![]() |
MAGMA
1.5.0
Matrix Algebra for GPU and Multicore Architectures
|
Functions | |
magma_int_t | magma_cheevd (magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, float *w, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
CHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. More... | |
magma_int_t | magma_cheevd_gpu (magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *dA, magma_int_t ldda, float *w, magmaFloatComplex *wA, magma_int_t ldwa, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
CHEEVD_GPU computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. More... | |
magma_int_t | magma_cheevd_m (magma_int_t nrgpu, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, float *w, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
CHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. More... | |
magma_int_t | magma_cheevdx (magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, float vl, float vu, magma_int_t il, magma_int_t iu, magma_int_t *m, float *w, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
CHEEVDX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. More... | |
magma_int_t | magma_cheevdx_2stage (magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, float vl, float vu, magma_int_t il, magma_int_t iu, magma_int_t *m, float *w, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
CHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. More... | |
magma_int_t | magma_cheevdx_2stage_m (magma_int_t nrgpu, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, float vl, float vu, magma_int_t il, magma_int_t iu, magma_int_t *m, float *w, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
CHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. More... | |
magma_int_t | magma_cheevdx_gpu (magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *dA, magma_int_t ldda, float vl, float vu, magma_int_t il, magma_int_t iu, magma_int_t *m, float *w, magmaFloatComplex *wA, magma_int_t ldwa, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
CHEEVDX_GPU computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. More... | |
magma_int_t | magma_cheevdx_m (magma_int_t nrgpu, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, float vl, float vu, magma_int_t il, magma_int_t iu, magma_int_t *m, float *w, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
CHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. More... | |
magma_int_t | magma_cheevr (magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, float vl, float vu, magma_int_t il, magma_int_t iu, float abstol, magma_int_t *m, float *w, magmaFloatComplex *Z, magma_int_t ldz, magma_int_t *isuppz, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
CHEEVR computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix T. More... | |
magma_int_t | magma_cheevr_gpu (magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *dA, magma_int_t ldda, float vl, float vu, magma_int_t il, magma_int_t iu, float abstol, magma_int_t *m, float *w, magmaFloatComplex *dZ, magma_int_t lddz, magma_int_t *isuppz, magmaFloatComplex *wA, magma_int_t ldwa, magmaFloatComplex *wZ, magma_int_t ldwz, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
CHEEVR computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix T. More... | |
magma_int_t | magma_cheevx (magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, float vl, float vu, magma_int_t il, magma_int_t iu, float abstol, magma_int_t *m, float *w, magmaFloatComplex *Z, magma_int_t ldz, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t *iwork, magma_int_t *ifail, magma_int_t *info) |
CHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. More... | |
magma_int_t | magma_cheevx_gpu (magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *dA, magma_int_t ldda, float vl, float vu, magma_int_t il, magma_int_t iu, float abstol, magma_int_t *m, float *w, magmaFloatComplex *dZ, magma_int_t lddz, magmaFloatComplex *wA, magma_int_t ldwa, magmaFloatComplex *wZ, magma_int_t ldwz, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t *iwork, magma_int_t *ifail, magma_int_t *info) |
CHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. More... | |
magma_int_t magma_cheevd | ( | magma_vec_t | jobz, |
magma_uplo_t | uplo, | ||
magma_int_t | n, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
float * | w, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
float * | rwork, | ||
magma_int_t | lrwork, | ||
magma_int_t * | iwork, | ||
magma_int_t | liwork, | ||
magma_int_t * | info | ||
) |
CHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[in] | jobz | magma_vec_t
|
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | COMPLEX array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A. If JOBZ = MagmaNoVec, then on exit the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed. |
[in] | lda | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[out] | w | REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. |
[out] | work | (workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. |
[in] | lwork | INTEGER The length of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LWORK >= N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ). NB can be obtained through magma_get_chetrd_nb(N). If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | rwork | (workspace) REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK. |
[in] | lrwork | INTEGER The dimension of the array RWORK. If N <= 1, LRWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LRWORK >= N. If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2. If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | iwork | (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. |
[in] | liwork | INTEGER The dimension of the array IWORK. If N <= 1, LIWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1. If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | info | INTEGER
|
Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
magma_int_t magma_cheevd_gpu | ( | magma_vec_t | jobz, |
magma_uplo_t | uplo, | ||
magma_int_t | n, | ||
magmaFloatComplex * | dA, | ||
magma_int_t | ldda, | ||
float * | w, | ||
magmaFloatComplex * | wA, | ||
magma_int_t | ldwa, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
float * | rwork, | ||
magma_int_t | lrwork, | ||
magma_int_t * | iwork, | ||
magma_int_t | liwork, | ||
magma_int_t * | info | ||
) |
CHEEVD_GPU computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[in] | jobz | magma_vec_t
|
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | dA | COMPLEX array on the GPU, dimension (LDDA, N). On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A. If JOBZ = MagmaNoVec, then on exit the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed. |
[in] | ldda | INTEGER The leading dimension of the array DA. LDDA >= max(1,N). |
[out] | w | REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. |
wA | (workspace) COMPLEX array, dimension (LDWA, N) | |
[in] | ldwa | INTEGER The leading dimension of the array wA. LDWA >= max(1,N). |
[out] | work | (workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. |
[in] | lwork | INTEGER The length of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LWORK >= N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ). NB can be obtained through magma_get_chetrd_nb(N). If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | rwork | (workspace) REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK. |
[in] | lrwork | INTEGER The dimension of the array RWORK. If N <= 1, LRWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LRWORK >= N. If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2. If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | iwork | (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. |
[in] | liwork | INTEGER The dimension of the array IWORK. If N <= 1, LIWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1. If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | info | INTEGER
|
Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
magma_int_t magma_cheevd_m | ( | magma_int_t | nrgpu, |
magma_vec_t | jobz, | ||
magma_uplo_t | uplo, | ||
magma_int_t | n, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
float * | w, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
float * | rwork, | ||
magma_int_t | lrwork, | ||
magma_int_t * | iwork, | ||
magma_int_t | liwork, | ||
magma_int_t * | info | ||
) |
CHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[in] | nrgpu | INTEGER Number of GPUs to use. |
[in] | jobz | magma_vec_t
|
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | COMPLEX array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A. If JOBZ = MagmaNoVec, then on exit the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed. |
[in] | lda | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[out] | w | REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. |
[out] | work | (workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
[in] | lwork | INTEGER The length of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LWORK >= N * (NB + 1). If JOBZ = MagmaVec and N > 1, LWORK >= 2*N + N**2. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | rwork | (workspace) REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. |
[in] | lrwork | INTEGER The dimension of the array RWORK. If N <= 1, LRWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LRWORK >= N. If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2. If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | iwork | (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. |
[in] | liwork | INTEGER The dimension of the array IWORK. If N <= 1, LIWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1. If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | info | INTEGER
|
Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
magma_int_t magma_cheevdx | ( | magma_vec_t | jobz, |
magma_range_t | range, | ||
magma_uplo_t | uplo, | ||
magma_int_t | n, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
float | vl, | ||
float | vu, | ||
magma_int_t | il, | ||
magma_int_t | iu, | ||
magma_int_t * | m, | ||
float * | w, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
float * | rwork, | ||
magma_int_t | lrwork, | ||
magma_int_t * | iwork, | ||
magma_int_t | liwork, | ||
magma_int_t * | info | ||
) |
CHEEVDX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.
Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[in] | jobz | magma_vec_t
|
[in] | range | magma_range_t
|
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | COMPLEX array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = MagmaVec, then if INFO = 0, the first m columns of A contains the required orthonormal eigenvectors of the matrix A. If JOBZ = MagmaNoVec, then on exit the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed. |
[in] | lda | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[in] | vl | REAL |
[in] | vu | REAL If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI. |
[in] | il | INTEGER |
[in] | iu | INTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV. |
[out] | m | INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1. |
[out] | w | REAL array, dimension (N) If INFO = 0, the required m eigenvalues in ascending order. |
[out] | work | (workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. |
[in] | lwork | INTEGER The length of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LWORK >= N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ). NB can be obtained through magma_get_chetrd_nb(N). If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | rwork | (workspace) REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK. |
[in] | lrwork | INTEGER The dimension of the array RWORK. If N <= 1, LRWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LRWORK >= N. If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2. If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | iwork | (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. |
[in] | liwork | INTEGER The dimension of the array IWORK. If N <= 1, LIWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1. If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | info | INTEGER
|
Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
magma_int_t magma_cheevdx_2stage | ( | magma_vec_t | jobz, |
magma_range_t | range, | ||
magma_uplo_t | uplo, | ||
magma_int_t | n, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
float | vl, | ||
float | vu, | ||
magma_int_t | il, | ||
magma_int_t | iu, | ||
magma_int_t * | m, | ||
float * | w, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
float * | rwork, | ||
magma_int_t | lrwork, | ||
magma_int_t * | iwork, | ||
magma_int_t | liwork, | ||
magma_int_t * | info | ||
) |
CHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.
It uses a two-stage algorithm for the tridiagonalization. If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[in] | jobz | magma_vec_t
|
[in] | range | magma_range_t
|
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | COMPLEX array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = MagmaVec, then if INFO = 0, the first m columns of A contains the required orthonormal eigenvectors of the matrix A. If JOBZ = MagmaNoVec, then on exit the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed. |
[in] | lda | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[in] | vl | REAL |
[in] | vu | REAL If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI. |
[in] | il | INTEGER |
[in] | iu | INTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV. |
[out] | m | INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1. |
[out] | w | REAL array, dimension (N) If INFO = 0, the required m eigenvalues in ascending order. |
[out] | work | (workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
[in] | lwork | INTEGER The length of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LWORK >= LQ2 + N * (NB + 1). If JOBZ = MagmaVec and N > 1, LWORK >= LQ2 + 2*N + N**2. where LQ2 is the size needed to store the Q2 matrix and is returned by magma_bulge_get_lq2. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | rwork | (workspace) REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. |
[in] | lrwork | INTEGER The dimension of the array RWORK. If N <= 1, LRWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LRWORK >= N. If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2. If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | iwork | (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. |
[in] | liwork | INTEGER The dimension of the array IWORK. If N <= 1, LIWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1. If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | info | INTEGER
|
Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
magma_int_t magma_cheevdx_2stage_m | ( | magma_int_t | nrgpu, |
magma_vec_t | jobz, | ||
magma_range_t | range, | ||
magma_uplo_t | uplo, | ||
magma_int_t | n, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
float | vl, | ||
float | vu, | ||
magma_int_t | il, | ||
magma_int_t | iu, | ||
magma_int_t * | m, | ||
float * | w, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
float * | rwork, | ||
magma_int_t | lrwork, | ||
magma_int_t * | iwork, | ||
magma_int_t | liwork, | ||
magma_int_t * | info | ||
) |
CHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.
It uses a two-stage algorithm for the tridiagonalization. If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[in] | nrgpu | INTEGER Number of GPUs to use. |
[in] | jobz | magma_vec_t
|
[in] | range | magma_range_t
|
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | COMPLEX array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = MagmaVec, then if INFO = 0, the first m columns of A contains the required orthonormal eigenvectors of the matrix A. If JOBZ = MagmaNoVec, then on exit the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed. |
[in] | lda | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[in] | vl | REAL |
[in] | vu | REAL If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI. |
[in] | il | INTEGER |
[in] | iu | INTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV. |
[out] | m | INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1. |
[out] | w | REAL array, dimension (N) If INFO = 0, the required m eigenvalues in ascending order. |
[out] | work | (workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
[in] | lwork | INTEGER The length of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LWORK >= LQ2 + N * (NB + 1). If JOBZ = MagmaVec and N > 1, LWORK >= LQ2 + 2*N + N**2. where LQ2 is the size needed to store the Q2 matrix and is returned by magma_bulge_get_lq2. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | rwork | (workspace) REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. |
[in] | lrwork | INTEGER The dimension of the array RWORK. If N <= 1, LRWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LRWORK >= N. If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2. If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | iwork | (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. |
[in] | liwork | INTEGER The dimension of the array IWORK. If N <= 1, LIWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1. If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | info | INTEGER
|
Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
magma_int_t magma_cheevdx_gpu | ( | magma_vec_t | jobz, |
magma_range_t | range, | ||
magma_uplo_t | uplo, | ||
magma_int_t | n, | ||
magmaFloatComplex * | dA, | ||
magma_int_t | ldda, | ||
float | vl, | ||
float | vu, | ||
magma_int_t | il, | ||
magma_int_t | iu, | ||
magma_int_t * | m, | ||
float * | w, | ||
magmaFloatComplex * | wA, | ||
magma_int_t | ldwa, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
float * | rwork, | ||
magma_int_t | lrwork, | ||
magma_int_t * | iwork, | ||
magma_int_t | liwork, | ||
magma_int_t * | info | ||
) |
CHEEVDX_GPU computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.
Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[in] | jobz | magma_vec_t
|
[in] | range | magma_range_t
|
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | dA | COMPLEX array on the GPU, dimension (LDDA, N). On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = MagmaVec, then if INFO = 0, the first m columns of A contains the required orthonormal eigenvectors of the matrix A. If JOBZ = MagmaNoVec, then on exit the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed. |
[in] | ldda | INTEGER The leading dimension of the array DA. LDDA >= max(1,N). |
[in] | vl | REAL |
[in] | vu | REAL If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI. |
[in] | il | INTEGER |
[in] | iu | INTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV. |
[out] | m | INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1. |
[out] | w | REAL array, dimension (N) If INFO = 0, the required m eigenvalues in ascending order. |
wA | (workspace) COMPLEX array, dimension (LDWA, N) | |
[in] | ldwa | INTEGER The leading dimension of the array wA. LDWA >= max(1,N). |
[out] | work | (workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. |
[in] | lwork | INTEGER The length of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LWORK >= N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ). NB can be obtained through magma_get_chetrd_nb(N). If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | rwork | (workspace) REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK. |
[in] | lrwork | INTEGER The dimension of the array RWORK. If N <= 1, LRWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LRWORK >= N. If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2. If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | iwork | (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. |
[in] | liwork | INTEGER The dimension of the array IWORK. If N <= 1, LIWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1. If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | info | INTEGER
|
Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
magma_int_t magma_cheevdx_m | ( | magma_int_t | nrgpu, |
magma_vec_t | jobz, | ||
magma_range_t | range, | ||
magma_uplo_t | uplo, | ||
magma_int_t | n, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
float | vl, | ||
float | vu, | ||
magma_int_t | il, | ||
magma_int_t | iu, | ||
magma_int_t * | m, | ||
float * | w, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
float * | rwork, | ||
magma_int_t | lrwork, | ||
magma_int_t * | iwork, | ||
magma_int_t | liwork, | ||
magma_int_t * | info | ||
) |
CHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[in] | nrgpu | INTEGER Number of GPUs to use. |
[in] | jobz | magma_vec_t
|
[in] | range | magma_range_t
|
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | COMPLEX array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A. If JOBZ = MagmaNoVec, then on exit the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed. |
[in] | lda | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[in] | vl | REAL |
[in] | vu | REAL If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI. |
[in] | il | INTEGER |
[in] | iu | INTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV. |
[out] | m | INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1. |
[out] | w | REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. |
[out] | work | (workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
[in] | lwork | INTEGER The length of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LWORK >= N * (NB + 1). If JOBZ = MagmaVec and N > 1, LWORK >= 2*N + N**2. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | rwork | (workspace) REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. |
[in] | lrwork | INTEGER The dimension of the array RWORK. If N <= 1, LRWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LRWORK >= N. If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2. If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | iwork | (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. |
[in] | liwork | INTEGER The dimension of the array IWORK. If N <= 1, LIWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1. If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
[out] | info | INTEGER
|
Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
magma_int_t magma_cheevr | ( | magma_vec_t | jobz, |
magma_range_t | range, | ||
magma_uplo_t | uplo, | ||
magma_int_t | n, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
float | vl, | ||
float | vu, | ||
magma_int_t | il, | ||
magma_int_t | iu, | ||
float | abstol, | ||
magma_int_t * | m, | ||
float * | w, | ||
magmaFloatComplex * | Z, | ||
magma_int_t | ldz, | ||
magma_int_t * | isuppz, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
float * | rwork, | ||
magma_int_t | lrwork, | ||
magma_int_t * | iwork, | ||
magma_int_t | liwork, | ||
magma_int_t * | info | ||
) |
CHEEVR computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix T.
Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
Whenever possible, CHEEVR calls CSTEGR to compute the eigenspectrum using Relatively Robust Representations. CSTEGR computes eigenvalues by the dqds algorithm, while orthogonal eigenvectors are computed from various "good" L D L^T representations (also known as Relatively Robust Representations). Gram-Schmidt orthogonalization is avoided as far as possible. More specifically, the various steps of the algorithm are as follows. For the i-th unreduced block of T,
For more details, see "A new O(n^2) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem", by Inderjit Dhillon, Computer Science Division Technical Report No. UCB//CSD-97-971, UC Berkeley, May 1997.
Note 1 : CHEEVR calls CSTEGR when the full spectrum is requested on machines which conform to the ieee-754 floating point standard. CHEEVR calls SSTEBZ and CSTEIN on non-ieee machines and when partial spectrum requests are made.
Normal execution of CSTEGR may create NaNs and infinities and hence may abort due to a floating point exception in environments which do not handle NaNs and infinities in the ieee standard default manner.
[in] | jobz | magma_vec_t
|
[in] | range | magma_range_t
|
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | COMPLEX array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed. |
[in] | lda | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[in] | vl | REAL |
[in] | vu | REAL If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI. |
[in] | il | INTEGER |
[in] | iu | INTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV. |
[in] | abstol | REAL The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( |a|,|b| ), where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing A to tridiagonal form. See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3. If high relative accuracy is important, set ABSTOL to SLAMCH( 'Safe minimum' ). Doing so will guarantee that eigenvalues are computed to high relative accuracy when possible in future releases. The current code does not make any guarantees about high relative accuracy, but furutre releases will. See J. Barlow and J. Demmel, "Computing Accurate Eigensystems of Scaled Diagonally Dominant Matrices", LAPACK Working Note #7, for a discussion of which matrices define their eigenvalues to high relative accuracy. |
[out] | m | INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1. |
[out] | w | REAL array, dimension (N) The first M elements contain the selected eigenvalues in ascending order. |
[out] | Z | COMPLEX array, dimension (LDZ, max(1,M)) If JOBZ = MagmaVec, then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = MagmaNoVec, then Z is not referenced. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = MagmaRangeV, the exact value of M is not known in advance and an upper bound must be used. |
[in] | ldz | INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = MagmaVec, LDZ >= max(1,N). |
[out] | isuppz | INTEGER ARRAY, dimension ( 2*max(1,M) ) The support of the eigenvectors in Z, i.e., the indices indicating the nonzero elements in Z. The i-th eigenvector is nonzero only in elements ISUPPZ( 2*i-1 ) through ISUPPZ( 2*i ). Implemented only for RANGE = MagmaRangeAll or MagmaRangeI and IU - IL = N - 1 |
[out] | work | (workspace) COMPLEX array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
[in] | lwork | INTEGER The length of the array WORK. LWORK >= max(1,2*N). For optimal efficiency, LWORK >= (NB+1)*N, where NB is the max of the blocksize for CHETRD and for CUNMTR as returned by ILAENV. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. |
[out] | rwork | (workspace) REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal (and minimal) LRWORK. |
[in] | lrwork | INTEGER The length of the array RWORK. LRWORK >= max(1,24*N). If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the RWORK array, returns this value as the first entry of the RWORK array, and no error message related to LRWORK is issued by XERBLA. |
[out] | iwork | (workspace) INTEGER array, dimension (LIWORK) On exit, if INFO = 0, IWORK(1) returns the optimal (and minimal) LIWORK. |
[in] | liwork | INTEGER The dimension of the array IWORK. LIWORK >= max(1,10*N). If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued by XERBLA. |
[out] | info | INTEGER
|
Based on contributions by Inderjit Dhillon, IBM Almaden, USA Osni Marques, LBNL/NERSC, USA Ken Stanley, Computer Science Division, University of California at Berkeley, USA
magma_int_t magma_cheevr_gpu | ( | magma_vec_t | jobz, |
magma_range_t | range, | ||
magma_uplo_t | uplo, | ||
magma_int_t | n, | ||
magmaFloatComplex * | dA, | ||
magma_int_t | ldda, | ||
float | vl, | ||
float | vu, | ||
magma_int_t | il, | ||
magma_int_t | iu, | ||
float | abstol, | ||
magma_int_t * | m, | ||
float * | w, | ||
magmaFloatComplex * | dZ, | ||
magma_int_t | lddz, | ||
magma_int_t * | isuppz, | ||
magmaFloatComplex * | wA, | ||
magma_int_t | ldwa, | ||
magmaFloatComplex * | wZ, | ||
magma_int_t | ldwz, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
float * | rwork, | ||
magma_int_t | lrwork, | ||
magma_int_t * | iwork, | ||
magma_int_t | liwork, | ||
magma_int_t * | info | ||
) |
CHEEVR computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix T.
Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
Whenever possible, CHEEVR calls CSTEGR to compute the eigenspectrum using Relatively Robust Representations. CSTEGR computes eigenvalues by the dqds algorithm, while orthogonal eigenvectors are computed from various "good" L D L^T representations (also known as Relatively Robust Representations). Gram-Schmidt orthogonalization is avoided as far as possible. More specifically, the various steps of the algorithm are as follows. For the i-th unreduced block of T,
For more details, see "A new O(n^2) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem", by Inderjit Dhillon, Computer Science Division Technical Report No. UCB//CSD-97-971, UC Berkeley, May 1997.
Note 1 : CHEEVR calls CSTEGR when the full spectrum is requested on machines which conform to the ieee-754 floating point standard. CHEEVR calls SSTEBZ and CSTEIN on non-ieee machines and when partial spectrum requests are made.
Normal execution of CSTEGR may create NaNs and infinities and hence may abort due to a floating point exception in environments which do not handle NaNs and infinities in the ieee standard default manner.
[in] | jobz | magma_vec_t
|
[in] | range | magma_range_t
|
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | dA | COMPLEX array, dimension (LDDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, DA is destroyed. |
[in] | ldda | INTEGER The leading dimension of the array A. LDDA >= max(1,N). |
[in] | vl | REAL |
[in] | vu | REAL If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI. |
[in] | il | INTEGER |
[in] | iu | INTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV. |
[in] | abstol | REAL The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( |a|,|b| ), where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing A to tridiagonal form. See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3. If high relative accuracy is important, set ABSTOL to SLAMCH( 'Safe minimum' ). Doing so will guarantee that eigenvalues are computed to high relative accuracy when possible in future releases. The current code does not make any guarantees about high relative accuracy, but furutre releases will. See J. Barlow and J. Demmel, "Computing Accurate Eigensystems of Scaled Diagonally Dominant Matrices", LAPACK Working Note #7, for a discussion of which matrices define their eigenvalues to high relative accuracy. |
[out] | m | INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1. |
[out] | w | REAL array, dimension (N) The first M elements contain the selected eigenvalues in ascending order. |
[out] | dZ | COMPLEX array, dimension (LDDZ, max(1,M)) If JOBZ = MagmaVec, then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = MagmaNoVec, then Z is not referenced. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = MagmaRangeV, the exact value of M is not known in advance and an upper bound must be used. (workspace) If FAST_HEMV is defined DZ should be (LDDZ, max(1,N)) in both cases. |
[in] | lddz | INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = MagmaVec, LDZ >= max(1,N). |
[out] | isuppz | INTEGER ARRAY, dimension ( 2*max(1,M) ) The support of the eigenvectors in Z, i.e., the indices indicating the nonzero elements in Z. The i-th eigenvector is nonzero only in elements ISUPPZ( 2*i-1 ) through ISUPPZ( 2*i ). Implemented only for RANGE = MagmaRangeAll or MagmaRangeI and IU - IL = N - 1 |
wA | (workspace) COMPLEX array, dimension (LDWA, N) | |
[in] | ldwa | INTEGER The leading dimension of the array wA. LDWA >= max(1,N). |
wZ | (workspace) COMPLEX array, dimension (LDWZ, max(1,M)) | |
[in] | ldwz | INTEGER The leading dimension of the array wZ. LDWZ >= 1, and if JOBZ = MagmaVec, LDWZ >= max(1,N). |
[out] | work | (workspace) COMPLEX array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
[in] | lwork | INTEGER The length of the array WORK. LWORK >= (NB+1)*N, where NB is the max of the blocksize for CHETRD If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. |
[out] | rwork | (workspace) REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal (and minimal) LRWORK. |
[in] | lrwork | INTEGER The length of the array RWORK. LRWORK >= max(1,24*N). If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the RWORK array, returns this value as the first entry of the RWORK array, and no error message related to LRWORK is issued by XERBLA. |
[out] | iwork | (workspace) INTEGER array, dimension (LIWORK) On exit, if INFO = 0, IWORK(1) returns the optimal (and minimal) LIWORK. |
[in] | liwork | INTEGER The dimension of the array IWORK. LIWORK >= max(1,10*N). If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued by XERBLA. |
[out] | info | INTEGER
|
Based on contributions by Inderjit Dhillon, IBM Almaden, USA Osni Marques, LBNL/NERSC, USA Ken Stanley, Computer Science Division, University of California at Berkeley, USA
magma_int_t magma_cheevx | ( | magma_vec_t | jobz, |
magma_range_t | range, | ||
magma_uplo_t | uplo, | ||
magma_int_t | n, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
float | vl, | ||
float | vu, | ||
magma_int_t | il, | ||
magma_int_t | iu, | ||
float | abstol, | ||
magma_int_t * | m, | ||
float * | w, | ||
magmaFloatComplex * | Z, | ||
magma_int_t | ldz, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
float * | rwork, | ||
magma_int_t * | iwork, | ||
magma_int_t * | ifail, | ||
magma_int_t * | info | ||
) |
CHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.
Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
[in] | jobz | magma_vec_t
|
[in] | range | magma_range_t
|
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | COMPLEX array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed. |
[in] | lda | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[in] | vl | REAL |
[in] | vu | REAL If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI. |
[in] | il | INTEGER |
[in] | iu | INTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV. |
[in] | abstol | REAL The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( |a|,|b| ), where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing A to tridiagonal form. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*SLAMCH('S'), not zero. If this routine returns with INFO > 0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*SLAMCH('S'). See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3. |
[out] | m | INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1. |
[out] | w | REAL array, dimension (N) On normal exit, the first M elements contain the selected eigenvalues in ascending order. |
[out] | Z | COMPLEX array, dimension (LDZ, max(1,M)) If JOBZ = MagmaVec, then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. If JOBZ = MagmaNoVec, then Z is not referenced. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = MagmaRangeV, the exact value of M is not known in advance and an upper bound must be used. |
[in] | ldz | INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = MagmaVec, LDZ >= max(1,N). |
[out] | work | (workspace) COMPLEX array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
[in] | lwork | INTEGER The length of the array WORK. LWORK >= max(1,2*N-1). For optimal efficiency, LWORK >= (NB+1)*N, where NB is the max of the blocksize for CHETRD and for CUNMTR as returned by ILAENV. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. |
rwork | (workspace) REAL array, dimension (7*N) | |
iwork | (workspace) INTEGER array, dimension (5*N) | |
[out] | ifail | INTEGER array, dimension (N) If JOBZ = MagmaVec, then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = MagmaNoVec, then IFAIL is not referenced. |
[out] | info | INTEGER
|
magma_int_t magma_cheevx_gpu | ( | magma_vec_t | jobz, |
magma_range_t | range, | ||
magma_uplo_t | uplo, | ||
magma_int_t | n, | ||
magmaFloatComplex * | dA, | ||
magma_int_t | ldda, | ||
float | vl, | ||
float | vu, | ||
magma_int_t | il, | ||
magma_int_t | iu, | ||
float | abstol, | ||
magma_int_t * | m, | ||
float * | w, | ||
magmaFloatComplex * | dZ, | ||
magma_int_t | lddz, | ||
magmaFloatComplex * | wA, | ||
magma_int_t | ldwa, | ||
magmaFloatComplex * | wZ, | ||
magma_int_t | ldwz, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
float * | rwork, | ||
magma_int_t * | iwork, | ||
magma_int_t * | ifail, | ||
magma_int_t * | info | ||
) |
CHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.
Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
[in] | jobz | magma_vec_t
|
[in] | range | magma_range_t
|
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | dA | COMPLEX array, dimension (LDDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed. |
[in] | ldda | INTEGER The leading dimension of the array DA. LDDA >= max(1,N). |
[in] | vl | REAL |
[in] | vu | REAL If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI. |
[in] | il | INTEGER |
[in] | iu | INTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV. |
[in] | abstol | REAL The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( |a|,|b| ), where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing A to tridiagonal form. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*SLAMCH('S'), not zero. If this routine returns with INFO > 0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*SLAMCH('S'). See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3. |
[out] | m | INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1. |
[out] | w | REAL array, dimension (N) On normal exit, the first M elements contain the selected eigenvalues in ascending order. |
[out] | dZ | COMPLEX array, dimension (LDDZ, max(1,M)) If JOBZ = MagmaVec, then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. If JOBZ = MagmaNoVec, then Z is not referenced. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = MagmaRangeV, the exact value of M is not known in advance and an upper bound must be used. (workspace) If FAST_HEMV is defined DZ should be (LDDZ, max(1,N)) in both cases. |
[in] | lddz | INTEGER The leading dimension of the array DZ. LDDZ >= 1, and if JOBZ = MagmaVec, LDDZ >= max(1,N). |
wA | (workspace) COMPLEX array, dimension (LDWA, N) | |
[in] | ldwa | INTEGER The leading dimension of the array wA. LDWA >= max(1,N). |
wZ | (workspace) COMPLEX array, dimension (LDWZ, max(1,M)) | |
[in] | ldwz | INTEGER The leading dimension of the array wZ. LDWZ >= 1, and if JOBZ = MagmaVec, LDWZ >= max(1,N). |
[out] | work | (workspace) COMPLEX array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
[in] | lwork | INTEGER The length of the array WORK. LWORK >= (NB+1)*N, where NB is the max of the blocksize for CHETRD. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. |
rwork | (workspace) REAL array, dimension (7*N) | |
iwork | (workspace) INTEGER array, dimension (5*N) | |
[out] | ifail | INTEGER array, dimension (N) If JOBZ = MagmaVec, then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = MagmaNoVec, then IFAIL is not referenced. |
[out] | info | INTEGER
|