Functions | |
magma_int_t | magma_ssyevd (magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, float *w, float *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
SSYEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. | |
magma_int_t | magma_ssyevd_gpu (magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, float *w, float *wA, magma_int_t ldwa, float *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
SSYEVD_GPU computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. | |
magma_int_t | magma_ssyevd_m (magma_int_t ngpu, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, float *w, float *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
SSYEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. | |
magma_int_t | magma_ssyevdx (magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, float vl, float vu, magma_int_t il, magma_int_t iu, magma_int_t *m, float *w, float *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
SSYEVDX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. | |
magma_int_t | magma_ssyevdx_2stage (magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, float vl, float vu, magma_int_t il, magma_int_t iu, magma_int_t *m, float *w, float *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
ZHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. | |
magma_int_t | magma_ssyevdx_2stage_m (magma_int_t ngpu, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, float vl, float vu, magma_int_t il, magma_int_t iu, magma_int_t *m, float *w, float *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
ZHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. | |
magma_int_t | magma_ssyevdx_gpu (magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, float vl, float vu, magma_int_t il, magma_int_t iu, magma_int_t *mout, float *w, float *wA, magma_int_t ldwa, float *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
SSYEVDX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. | |
magma_int_t | magma_ssyevdx_m (magma_int_t ngpu, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, float vl, float vu, magma_int_t il, magma_int_t iu, magma_int_t *m, float *w, float *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) |
SSYEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. |
magma_int_t magma_ssyevd | ( | magma_vec_t | jobz, | |
magma_uplo_t | uplo, | |||
magma_int_t | n, | |||
float * | A, | |||
magma_int_t | lda, | |||
float * | w, | |||
float * | work, | |||
magma_int_t | lwork, | |||
float * | rwork, | |||
magma_int_t | lrwork, | |||
magma_int_t * | iwork, | |||
magma_int_t | liwork, | |||
magma_int_t * | info | |||
) |
SSYEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric 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 | REAL array, dimension (LDA, N) On entry, the symmetric 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) REAL 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 >= 2*N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ). NB can be obtained through magma_get_ssytrd_nb(N). If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK 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 and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. |
[out] | info | INTEGER
|
Further Details --------------- 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_ssyevd_gpu | ( | magma_vec_t | jobz, | |
magma_uplo_t | uplo, | |||
magma_int_t | n, | |||
magmaFloat_ptr | dA, | |||
magma_int_t | ldda, | |||
float * | w, | |||
float * | wA, | |||
magma_int_t | ldwa, | |||
float * | work, | |||
magma_int_t | lwork, | |||
float * | rwork, | |||
magma_int_t | lrwork, | |||
magma_int_t * | iwork, | |||
magma_int_t | liwork, | |||
magma_int_t * | info | |||
) |
SSYEVD_GPU computes all eigenvalues and, optionally, eigenvectors of a real symmetric 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 | REAL array on the GPU, dimension (LDDA, N). On entry, the symmetric 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) REAL array, dimension (LDWA, N) | |
[in] | ldwa | INTEGER The leading dimension of the array wA. LDWA >= max(1,N). |
[out] | work | (workspace) REAL 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 >= 2*N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ). NB can be obtained through magma_get_ssytrd_nb(N). If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK 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 and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. |
[out] | info | INTEGER
|
Further Details --------------- 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_ssyevd_m | ( | magma_int_t | ngpu, | |
magma_vec_t | jobz, | |||
magma_uplo_t | uplo, | |||
magma_int_t | n, | |||
float * | A, | |||
magma_int_t | lda, | |||
float * | w, | |||
float * | work, | |||
magma_int_t | lwork, | |||
float * | rwork, | |||
magma_int_t | lrwork, | |||
magma_int_t * | iwork, | |||
magma_int_t | liwork, | |||
magma_int_t * | info | |||
) |
SSYEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric 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] | ngpu | INTEGER Number of GPUs to use. ngpu > 0. |
[in] | jobz | magma_vec_t
|
[in] | uplo | magma_uplo_t
|
[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | REAL array, dimension (LDA, N) On entry, the symmetric 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) REAL 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 >= 2*N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ). NB can be obtained through magma_get_ssytrd_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] | 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
|
Further Details --------------- 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_ssyevdx | ( | magma_vec_t | jobz, | |
magma_range_t | range, | |||
magma_uplo_t | uplo, | |||
magma_int_t | n, | |||
float * | A, | |||
magma_int_t | lda, | |||
float | vl, | |||
float | vu, | |||
magma_int_t | il, | |||
magma_int_t | iu, | |||
magma_int_t * | m, | |||
float * | w, | |||
float * | work, | |||
magma_int_t | lwork, | |||
float * | rwork, | |||
magma_int_t | lrwork, | |||
magma_int_t * | iwork, | |||
magma_int_t | liwork, | |||
magma_int_t * | info | |||
) |
SSYEVDX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric 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 | REAL array, dimension (LDA, N) On entry, the symmetric 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 required m eigenvalues in ascending order. |
[out] | work | (workspace) REAL 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 >= 2*N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ). NB can be obtained through magma_get_ssytrd_nb(N). If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK 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 and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. |
[out] | info | INTEGER
|
Further Details --------------- 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_ssyevdx_2stage | ( | magma_vec_t | jobz, | |
magma_range_t | range, | |||
magma_uplo_t | uplo, | |||
magma_int_t | n, | |||
float * | A, | |||
magma_int_t | lda, | |||
float | vl, | |||
float | vu, | |||
magma_int_t | il, | |||
magma_int_t | iu, | |||
magma_int_t * | m, | |||
float * | w, | |||
float * | work, | |||
magma_int_t | lwork, | |||
float * | rwork, | |||
magma_int_t | lrwork, | |||
magma_int_t * | iwork, | |||
magma_int_t | liwork, | |||
magma_int_t * | info | |||
) |
ZHEEVD_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 | REAL 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) REAL 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 >= LQ2 + 2*N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= LQ2 + 1 + 6*N + 2*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] | 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
|
Further Details --------------- 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_ssyevdx_2stage_m | ( | magma_int_t | ngpu, | |
magma_vec_t | jobz, | |||
magma_range_t | range, | |||
magma_uplo_t | uplo, | |||
magma_int_t | n, | |||
float * | A, | |||
magma_int_t | lda, | |||
float | vl, | |||
float | vu, | |||
magma_int_t | il, | |||
magma_int_t | iu, | |||
magma_int_t * | m, | |||
float * | w, | |||
float * | work, | |||
magma_int_t | lwork, | |||
float * | rwork, | |||
magma_int_t | lrwork, | |||
magma_int_t * | iwork, | |||
magma_int_t | liwork, | |||
magma_int_t * | info | |||
) |
ZHEEVD_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] | ngpu | INTEGER Number of GPUs to use. ngpu > 0. |
[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 | REAL 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) REAL 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 >= LQ2 + 2*N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= LQ2 + 1 + 6*N + 2*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] | 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
|
Further Details --------------- 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_ssyevdx_gpu | ( | magma_vec_t | jobz, | |
magma_range_t | range, | |||
magma_uplo_t | uplo, | |||
magma_int_t | n, | |||
magmaFloat_ptr | dA, | |||
magma_int_t | ldda, | |||
float | vl, | |||
float | vu, | |||
magma_int_t | il, | |||
magma_int_t | iu, | |||
magma_int_t * | mout, | |||
float * | w, | |||
float * | wA, | |||
magma_int_t | ldwa, | |||
float * | work, | |||
magma_int_t | lwork, | |||
float * | rwork, | |||
magma_int_t | lrwork, | |||
magma_int_t * | iwork, | |||
magma_int_t | liwork, | |||
magma_int_t * | info | |||
) |
SSYEVDX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric 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 | REAL array on the GPU, dimension (LDDA, N). On entry, the symmetric 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 mout 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] | mout | INTEGER The total number of eigenvalues found. 0 <= MOUT <= N. If RANGE = MagmaRangeAll, MOUT = N, and if RANGE = MagmaRangeI, MOUT = IU-IL+1. |
[out] | w | REAL array, dimension (N) If INFO = 0, the required mout eigenvalues in ascending order. |
wA | (workspace) REAL array, dimension (LDWA, N) | |
[in] | ldwa | INTEGER The leading dimension of the array wA. LDWA >= max(1,N). |
[out] | work | (workspace) REAL 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 >= 2*N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ). NB can be obtained through magma_get_ssytrd_nb(N). If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK 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 and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. |
[out] | info | INTEGER
|
Further Details --------------- 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_ssyevdx_m | ( | magma_int_t | ngpu, | |
magma_vec_t | jobz, | |||
magma_range_t | range, | |||
magma_uplo_t | uplo, | |||
magma_int_t | n, | |||
float * | A, | |||
magma_int_t | lda, | |||
float | vl, | |||
float | vu, | |||
magma_int_t | il, | |||
magma_int_t | iu, | |||
magma_int_t * | m, | |||
float * | w, | |||
float * | work, | |||
magma_int_t | lwork, | |||
float * | rwork, | |||
magma_int_t | lrwork, | |||
magma_int_t * | iwork, | |||
magma_int_t | liwork, | |||
magma_int_t * | info | |||
) |
SSYEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric 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] | ngpu | INTEGER Number of GPUs to use. ngpu > 0. |
[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 | REAL array, dimension (LDA, N) On entry, the symmetric 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) REAL 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 >= 2*N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ). NB can be obtained through magma_get_ssytrd_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] | 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
|
Further Details --------------- Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.