217862ee4b820b9cd9d4b343bfae}{P\-L\-A\-S\-M\-A\-\_\-cgesv} 

\hyperlink{group__double_gae380e95b53e07b9b1261aec244191c0f_gae380e95b53e07b9b1261aec244191c0f}{P\-L\-A\-S\-M\-A\-\_\-dgesv} 

\hyperlink{group__float_ga39018420f926f77ef11c50c82f66da77_ga39018420f926f77ef11c50c82f66da77}{P\-L\-A\-S\-M\-A\-\_\-sgesv} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga27916109c8ac4bed6d101fcb98b27fad_ga27916109c8ac4bed6d101fcb98b27fad}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zgesv\-\_\-incpiv@{P\-L\-A\-S\-M\-A\-\_\-zgesv\-\_\-incpiv}}
\index{P\-L\-A\-S\-M\-A\-\_\-zgesv\-\_\-incpiv@{P\-L\-A\-S\-M\-A\-\_\-zgesv\-\_\-incpiv}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zgesv\-\_\-incpiv}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zgesv\-\_\-incpiv (
\begin{DoxyParamCaption}
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-L, }
\item[{int $\ast$}]{I\-P\-I\-V, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga27916109c8ac4bed6d101fcb98b27fad_ga27916109c8ac4bed6d101fcb98b27fad}
P\-L\-A\-S\-M\-A\-\_\-zgesv\-\_\-incpiv -\/ Computes the solution to a system of linear equations A $\ast$ X = B, where A is an N-\/by-\/\-N matrix and X and B are N-\/by-\/\-N\-R\-H\-S matrices. The tile L\-U decomposition with partial tile pivoting and row interchanges is used to factor A. The factored form of A is then used to solve the system of equations A $\ast$ X = B.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em N} & The number of linear equations, i.\-e., the order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of right hand sides, i.\-e., the number of columns of the matrix B. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the N-\/by-\/\-N coefficient matrix A. On exit, the tile L and U factors from the factorization (not equivalent to L\-A\-P\-A\-C\-K).\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt out}  & {\em desc\-L} & On exit, auxiliary factorization data, related to the tile L factor, necessary to solve the system of equations.\\
\hline
\mbox{\tt out}  & {\em I\-P\-I\-V} & On exit, the pivot indices that define the permutations (not equivalent to L\-A\-P\-A\-C\-K).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\-N\-R\-H\-S matrix of right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\-N\-R\-H\-S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gab1992fd7d128b9101dfcf9da53238cec_gab1992fd7d128b9101dfcf9da53238cec}{P\-L\-A\-S\-M\-A\-\_\-zgesv\-\_\-incpiv\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga249ca8742ffa280cbd62c4bdad362ee7_ga249ca8742ffa280cbd62c4bdad362ee7}{P\-L\-A\-S\-M\-A\-\_\-zgesv\-\_\-incpiv\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gade54f0cdad2648b241e2701e0e07cbce_gade54f0cdad2648b241e2701e0e07cbce}{P\-L\-A\-S\-M\-A\-\_\-cgesv\-\_\-incpiv} 

\hyperlink{group__double_gaaf143240840f5315cf672d66dead1111_gaaf143240840f5315cf672d66dead1111}{P\-L\-A\-S\-M\-A\-\_\-dgesv\-\_\-incpiv} 

\hyperlink{group__float_gab9dab6c3f22b6cf8dad0fa2f1b563988_gab9dab6c3f22b6cf8dad0fa2f1b563988}{P\-L\-A\-S\-M\-A\-\_\-sgesv\-\_\-incpiv} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga36fc556f67632e00105090a60657dab2_ga36fc556f67632e00105090a60657dab2}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zgesvd@{P\-L\-A\-S\-M\-A\-\_\-zgesvd}}
\index{P\-L\-A\-S\-M\-A\-\_\-zgesvd@{P\-L\-A\-S\-M\-A\-\_\-zgesvd}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zgesvd}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zgesvd (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{jobu, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{jobvt, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{double $\ast$}]{S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{U, }
\item[{int}]{L\-D\-U, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{V\-T, }
\item[{int}]{L\-D\-V\-T, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga36fc556f67632e00105090a60657dab2_ga36fc556f67632e00105090a60657dab2}
P\-L\-A\-S\-M\-A\-\_\-zgesvd -\/ computes the singular value decomposition (S\-V\-D) of a complex M-\/by-\/\-N matrix A, optionally computing the left and/or right singular vectors. The S\-V\-D is written \begin{DoxyVerb} A = U * SIGMA * transpose(V)
\end{DoxyVerb}


where S\-I\-G\-M\-A is an M-\/by-\/\-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-\/by-\/\-M orthogonal matrix, and V is an N-\/by-\/\-N orthogonal matrix. The diagonal elements of S\-I\-G\-M\-A are the singular values of A; they are real and non-\/negative, and are returned in descending order. The first min(m,n) columns of U and V are the left and right singular vectors of A.

Note that the routine returns V$\ast$$\ast$\-T, not V. Not L\-A\-P\-A\-C\-K Compliant for now! Note\-: Only Plasma\-No\-Vec supported!


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em jobu} & Specifies options for computing all or part of the matrix U. Intended usage\-: = Plasma\-Vec\-: all M columns of U are returned in array U; = Plasma\-No\-Vec\-: no columns of U (no left singular vectors) are computed. Note\-: Only Plasma\-No\-Vec supported!\\
\hline
\mbox{\tt in}  & {\em jobvt} & Specifies options for computing all or part of the matrix V$\ast$$\ast$\-H. Intended usage\-: = Plasma\-Vec\-: all M columns of U are returned in array U; = Plasma\-No\-Vec\-: no columns of U (no left singular vectors) are computed. Note\-: Only Plasma\-No\-Vec supported!\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\-N matrix A. On exit, if J\-O\-B\-U = 'O', A is overwritten with the first min(m,n) columns of U (the left singular vectors, stored columnwise); if J\-O\-B\-V\-T = 'O', A is overwritten with the first min(m,n) rows of V$\ast$$\ast$\-H (the right singular vectors, stored rowwise); if J\-O\-B\-U .ne. 'O' and J\-O\-B\-V\-T .ne. 'O', the contents of A are destroyed.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt out}  & {\em S} & The double precision singular values of A, sorted so that S(i) $>$= S(i+1).\\
\hline
\mbox{\tt out}  & {\em U} & (L\-D\-U,M) if J\-O\-B\-U = 'A' or (L\-D\-U,min(\-M,\-N)) if J\-O\-B\-U = 'S'. If J\-O\-B\-U = 'A', U contains the M-\/by-\/\-M unitary matrix U; if J\-O\-B\-U = 'S', U contains the first min(m,n) columns of U (the left singular vectors, stored columnwise); if J\-O\-B\-U = 'N' or 'O', U is not referenced.\\
\hline
\mbox{\tt in}  & {\em L\-D\-U} & The leading dimension of the array U. L\-D\-U $>$= 1; if J\-O\-B\-U = 'S' or 'A', L\-D\-U $>$= M.\\
\hline
\mbox{\tt out}  & {\em V\-T} & If J\-O\-B\-V\-T = 'A', V\-T contains the N-\/by-\/\-N unitary matrix V$\ast$$\ast$\-H; if J\-O\-B\-V\-T = 'S', V\-T contains the first min(m,n) rows of V$\ast$$\ast$\-H (the right singular vectors, stored rowwise); if J\-O\-B\-V\-T = 'N' or 'O', V\-T is not referenced.\\
\hline
\mbox{\tt in}  & {\em L\-D\-V\-T} & The leading dimension of the array V\-T. L\-D\-V\-T $>$= 1; if J\-O\-B\-V\-T = 'A', L\-D\-V\-T $>$= N; if J\-O\-B\-V\-T = 'S', L\-D\-V\-T $>$= min(\-M,\-N).\\
\hline
\mbox{\tt in,out}  & {\em desc\-T} & On entry, descriptor as return by P\-L\-A\-S\-M\-A\-\_\-\-Alloc\-\_\-\-Workspace\-\_\-zgesvd On exit, contains auxiliary factorization data.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga025036ca043dbc70234c596eaf890b09_ga025036ca043dbc70234c596eaf890b09}{P\-L\-A\-S\-M\-A\-\_\-zgesvd\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gaeeee9490a0606f1160863b3de568b8fe_gaeeee9490a0606f1160863b3de568b8fe}{P\-L\-A\-S\-M\-A\-\_\-zgesvd\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga2c71687d9af24541b259570cb46fbce0_ga2c71687d9af24541b259570cb46fbce0}{P\-L\-A\-S\-M\-A\-\_\-cgesvd} 

\hyperlink{group__double_ga033944c3892f07b32ae0275788e51b00_ga033944c3892f07b32ae0275788e51b00}{P\-L\-A\-S\-M\-A\-\_\-dgesvd} 

\hyperlink{group__float_ga5f1c967294c4214329ed839f41988e2b_ga5f1c967294c4214329ed839f41988e2b}{P\-L\-A\-S\-M\-A\-\_\-sgesvd} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga03449aa4e83b2f2223dad281d122697d_ga03449aa4e83b2f2223dad281d122697d}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zgetrf@{P\-L\-A\-S\-M\-A\-\_\-zgetrf}}
\index{P\-L\-A\-S\-M\-A\-\_\-zgetrf@{P\-L\-A\-S\-M\-A\-\_\-zgetrf}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zgetrf}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zgetrf (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{int $\ast$}]{I\-P\-I\-V}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga03449aa4e83b2f2223dad281d122697d_ga03449aa4e83b2f2223dad281d122697d}
P\-L\-A\-S\-M\-A\-\_\-zgetrf -\/ Computes an L\-U factorization of a general M-\/by-\/\-N matrix A using the tile L\-U algorithm with partial tile pivoting with row interchanges.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\-N matrix to be factored. On exit, the tile factors L and U from the factorization.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt out}  & {\em I\-P\-I\-V} & The pivot indices that define the permutations.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gabaabd34550ca8a2ba83245af3c44bea0_gabaabd34550ca8a2ba83245af3c44bea0}{P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga8005f834cea1750e617b078d2cfa39d2_ga8005f834cea1750e617b078d2cfa39d2}{P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga9a372dbe56f1ef00531a284e1bf3a694_ga9a372dbe56f1ef00531a284e1bf3a694}{P\-L\-A\-S\-M\-A\-\_\-cgetrf} 

\hyperlink{group__double_gaa626e37ec710bfb5c98fef7b00511ea8_gaa626e37ec710bfb5c98fef7b00511ea8}{P\-L\-A\-S\-M\-A\-\_\-dgetrf} 

\hyperlink{group__float_ga8bf6af99c20539f64fa60b64d99fc1be_ga8bf6af99c20539f64fa60b64d99fc1be}{P\-L\-A\-S\-M\-A\-\_\-sgetrf} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga085b5e62180512c7c603e72a9092ad8d_ga085b5e62180512c7c603e72a9092ad8d}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv@{P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv}}
\index{P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv@{P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-L, }
\item[{int $\ast$}]{I\-P\-I\-V}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga085b5e62180512c7c603e72a9092ad8d_ga085b5e62180512c7c603e72a9092ad8d}
P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv -\/ Computes an L\-U factorization of a general M-\/by-\/\-N matrix A using the tile L\-U algorithm with partial tile pivoting with row interchanges.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the M-\/by-\/\-N matrix to be factored. On exit, the tile factors L and U from the factorization.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt out}  & {\em desc\-L} & On exit, auxiliary factorization data, related to the tile L factor, required by P\-L\-A\-S\-M\-A\-\_\-zgetrs\-\_\-incpiv to solve the system of equations.\\
\hline
\mbox{\tt out}  & {\em I\-P\-I\-V} & The pivot indices that define the permutations (not equivalent to L\-A\-P\-A\-C\-K).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga767b9ff4ff1b5289e680ea42b05786e1_ga767b9ff4ff1b5289e680ea42b05786e1}{P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gaa9d5a18c3cd7ddfb551cfcffe7d90f2d_gaa9d5a18c3cd7ddfb551cfcffe7d90f2d}{P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gaaeca906ffb473a1bc1772671fb4f558f_gaaeca906ffb473a1bc1772671fb4f558f}{P\-L\-A\-S\-M\-A\-\_\-cgetrf\-\_\-incpiv} 

\hyperlink{group__double_gad1a9ffdf2bf95696d94eac58177c3964_gad1a9ffdf2bf95696d94eac58177c3964}{P\-L\-A\-S\-M\-A\-\_\-dgetrf\-\_\-incpiv} 

\hyperlink{group__float_ga2980cac88a14ba51d0ef99036f5ace69_ga2980cac88a14ba51d0ef99036f5ace69}{P\-L\-A\-S\-M\-A\-\_\-sgetrf\-\_\-incpiv} 

\hyperlink{group__PLASMA__Complex64__t_ga421d402c25832837b8247720d1ce79d5_ga421d402c25832837b8247720d1ce79d5}{P\-L\-A\-S\-M\-A\-\_\-zgetrs\-\_\-incpiv} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga96b45d431296d17561924b09a770ce17_ga96b45d431296d17561924b09a770ce17}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zgetri@{P\-L\-A\-S\-M\-A\-\_\-zgetri}}
\index{P\-L\-A\-S\-M\-A\-\_\-zgetri@{P\-L\-A\-S\-M\-A\-\_\-zgetri}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zgetri}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zgetri (
\begin{DoxyParamCaption}
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{int $\ast$}]{I\-P\-I\-V}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga96b45d431296d17561924b09a770ce17_ga96b45d431296d17561924b09a770ce17}
P\-L\-A\-S\-M\-A\-\_\-zgetri -\/ Computes the inverse of a matrix using the L\-U factorization computed by P\-L\-A\-S\-M\-A\-\_\-zgetrf. This method inverts U and then computes inv(\-A) by solving the system inv(\-A)$\ast$\-L = inv(\-U) for inv(\-A).


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the triangular factor L or U from the factorization A = P$\ast$\-L$\ast$\-U as computed by P\-L\-A\-S\-M\-A\-\_\-zgetrf. On exit, if return value = 0, the inverse of the original matrix A.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in}  & {\em I\-P\-I\-V} & The pivot indices that define the permutations as returned by P\-L\-A\-S\-M\-A\-\_\-zgetrf.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, the (i,i) element of the factor U is exactly zero; The matrix is singular and its inverse could not be computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga7da186dd28a5bd5551d4c18ebb8e38ea_ga7da186dd28a5bd5551d4c18ebb8e38ea}{P\-L\-A\-S\-M\-A\-\_\-zgetri\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga128683abcbdcfef6eda7503f0ff45d0d_ga128683abcbdcfef6eda7503f0ff45d0d}{P\-L\-A\-S\-M\-A\-\_\-zgetri\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gaecd124d0a04fc7a679385fd13018fa02_gaecd124d0a04fc7a679385fd13018fa02}{P\-L\-A\-S\-M\-A\-\_\-cgetri} 

\hyperlink{group__double_gaef9247e762016885c0b31dc28356bab7_gaef9247e762016885c0b31dc28356bab7}{P\-L\-A\-S\-M\-A\-\_\-dgetri} 

\hyperlink{group__float_gadb78715cdd99791aa77c2640f1325f8e_gadb78715cdd99791aa77c2640f1325f8e}{P\-L\-A\-S\-M\-A\-\_\-sgetri} 

\hyperlink{group__PLASMA__Complex64__t_ga03449aa4e83b2f2223dad281d122697d_ga03449aa4e83b2f2223dad281d122697d}{P\-L\-A\-S\-M\-A\-\_\-zgetrf} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gad7b041e52be07ced12ad09ca2c51ddc6_gad7b041e52be07ced12ad09ca2c51ddc6}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zgetrs@{P\-L\-A\-S\-M\-A\-\_\-zgetrs}}
\index{P\-L\-A\-S\-M\-A\-\_\-zgetrs@{P\-L\-A\-S\-M\-A\-\_\-zgetrs}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zgetrs}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zgetrs (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans, }
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{int $\ast$}]{I\-P\-I\-V, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gad7b041e52be07ced12ad09ca2c51ddc6_gad7b041e52be07ced12ad09ca2c51ddc6}
P\-L\-A\-S\-M\-A\-\_\-zgetrs -\/ Solves a system of linear equations A $\ast$ X = B, with a general N-\/by-\/\-N matrix A using the tile L\-U factorization computed by P\-L\-A\-S\-M\-A\-\_\-zgetrf.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em trans} & Intended to specify the the form of the system of equations\-: = Plasma\-No\-Trans\-: A $\ast$ X = B (No transpose) = Plasma\-Trans\-: A$\ast$$\ast$\-T $\ast$ X = B (Transpose) = Plasma\-Conj\-Trans\-: A$\ast$$\ast$\-H $\ast$ X = B (Conjugate transpose)\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of right hand sides, i.\-e., the number of columns of the matrix B. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The tile factors L and U from the factorization, computed by P\-L\-A\-S\-M\-A\-\_\-zgetrf.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in}  & {\em I\-P\-I\-V} & The pivot indices from P\-L\-A\-S\-M\-A\-\_\-zgetrf.\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\-N\-R\-H\-S matrix of right hand side matrix B. On exit, the solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
\end{DoxyRetVals}
\begin{DoxyReturn}{Returns}
$<$0 if -\/i, the i-\/th argument had an illegal value
\end{DoxyReturn}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga7a5cc3d203a14369272322ed4b9922ca_ga7a5cc3d203a14369272322ed4b9922ca}{P\-L\-A\-S\-M\-A\-\_\-zgetrs\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga8c9e7f91287449767222b5156a57a384_ga8c9e7f91287449767222b5156a57a384}{P\-L\-A\-S\-M\-A\-\_\-zgetrs\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gaa63ca86deb84eae5320d832f5dffd2fc_gaa63ca86deb84eae5320d832f5dffd2fc}{P\-L\-A\-S\-M\-A\-\_\-cgetrs} 

\hyperlink{group__double_ga5b08c48445d3d72e892aceafa3f5b788_ga5b08c48445d3d72e892aceafa3f5b788}{P\-L\-A\-S\-M\-A\-\_\-dgetrs} 

\hyperlink{group__float_gabd57d3c25369b07e888ef602d8771285_gabd57d3c25369b07e888ef602d8771285}{P\-L\-A\-S\-M\-A\-\_\-sgetrs} 

\hyperlink{group__PLASMA__Complex64__t_ga03449aa4e83b2f2223dad281d122697d_ga03449aa4e83b2f2223dad281d122697d}{P\-L\-A\-S\-M\-A\-\_\-zgetrf} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga421d402c25832837b8247720d1ce79d5_ga421d402c25832837b8247720d1ce79d5}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zgetrs\-\_\-incpiv@{P\-L\-A\-S\-M\-A\-\_\-zgetrs\-\_\-incpiv}}
\index{P\-L\-A\-S\-M\-A\-\_\-zgetrs\-\_\-incpiv@{P\-L\-A\-S\-M\-A\-\_\-zgetrs\-\_\-incpiv}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zgetrs\-\_\-incpiv}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zgetrs\-\_\-incpiv (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans, }
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-L, }
\item[{int $\ast$}]{I\-P\-I\-V, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga421d402c25832837b8247720d1ce79d5_ga421d402c25832837b8247720d1ce79d5}
P\-L\-A\-S\-M\-A\-\_\-zgetrs\-\_\-incpiv -\/ Solves a system of linear equations A $\ast$ X = B, with a general N-\/by-\/\-N matrix A using the tile L\-U factorization computed by P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em trans} & Intended to specify the the form of the system of equations\-: = Plasma\-No\-Trans\-: A $\ast$ X = B (No transpose) = Plasma\-Trans\-: A$\ast$$\ast$\-T $\ast$ X = B (Transpose) = Plasma\-Conj\-Trans\-: A$\ast$$\ast$\-H $\ast$ X = B (Conjugate transpose) Currently only Plasma\-No\-Trans is supported.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of right hand sides, i.\-e., the number of columns of the matrix B. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The tile factors L and U from the factorization, computed by P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in}  & {\em desc\-L} & Auxiliary factorization data, related to the tile L factor, computed by P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv.\\
\hline
\mbox{\tt in}  & {\em I\-P\-I\-V} & The pivot indices from P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv (not equivalent to L\-A\-P\-A\-C\-K).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\-N\-R\-H\-S matrix of right hand side matrix B. On exit, the solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
\end{DoxyRetVals}
\begin{DoxyReturn}{Returns}
$<$0 if -\/i, the i-\/th argument had an illegal value
\end{DoxyReturn}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga98dfc8fc95ebd0886aaacec0694600ba_ga98dfc8fc95ebd0886aaacec0694600ba}{P\-L\-A\-S\-M\-A\-\_\-zgetrs\-\_\-incpiv\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga6a3ffe51ae54b35174d9f106c563ac64_ga6a3ffe51ae54b35174d9f106c563ac64}{P\-L\-A\-S\-M\-A\-\_\-zgetrs\-\_\-incpiv\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga76f71e3044a34898fcf7f5c8a9522183_ga76f71e3044a34898fcf7f5c8a9522183}{P\-L\-A\-S\-M\-A\-\_\-cgetrs\-\_\-incpiv} 

\hyperlink{group__double_gac66423b6f925105bbb478f55e2ff98ee_gac66423b6f925105bbb478f55e2ff98ee}{P\-L\-A\-S\-M\-A\-\_\-dgetrs\-\_\-incpiv} 

\hyperlink{group__float_ga2fecfebe8c2992a7eac4b8006068cd22_ga2fecfebe8c2992a7eac4b8006068cd22}{P\-L\-A\-S\-M\-A\-\_\-sgetrs\-\_\-incpiv} 

\hyperlink{group__PLASMA__Complex64__t_ga085b5e62180512c7c603e72a9092ad8d_ga085b5e62180512c7c603e72a9092ad8d}{P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gad148e141c13feede49709370caea9c2a_gad148e141c13feede49709370caea9c2a}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zheev@{P\-L\-A\-S\-M\-A\-\_\-zheev}}
\index{P\-L\-A\-S\-M\-A\-\_\-zheev@{P\-L\-A\-S\-M\-A\-\_\-zheev}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zheev}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zheev (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{jobz, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{double $\ast$}]{W, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{Q, }
\item[{int}]{L\-D\-Q}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gad148e141c13feede49709370caea9c2a_gad148e141c13feede49709370caea9c2a}
P\-L\-A\-S\-M\-A\-\_\-zheev -\/ Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. The matrix A is preliminary reduced to tridiagonal form using a two-\/stage approach\-: First stage\-: reduction to band tridiagonal form; Second stage\-: reduction from band to tridiagonal form.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em jobz} & Intended usage\-: = Plasma\-No\-Vec\-: computes eigenvalues only; = Plasma\-Vec\-: computes eigenvalues and eigenvectors.\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\-: = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric (or Hermitian) matrix A. If uplo = Plasma\-Upper, the leading N-\/by-\/\-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\-Lower, the leading N-\/by-\/\-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the lower triangle (if uplo = Plasma\-Lower) or the upper triangle (if uplo = Plasma\-Upper) of A, including the diagonal, is destroyed.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt out}  & {\em W} & On exit, if info = 0, the eigenvalues.\\
\hline
\mbox{\tt in,out}  & {\em desc\-T} & On entry, descriptor as return by P\-L\-A\-S\-M\-A\-\_\-\-Alloc\-\_\-\-Workspace\-\_\-zheev On exit, contains auxiliary factorization data.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, if jobz = Plasma\-Vec and info = 0, the eigenvectors.\\
\hline
\mbox{\tt in}  & {\em L\-D\-Q} & The leading dimension of the array Q. L\-D\-Q $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if I\-N\-F\-O = i, the algorithm failed to converge; i off-\/diagonal elements of an intermediate tridiagonal form did not converge to zero.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga8950fc5b8aad1db5b23a369c7971f935_ga8950fc5b8aad1db5b23a369c7971f935}{P\-L\-A\-S\-M\-A\-\_\-zheev\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga60a2e9e10307ed2e539bc1ff997465b7_ga60a2e9e10307ed2e539bc1ff997465b7}{P\-L\-A\-S\-M\-A\-\_\-zheev\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga0d2fe45268be2c3d25593d80dd0c547f_ga0d2fe45268be2c3d25593d80dd0c547f}{P\-L\-A\-S\-M\-A\-\_\-cheev} 

\hyperlink{group__double_gac7ea19b1441c1325f45c0f6a9cfd8a8a_gac7ea19b1441c1325f45c0f6a9cfd8a8a}{P\-L\-A\-S\-M\-A\-\_\-dsyev} 

\hyperlink{group__float_ga92b57475b852b71b42bc39cd0d1ec356_ga92b57475b852b71b42bc39cd0d1ec356}{P\-L\-A\-S\-M\-A\-\_\-ssyev} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gad7de537e69c66566cc4e8e0b9fbfdb87_gad7de537e69c66566cc4e8e0b9fbfdb87}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zheevd@{P\-L\-A\-S\-M\-A\-\_\-zheevd}}
\index{P\-L\-A\-S\-M\-A\-\_\-zheevd@{P\-L\-A\-S\-M\-A\-\_\-zheevd}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zheevd}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zheevd (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{jobz, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{double $\ast$}]{W, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{Q, }
\item[{int}]{L\-D\-Q}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gad7de537e69c66566cc4e8e0b9fbfdb87_gad7de537e69c66566cc4e8e0b9fbfdb87}
P\-L\-A\-S\-M\-A\-\_\-zheevd -\/ Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. The matrix A is preliminary reduced to tridiagonal form using a two-\/stage approach\-: First stage\-: reduction to band tridiagonal form; Second stage\-: reduction from band to tridiagonal form.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em jobz} & Intended usage\-: = Plasma\-No\-Vec\-: computes eigenvalues only; = Plasma\-Vec\-: computes eigenvalues and eigenvectors.\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\-: = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric (or Hermitian) matrix A. If uplo = Plasma\-Upper, the leading N-\/by-\/\-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\-Lower, the leading N-\/by-\/\-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the lower triangle (if uplo = Plasma\-Lower) or the upper triangle (if uplo = Plasma\-Upper) of A, including the diagonal, is destroyed.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt out}  & {\em W} & On exit, if info = 0, the eigenvalues.\\
\hline
\mbox{\tt in,out}  & {\em desc\-T} & On entry, descriptor as return by P\-L\-A\-S\-M\-A\-\_\-\-Alloc\-\_\-\-Workspace\-\_\-zheevd On exit, contains auxiliary factorization data.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, if jobz = Plasma\-Vec and info = 0, the eigenvectors.\\
\hline
\mbox{\tt in}  & {\em L\-D\-Q} & The leading dimension of the array Q. L\-D\-Q $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if I\-N\-F\-O = i, the algorithm failed to converge; i off-\/diagonal elements of an intermediate tridiagonal form did not converge to zero.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gacf562f4797071417427688a0bcb590e9_gacf562f4797071417427688a0bcb590e9}{P\-L\-A\-S\-M\-A\-\_\-zheevd\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga6a7d30d39380d93ed1aacc15a79bde8f_ga6a7d30d39380d93ed1aacc15a79bde8f}{P\-L\-A\-S\-M\-A\-\_\-zheevd\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga73b59abe87bcb46382a26a50c70345ad_ga73b59abe87bcb46382a26a50c70345ad}{P\-L\-A\-S\-M\-A\-\_\-cheevd} 

\hyperlink{group__double_gac7ea19b1441c1325f45c0f6a9cfd8a8a_gac7ea19b1441c1325f45c0f6a9cfd8a8a}{P\-L\-A\-S\-M\-A\-\_\-dsyev} 

\hyperlink{group__float_ga92b57475b852b71b42bc39cd0d1ec356_ga92b57475b852b71b42bc39cd0d1ec356}{P\-L\-A\-S\-M\-A\-\_\-ssyev} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga387eb7a21f8b3d03aec26324255e7510_ga387eb7a21f8b3d03aec26324255e7510}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zhegst@{P\-L\-A\-S\-M\-A\-\_\-zhegst}}
\index{P\-L\-A\-S\-M\-A\-\_\-zhegst@{P\-L\-A\-S\-M\-A\-\_\-zhegst}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zhegst}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zhegst (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{itype, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga387eb7a21f8b3d03aec26324255e7510_ga387eb7a21f8b3d03aec26324255e7510}
P\-L\-A\-S\-M\-A\-\_\-zhegst -\/ reduces a complex Hermitian-\/definite generalized eigenproblem to standard form. If Plasma\-Itype == 1, the problem is A$\ast$x = lambda$\ast$\-B$\ast$x, and A is overwritten by inv(\-U$\ast$$\ast$\-H)$\ast$\-A$\ast$inv(U) or inv(\-L)$\ast$\-A$\ast$inv(L$\ast$$\ast$\-H) If Plasma\-Itype == 2 or 3, the problem is A$\ast$\-B$\ast$x = lambda$\ast$x or B$\ast$\-A$\ast$x = lambda$\ast$x, and A is overwritten by U$\ast$\-A$\ast$\-U$\ast$$\ast$\-H or L$\ast$$\ast$\-H$\ast$\-A$\ast$\-L. B must have been previously factorized as U$\ast$$\ast$\-H$\ast$\-U or L$\ast$\-L$\ast$$\ast$\-H by P\-L\-A\-S\-M\-A\-\_\-\-Z\-P\-O\-T\-R\-F.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em itype} & Intended usage\-: = 1\-: A$\ast$x=(lambda)$\ast$\-B$\ast$x = 2\-: A$\ast$\-Bx=(lambda)$\ast$x = 3\-: B$\ast$\-A$\ast$x=(lambda)$\ast$x\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\-: = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrices A and B. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric (or Hermitian) matrix A. If uplo = Plasma\-Upper, the leading N-\/by-\/\-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\-Lower, the leading N-\/by-\/\-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if return value == 0, the transformed matrix, stored in the same format as A.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the triangular factor from the Cholesky factorization of B, as returned by P\-L\-A\-S\-M\-A\-\_\-\-Z\-P\-O\-T\-R\-F.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gaa28f6da2b7b8e8af7abf429f7f01047d_gaa28f6da2b7b8e8af7abf429f7f01047d}{P\-L\-A\-S\-M\-A\-\_\-zhegst\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga2b7df2f947d4f57750cf4f0145c80624_ga2b7df2f947d4f57750cf4f0145c80624}{P\-L\-A\-S\-M\-A\-\_\-zhegst\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gac4b81a8ac8396c84a27d8a0b719bc379_gac4b81a8ac8396c84a27d8a0b719bc379}{P\-L\-A\-S\-M\-A\-\_\-chegst} 

\hyperlink{group__double_ga7ab44c615960d36295086012efc45a7d_ga7ab44c615960d36295086012efc45a7d}{P\-L\-A\-S\-M\-A\-\_\-dsygst} 

\hyperlink{group__float_ga66b77c0de44f80760c4184756250e75e_ga66b77c0de44f80760c4184756250e75e}{P\-L\-A\-S\-M\-A\-\_\-ssygst} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gaec004491cb00c99f63f9604c84ef8f43_gaec004491cb00c99f63f9604c84ef8f43}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zhegv@{P\-L\-A\-S\-M\-A\-\_\-zhegv}}
\index{P\-L\-A\-S\-M\-A\-\_\-zhegv@{P\-L\-A\-S\-M\-A\-\_\-zhegv}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zhegv}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zhegv (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{itype, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{jobz, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B, }
\item[{double $\ast$}]{W, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{Q, }
\item[{int}]{L\-D\-Q}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gaec004491cb00c99f63f9604c84ef8f43_gaec004491cb00c99f63f9604c84ef8f43}
P\-L\-A\-S\-M\-A\-\_\-zhegv -\/ Computes all eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian-\/definite eigenproblem of the form\-: A$\ast$x=(lambda)$\ast$\-B$\ast$x, A$\ast$\-Bx=(lambda)$\ast$x, or B$\ast$\-A$\ast$x=(lambda)$\ast$x. Here A and B are assumed to be Hermitian and B is also positive definite.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em itype} & Intended usage\-: = 1\-: A$\ast$x=(lambda)$\ast$\-B$\ast$x = 2\-: A$\ast$\-Bx=(lambda)$\ast$x = 3\-: B$\ast$\-A$\ast$x=(lambda)$\ast$x\\
\hline
\mbox{\tt in}  & {\em jobz} & Intended usage\-: = Plasma\-No\-Vec\-: computes eigenvalues only; = Plasma\-Vec\-: computes eigenvalues and eigenvectors.\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\-: = Plasma\-Upper\-: Upper triangle of A and B are stored; = Plasma\-Lower\-: Lower triangle of A and B are stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric (or Hermitian) matrix A. If uplo = Plasma\-Upper, the leading N-\/by-\/\-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\-Lower, the leading N-\/by-\/\-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if jobz = Plasma\-Vec, then if return value = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows\-: if I\-T\-Y\-P\-E = 1 or 2, Z$\ast$$\ast$\-H$\ast$\-B$\ast$\-Z = I; if I\-T\-Y\-P\-E = 3, Z$\ast$$\ast$\-H$\ast$inv(B)$\ast$\-Z = I. If jobz = Plasma\-No\-Vec, then on exit the lower triangle (if uplo = Plasma\-Lower) or the upper triangle (if uplo = Plasma\-Upper) of A, including the diagonal, is destroyed.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the symmetric (or Hermitian) positive definite matrix B. If uplo = Plasma\-Upper, the leading N-\/by-\/\-N upper triangular part of B contains the upper triangular part of the matrix B, and the strictly lower triangular part of B is not referenced. If uplo = Plasma\-Lower, the leading N-\/by-\/\-N lower triangular part of B contains the lower triangular part of the matrix B, and the strictly upper triangular part of B is not referenced. On exit, if return value $<$= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U$\ast$$\ast$\-H$\ast$\-U or B = L$\ast$\-L$\ast$$\ast$\-H.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt out}  & {\em W} & On exit, if info = 0, the eigenvalues.\\
\hline
\mbox{\tt in,out}  & {\em desc\-T} & On entry, descriptor as return by P\-L\-A\-S\-M\-A\-\_\-\-Alloc\-\_\-\-Workspace\-\_\-zhegv On exit, contains auxiliary factorization data.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, if jobz = Plasma\-Vec and info = 0, the eigenvectors.\\
\hline
\mbox{\tt in}  & {\em L\-D\-Q} & The leading dimension of Q.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $<$=\-N} & if I\-N\-F\-O = i, plasma\-\_\-zhegv failed to converge; i off-\/diagonal elements of an intermediate tridiagonal form did not converge to zero. \\
\hline
{\em $>$\-N} & if I\-N\-F\-O = N + i, for 1 $<$= i $<$= N, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gaf4bdf938225d0259e4df04006bd80655_gaf4bdf938225d0259e4df04006bd80655}{P\-L\-A\-S\-M\-A\-\_\-zhegv\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga0a534f6761d13d19f35b9944934bff2e_ga0a534f6761d13d19f35b9944934bff2e}{P\-L\-A\-S\-M\-A\-\_\-zhegv\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga7d0aad7dba26173b3cc6f35a74f6eaf0_ga7d0aad7dba26173b3cc6f35a74f6eaf0}{P\-L\-A\-S\-M\-A\-\_\-chegv} 

\hyperlink{group__double_ga7efdf7cffbb28696c69310d1627a100d_ga7efdf7cffbb28696c69310d1627a100d}{P\-L\-A\-S\-M\-A\-\_\-dsygv} 

\hyperlink{group__float_gaa5deb8e85d037eff767d9a9e5e99fad9_gaa5deb8e85d037eff767d9a9e5e99fad9}{P\-L\-A\-S\-M\-A\-\_\-ssygv} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga6ee549df75bf7738aa6066c564ff72a9_ga6ee549df75bf7738aa6066c564ff72a9}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zhegvd@{P\-L\-A\-S\-M\-A\-\_\-zhegvd}}
\index{P\-L\-A\-S\-M\-A\-\_\-zhegvd@{P\-L\-A\-S\-M\-A\-\_\-zhegvd}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zhegvd}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zhegvd (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{itype, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{jobz, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B, }
\item[{double $\ast$}]{W, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{Q, }
\item[{int}]{L\-D\-Q}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga6ee549df75bf7738aa6066c564ff72a9_ga6ee549df75bf7738aa6066c564ff72a9}
P\-L\-A\-S\-M\-A\-\_\-zhegvd -\/ Computes all eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian-\/definite eigenproblem of the form\-: A$\ast$x=(lambda)$\ast$\-B$\ast$x, A$\ast$\-Bx=(lambda)$\ast$x, or B$\ast$\-A$\ast$x=(lambda)$\ast$x. Here A and B are assumed to be Hermitian and B is also positive definite.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em itype} & Intended usage\-: = 1\-: A$\ast$x=(lambda)$\ast$\-B$\ast$x = 2\-: A$\ast$\-Bx=(lambda)$\ast$x = 3\-: B$\ast$\-A$\ast$x=(lambda)$\ast$x\\
\hline
\mbox{\tt in}  & {\em jobz} & Intended usage\-: = Plasma\-No\-Vec\-: computes eigenvalues only; = Plasma\-Vec\-: computes eigenvalues and eigenvectors.\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\-: = Plasma\-Upper\-: Upper triangle of A and B are stored; = Plasma\-Lower\-: Lower triangle of A and B are stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric (or Hermitian) matrix A. If uplo = Plasma\-Upper, the leading N-\/by-\/\-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\-Lower, the leading N-\/by-\/\-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if jobz = Plasma\-Vec, then if return value = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows\-: if I\-T\-Y\-P\-E = 1 or 2, Z$\ast$$\ast$\-H$\ast$\-B$\ast$\-Z = I; if I\-T\-Y\-P\-E = 3, Z$\ast$$\ast$\-H$\ast$inv(B)$\ast$\-Z = I. If jobz = Plasma\-No\-Vec, then on exit the lower triangle (if uplo = Plasma\-Lower) or the upper triangle (if uplo = Plasma\-Upper) of A, including the diagonal, is destroyed.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the symmetric (or Hermitian) positive definite matrix B. If uplo = Plasma\-Upper, the leading N-\/by-\/\-N upper triangular part of B contains the upper triangular part of the matrix B, and the strictly lower triangular part of B is not referenced. If uplo = Plasma\-Lower, the leading N-\/by-\/\-N lower triangular part of B contains the lower triangular part of the matrix B, and the strictly upper triangular part of B is not referenced. On exit, if return value $<$= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U$\ast$$\ast$\-H$\ast$\-U or B = L$\ast$\-L$\ast$$\ast$\-H.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt out}  & {\em W} & On exit, if info = 0, the eigenvalues.\\
\hline
\mbox{\tt in,out}  & {\em desc\-T} & On entry, descriptor as return by P\-L\-A\-S\-M\-A\-\_\-\-Alloc\-\_\-\-Workspace\-\_\-zhegvd On exit, contains auxiliary factorization data.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, if jobz = Plasma\-Vec and info = 0, the eigenvectors.\\
\hline
\mbox{\tt in}  & {\em L\-D\-Q} & The leading dimension of Q.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $<$=\-N} & if I\-N\-F\-O = i, plasma\-\_\-zhegvd failed to converge; i off-\/diagonal elements of an intermediate tridiagonal form did not converge to zero. \\
\hline
{\em $>$\-N} & if I\-N\-F\-O = N + i, for 1 $<$= i $<$= N, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gadbe098059f3edfb837f3294d4391bf02_gadbe098059f3edfb837f3294d4391bf02}{P\-L\-A\-S\-M\-A\-\_\-zhegvd\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga6065f0455ac9f6b971845fd193055758_ga6065f0455ac9f6b971845fd193055758}{P\-L\-A\-S\-M\-A\-\_\-zhegvd\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga7c4d8cc52849439d387178748f08d45b_ga7c4d8cc52849439d387178748f08d45b}{P\-L\-A\-S\-M\-A\-\_\-chegvd} 

\hyperlink{group__double_ga10b8c70c33dfee0cbbe6acb17217f717_ga10b8c70c33dfee0cbbe6acb17217f717}{P\-L\-A\-S\-M\-A\-\_\-dsygvd} 

\hyperlink{group__float_ga366bd2466847e2b9f29bd39a9d699fb9_ga366bd2466847e2b9f29bd39a9d699fb9}{P\-L\-A\-S\-M\-A\-\_\-ssygvd} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gad53a9ae69e0ff46c3859f19c16b97081_gad53a9ae69e0ff46c3859f19c16b97081}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zhemm@{P\-L\-A\-S\-M\-A\-\_\-zhemm}}
\index{P\-L\-A\-S\-M\-A\-\_\-zhemm@{P\-L\-A\-S\-M\-A\-\_\-zhemm}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zhemm}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zhemm (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{side, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{alpha, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{beta, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{C, }
\item[{int}]{L\-D\-C}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gad53a9ae69e0ff46c3859f19c16b97081_gad53a9ae69e0ff46c3859f19c16b97081}
P\-L\-A\-S\-M\-A\-\_\-zhemm -\/ Performs one of the matrix-\/matrix operations

\[ C = \alpha \times A \times B + \beta \times C \]

or

\[ C = \alpha \times B \times A + \beta \times C \]

where alpha and beta are scalars, A is an hermitian matrix and B and C are m by n matrices.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em side} & Specifies whether the hermitian matrix A appears on the left or right in the operation as follows\-: = Plasma\-Left\-: \[ C = \alpha \times A \times B + \beta \times C \] = Plasma\-Right\-: \[ C = \alpha \times B \times A + \beta \times C \]\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the upper or lower triangular part of the hermitian matrix A is to be referenced as follows\-: = Plasma\-Lower\-: Only the lower triangular part of the hermitian matrix A is to be referenced. = Plasma\-Upper\-: Only the upper triangular part of the hermitian matrix A is to be referenced.\\
\hline
\mbox{\tt in}  & {\em M} & Specifies the number of rows of the matrix C. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & Specifies the number of columns of the matrix C. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & Specifies the scalar alpha.\\
\hline
\mbox{\tt in}  & {\em A} & A is a L\-D\-A-\/by-\/ka matrix, where ka is M when side = Plasma\-Left, and is N otherwise. Only the uplo triangular part is referenced.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,ka).\\
\hline
\mbox{\tt in}  & {\em B} & B is a L\-D\-B-\/by-\/\-N matrix, where the leading M-\/by-\/\-N part of the array B must contain the matrix B.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-M).\\
\hline
\mbox{\tt in}  & {\em beta} & Specifies the scalar beta.\\
\hline
\mbox{\tt in,out}  & {\em C} & C is a L\-D\-C-\/by-\/\-N matrix. On exit, the array is overwritten by the M by N updated matrix.\\
\hline
\mbox{\tt in}  & {\em L\-D\-C} & The leading dimension of the array C. L\-D\-C $>$= max(1,\-M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga7f8b661b2774dd77bc0eef260f1eef3c_ga7f8b661b2774dd77bc0eef260f1eef3c}{P\-L\-A\-S\-M\-A\-\_\-zhemm\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex32__t_ga5eccc301c2b8ed5497c8149d002d3ca8_ga5eccc301c2b8ed5497c8149d002d3ca8}{P\-L\-A\-S\-M\-A\-\_\-chemm} 

P\-L\-A\-S\-M\-A\-\_\-dhemm 

P\-L\-A\-S\-M\-A\-\_\-shemm 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga1086284f7bd6db0de2341eeaa3a3e655_ga1086284f7bd6db0de2341eeaa3a3e655}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zher2k@{P\-L\-A\-S\-M\-A\-\_\-zher2k}}
\index{P\-L\-A\-S\-M\-A\-\_\-zher2k@{P\-L\-A\-S\-M\-A\-\_\-zher2k}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zher2k}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zher2k (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{alpha, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B, }
\item[{double}]{beta, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{C, }
\item[{int}]{L\-D\-C}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga1086284f7bd6db0de2341eeaa3a3e655_ga1086284f7bd6db0de2341eeaa3a3e655}
P\-L\-A\-S\-M\-A\-\_\-zher2k -\/ Performs one of the hermitian rank 2k operations

\[ C = \alpha [ op( A ) \times conjg( op( B )' )] + conjg( \alpha ) [ op( B ) \times conjg( op( A )' )] + \beta C \], or \[ C = \alpha [ conjg( op( A )' ) \times op( B ) ] + conjg( \alpha ) [ conjg( op( B )' ) \times op( A ) ] + \beta C \],

where op( X ) is one of

op( X ) = X or op( X ) = conjg( X' )

where alpha and beta are real scalars, C is an n-\/by-\/n symmetric matrix and A and B are an n-\/by-\/k matrices the first case and k-\/by-\/n matrices in the second case.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\-Upper\-: Upper triangle of C is stored; = Plasma\-Lower\-: Lower triangle of C is stored.\\
\hline
\mbox{\tt in}  & {\em trans} & Specifies whether the matrix A is transposed or conjugate transposed\-: = Plasma\-No\-Trans\-: \[ C = \alpha [ op( A ) \times conjg( op( B )' )] + conjg( \alpha ) [ op( B ) \times conjg( op( A )' )] + \beta C \] = Plasma\-Conj\-Trans\-: \[ C = \alpha [ conjg( op( A )' ) \times op( B ) ] + conjg( \alpha ) [ conjg( op( B )' ) \times op( A ) ] + \beta C \]\\
\hline
\mbox{\tt in}  & {\em N} & N specifies the order of the matrix C. N must be at least zero.\\
\hline
\mbox{\tt in}  & {\em K} & K specifies the number of columns of the A and B matrices with trans = Plasma\-No\-Trans. K specifies the number of rows of the A and B matrices with trans = Plasma\-Trans.\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha.\\
\hline
\mbox{\tt in}  & {\em A} & A is a L\-D\-A-\/by-\/ka matrix, where ka is K when trans = Plasma\-No\-Trans, and is N otherwise.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A must be at least max( 1, N ), otherwise L\-D\-A must be at least max( 1, K ).\\
\hline
\mbox{\tt in}  & {\em B} & B is a L\-D\-B-\/by-\/kb matrix, where kb is K when trans = Plasma\-No\-Trans, and is N otherwise.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B must be at least max( 1, N ), otherwise L\-D\-B must be at least max( 1, K ).\\
\hline
\mbox{\tt in}  & {\em beta} & beta specifies the scalar beta.\\
\hline
\mbox{\tt in,out}  & {\em C} & C is a L\-D\-C-\/by-\/\-N matrix. On exit, the array uplo part of the matrix is overwritten by the uplo part of the updated matrix.\\
\hline
\mbox{\tt in}  & {\em L\-D\-C} & The leading dimension of the array C. L\-D\-C $>$= max( 1, N ).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gad2435eb3d2c1e66f89023aae6089cd04_gad2435eb3d2c1e66f89023aae6089cd04}{P\-L\-A\-S\-M\-A\-\_\-zher2k\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex32__t_ga2174f460c8b3a319d83f5890688c53af_ga2174f460c8b3a319d83f5890688c53af}{P\-L\-A\-S\-M\-A\-\_\-cher2k} 

P\-L\-A\-S\-M\-A\-\_\-dher2k 

P\-L\-A\-S\-M\-A\-\_\-sher2k 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga37897923ff4fb613bbd5a69a58b12fb8_ga37897923ff4fb613bbd5a69a58b12fb8}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zherk@{P\-L\-A\-S\-M\-A\-\_\-zherk}}
\index{P\-L\-A\-S\-M\-A\-\_\-zherk@{P\-L\-A\-S\-M\-A\-\_\-zherk}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zherk}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zherk (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{double}]{alpha, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{double}]{beta, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{C, }
\item[{int}]{L\-D\-C}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga37897923ff4fb613bbd5a69a58b12fb8_ga37897923ff4fb613bbd5a69a58b12fb8}
P\-L\-A\-S\-M\-A\-\_\-zherk -\/ Performs one of the hermitian rank k operations

\[ C = \alpha [ op( A ) \times conjg( op( A )' )] + \beta C \],

where op( X ) is one of

op( X ) = X or op( X ) = conjg( X' )

where alpha and beta are real scalars, C is an n-\/by-\/n hermitian matrix and A is an n-\/by-\/k matrix in the first case and a k-\/by-\/n matrix in the second case.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\-Upper\-: Upper triangle of C is stored; = Plasma\-Lower\-: Lower triangle of C is stored.\\
\hline
\mbox{\tt in}  & {\em trans} & Specifies whether the matrix A is transposed or conjugate transposed\-: = Plasma\-No\-Trans\-: A is not transposed; = Plasma\-Conj\-Trans\-: A is conjugate transposed.\\
\hline
\mbox{\tt in}  & {\em N} & N specifies the order of the matrix C. N must be at least zero.\\
\hline
\mbox{\tt in}  & {\em K} & K specifies the number of columns of the matrix op( A ).\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha.\\
\hline
\mbox{\tt in}  & {\em A} & A is a L\-D\-A-\/by-\/ka matrix, where ka is K when trans = Plasma\-No\-Trans, and is N otherwise.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A must be at least max( 1, N ) if trans == Plasma\-No\-Trans, otherwise L\-D\-A must be at least max( 1, K ).\\
\hline
\mbox{\tt in}  & {\em beta} & beta specifies the scalar beta\\
\hline
\mbox{\tt in,out}  & {\em C} & C is a L\-D\-C-\/by-\/\-N matrix. On exit, the array uplo part of the matrix is overwritten by the uplo part of the updated matrix.\\
\hline
\mbox{\tt in}  & {\em L\-D\-C} & The leading dimension of the array C. L\-D\-C $>$= max( 1, N ).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga01560f3e4d486a5576c6ed9b67756d67_ga01560f3e4d486a5576c6ed9b67756d67}{P\-L\-A\-S\-M\-A\-\_\-zherk\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex32__t_ga218b2a902b2a05b10c19161c88b2065a_ga218b2a902b2a05b10c19161c88b2065a}{P\-L\-A\-S\-M\-A\-\_\-cherk} 

P\-L\-A\-S\-M\-A\-\_\-dherk 

P\-L\-A\-S\-M\-A\-\_\-sherk 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gadeaa16b417f2033a10685c130db081fb_gadeaa16b417f2033a10685c130db081fb}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zhetrd@{P\-L\-A\-S\-M\-A\-\_\-zhetrd}}
\index{P\-L\-A\-S\-M\-A\-\_\-zhetrd@{P\-L\-A\-S\-M\-A\-\_\-zhetrd}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zhetrd}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zhetrd (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{jobz, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{double $\ast$}]{D, }
\item[{double $\ast$}]{E, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{Q, }
\item[{int}]{L\-D\-Q}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gadeaa16b417f2033a10685c130db081fb_gadeaa16b417f2033a10685c130db081fb}
P\-L\-A\-S\-M\-A\-\_\-zhetrd -\/ reduces a complex Hermitian matrix A to real symmetric tridiagonal form S using a two-\/stage approach First stage\-: reduction to band tridiagonal form (unitary Q1); Second stage\-: reduction from band to tridiagonal form (unitary Q2). Let Q = Q1 $\ast$ Q2 be the global unitary transformation; Q$\ast$$\ast$\-H $\ast$ A $\ast$ Q = S.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em jobz} & Intended usage\-: = Plasma\-No\-Vec\-: computes tridiagonal only; = Plasma\-Vec\-: computes tridiagonal and generate the orthogonal matrix Q.\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\-: = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric (or Hermitian) matrix A. If uplo = Plasma\-Upper, the leading N-\/by-\/\-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\-Lower, the leading N-\/by-\/\-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the lower triangle (if uplo = Plasma\-Lower) or the upper triangle (if uplo = Plasma\-Upper) of A, including the diagonal, is destroyed.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt out}  & {\em D} & On exit, the diagonal elements of the tridiagonal matrix\-: D(i) = A(i,i).\\
\hline
\mbox{\tt out}  & {\em E} & On exit, he off-\/diagonal elements of the tridiagonal matrix\-: E(i) = A(i,i+1) if uplo = Plasma\-Upper, E(i) = A(i+1,i) if uplo = Plasma\-Lower.\\
\hline
\mbox{\tt out}  & {\em desc\-T} & On entry, descriptor as return by P\-L\-A\-S\-M\-A\-\_\-\-Alloc\-\_\-\-Workspace\-\_\-zhetrd On exit, contains auxiliary factorization data.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, if jobz = Plasma\-Vec, then if return value = 0, Q contains the N-\/by-\/\-N unitary matrix Q. If jobz = Plasma\-No\-Vec, then it is not referenced.\\
\hline
\mbox{\tt in}  & {\em L\-D\-Q} & The leading dimension of the array Q. L\-D\-Q $>$= N.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if I\-N\-F\-O = i, the algorithm failed to converge; i off-\/diagonal elements of an intermediate tridiagonal form did not converge to zero.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gafced4fe39f5fa98ab1c9b8d857e2b7c4_gafced4fe39f5fa98ab1c9b8d857e2b7c4}{P\-L\-A\-S\-M\-A\-\_\-zhetrd\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga857cb7f326bb74e4a282c99bb2d9b557_ga857cb7f326bb74e4a282c99bb2d9b557}{P\-L\-A\-S\-M\-A\-\_\-zhetrd\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga72efb6e6664acbda79f267c167eae41c_ga72efb6e6664acbda79f267c167eae41c}{P\-L\-A\-S\-M\-A\-\_\-chetrd} 

\hyperlink{group__double_gaebb037c30606f77404ffef513f255d5c_gaebb037c30606f77404ffef513f255d5c}{P\-L\-A\-S\-M\-A\-\_\-dsytrd} 

\hyperlink{group__float_gadfee26871dee9a24b201bc329fccd81b_gadfee26871dee9a24b201bc329fccd81b}{P\-L\-A\-S\-M\-A\-\_\-ssytrd} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga8502c982b63153d2a7c11c05fe51cd39_ga8502c982b63153d2a7c11c05fe51cd39}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zlacpy@{P\-L\-A\-S\-M\-A\-\_\-zlacpy}}
\index{P\-L\-A\-S\-M\-A\-\_\-zlacpy@{P\-L\-A\-S\-M\-A\-\_\-zlacpy}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zlacpy}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zlacpy (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga8502c982b63153d2a7c11c05fe51cd39_ga8502c982b63153d2a7c11c05fe51cd39}
P\-L\-A\-S\-M\-A\-\_\-zlacpy copies all or part of a two-\/dimensional matrix A to another matrix B


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & Specifies the part of the matrix A to be copied to B. = Plasma\-Upper\-Lower\-: All the matrix A = Plasma\-Upper\-: Upper triangular part = Plasma\-Lower\-: Lower triangular part\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The M-\/by-\/\-N matrix A. If uplo = Plasma\-Upper, only the upper trapezium is accessed; if U\-P\-L\-O = Plasma\-Lower, only the lower trapezium is accessed.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt out}  & {\em B} & The M-\/by-\/\-N matrix B. On exit, B = A in the locations specified by U\-P\-L\-O.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-M).\\
\hline
\end{DoxyParams}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga59a20a10bc1d75d0a51db239183d19fb_ga59a20a10bc1d75d0a51db239183d19fb}{P\-L\-A\-S\-M\-A\-\_\-zlacpy\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gae38a72f65089e76fd46a2e978b46565f_gae38a72f65089e76fd46a2e978b46565f}{P\-L\-A\-S\-M\-A\-\_\-zlacpy\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga898cba57b9144416a37de9c72386c58a_ga898cba57b9144416a37de9c72386c58a}{P\-L\-A\-S\-M\-A\-\_\-clacpy} 

\hyperlink{group__double_gaa1c69f5b82fa24bd925055b4e0595dab_gaa1c69f5b82fa24bd925055b4e0595dab}{P\-L\-A\-S\-M\-A\-\_\-dlacpy} 

\hyperlink{group__float_ga2ae5e8cc7cf6222bf521a6decd6c27a1_ga2ae5e8cc7cf6222bf521a6decd6c27a1}{P\-L\-A\-S\-M\-A\-\_\-slacpy} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga89327462733d7b77d403e9612954474d_ga89327462733d7b77d403e9612954474d}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zlange@{P\-L\-A\-S\-M\-A\-\_\-zlange}}
\index{P\-L\-A\-S\-M\-A\-\_\-zlange@{P\-L\-A\-S\-M\-A\-\_\-zlange}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zlange}]{\setlength{\rightskip}{0pt plus 5cm}double P\-L\-A\-S\-M\-A\-\_\-zlange (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{norm, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{double $\ast$}]{work}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga89327462733d7b77d403e9612954474d_ga89327462733d7b77d403e9612954474d}
P\-L\-A\-S\-M\-A\-\_\-zlange returns the value

zlange = ( max(abs(A(i,j))), N\-O\-R\-M = Plasma\-Max\-Norm ( ( norm1(\-A), N\-O\-R\-M = Plasma\-One\-Norm ( ( norm\-I(\-A), N\-O\-R\-M = Plasma\-Inf\-Norm ( ( norm\-F(\-A), N\-O\-R\-M = Plasma\-Frobenius\-Norm

where norm1 denotes the one norm of a matrix (maximum column sum), norm\-I denotes the infinity norm of a matrix (maximum row sum) and norm\-F denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em norm} & = Plasma\-Max\-Norm\-: Max norm = Plasma\-One\-Norm\-: One norm = Plasma\-Inf\-Norm\-: Infinity norm = Plasma\-Frobenius\-Norm\-: Frobenius norm\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0. When M = 0, the returned value is set to zero.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0. When N = 0, the returned value is set to zero.\\
\hline
\mbox{\tt in}  & {\em A} & The M-\/by-\/\-N matrix A.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt in}  & {\em work} & double precision array of dimension (M\-A\-X(1,\-L\-W\-O\-R\-K)), where L\-W\-O\-R\-K $>$= M when N\-O\-R\-M = Plasma\-Inf\-Norm; otherwise, W\-O\-R\-K is not referenced.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em the} & norm described above.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga0f059e1eba1f049750759097e441a1a4_ga0f059e1eba1f049750759097e441a1a4}{P\-L\-A\-S\-M\-A\-\_\-zlange\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga57d6df0183911637315c83c07820d56d_ga57d6df0183911637315c83c07820d56d}{P\-L\-A\-S\-M\-A\-\_\-zlange\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga4520d4c444c0e4966fe0d261b175c3cd_ga4520d4c444c0e4966fe0d261b175c3cd}{P\-L\-A\-S\-M\-A\-\_\-clange} 

\hyperlink{group__double_gae51aee6b673e80bd606956ae6af92fbd_gae51aee6b673e80bd606956ae6af92fbd}{P\-L\-A\-S\-M\-A\-\_\-dlange} 

\hyperlink{group__float_ga778abdd6cc24bde2e6c7d41a2a563479_ga778abdd6cc24bde2e6c7d41a2a563479}{P\-L\-A\-S\-M\-A\-\_\-slange} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga3667b32ec418aa44fe1e28b78a670af6_ga3667b32ec418aa44fe1e28b78a670af6}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zlanhe@{P\-L\-A\-S\-M\-A\-\_\-zlanhe}}
\index{P\-L\-A\-S\-M\-A\-\_\-zlanhe@{P\-L\-A\-S\-M\-A\-\_\-zlanhe}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zlanhe}]{\setlength{\rightskip}{0pt plus 5cm}double P\-L\-A\-S\-M\-A\-\_\-zlanhe (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{norm, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{double $\ast$}]{work}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga3667b32ec418aa44fe1e28b78a670af6_ga3667b32ec418aa44fe1e28b78a670af6}
P\-L\-A\-S\-M\-A\-\_\-zlanhe returns the value

zlanhe = ( max(abs(A(i,j))), N\-O\-R\-M = Plasma\-Max\-Norm ( ( norm1(\-A), N\-O\-R\-M = Plasma\-One\-Norm ( ( norm\-I(\-A), N\-O\-R\-M = Plasma\-Inf\-Norm ( ( norm\-F(\-A), N\-O\-R\-M = Plasma\-Frobenius\-Norm

where norm1 denotes the one norm of a matrix (maximum column sum), norm\-I denotes the infinity norm of a matrix (maximum row sum) and norm\-F denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em norm} & = Plasma\-Max\-Norm\-: Max norm = Plasma\-One\-Norm\-: One norm = Plasma\-Inf\-Norm\-: Infinity norm = Plasma\-Frobenius\-Norm\-: Frobenius norm\\
\hline
\mbox{\tt in}  & {\em uplo} & = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns/rows of the matrix A. N $>$= 0. When N = 0, the returned value is set to zero.\\
\hline
\mbox{\tt in}  & {\em A} & The N-\/by-\/\-N matrix A.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in}  & {\em work} & double precision array of dimension P\-L\-A\-S\-M\-A\-\_\-\-S\-I\-Z\-E is P\-L\-A\-S\-M\-A\-\_\-\-S\-T\-A\-T\-I\-C\-\_\-\-S\-C\-H\-E\-D\-U\-L\-I\-N\-G is used, and N\-U\-L\-L otherwise.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em the} & norm described above.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga8ae849081c7c03c3f94169cdb9210db3_ga8ae849081c7c03c3f94169cdb9210db3}{P\-L\-A\-S\-M\-A\-\_\-zlanhe\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gaa6c26d48d48916841db34110002146c6_gaa6c26d48d48916841db34110002146c6}{P\-L\-A\-S\-M\-A\-\_\-zlanhe\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gaf609bd2319064273abdfacf8c733340f_gaf609bd2319064273abdfacf8c733340f}{P\-L\-A\-S\-M\-A\-\_\-clanhe} 

P\-L\-A\-S\-M\-A\-\_\-dlanhe 

P\-L\-A\-S\-M\-A\-\_\-slanhe 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga56ed091feed59f955ba15b8c6204e06a_ga56ed091feed59f955ba15b8c6204e06a}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zlansy@{P\-L\-A\-S\-M\-A\-\_\-zlansy}}
\index{P\-L\-A\-S\-M\-A\-\_\-zlansy@{P\-L\-A\-S\-M\-A\-\_\-zlansy}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zlansy}]{\setlength{\rightskip}{0pt plus 5cm}double P\-L\-A\-S\-M\-A\-\_\-zlansy (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{norm, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{double $\ast$}]{work}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga56ed091feed59f955ba15b8c6204e06a_ga56ed091feed59f955ba15b8c6204e06a}
P\-L\-A\-S\-M\-A\-\_\-zlansy returns the value

zlansy = ( max(abs(A(i,j))), N\-O\-R\-M = Plasma\-Max\-Norm ( ( norm1(\-A), N\-O\-R\-M = Plasma\-One\-Norm ( ( norm\-I(\-A), N\-O\-R\-M = Plasma\-Inf\-Norm ( ( norm\-F(\-A), N\-O\-R\-M = Plasma\-Frobenius\-Norm

where norm1 denotes the one norm of a matrix (maximum column sum), norm\-I denotes the infinity norm of a matrix (maximum row sum) and norm\-F denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em norm} & = Plasma\-Max\-Norm\-: Max norm = Plasma\-One\-Norm\-: One norm = Plasma\-Inf\-Norm\-: Infinity norm = Plasma\-Frobenius\-Norm\-: Frobenius norm\\
\hline
\mbox{\tt in}  & {\em uplo} & = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns/rows of the matrix A. N $>$= 0. When N = 0, the returned value is set to zero.\\
\hline
\mbox{\tt in}  & {\em A} & The N-\/by-\/\-N matrix A.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in}  & {\em work} & double precision array of dimension P\-L\-A\-S\-M\-A\-\_\-\-S\-I\-Z\-E is P\-L\-A\-S\-M\-A\-\_\-\-S\-T\-A\-T\-I\-C\-\_\-\-S\-C\-H\-E\-D\-U\-L\-I\-N\-G is used, and N\-U\-L\-L otherwise.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em the} & norm described above.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga857a208027710b6bd8f92a4706c2cb69_ga857a208027710b6bd8f92a4706c2cb69}{P\-L\-A\-S\-M\-A\-\_\-zlansy\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gac8468328525f1254a6b83925d71c62cf_gac8468328525f1254a6b83925d71c62cf}{P\-L\-A\-S\-M\-A\-\_\-zlansy\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga4c705dba935087686f8fdaa1e676b9f8_ga4c705dba935087686f8fdaa1e676b9f8}{P\-L\-A\-S\-M\-A\-\_\-clansy} 

\hyperlink{group__double_ga541f5864b15b169ab01998abb2c776ec_ga541f5864b15b169ab01998abb2c776ec}{P\-L\-A\-S\-M\-A\-\_\-dlansy} 

\hyperlink{group__float_gaa06de2986c0e12814a57e4def6110223_gaa06de2986c0e12814a57e4def6110223}{P\-L\-A\-S\-M\-A\-\_\-slansy} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga54817e0733e678bcdfdfeaa76ab486f6_ga54817e0733e678bcdfdfeaa76ab486f6}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-z\-Lapack\-\_\-to\-\_\-\-Tile@{P\-L\-A\-S\-M\-A\-\_\-z\-Lapack\-\_\-to\-\_\-\-Tile}}
\index{P\-L\-A\-S\-M\-A\-\_\-z\-Lapack\-\_\-to\-\_\-\-Tile@{P\-L\-A\-S\-M\-A\-\_\-z\-Lapack\-\_\-to\-\_\-\-Tile}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-z\-Lapack\-\_\-to\-\_\-\-Tile}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-z\-Lapack\-\_\-to\-\_\-\-Tile (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{Af77, }
\item[{int}]{L\-D\-A, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{A}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga54817e0733e678bcdfdfeaa76ab486f6_ga54817e0733e678bcdfdfeaa76ab486f6}
P\-L\-A\-S\-M\-A\-\_\-z\-Lapack\-\_\-to\-\_\-\-Tile -\/ Conversion from L\-A\-P\-A\-C\-K layout to tile layout.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em Af77} & L\-A\-P\-A\-C\-K matrix.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the matrix Af77.\\
\hline
\mbox{\tt in,out}  & {\em A} & Descriptor of the P\-L\-A\-S\-M\-A matrix in tile layout. If P\-L\-A\-S\-M\-A\-\_\-\-T\-R\-A\-N\-S\-L\-A\-T\-I\-O\-N\-\_\-\-M\-O\-D\-E is set to P\-L\-A\-S\-M\-A\-\_\-\-I\-N\-P\-L\-A\-C\-E, A-\/$>$mat is not used and set to Af77 when returns, else if P\-L\-A\-S\-M\-A\-\_\-\-T\-R\-A\-N\-S\-L\-A\-T\-I\-O\-N\-\_\-\-M\-O\-D\-E is set to P\-L\-A\-S\-M\-A\-\_\-\-O\-U\-T\-O\-F\-P\-L\-A\-C\-E, A-\/$>$mat has to be allocated before.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga3a85e3d7fff8991650e1b1f9761c9153_ga3a85e3d7fff8991650e1b1f9761c9153}{P\-L\-A\-S\-M\-A\-\_\-z\-Lapack\-\_\-to\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex64__t_ga8df0b9fdc5537a648d7544b528c9e6e3_ga8df0b9fdc5537a648d7544b528c9e6e3}{P\-L\-A\-S\-M\-A\-\_\-z\-Tile\-\_\-to\-\_\-\-Lapack} 

\hyperlink{group__PLASMA__Complex32__t_ga44c99c1388a7830a6efbc4fc1ab328f3_ga44c99c1388a7830a6efbc4fc1ab328f3}{P\-L\-A\-S\-M\-A\-\_\-c\-Lapack\-\_\-to\-\_\-\-Tile} 

\hyperlink{group__double_ga36e9254b8f24778e1aed6bcee1165450_ga36e9254b8f24778e1aed6bcee1165450}{P\-L\-A\-S\-M\-A\-\_\-d\-Lapack\-\_\-to\-\_\-\-Tile} 

\hyperlink{group__float_gaad3dd3212d3d774f44094c3f0835ef22_gaad3dd3212d3d774f44094c3f0835ef22}{P\-L\-A\-S\-M\-A\-\_\-s\-Lapack\-\_\-to\-\_\-\-Tile} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gad41de0032d2290e448cfc67683dc01bb_gad41de0032d2290e448cfc67683dc01bb}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zlaset@{P\-L\-A\-S\-M\-A\-\_\-zlaset}}
\index{P\-L\-A\-S\-M\-A\-\_\-zlaset@{P\-L\-A\-S\-M\-A\-\_\-zlaset}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zlaset}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zlaset (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{alpha, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{beta, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gad41de0032d2290e448cfc67683dc01bb_gad41de0032d2290e448cfc67683dc01bb}
P\-L\-A\-S\-M\-A\-\_\-zlaset copies all or part of a two-\/dimensional matrix A to another matrix B


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & Specifies the part of the matrix A to be copied to B. = Plasma\-Upper\-Lower\-: All the matrix A = Plasma\-Upper\-: Upper triangular part is set. The lower triangle is unchanged. = Plasma\-Lower\-: Lower triangular part is set. The upper triangle is unchange.\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix A. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & All the offdiagonal array elements are set to alpha.\\
\hline
\mbox{\tt in}  & {\em beta} & All the diagonal array elements are set to beta.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the m by n matrix A. On exit, A(i,j) = A\-L\-P\-H\-A, 1 $<$= i $<$= m, 1 $<$= j $<$= n, i.\-ne.\-j; A(i,i) = B\-E\-T\-A, 1 $<$= i $<$= min(m,n)\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\end{DoxyParams}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gab13674b53c6109c3da58d05a35e5a990_gab13674b53c6109c3da58d05a35e5a990}{P\-L\-A\-S\-M\-A\-\_\-zlaset\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga2c72b62b08b3a1e461e4dbc4bb7bdd5c_ga2c72b62b08b3a1e461e4dbc4bb7bdd5c}{P\-L\-A\-S\-M\-A\-\_\-zlaset\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gabe5cbe444d3395d525dad261b92295f0_gabe5cbe444d3395d525dad261b92295f0}{P\-L\-A\-S\-M\-A\-\_\-claset} 

\hyperlink{group__double_ga2b2e191b49f6e0fede1bcd352bcd14af_ga2b2e191b49f6e0fede1bcd352bcd14af}{P\-L\-A\-S\-M\-A\-\_\-dlaset} 

\hyperlink{group__float_gaeb7486c1cb46dd4a81c11981605c093c_gaeb7486c1cb46dd4a81c11981605c093c}{P\-L\-A\-S\-M\-A\-\_\-slaset} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga33f553c60d1f95a0d7da9e7e17e2a160_ga33f553c60d1f95a0d7da9e7e17e2a160}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zlaswp@{P\-L\-A\-S\-M\-A\-\_\-zlaswp}}
\index{P\-L\-A\-S\-M\-A\-\_\-zlaswp@{P\-L\-A\-S\-M\-A\-\_\-zlaswp}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zlaswp}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zlaswp (
\begin{DoxyParamCaption}
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{int}]{K1, }
\item[{int}]{K2, }
\item[{int $\ast$}]{I\-P\-I\-V, }
\item[{int}]{I\-N\-C\-X}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga33f553c60d1f95a0d7da9e7e17e2a160_ga33f553c60d1f95a0d7da9e7e17e2a160}
P\-L\-A\-S\-M\-A\-\_\-zlaswp -\/ performs a series of row interchanges on the matrix A. One row interchange is initiated for each of rows K1 through K2 of A.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The tile factors L and U from the factorization, computed by P\-L\-A\-S\-M\-A\-\_\-zgetrf.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in}  & {\em K1} & The first element of I\-P\-I\-V for which a row interchange will be done.\\
\hline
\mbox{\tt in}  & {\em K2} & The last element of I\-P\-I\-V for which a row interchange will be done.\\
\hline
\mbox{\tt in}  & {\em I\-P\-I\-V} & The pivot indices from P\-L\-A\-S\-M\-A\-\_\-zgetrf.\\
\hline
\mbox{\tt in}  & {\em I\-N\-C\-X} & The increment between successive values of I\-P\-I\-V. If I\-P\-I\-V is negative, the pivots are applied in reverse order.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
\end{DoxyRetVals}
\begin{DoxyReturn}{Returns}
$<$0 if -\/i, the i-\/th argument had an illegal value
\end{DoxyReturn}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga8b7d50bff2ba16b61f69e14f70ff79b7_ga8b7d50bff2ba16b61f69e14f70ff79b7}{P\-L\-A\-S\-M\-A\-\_\-zlaswp\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gac1b6a0ba1f451d1b3e60bb8bce8f086b_gac1b6a0ba1f451d1b3e60bb8bce8f086b}{P\-L\-A\-S\-M\-A\-\_\-zlaswp\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gace22856d1d438d8d04c90b7423eac23c_gace22856d1d438d8d04c90b7423eac23c}{P\-L\-A\-S\-M\-A\-\_\-claswp} 

\hyperlink{group__double_ga69516426acd62eb6dadfc92097b9f624_ga69516426acd62eb6dadfc92097b9f624}{P\-L\-A\-S\-M\-A\-\_\-dlaswp} 

\hyperlink{group__float_ga871c63746a94adb61e6c06ebc9126671_ga871c63746a94adb61e6c06ebc9126671}{P\-L\-A\-S\-M\-A\-\_\-slaswp} 

\hyperlink{group__PLASMA__Complex64__t_ga03449aa4e83b2f2223dad281d122697d_ga03449aa4e83b2f2223dad281d122697d}{P\-L\-A\-S\-M\-A\-\_\-zgetrf} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gae7d7a89512a3d4c6e733de30a25dc5cc_gae7d7a89512a3d4c6e733de30a25dc5cc}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zlaswpc@{P\-L\-A\-S\-M\-A\-\_\-zlaswpc}}
\index{P\-L\-A\-S\-M\-A\-\_\-zlaswpc@{P\-L\-A\-S\-M\-A\-\_\-zlaswpc}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zlaswpc}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zlaswpc (
\begin{DoxyParamCaption}
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{int}]{K1, }
\item[{int}]{K2, }
\item[{int $\ast$}]{I\-P\-I\-V, }
\item[{int}]{I\-N\-C\-X}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gae7d7a89512a3d4c6e733de30a25dc5cc_gae7d7a89512a3d4c6e733de30a25dc5cc}
P\-L\-A\-S\-M\-A\-\_\-zlaswpc -\/ performs a series of row interchanges on the matrix A. One row interchange is initiated for each of rows K1 through K2 of A.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The tile factors L and U from the factorization, computed by P\-L\-A\-S\-M\-A\-\_\-zgetrf.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in}  & {\em K1} & The first element of I\-P\-I\-V for which a row interchange will be done.\\
\hline
\mbox{\tt in}  & {\em K2} & The last element of I\-P\-I\-V for which a row interchange will be done.\\
\hline
\mbox{\tt in}  & {\em I\-P\-I\-V} & The pivot indices from P\-L\-A\-S\-M\-A\-\_\-zgetrf.\\
\hline
\mbox{\tt in}  & {\em I\-N\-C\-X} & The increment between successive values of I\-P\-I\-V. If I\-P\-I\-V is negative, the pivots are applied in reverse order.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
\end{DoxyRetVals}
\begin{DoxyReturn}{Returns}
$<$0 if -\/i, the i-\/th argument had an illegal value
\end{DoxyReturn}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga3f6d1642862f998a9c0722c57d3e66b4_ga3f6d1642862f998a9c0722c57d3e66b4}{P\-L\-A\-S\-M\-A\-\_\-zlaswpc\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gad282a71e25e9a5d0a19fab88d9270f5f_gad282a71e25e9a5d0a19fab88d9270f5f}{P\-L\-A\-S\-M\-A\-\_\-zlaswpc\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gae439a74f48cce6f172f129f5e761b089_gae439a74f48cce6f172f129f5e761b089}{P\-L\-A\-S\-M\-A\-\_\-claswpc} 

\hyperlink{group__double_gab4cabd8330cc58001b4b1c16552abbde_gab4cabd8330cc58001b4b1c16552abbde}{P\-L\-A\-S\-M\-A\-\_\-dlaswpc} 

\hyperlink{group__float_ga9172c5d4cdc40b0dae8e87b82ee23b6e_ga9172c5d4cdc40b0dae8e87b82ee23b6e}{P\-L\-A\-S\-M\-A\-\_\-slaswpc} 

\hyperlink{group__PLASMA__Complex64__t_ga03449aa4e83b2f2223dad281d122697d_ga03449aa4e83b2f2223dad281d122697d}{P\-L\-A\-S\-M\-A\-\_\-zgetrf} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga0e1f064db19e3855c590172274fbdf43_ga0e1f064db19e3855c590172274fbdf43}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zlauum@{P\-L\-A\-S\-M\-A\-\_\-zlauum}}
\index{P\-L\-A\-S\-M\-A\-\_\-zlauum@{P\-L\-A\-S\-M\-A\-\_\-zlauum}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zlauum}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zlauum (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga0e1f064db19e3855c590172274fbdf43_ga0e1f064db19e3855c590172274fbdf43}
P\-L\-A\-S\-M\-A\-\_\-zlauum -\/ Computes the product U $\ast$ U' or L' $\ast$ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A.

If U\-P\-L\-O = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A. If U\-P\-L\-O = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the triangular factor U or L. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the triangular factor U or L. On exit, if U\-P\-L\-O = 'U', the upper triangle of A is overwritten with the upper triangle of the product U $\ast$ U'; if U\-P\-L\-O = 'L', the lower triangle of A is overwritten with the lower triangle of the product L' $\ast$ L.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga50322b286ba5e26cfa918ed2be8860c9_ga50322b286ba5e26cfa918ed2be8860c9}{P\-L\-A\-S\-M\-A\-\_\-zlauum\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga425208ce23f59b3120b5bfa7923b50ae_ga425208ce23f59b3120b5bfa7923b50ae}{P\-L\-A\-S\-M\-A\-\_\-zlauum\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga937589f5f8ae6b95a4e81589f5471d3e_ga937589f5f8ae6b95a4e81589f5471d3e}{P\-L\-A\-S\-M\-A\-\_\-clauum} 

\hyperlink{group__double_ga67ff8abfce111a501fb5cec37333756f_ga67ff8abfce111a501fb5cec37333756f}{P\-L\-A\-S\-M\-A\-\_\-dlauum} 

\hyperlink{group__float_gaafb49f230a9c4dbdc635144f46f680f6_gaafb49f230a9c4dbdc635144f46f680f6}{P\-L\-A\-S\-M\-A\-\_\-slauum} 

\hyperlink{group__PLASMA__Complex64__t_ga6dd563144dd8c7f29a58659f220f44a0_ga6dd563144dd8c7f29a58659f220f44a0}{P\-L\-A\-S\-M\-A\-\_\-zpotri} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga3a50559a69450b4f13a23c4af092c60e_ga3a50559a69450b4f13a23c4af092c60e}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zplghe@{P\-L\-A\-S\-M\-A\-\_\-zplghe}}
\index{P\-L\-A\-S\-M\-A\-\_\-zplghe@{P\-L\-A\-S\-M\-A\-\_\-zplghe}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zplghe}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zplghe (
\begin{DoxyParamCaption}
\item[{double}]{bump, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{unsigned long long int}]{seed}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga3a50559a69450b4f13a23c4af092c60e_ga3a50559a69450b4f13a23c4af092c60e}
P\-L\-A\-S\-M\-A\-\_\-zplghe -\/ Generate a random hermitian matrix by tiles.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em bump} & The value to add to the diagonal to be sure to have a positive definite matrix.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt out}  & {\em A} & On exit, The random hermitian matrix A generated.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt in}  & {\em seed} & The seed used in the random generation.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gaf494256f8af8223468c1e0a2315dbfb7_gaf494256f8af8223468c1e0a2315dbfb7}{P\-L\-A\-S\-M\-A\-\_\-zplghe\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga87167295ebd4bad3452479a53981bb9b_ga87167295ebd4bad3452479a53981bb9b}{P\-L\-A\-S\-M\-A\-\_\-zplghe\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gab2e8cb228186ddf8555009ee5b678b1c_gab2e8cb228186ddf8555009ee5b678b1c}{P\-L\-A\-S\-M\-A\-\_\-cplghe} 

P\-L\-A\-S\-M\-A\-\_\-dplghe 

P\-L\-A\-S\-M\-A\-\_\-splghe 

\hyperlink{group__PLASMA__Complex64__t_gaed78cffc7c2835c485ef7c8e3761d127_gaed78cffc7c2835c485ef7c8e3761d127}{P\-L\-A\-S\-M\-A\-\_\-zplrnt} 

\hyperlink{group__PLASMA__Complex64__t_ga065c2bc2190fc079035e1de4d16e4e60_ga065c2bc2190fc079035e1de4d16e4e60}{P\-L\-A\-S\-M\-A\-\_\-zplgsy} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga065c2bc2190fc079035e1de4d16e4e60_ga065c2bc2190fc079035e1de4d16e4e60}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zplgsy@{P\-L\-A\-S\-M\-A\-\_\-zplgsy}}
\index{P\-L\-A\-S\-M\-A\-\_\-zplgsy@{P\-L\-A\-S\-M\-A\-\_\-zplgsy}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zplgsy}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zplgsy (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{bump, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{unsigned long long int}]{seed}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga065c2bc2190fc079035e1de4d16e4e60_ga065c2bc2190fc079035e1de4d16e4e60}
P\-L\-A\-S\-M\-A\-\_\-zplgsy -\/ Generate a random hermitian matrix by tiles.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em bump} & The value to add to the diagonal to be sure to have a positive definite matrix.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt out}  & {\em A} & On exit, The random hermitian matrix A generated.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt in}  & {\em seed} & The seed used in the random generation.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga5009d502bba79bde803f883aff293921_ga5009d502bba79bde803f883aff293921}{P\-L\-A\-S\-M\-A\-\_\-zplgsy\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gadd20ad669ca318409d2ac938bb13afa2_gadd20ad669ca318409d2ac938bb13afa2}{P\-L\-A\-S\-M\-A\-\_\-zplgsy\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga3fc244eb71f8484ede01d0a8fb8b7243_ga3fc244eb71f8484ede01d0a8fb8b7243}{P\-L\-A\-S\-M\-A\-\_\-cplgsy} 

\hyperlink{group__double_ga267c9f85256181c2024279e1dc55e84b_ga267c9f85256181c2024279e1dc55e84b}{P\-L\-A\-S\-M\-A\-\_\-dplgsy} 

\hyperlink{group__float_ga949e065a6843e3d20ebc74741ccec2e2_ga949e065a6843e3d20ebc74741ccec2e2}{P\-L\-A\-S\-M\-A\-\_\-splgsy} 

\hyperlink{group__PLASMA__Complex64__t_gaed78cffc7c2835c485ef7c8e3761d127_gaed78cffc7c2835c485ef7c8e3761d127}{P\-L\-A\-S\-M\-A\-\_\-zplrnt} 

\hyperlink{group__PLASMA__Complex64__t_ga065c2bc2190fc079035e1de4d16e4e60_ga065c2bc2190fc079035e1de4d16e4e60}{P\-L\-A\-S\-M\-A\-\_\-zplgsy} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gaed78cffc7c2835c485ef7c8e3761d127_gaed78cffc7c2835c485ef7c8e3761d127}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zplrnt@{P\-L\-A\-S\-M\-A\-\_\-zplrnt}}
\index{P\-L\-A\-S\-M\-A\-\_\-zplrnt@{P\-L\-A\-S\-M\-A\-\_\-zplrnt}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zplrnt}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zplrnt (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{unsigned long long int}]{seed}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gaed78cffc7c2835c485ef7c8e3761d127_gaed78cffc7c2835c485ef7c8e3761d127}
P\-L\-A\-S\-M\-A\-\_\-zplrnt -\/ Generate a random matrix by tiles.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of A.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt out}  & {\em A} & On exit, The random matrix A generated.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt in}  & {\em seed} & The seed used in the random generation.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga7e7cf88c4295f8b364b66cbadd023557_ga7e7cf88c4295f8b364b66cbadd023557}{P\-L\-A\-S\-M\-A\-\_\-zplrnt\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga9c7ab272adb91b3c38af66f649223e4e_ga9c7ab272adb91b3c38af66f649223e4e}{P\-L\-A\-S\-M\-A\-\_\-zplrnt\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gadc1ab86fbc4e1acd67411bcf7d18ccc1_gadc1ab86fbc4e1acd67411bcf7d18ccc1}{P\-L\-A\-S\-M\-A\-\_\-cplrnt} 

\hyperlink{group__double_gafca5b7ac3183e0a107df9f88ecde4cdf_gafca5b7ac3183e0a107df9f88ecde4cdf}{P\-L\-A\-S\-M\-A\-\_\-dplrnt} 

\hyperlink{group__float_ga1ab9b8f017c16245b0f44ab6f4798dfd_ga1ab9b8f017c16245b0f44ab6f4798dfd}{P\-L\-A\-S\-M\-A\-\_\-splrnt} 

\hyperlink{group__PLASMA__Complex64__t_ga3a50559a69450b4f13a23c4af092c60e_ga3a50559a69450b4f13a23c4af092c60e}{P\-L\-A\-S\-M\-A\-\_\-zplghe} 

\hyperlink{group__PLASMA__Complex64__t_ga065c2bc2190fc079035e1de4d16e4e60_ga065c2bc2190fc079035e1de4d16e4e60}{P\-L\-A\-S\-M\-A\-\_\-zplgsy} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gaed71622155778ea4372e34879184e742_gaed71622155778ea4372e34879184e742}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zposv@{P\-L\-A\-S\-M\-A\-\_\-zposv}}
\index{P\-L\-A\-S\-M\-A\-\_\-zposv@{P\-L\-A\-S\-M\-A\-\_\-zposv}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zposv}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zposv (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gaed71622155778ea4372e34879184e742_gaed71622155778ea4372e34879184e742}
P\-L\-A\-S\-M\-A\-\_\-zposv -\/ Computes the solution to a system of linear equations A $\ast$ X = B, where A is an N-\/by-\/\-N symmetric positive definite (or Hermitian positive definite in the complex case) matrix and X and B are N-\/by-\/\-N\-R\-H\-S matrices. The Cholesky decomposition is used to factor A as

\[ A = \{_{L\times L^H, if uplo = PlasmaLower}^{U^H\times U, if uplo = PlasmaUpper} \]

where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A $\ast$ X = B.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\-: = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The number of linear equations, i.\-e., the order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of right hand sides, i.\-e., the number of columns of the matrix B. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric positive definite (or Hermitian) matrix A. If uplo = Plasma\-Upper, the leading N-\/by-\/\-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If U\-P\-L\-O = 'L', the leading N-\/by-\/\-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if return value = 0, the factor U or L from the Cholesky factorization A = U$\ast$$\ast$\-H$\ast$\-U or A = L$\ast$\-L$\ast$$\ast$\-H.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\-N\-R\-H\-S right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\-N\-R\-H\-S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gaf7050f109b30dcdea1cedd1a6577d2b9_gaf7050f109b30dcdea1cedd1a6577d2b9}{P\-L\-A\-S\-M\-A\-\_\-zposv\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gaf25c91026a678c4b6489edf98d8f02b1_gaf25c91026a678c4b6489edf98d8f02b1}{P\-L\-A\-S\-M\-A\-\_\-zposv\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gacb9e52ca26891e283878a10c6b7f24b7_gacb9e52ca26891e283878a10c6b7f24b7}{P\-L\-A\-S\-M\-A\-\_\-cposv} 

\hyperlink{group__double_ga83015e9476d13f0c9f056eac9b54804f_ga83015e9476d13f0c9f056eac9b54804f}{P\-L\-A\-S\-M\-A\-\_\-dposv} 

\hyperlink{group__float_ga113c09b4a9f41fc4c19358a52477d685_ga113c09b4a9f41fc4c19358a52477d685}{P\-L\-A\-S\-M\-A\-\_\-sposv} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga850a6c9da7c5632d160b28f211cdf2eb_ga850a6c9da7c5632d160b28f211cdf2eb}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zpotrf@{P\-L\-A\-S\-M\-A\-\_\-zpotrf}}
\index{P\-L\-A\-S\-M\-A\-\_\-zpotrf@{P\-L\-A\-S\-M\-A\-\_\-zpotrf}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zpotrf}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zpotrf (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga850a6c9da7c5632d160b28f211cdf2eb_ga850a6c9da7c5632d160b28f211cdf2eb}
P\-L\-A\-S\-M\-A\-\_\-zpotrf -\/ Computes the Cholesky factorization of a symmetric positive definite (or Hermitian positive definite in the complex case) matrix A. The factorization has the form

\[ A = \{_{L\times L^H, if uplo = PlasmaLower}^{U^H\times U, if uplo = PlasmaUpper} \]

where U is an upper triangular matrix and L is a lower triangular matrix.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the symmetric positive definite (or Hermitian) matrix A. If uplo = Plasma\-Upper, the leading N-\/by-\/\-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If U\-P\-L\-O = 'L', the leading N-\/by-\/\-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if return value = 0, the factor U or L from the Cholesky factorization A = U$\ast$$\ast$\-H$\ast$\-U or A = L$\ast$\-L$\ast$$\ast$\-H.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gaf062088380cfda1a7dc01bf9596c91e3_gaf062088380cfda1a7dc01bf9596c91e3}{P\-L\-A\-S\-M\-A\-\_\-zpotrf\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gaecab84c31c6e1658b18868b33478de53_gaecab84c31c6e1658b18868b33478de53}{P\-L\-A\-S\-M\-A\-\_\-zpotrf\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga9a02052646386252f5b41c09c8d18684_ga9a02052646386252f5b41c09c8d18684}{P\-L\-A\-S\-M\-A\-\_\-cpotrf} 

\hyperlink{group__double_ga08c3851e861086761123a375b8472df2_ga08c3851e861086761123a375b8472df2}{P\-L\-A\-S\-M\-A\-\_\-dpotrf} 

\hyperlink{group__float_ga3ada27ebefe8e378bc6f9d25ab72d217_ga3ada27ebefe8e378bc6f9d25ab72d217}{P\-L\-A\-S\-M\-A\-\_\-spotrf} 

\hyperlink{group__PLASMA__Complex64__t_gafa3392d835a508f57674c601c46eb331_gafa3392d835a508f57674c601c46eb331}{P\-L\-A\-S\-M\-A\-\_\-zpotrs} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga6dd563144dd8c7f29a58659f220f44a0_ga6dd563144dd8c7f29a58659f220f44a0}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zpotri@{P\-L\-A\-S\-M\-A\-\_\-zpotri}}
\index{P\-L\-A\-S\-M\-A\-\_\-zpotri@{P\-L\-A\-S\-M\-A\-\_\-zpotri}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zpotri}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zpotri (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga6dd563144dd8c7f29a58659f220f44a0_ga6dd563144dd8c7f29a58659f220f44a0}
P\-L\-A\-S\-M\-A\-\_\-zpotri -\/ Computes the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U$\ast$$\ast$\-H$\ast$\-U or A = L$\ast$\-L$\ast$$\ast$\-H computed by P\-L\-A\-S\-M\-A\-\_\-zpotrf.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the triangular factor U or L from the Cholesky factorization A = U$\ast$$\ast$\-H$\ast$\-U or A = L$\ast$\-L$\ast$$\ast$\-H, as computed by P\-L\-A\-S\-M\-A\-\_\-zpotrf. On exit, the upper or lower triangle of the (Hermitian) inverse of A, overwriting the input factor U or L.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, the (i,i) element of the factor U or L is zero, and the inverse could not be computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga30d9bbba83e9e9098c6444553d20f47a_ga30d9bbba83e9e9098c6444553d20f47a}{P\-L\-A\-S\-M\-A\-\_\-zpotri\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga9c9b672c28f4f191528f07cd0d66774e_ga9c9b672c28f4f191528f07cd0d66774e}{P\-L\-A\-S\-M\-A\-\_\-zpotri\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga2bbe242c5e06f243640fb6287b4a85ab_ga2bbe242c5e06f243640fb6287b4a85ab}{P\-L\-A\-S\-M\-A\-\_\-cpotri} 

\hyperlink{group__double_ga01b70786730b5e4c314b4584fe3697c5_ga01b70786730b5e4c314b4584fe3697c5}{P\-L\-A\-S\-M\-A\-\_\-dpotri} 

\hyperlink{group__float_gaf35cf8d73bf326a683f4be4943ef9b38_gaf35cf8d73bf326a683f4be4943ef9b38}{P\-L\-A\-S\-M\-A\-\_\-spotri} 

\hyperlink{group__PLASMA__Complex64__t_ga850a6c9da7c5632d160b28f211cdf2eb_ga850a6c9da7c5632d160b28f211cdf2eb}{P\-L\-A\-S\-M\-A\-\_\-zpotrf} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gafa3392d835a508f57674c601c46eb331_gafa3392d835a508f57674c601c46eb331}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zpotrs@{P\-L\-A\-S\-M\-A\-\_\-zpotrs}}
\index{P\-L\-A\-S\-M\-A\-\_\-zpotrs@{P\-L\-A\-S\-M\-A\-\_\-zpotrs}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zpotrs}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zpotrs (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gafa3392d835a508f57674c601c46eb331_gafa3392d835a508f57674c601c46eb331}
P\-L\-A\-S\-M\-A\-\_\-zpotrs -\/ Solves a system of linear equations A $\ast$ X = B with a symmetric positive definite (or Hermitian positive definite in the complex case) matrix A using the Cholesky factorization A = U$\ast$$\ast$\-H$\ast$\-U or A = L$\ast$\-L$\ast$$\ast$\-H computed by P\-L\-A\-S\-M\-A\-\_\-zpotrf.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of right hand sides, i.\-e., the number of columns of the matrix B. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The triangular factor U or L from the Cholesky factorization A = U$\ast$$\ast$\-H$\ast$\-U or A = L$\ast$\-L$\ast$$\ast$\-H, computed by P\-L\-A\-S\-M\-A\-\_\-zpotrf.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\-N\-R\-H\-S right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\-N\-R\-H\-S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gad13147593a1970092f560e8cb54925b8_gad13147593a1970092f560e8cb54925b8}{P\-L\-A\-S\-M\-A\-\_\-zpotrs\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga493aec60380a3935c89f40c976fbb705_ga493aec60380a3935c89f40c976fbb705}{P\-L\-A\-S\-M\-A\-\_\-zpotrs\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gaf429b7116507625912226d3c91bdfecc_gaf429b7116507625912226d3c91bdfecc}{P\-L\-A\-S\-M\-A\-\_\-cpotrs} 

\hyperlink{group__double_ga2d3c0509f11f1e9a9cf06b95109e62f5_ga2d3c0509f11f1e9a9cf06b95109e62f5}{P\-L\-A\-S\-M\-A\-\_\-dpotrs} 

\hyperlink{group__float_gab813bd6d81c21feae7ce6553c9ba255a_gab813bd6d81c21feae7ce6553c9ba255a}{P\-L\-A\-S\-M\-A\-\_\-spotrs} 

\hyperlink{group__PLASMA__Complex64__t_ga850a6c9da7c5632d160b28f211cdf2eb_ga850a6c9da7c5632d160b28f211cdf2eb}{P\-L\-A\-S\-M\-A\-\_\-zpotrf} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga78d0974b51b7d019e0606422b3292b46_ga78d0974b51b7d019e0606422b3292b46}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zsymm@{P\-L\-A\-S\-M\-A\-\_\-zsymm}}
\index{P\-L\-A\-S\-M\-A\-\_\-zsymm@{P\-L\-A\-S\-M\-A\-\_\-zsymm}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zsymm}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zsymm (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{side, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{alpha, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{beta, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{C, }
\item[{int}]{L\-D\-C}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga78d0974b51b7d019e0606422b3292b46_ga78d0974b51b7d019e0606422b3292b46}
P\-L\-A\-S\-M\-A\-\_\-zsymm -\/ Performs one of the matrix-\/matrix operations

\[ C = \alpha \times A \times B + \beta \times C \]

or

\[ C = \alpha \times B \times A + \beta \times C \]

where alpha and beta are scalars, A is an symmetric matrix and B and C are m by n matrices.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em side} & Specifies whether the symmetric matrix A appears on the left or right in the operation as follows\-: = Plasma\-Left\-: \[ C = \alpha \times A \times B + \beta \times C \] = Plasma\-Right\-: \[ C = \alpha \times B \times A + \beta \times C \]\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced as follows\-: = Plasma\-Lower\-: Only the lower triangular part of the symmetric matrix A is to be referenced. = Plasma\-Upper\-: Only the upper triangular part of the symmetric matrix A is to be referenced.\\
\hline
\mbox{\tt in}  & {\em M} & Specifies the number of rows of the matrix C. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & Specifies the number of columns of the matrix C. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & Specifies the scalar alpha.\\
\hline
\mbox{\tt in}  & {\em A} & A is a L\-D\-A-\/by-\/ka matrix, where ka is M when side = Plasma\-Left, and is N otherwise. Only the uplo triangular part is referenced.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,ka).\\
\hline
\mbox{\tt in}  & {\em B} & B is a L\-D\-B-\/by-\/\-N matrix, where the leading M-\/by-\/\-N part of the array B must contain the matrix B.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-M).\\
\hline
\mbox{\tt in}  & {\em beta} & Specifies the scalar beta.\\
\hline
\mbox{\tt in,out}  & {\em C} & C is a L\-D\-C-\/by-\/\-N matrix. On exit, the array is overwritten by the M by N updated matrix.\\
\hline
\mbox{\tt in}  & {\em L\-D\-C} & The leading dimension of the array C. L\-D\-C $>$= max(1,\-M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga87921acde0e9798ffdb9f011b083385b_ga87921acde0e9798ffdb9f011b083385b}{P\-L\-A\-S\-M\-A\-\_\-zsymm\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex32__t_gac62cd0bd5b290a074c3af371972266a4_gac62cd0bd5b290a074c3af371972266a4}{P\-L\-A\-S\-M\-A\-\_\-csymm} 

\hyperlink{group__double_ga1ab6ee29131efe4804f5ff940eeb699a_ga1ab6ee29131efe4804f5ff940eeb699a}{P\-L\-A\-S\-M\-A\-\_\-dsymm} 

\hyperlink{group__float_gaaffcd386f207f3e3a3073a803e27e3f1_gaaffcd386f207f3e3a3073a803e27e3f1}{P\-L\-A\-S\-M\-A\-\_\-ssymm} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga575230c6f1629fabf7ba151a09e4c7a7_ga575230c6f1629fabf7ba151a09e4c7a7}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zsyr2k@{P\-L\-A\-S\-M\-A\-\_\-zsyr2k}}
\index{P\-L\-A\-S\-M\-A\-\_\-zsyr2k@{P\-L\-A\-S\-M\-A\-\_\-zsyr2k}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zsyr2k}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zsyr2k (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{alpha, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{beta, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{C, }
\item[{int}]{L\-D\-C}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga575230c6f1629fabf7ba151a09e4c7a7_ga575230c6f1629fabf7ba151a09e4c7a7}
P\-L\-A\-S\-M\-A\-\_\-zsyr2k -\/ Performs one of the symmetric rank 2k operations

\[ C = \alpha [ op( A ) \times conjg( op( B )' )] + \alpha [ op( B ) \times conjg( op( A )' )] + \beta C \], or \[ C = \alpha [ conjg( op( A )' ) \times op( B ) ] + \alpha [ conjg( op( B )' ) \times op( A ) ] + \beta C \],

where op( X ) is one of

op( X ) = X or op( X ) = conjg( X' )

where alpha and beta are real scalars, C is an n-\/by-\/n symmetric matrix and A and B are an n-\/by-\/k matrices the first case and k-\/by-\/n matrices in the second case.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\-Upper\-: Upper triangle of C is stored; = Plasma\-Lower\-: Lower triangle of C is stored.\\
\hline
\mbox{\tt in}  & {\em trans} & Specifies whether the matrix A is transposed or conjugate transposed\-: = Plasma\-No\-Trans\-: \[ C = \alpha [ op( A ) \times conjg( op( B )' )] + \alpha [ op( B ) \times conjg( op( A )' )] + \beta C \] = Plasma\-Trans\-: \[ C = \alpha [ conjg( op( A )' ) \times op( B ) ] + \alpha [ conjg( op( B )' ) \times op( A ) ] + \beta C \]\\
\hline
\mbox{\tt in}  & {\em N} & N specifies the order of the matrix C. N must be at least zero.\\
\hline
\mbox{\tt in}  & {\em K} & K specifies the number of columns of the A and B matrices with trans = Plasma\-No\-Trans. K specifies the number of rows of the A and B matrices with trans = Plasma\-Trans.\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha.\\
\hline
\mbox{\tt in}  & {\em A} & A is a L\-D\-A-\/by-\/ka matrix, where ka is K when trans = Plasma\-No\-Trans, and is N otherwise.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A must be at least max( 1, N ), otherwise L\-D\-A must be at least max( 1, K ).\\
\hline
\mbox{\tt in}  & {\em B} & B is a L\-D\-B-\/by-\/kb matrix, where kb is K when trans = Plasma\-No\-Trans, and is N otherwise.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B must be at least max( 1, N ), otherwise L\-D\-B must be at least max( 1, K ).\\
\hline
\mbox{\tt in}  & {\em beta} & beta specifies the scalar beta.\\
\hline
\mbox{\tt in,out}  & {\em C} & C is a L\-D\-C-\/by-\/\-N matrix. On exit, the array uplo part of the matrix is overwritten by the uplo part of the updated matrix.\\
\hline
\mbox{\tt in}  & {\em L\-D\-C} & The leading dimension of the array C. L\-D\-C $>$= max( 1, N ).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga84266642d3b1d97fafcfc81d695cc3d5_ga84266642d3b1d97fafcfc81d695cc3d5}{P\-L\-A\-S\-M\-A\-\_\-zsyr2k\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex32__t_ga5a48c1ff1b73920651249deb75b9d0b7_ga5a48c1ff1b73920651249deb75b9d0b7}{P\-L\-A\-S\-M\-A\-\_\-csyr2k} 

\hyperlink{group__double_gaf9fa0e62110092a132cd17d8f48561f0_gaf9fa0e62110092a132cd17d8f48561f0}{P\-L\-A\-S\-M\-A\-\_\-dsyr2k} 

\hyperlink{group__float_gafac964a38a7c62696c3b95d35108ad9b_gafac964a38a7c62696c3b95d35108ad9b}{P\-L\-A\-S\-M\-A\-\_\-ssyr2k} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gaae2f934da463e7256c82500587c3042b_gaae2f934da463e7256c82500587c3042b}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zsyrk@{P\-L\-A\-S\-M\-A\-\_\-zsyrk}}
\index{P\-L\-A\-S\-M\-A\-\_\-zsyrk@{P\-L\-A\-S\-M\-A\-\_\-zsyrk}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zsyrk}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zsyrk (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{alpha, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{beta, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{C, }
\item[{int}]{L\-D\-C}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gaae2f934da463e7256c82500587c3042b_gaae2f934da463e7256c82500587c3042b}
P\-L\-A\-S\-M\-A\-\_\-zsyrk -\/ Performs one of the hermitian rank k operations

\[ C = \alpha [ op( A ) \times conjg( op( A )' )] + \beta C \],

where op( X ) is one of

op( X ) = X or op( X ) = conjg( X' )

where alpha and beta are real scalars, C is an n-\/by-\/n hermitian matrix and A is an n-\/by-\/k matrix in the first case and a k-\/by-\/n matrix in the second case.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\-Upper\-: Upper triangle of C is stored; = Plasma\-Lower\-: Lower triangle of C is stored.\\
\hline
\mbox{\tt in}  & {\em trans} & Specifies whether the matrix A is transposed or conjugate transposed\-: = Plasma\-No\-Trans\-: A is not transposed; = Plasma\-Trans \-: A is transposed.\\
\hline
\mbox{\tt in}  & {\em N} & N specifies the order of the matrix C. N must be at least zero.\\
\hline
\mbox{\tt in}  & {\em K} & K specifies the number of columns of the matrix op( A ).\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha.\\
\hline
\mbox{\tt in}  & {\em A} & A is a L\-D\-A-\/by-\/ka matrix, where ka is K when trans = Plasma\-No\-Trans, and is N otherwise.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A must be at least max( 1, N ) if trans == Plasma\-No\-Trans, otherwise L\-D\-A must be at least max( 1, K ).\\
\hline
\mbox{\tt in}  & {\em beta} & beta specifies the scalar beta\\
\hline
\mbox{\tt in,out}  & {\em C} & C is a L\-D\-C-\/by-\/\-N matrix. On exit, the array uplo part of the matrix is overwritten by the uplo part of the updated matrix.\\
\hline
\mbox{\tt in}  & {\em L\-D\-C} & The leading dimension of the array C. L\-D\-C $>$= max( 1, N ).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga562df1ff0cbc44d96feff13cb26cd8ec_ga562df1ff0cbc44d96feff13cb26cd8ec}{P\-L\-A\-S\-M\-A\-\_\-zsyrk\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex32__t_gad7bae1673afbf5b73da18c20f376cb89_gad7bae1673afbf5b73da18c20f376cb89}{P\-L\-A\-S\-M\-A\-\_\-csyrk} 

\hyperlink{group__double_gacfdac462cfb1b2d6696e353bec9fd079_gacfdac462cfb1b2d6696e353bec9fd079}{P\-L\-A\-S\-M\-A\-\_\-dsyrk} 

\hyperlink{group__float_gae83f0347570d23dc62dd8b298eb14ad6_gae83f0347570d23dc62dd8b298eb14ad6}{P\-L\-A\-S\-M\-A\-\_\-ssyrk} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga8df0b9fdc5537a648d7544b528c9e6e3_ga8df0b9fdc5537a648d7544b528c9e6e3}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-z\-Tile\-\_\-to\-\_\-\-Lapack@{P\-L\-A\-S\-M\-A\-\_\-z\-Tile\-\_\-to\-\_\-\-Lapack}}
\index{P\-L\-A\-S\-M\-A\-\_\-z\-Tile\-\_\-to\-\_\-\-Lapack@{P\-L\-A\-S\-M\-A\-\_\-z\-Tile\-\_\-to\-\_\-\-Lapack}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-z\-Tile\-\_\-to\-\_\-\-Lapack}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-z\-Tile\-\_\-to\-\_\-\-Lapack (
\begin{DoxyParamCaption}
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{Af77, }
\item[{int}]{L\-D\-A}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga8df0b9fdc5537a648d7544b528c9e6e3_ga8df0b9fdc5537a648d7544b528c9e6e3}
P\-L\-A\-S\-M\-A\-\_\-\-Tile\-\_\-to\-\_\-\-Lapack -\/ Conversion from tile layout to L\-A\-P\-A\-C\-K layout.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em A} & Descriptor of the P\-L\-A\-S\-M\-A matrix in tile layout.\\
\hline
\mbox{\tt in,out}  & {\em Af77} & L\-A\-P\-A\-C\-K matrix. If P\-L\-A\-S\-M\-A\-\_\-\-T\-R\-A\-N\-S\-L\-A\-T\-I\-O\-N\-\_\-\-M\-O\-D\-E is set to P\-L\-A\-S\-M\-A\-\_\-\-I\-N\-P\-L\-A\-C\-E, Af77 has to be A-\/$>$mat, else if P\-L\-A\-S\-M\-A\-\_\-\-T\-R\-A\-N\-S\-L\-A\-T\-I\-O\-N\-\_\-\-M\-O\-D\-E is set to P\-L\-A\-S\-M\-A\-\_\-\-O\-U\-T\-O\-F\-P\-L\-A\-C\-E, Af77 has to be allocated before.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the matrix Af77.\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga27044f3ec4b95defcb842009096ff2a3_ga27044f3ec4b95defcb842009096ff2a3}{P\-L\-A\-S\-M\-A\-\_\-z\-Tile\-\_\-to\-\_\-\-Lapack\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex64__t_ga54817e0733e678bcdfdfeaa76ab486f6_ga54817e0733e678bcdfdfeaa76ab486f6}{P\-L\-A\-S\-M\-A\-\_\-z\-Lapack\-\_\-to\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex32__t_ga7dce142b920d792a0443efcc922c71fc_ga7dce142b920d792a0443efcc922c71fc}{P\-L\-A\-S\-M\-A\-\_\-c\-Tile\-\_\-to\-\_\-\-Lapack} 

\hyperlink{group__double_ga1a9152c4ac00de6cafe8a5a4ad6718df_ga1a9152c4ac00de6cafe8a5a4ad6718df}{P\-L\-A\-S\-M\-A\-\_\-d\-Tile\-\_\-to\-\_\-\-Lapack} 

\hyperlink{group__float_gacfc6859eb0da6e5c246a70178b5567be_gacfc6859eb0da6e5c246a70178b5567be}{P\-L\-A\-S\-M\-A\-\_\-s\-Tile\-\_\-to\-\_\-\-Lapack} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga9d25baa9dfdb84cd69270558338ce9b1_ga9d25baa9dfdb84cd69270558338ce9b1}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-ztrmm@{P\-L\-A\-S\-M\-A\-\_\-ztrmm}}
\index{P\-L\-A\-S\-M\-A\-\_\-ztrmm@{P\-L\-A\-S\-M\-A\-\_\-ztrmm}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-ztrmm}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-ztrmm (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{side, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{diag, }
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{alpha, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga9d25baa9dfdb84cd69270558338ce9b1_ga9d25baa9dfdb84cd69270558338ce9b1}
P\-L\-A\-S\-M\-A\-\_\-ztrmm -\/ Computes B = alpha$\ast$op( A )$\ast$\-B or B = alpha$\ast$\-B$\ast$op( A ).


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em side} & Specifies whether A appears on the left or on the right of X\-: = Plasma\-Left\-: A$\ast$\-X = B = Plasma\-Right\-: X$\ast$\-A = B\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\-: = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em trans\-A} & Specifies whether the matrix A is transposed, not transposed or conjugate transposed\-: = Plasma\-No\-Trans\-: A is transposed; = Plasma\-Trans\-: A is not transposed; = Plasma\-Conj\-Trans\-: A is conjugate transposed.\\
\hline
\mbox{\tt in}  & {\em diag} & Specifies whether or not A is unit triangular\-: = Plasma\-Non\-Unit\-: A is non unit; = Plasma\-Unit\-: A us unit.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of right hand sides, i.\-e., the number of columns of the matrix B. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha.\\
\hline
\mbox{\tt in}  & {\em A} & The triangular matrix A. If uplo = Plasma\-Upper, the leading N-\/by-\/\-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\-Lower, the leading N-\/by-\/\-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If diag = Plasma\-Unit, the diagonal elements of A are also not referenced and are assumed to be 1.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\-N\-R\-H\-S right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\-N\-R\-H\-S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga4ecbc28dd8c924fff262c73b5662eba7_ga4ecbc28dd8c924fff262c73b5662eba7}{P\-L\-A\-S\-M\-A\-\_\-ztrmm\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga6fe9ba44646a8e7bc93a7a2cd20bf862_ga6fe9ba44646a8e7bc93a7a2cd20bf862}{P\-L\-A\-S\-M\-A\-\_\-ztrmm\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga17234cfdde42bd11866b3435a9a8295a_ga17234cfdde42bd11866b3435a9a8295a}{P\-L\-A\-S\-M\-A\-\_\-ctrmm} 

\hyperlink{group__double_ga16876a8b4e9148ba2c8f4d37dca9eef4_ga16876a8b4e9148ba2c8f4d37dca9eef4}{P\-L\-A\-S\-M\-A\-\_\-dtrmm} 

\hyperlink{group__float_gabbc2cf7c018815bd2c1ce8a6623b2813_gabbc2cf7c018815bd2c1ce8a6623b2813}{P\-L\-A\-S\-M\-A\-\_\-strmm} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga36cf60d55716c7ab0c2fba7fb8833e2c_ga36cf60d55716c7ab0c2fba7fb8833e2c}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-ztrsm@{P\-L\-A\-S\-M\-A\-\_\-ztrsm}}
\index{P\-L\-A\-S\-M\-A\-\_\-ztrsm@{P\-L\-A\-S\-M\-A\-\_\-ztrsm}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-ztrsm}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-ztrsm (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{side, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{diag, }
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{alpha, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga36cf60d55716c7ab0c2fba7fb8833e2c_ga36cf60d55716c7ab0c2fba7fb8833e2c}
P\-L\-A\-S\-M\-A\-\_\-ztrsm -\/ Computes triangular solve A$\ast$\-X = B or X$\ast$\-A = B.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em side} & Specifies whether A appears on the left or on the right of X\-: = Plasma\-Left\-: A$\ast$\-X = B = Plasma\-Right\-: X$\ast$\-A = B\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\-: = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em trans\-A} & Specifies whether the matrix A is transposed, not transposed or conjugate transposed\-: = Plasma\-No\-Trans\-: A is transposed; = Plasma\-Trans\-: A is not transposed; = Plasma\-Conj\-Trans\-: A is conjugate transposed.\\
\hline
\mbox{\tt in}  & {\em diag} & Specifies whether or not A is unit triangular\-: = Plasma\-Non\-Unit\-: A is non unit; = Plasma\-Unit\-: A us unit.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of right hand sides, i.\-e., the number of columns of the matrix B. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha.\\
\hline
\mbox{\tt in}  & {\em A} & The triangular matrix A. If uplo = Plasma\-Upper, the leading N-\/by-\/\-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\-Lower, the leading N-\/by-\/\-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If diag = Plasma\-Unit, the diagonal elements of A are also not referenced and are assumed to be 1.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\-N\-R\-H\-S right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\-N\-R\-H\-S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gaa30141c5d48339be52806a6d01a6de1d_gaa30141c5d48339be52806a6d01a6de1d}{P\-L\-A\-S\-M\-A\-\_\-ztrsm\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gaaa1f664d00ac743bd6f9dd0c116e72a5_gaaa1f664d00ac743bd6f9dd0c116e72a5}{P\-L\-A\-S\-M\-A\-\_\-ztrsm\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga59907687253f7978f60e1d56d6fe941c_ga59907687253f7978f60e1d56d6fe941c}{P\-L\-A\-S\-M\-A\-\_\-ctrsm} 

\hyperlink{group__double_ga7dab3739b47f3f77f68cb6166638f507_ga7dab3739b47f3f77f68cb6166638f507}{P\-L\-A\-S\-M\-A\-\_\-dtrsm} 

\hyperlink{group__float_ga572e80d04d4e9701bf3dd73d1f96d54c_ga572e80d04d4e9701bf3dd73d1f96d54c}{P\-L\-A\-S\-M\-A\-\_\-strsm} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gac1801a329693ff71b7ee1bd772f76994_gac1801a329693ff71b7ee1bd772f76994}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-ztrsmpl@{P\-L\-A\-S\-M\-A\-\_\-ztrsmpl}}
\index{P\-L\-A\-S\-M\-A\-\_\-ztrsmpl@{P\-L\-A\-S\-M\-A\-\_\-ztrsmpl}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-ztrsmpl}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-ztrsmpl (
\begin{DoxyParamCaption}
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-L, }
\item[{int $\ast$}]{I\-P\-I\-V, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gac1801a329693ff71b7ee1bd772f76994_gac1801a329693ff71b7ee1bd772f76994}
P\-L\-A\-S\-M\-A\-\_\-ztrsmpl -\/ Performs the forward substitution step of solving a system of linear equations after the tile L\-U factorization of the matrix.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of right hand sides, i.\-e., the number of columns of the matrix B. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & The tile factor L from the factorization, computed by P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in}  & {\em desc\-L} & Auxiliary factorization data, related to the tile L factor, computed by P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv.\\
\hline
\mbox{\tt in}  & {\em I\-P\-I\-V} & The pivot indices from P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv (not equivalent to L\-A\-P\-A\-C\-K).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\-N\-R\-H\-S right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\-N\-R\-H\-S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga4d6411e08ef6faaf5b407ae7e9b46378_ga4d6411e08ef6faaf5b407ae7e9b46378}{P\-L\-A\-S\-M\-A\-\_\-ztrsmpl\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga53d217149357f44e30add1d419e30475_ga53d217149357f44e30add1d419e30475}{P\-L\-A\-S\-M\-A\-\_\-ztrsmpl\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga09e57f11d290244163f0dd6ede7952d5_ga09e57f11d290244163f0dd6ede7952d5}{P\-L\-A\-S\-M\-A\-\_\-ctrsmpl} 

\hyperlink{group__double_ga524dd7f9010a6a4c113d35e58316fd4e_ga524dd7f9010a6a4c113d35e58316fd4e}{P\-L\-A\-S\-M\-A\-\_\-dtrsmpl} 

\hyperlink{group__float_ga6474e57f7e75df01781a9b2ff4d2fc18_ga6474e57f7e75df01781a9b2ff4d2fc18}{P\-L\-A\-S\-M\-A\-\_\-strsmpl} 

\hyperlink{group__PLASMA__Complex64__t_ga085b5e62180512c7c603e72a9092ad8d_ga085b5e62180512c7c603e72a9092ad8d}{P\-L\-A\-S\-M\-A\-\_\-zgetrf\-\_\-incpiv} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gadc613ba744f045286d0869bbbf6765ac_gadc613ba744f045286d0869bbbf6765ac}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-ztrsmrv@{P\-L\-A\-S\-M\-A\-\_\-ztrsmrv}}
\index{P\-L\-A\-S\-M\-A\-\_\-ztrsmrv@{P\-L\-A\-S\-M\-A\-\_\-ztrsmrv}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-ztrsmrv}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-ztrsmrv (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{side, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{diag, }
\item[{int}]{N, }
\item[{int}]{N\-R\-H\-S, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t}]{alpha, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{B, }
\item[{int}]{L\-D\-B}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gadc613ba744f045286d0869bbbf6765ac_gadc613ba744f045286d0869bbbf6765ac}
P\-L\-A\-S\-M\-A\-\_\-ztrsmrv -\/ Computes triangular solve A$\ast$\-X = B or X$\ast$\-A = B.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em side} & Specifies whether A appears on the left or on the right of X\-: = Plasma\-Left\-: A$\ast$\-X = B = Plasma\-Right\-: X$\ast$\-A = B\\
\hline
\mbox{\tt in}  & {\em uplo} & Specifies whether the matrix A is upper triangular or lower triangular\-: = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em trans\-A} & Specifies whether the matrix A is transposed, not transposed or conjugate transposed\-: = Plasma\-No\-Trans\-: A is transposed; = Plasma\-Trans\-: A is not transposed; = Plasma\-Conj\-Trans\-: A is conjugate transposed.\\
\hline
\mbox{\tt in}  & {\em diag} & Specifies whether or not A is unit triangular\-: = Plasma\-Non\-Unit\-: A is non unit; = Plasma\-Unit\-: A us unit.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N\-R\-H\-S} & The number of right hand sides, i.\-e., the number of columns of the matrix B. N\-R\-H\-S $>$= 0.\\
\hline
\mbox{\tt in}  & {\em alpha} & alpha specifies the scalar alpha.\\
\hline
\mbox{\tt in}  & {\em A} & The triangular matrix A. If uplo = Plasma\-Upper, the leading N-\/by-\/\-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If uplo = Plasma\-Lower, the leading N-\/by-\/\-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If diag = Plasma\-Unit, the diagonal elements of A are also not referenced and are assumed to be 1.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in,out}  & {\em B} & On entry, the N-\/by-\/\-N\-R\-H\-S right hand side matrix B. On exit, if return value = 0, the N-\/by-\/\-N\-R\-H\-S solution matrix X.\\
\hline
\mbox{\tt in}  & {\em L\-D\-B} & The leading dimension of the array B. L\-D\-B $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga8b1fcefe28db01449afb53ea924bf889_ga8b1fcefe28db01449afb53ea924bf889}{P\-L\-A\-S\-M\-A\-\_\-ztrsmrv\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga0ed911d979585a7940b8436a4b90d494_ga0ed911d979585a7940b8436a4b90d494}{P\-L\-A\-S\-M\-A\-\_\-ztrsmrv\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga4932d66d31f7970a6cab8381d373eb12_ga4932d66d31f7970a6cab8381d373eb12}{P\-L\-A\-S\-M\-A\-\_\-ctrsmrv} 

\hyperlink{group__double_ga01879443f745172ea8165d4882136d36_ga01879443f745172ea8165d4882136d36}{P\-L\-A\-S\-M\-A\-\_\-dtrsmrv} 

\hyperlink{group__float_ga7713151eac0c0ff54c5a6aac1957b5e0_ga7713151eac0c0ff54c5a6aac1957b5e0}{P\-L\-A\-S\-M\-A\-\_\-strsmrv} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gaf634d0dec7f2b59a571b5aafa19892d1_gaf634d0dec7f2b59a571b5aafa19892d1}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-ztrtri@{P\-L\-A\-S\-M\-A\-\_\-ztrtri}}
\index{P\-L\-A\-S\-M\-A\-\_\-ztrtri@{P\-L\-A\-S\-M\-A\-\_\-ztrtri}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-ztrtri}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-ztrtri (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{uplo, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{diag, }
\item[{int}]{N, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gaf634d0dec7f2b59a571b5aafa19892d1_gaf634d0dec7f2b59a571b5aafa19892d1}
P\-L\-A\-S\-M\-A\-\_\-ztrtri -\/ Computes the inverse of a complex upper or lower triangular matrix A.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em uplo} & = Plasma\-Upper\-: Upper triangle of A is stored; = Plasma\-Lower\-: Lower triangle of A is stored.\\
\hline
\mbox{\tt in}  & {\em diag} & = Plasma\-Non\-Unit\-: A is non-\/unit triangular; = Plasma\-Unit\-: A is unit triangular.\\
\hline
\mbox{\tt in}  & {\em N} & The order of the matrix A. N $>$= 0.\\
\hline
\mbox{\tt in,out}  & {\em A} & On entry, the triangular matrix A. If U\-P\-L\-O = 'U', the leading N-\/by-\/\-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If U\-P\-L\-O = 'L', the leading N-\/by-\/\-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If D\-I\-A\-G = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-N).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value \\
\hline
{\em $>$0} & if i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse can not be computed.\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga3f573d99647fde05cf8db6dca201a564_ga3f573d99647fde05cf8db6dca201a564}{P\-L\-A\-S\-M\-A\-\_\-ztrtri\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gadfb88a401f30764bde58c38748e894bd_gadfb88a401f30764bde58c38748e894bd}{P\-L\-A\-S\-M\-A\-\_\-ztrtri\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga25e718997c7c1fd6f599d7b3a04fddad_ga25e718997c7c1fd6f599d7b3a04fddad}{P\-L\-A\-S\-M\-A\-\_\-ctrtri} 

\hyperlink{group__double_ga3968f78f69610b681ab7d6c411f92796_ga3968f78f69610b681ab7d6c411f92796}{P\-L\-A\-S\-M\-A\-\_\-dtrtri} 

\hyperlink{group__float_gaaf0df7b8ff03a270a25da71b9f133abb_gaaf0df7b8ff03a270a25da71b9f133abb}{P\-L\-A\-S\-M\-A\-\_\-strtri} 

\hyperlink{group__PLASMA__Complex64__t_ga6dd563144dd8c7f29a58659f220f44a0_ga6dd563144dd8c7f29a58659f220f44a0}{P\-L\-A\-S\-M\-A\-\_\-zpotri} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga8d2c7940bdd249a0a1e633b0ac6d107c_ga8d2c7940bdd249a0a1e633b0ac6d107c}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zunglq@{P\-L\-A\-S\-M\-A\-\_\-zunglq}}
\index{P\-L\-A\-S\-M\-A\-\_\-zunglq@{P\-L\-A\-S\-M\-A\-\_\-zunglq}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zunglq}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zunglq (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{Q, }
\item[{int}]{L\-D\-Q}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga8d2c7940bdd249a0a1e633b0ac6d107c_ga8d2c7940bdd249a0a1e633b0ac6d107c}
P\-L\-A\-S\-M\-A\-\_\-zunglq -\/ Generates an M-\/by-\/\-N matrix Q with orthonormal rows, which is defined as the first M rows of a product of the elementary reflectors returned by P\-L\-A\-S\-M\-A\-\_\-zgelqf.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix Q. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix Q. N $>$= M.\\
\hline
\mbox{\tt in}  & {\em K} & The number of rows of elementary tile reflectors whose product defines the matrix Q. M $>$= K $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & Details of the L\-Q factorization of the original matrix A as returned by P\-L\-A\-S\-M\-A\-\_\-zgelqf.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt in}  & {\em desc\-T} & Auxiliary factorization data, computed by P\-L\-A\-S\-M\-A\-\_\-zgelqf.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, the M-\/by-\/\-N matrix Q.\\
\hline
\mbox{\tt in}  & {\em L\-D\-Q} & The leading dimension of the array Q. L\-D\-Q $>$= max(1,\-M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & $<$0 if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga6b36db3de0fe6436ea85432a40fb4024_ga6b36db3de0fe6436ea85432a40fb4024}{P\-L\-A\-S\-M\-A\-\_\-zunglq\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga88e23a6307f8d2f1de2343b33954be5b_ga88e23a6307f8d2f1de2343b33954be5b}{P\-L\-A\-S\-M\-A\-\_\-zunglq\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gad8f450a6bb48fac4dc912211fef0e912_gad8f450a6bb48fac4dc912211fef0e912}{P\-L\-A\-S\-M\-A\-\_\-cunglq} 

\hyperlink{group__double_gae71a8dbbe843b68aca052074db93409d_gae71a8dbbe843b68aca052074db93409d}{P\-L\-A\-S\-M\-A\-\_\-dorglq} 

\hyperlink{group__float_ga2f8b6c06f4346761e024c9fa00427a61_ga2f8b6c06f4346761e024c9fa00427a61}{P\-L\-A\-S\-M\-A\-\_\-sorglq} 

\hyperlink{group__PLASMA__Complex64__t_ga8990facf0cb04df2a107c02e5dd5f3f7_ga8990facf0cb04df2a107c02e5dd5f3f7}{P\-L\-A\-S\-M\-A\-\_\-zgelqf} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_gafedf859d9373a2738b24e5780360ec5b_gafedf859d9373a2738b24e5780360ec5b}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zungqr@{P\-L\-A\-S\-M\-A\-\_\-zungqr}}
\index{P\-L\-A\-S\-M\-A\-\_\-zungqr@{P\-L\-A\-S\-M\-A\-\_\-zungqr}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zungqr}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zungqr (
\begin{DoxyParamCaption}
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{Q, }
\item[{int}]{L\-D\-Q}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_gafedf859d9373a2738b24e5780360ec5b_gafedf859d9373a2738b24e5780360ec5b}
P\-L\-A\-S\-M\-A\-\_\-zungqr -\/ Generates an M-\/by-\/\-N matrix Q with orthonormal columns, which is defined as the first N columns of a product of the elementary reflectors returned by P\-L\-A\-S\-M\-A\-\_\-zgeqrf.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em M} & The number of rows of the matrix Q. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix Q. N $>$= M.\\
\hline
\mbox{\tt in}  & {\em K} & The number of columns of elementary tile reflectors whose product defines the matrix Q. M $>$= K $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & Details of the Q\-R factorization of the original matrix A as returned by P\-L\-A\-S\-M\-A\-\_\-zgeqrf.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-M).\\
\hline
\mbox{\tt in}  & {\em desc\-T} & Auxiliary factorization data, computed by P\-L\-A\-S\-M\-A\-\_\-zgeqrf.\\
\hline
\mbox{\tt out}  & {\em Q} & On exit, the M-\/by-\/\-N matrix Q.\\
\hline
\mbox{\tt in}  & {\em L\-D\-Q} & The leading dimension of the array Q. L\-D\-Q $>$= max(1,\-M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga95b4202db333c7547d3459d7b909fcd6_ga95b4202db333c7547d3459d7b909fcd6}{P\-L\-A\-S\-M\-A\-\_\-zungqr\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_gafc2a8fdc018edb78cfa3fb1e671e16f4_gafc2a8fdc018edb78cfa3fb1e671e16f4}{P\-L\-A\-S\-M\-A\-\_\-zungqr\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_ga6c696165c8c276260ba80eff16e4d291_ga6c696165c8c276260ba80eff16e4d291}{P\-L\-A\-S\-M\-A\-\_\-cungqr} 

\hyperlink{group__double_ga5137c6e07ebf2faddae220daa28999ba_ga5137c6e07ebf2faddae220daa28999ba}{P\-L\-A\-S\-M\-A\-\_\-dorgqr} 

\hyperlink{group__float_ga4b6a6aa9e5da7961424f3afb62a69562_ga4b6a6aa9e5da7961424f3afb62a69562}{P\-L\-A\-S\-M\-A\-\_\-sorgqr} 

\hyperlink{group__PLASMA__Complex64__t_ga9d4fae8697b364c384faa7480aea3118_ga9d4fae8697b364c384faa7480aea3118}{P\-L\-A\-S\-M\-A\-\_\-zgeqrf} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga2c015740671fa101298fb9841b25f5d2_ga2c015740671fa101298fb9841b25f5d2}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zunmlq@{P\-L\-A\-S\-M\-A\-\_\-zunmlq}}
\index{P\-L\-A\-S\-M\-A\-\_\-zunmlq@{P\-L\-A\-S\-M\-A\-\_\-zunmlq}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zunmlq}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zunmlq (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{side, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{C, }
\item[{int}]{L\-D\-C}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga2c015740671fa101298fb9841b25f5d2_ga2c015740671fa101298fb9841b25f5d2}
P\-L\-A\-S\-M\-A\-\_\-zunmlq -\/ Overwrites the general complex M-\/by-\/\-N matrix C with \begin{DoxyVerb}            SIDE = 'L'     SIDE = 'R'
\end{DoxyVerb}
 T\-R\-A\-N\-S = 'N'\-: Q $\ast$ C C $\ast$ Q T\-R\-A\-N\-S = 'C'\-: Q$\ast$$\ast$\-H $\ast$ C C $\ast$ Q$\ast$$\ast$\-H

where Q is a complex unitary matrix defined as the product of k elementary reflectors \begin{DoxyVerb}  Q = H(1) H(2) . . . H(k)
\end{DoxyVerb}


as returned by P\-L\-A\-S\-M\-A\-\_\-zgeqrf. Q is of order M if S\-I\-D\-E = Plasma\-Left and of order N if S\-I\-D\-E = Plasma\-Right.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em side} & Intended usage\-: = Plasma\-Left\-: apply Q or Q$\ast$$\ast$\-H from the left; = Plasma\-Right\-: apply Q or Q$\ast$$\ast$\-H from the right.\\
\hline
\mbox{\tt in}  & {\em trans} & Intended usage\-: = Plasma\-No\-Trans\-: no transpose, apply Q; = Plasma\-Conj\-Trans\-: conjugate transpose, apply Q$\ast$$\ast$\-H.\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix C. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix C. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em K} & The number of rows of elementary tile reflectors whose product defines the matrix Q. If side == Plasma\-Left, M $>$= K $>$= 0. If side == Plasma\-Right, N $>$= K $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & Details of the L\-Q factorization of the original matrix A as returned by P\-L\-A\-S\-M\-A\-\_\-zgelqf.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. L\-D\-A $>$= max(1,\-K).\\
\hline
\mbox{\tt in}  & {\em desc\-T} & Auxiliary factorization data, computed by P\-L\-A\-S\-M\-A\-\_\-zgelqf.\\
\hline
\mbox{\tt in,out}  & {\em C} & On entry, the M-\/by-\/\-N matrix C. On exit, C is overwritten by Q$\ast$\-C or Q$\ast$$\ast$\-H$\ast$\-C.\\
\hline
\mbox{\tt in}  & {\em L\-D\-C} & The leading dimension of the array C. L\-D\-C $>$= max(1,\-M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_gad9b76883d0fe796b0dd8eaadef158d6b_gad9b76883d0fe796b0dd8eaadef158d6b}{P\-L\-A\-S\-M\-A\-\_\-zunmlq\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga5a5533f0e5deb266bd38699d1361e25f_ga5a5533f0e5deb266bd38699d1361e25f}{P\-L\-A\-S\-M\-A\-\_\-zunmlq\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gac9aca2d8444a6e5630fe4674505a2afd_gac9aca2d8444a6e5630fe4674505a2afd}{P\-L\-A\-S\-M\-A\-\_\-cunmlq} 

\hyperlink{group__double_ga7c70d5b53e69f9ab564126c78938002a_ga7c70d5b53e69f9ab564126c78938002a}{P\-L\-A\-S\-M\-A\-\_\-dormlq} 

\hyperlink{group__float_ga4f42eb41e34bdf290b36fe5ce8e576b7_ga4f42eb41e34bdf290b36fe5ce8e576b7}{P\-L\-A\-S\-M\-A\-\_\-sormlq} 

\hyperlink{group__PLASMA__Complex64__t_ga8990facf0cb04df2a107c02e5dd5f3f7_ga8990facf0cb04df2a107c02e5dd5f3f7}{P\-L\-A\-S\-M\-A\-\_\-zgelqf} 
\end{DoxySeeAlso}
\hypertarget{group__PLASMA__Complex64__t_ga2a00379e9ae15c89c8a21d7dfa945e8f_ga2a00379e9ae15c89c8a21d7dfa945e8f}{\index{Simple Interface -\/ Double Complex@{Simple Interface -\/ Double Complex}!P\-L\-A\-S\-M\-A\-\_\-zunmqr@{P\-L\-A\-S\-M\-A\-\_\-zunmqr}}
\index{P\-L\-A\-S\-M\-A\-\_\-zunmqr@{P\-L\-A\-S\-M\-A\-\_\-zunmqr}!Simple Interface - Double Complex@{Simple Interface -\/ Double Complex}}
\subsubsection[{P\-L\-A\-S\-M\-A\-\_\-zunmqr}]{\setlength{\rightskip}{0pt plus 5cm}int P\-L\-A\-S\-M\-A\-\_\-zunmqr (
\begin{DoxyParamCaption}
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{side, }
\item[{P\-L\-A\-S\-M\-A\-\_\-enum}]{trans, }
\item[{int}]{M, }
\item[{int}]{N, }
\item[{int}]{K, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{A, }
\item[{int}]{L\-D\-A, }
\item[{{\bf P\-L\-A\-S\-M\-A\-\_\-desc} $\ast$}]{desc\-T, }
\item[{P\-L\-A\-S\-M\-A\-\_\-\-Complex64\-\_\-t $\ast$}]{C, }
\item[{int}]{L\-D\-C}
\end{DoxyParamCaption}
)}}\label{group__PLASMA__Complex64__t_ga2a00379e9ae15c89c8a21d7dfa945e8f_ga2a00379e9ae15c89c8a21d7dfa945e8f}
P\-L\-A\-S\-M\-A\-\_\-zunmqr -\/ Overwrites the general complex M-\/by-\/\-N matrix C with \begin{DoxyVerb}            SIDE = 'L'     SIDE = 'R'
\end{DoxyVerb}
 T\-R\-A\-N\-S = 'N'\-: Q $\ast$ C C $\ast$ Q T\-R\-A\-N\-S = 'C'\-: Q$\ast$$\ast$\-H $\ast$ C C $\ast$ Q$\ast$$\ast$\-H

where Q is a complex unitary matrix defined as the product of k elementary reflectors \begin{DoxyVerb}  Q = H(1) H(2) . . . H(k)
\end{DoxyVerb}


as returned by P\-L\-A\-S\-M\-A\-\_\-zgeqrf. Q is of order M if S\-I\-D\-E = Plasma\-Left and of order N if S\-I\-D\-E = Plasma\-Right.


\begin{DoxyParams}[1]{Parameters}
\mbox{\tt in}  & {\em side} & Intended usage\-: = Plasma\-Left\-: apply Q or Q$\ast$$\ast$\-H from the left; = Plasma\-Right\-: apply Q or Q$\ast$$\ast$\-H from the right.\\
\hline
\mbox{\tt in}  & {\em trans} & Intended usage\-: = Plasma\-No\-Trans\-: no transpose, apply Q; = Plasma\-Conj\-Trans\-: conjugate transpose, apply Q$\ast$$\ast$\-H.\\
\hline
\mbox{\tt in}  & {\em M} & The number of rows of the matrix C. M $>$= 0.\\
\hline
\mbox{\tt in}  & {\em N} & The number of columns of the matrix C. N $>$= 0.\\
\hline
\mbox{\tt in}  & {\em K} & The number of elementary reflectors whose product defines the matrix Q. If side == Plasma\-Left, M $>$= K $>$= 0. If side == Plasma\-Right, N $>$= K $>$= 0.\\
\hline
\mbox{\tt in}  & {\em A} & Details of the Q\-R factorization of the original matrix A as returned by P\-L\-A\-S\-M\-A\-\_\-zgeqrf.\\
\hline
\mbox{\tt in}  & {\em L\-D\-A} & The leading dimension of the array A. If side == Plasma\-Left, L\-D\-A $>$= max(1,\-M). If side == Plasma\-Right, L\-D\-A $>$= max(1,\-N).\\
\hline
\mbox{\tt in}  & {\em desc\-T} & Auxiliary factorization data, computed by P\-L\-A\-S\-M\-A\-\_\-zgeqrf.\\
\hline
\mbox{\tt in,out}  & {\em C} & On entry, the M-\/by-\/\-N matrix C. On exit, C is overwritten by Q$\ast$\-C or Q$\ast$$\ast$\-H$\ast$\-C.\\
\hline
\mbox{\tt in}  & {\em L\-D\-C} & The leading dimension of the array C. L\-D\-C $>$= max(1,\-M).\\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}

\end{DoxyReturn}

\begin{DoxyRetVals}{Return values}
{\em P\-L\-A\-S\-M\-A\-\_\-\-S\-U\-C\-C\-E\-S\-S} & successful exit \\
\hline
{\em $<$0} & if -\/i, the i-\/th argument had an illegal value\\
\hline
\end{DoxyRetVals}
\begin{DoxySeeAlso}{See Also}
\hyperlink{group__PLASMA__Complex64__t__Tile_ga52c9965e4609c082ae9b976764fdd1c7_ga52c9965e4609c082ae9b976764fdd1c7}{P\-L\-A\-S\-M\-A\-\_\-zunmqr\-\_\-\-Tile} 

\hyperlink{group__PLASMA__Complex64__t__Tile__Async_ga65bce78bfc91e50cd35cdb87521ce9a4_ga65bce78bfc91e50cd35cdb87521ce9a4}{P\-L\-A\-S\-M\-A\-\_\-zunmqr\-\_\-\-Tile\-\_\-\-Async} 

\hyperlink{group__PLASMA__Complex32__t_gac4f6c16a5e7d9bc92ec6addcaa42bad1_gac4f6c16a5e7d9bc92ec6addcaa42bad1}{P\-L\-A\-S\-M\-A\-\_\-cunmqr} 

\hyperlink{group__double_ga9623493d89eb656c0f5aa44c7772294c_ga9623493d89eb656c0f5aa44c7772294c}{P\-L\-A\-S\-M\-A\-\_\-dormqr} 

\hyperlink{group__float_ga3d2c263d860db4a6d63fd13156262bd2_ga3d2c263d860db4a6d63fd13156262bd2}{P\-L\-A\-S\-M\-A\-\_\-sormqr} 

\hyperlink{group__PLASMA__Complex64__t_ga9d4fae8697b364c384faa7480aea3118_ga9d4fae8697b364c384faa7480aea3118}{P\-L\-A\-S\-M\-A\-\_\-zgeqrf} 
\end{DoxySeeAlso}
