MAGMA 2.9.0
Matrix Algebra for GPU and Multicore Architectures
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Functions
or/unmtr: Multiply by Q from tridiagonal reduction
Dense LA » Eigenvalues » Symmetric/Hermitian eigenvalues

Functions

magma_int_t magma_cunmtr (magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_int_t m, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *C, magma_int_t ldc, magmaFloatComplex *work, magma_int_t lwork, magma_int_t *info)
 CUNMTR overwrites the general complex M-by-N matrix C with.
 
magma_int_t magma_cunmtr_gpu (magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_int_t m, magma_int_t n, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex *tau, magmaFloatComplex_ptr dC, magma_int_t lddc, const magmaFloatComplex *wA, magma_int_t ldwa, magma_int_t *info)
 CUNMTR overwrites the general complex M-by-N matrix C with.
 
magma_int_t magma_cunmtr_m (magma_int_t ngpu, magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_int_t m, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *C, magma_int_t ldc, magmaFloatComplex *work, magma_int_t lwork, magma_int_t *info)
 CUNMTR overwrites the general complex M-by-N matrix C with.
 
magma_int_t magma_dormtr (magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_int_t m, magma_int_t n, double *A, magma_int_t lda, double *tau, double *C, magma_int_t ldc, double *work, magma_int_t lwork, magma_int_t *info)
 DORMTR overwrites the general real M-by-N matrix C with.
 
magma_int_t magma_dormtr_gpu (magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_int_t m, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, double *tau, magmaDouble_ptr dC, magma_int_t lddc, const double *wA, magma_int_t ldwa, magma_int_t *info)
 DORMTR overwrites the general real M-by-N matrix C with.
 
magma_int_t magma_dormtr_m (magma_int_t ngpu, magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_int_t m, magma_int_t n, double *A, magma_int_t lda, double *tau, double *C, magma_int_t ldc, double *work, magma_int_t lwork, magma_int_t *info)
 DORMTR overwrites the general real M-by-N matrix C with.
 
magma_int_t magma_sormtr (magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_int_t m, magma_int_t n, float *A, magma_int_t lda, float *tau, float *C, magma_int_t ldc, float *work, magma_int_t lwork, magma_int_t *info)
 SORMTR overwrites the general real M-by-N matrix C with.
 
magma_int_t magma_sormtr_gpu (magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, float *tau, magmaFloat_ptr dC, magma_int_t lddc, const float *wA, magma_int_t ldwa, magma_int_t *info)
 SORMTR overwrites the general real M-by-N matrix C with.
 
magma_int_t magma_sormtr_m (magma_int_t ngpu, magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_int_t m, magma_int_t n, float *A, magma_int_t lda, float *tau, float *C, magma_int_t ldc, float *work, magma_int_t lwork, magma_int_t *info)
 SORMTR overwrites the general real M-by-N matrix C with.
 
magma_int_t magma_zunmtr (magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_int_t m, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex *tau, magmaDoubleComplex *C, magma_int_t ldc, magmaDoubleComplex *work, magma_int_t lwork, magma_int_t *info)
 ZUNMTR overwrites the general complex M-by-N matrix C with.
 
magma_int_t magma_zunmtr_gpu (magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_int_t m, magma_int_t n, magmaDoubleComplex_ptr dA, magma_int_t ldda, magmaDoubleComplex *tau, magmaDoubleComplex_ptr dC, magma_int_t lddc, const magmaDoubleComplex *wA, magma_int_t ldwa, magma_int_t *info)
 ZUNMTR overwrites the general complex M-by-N matrix C with.
 
magma_int_t magma_zunmtr_m (magma_int_t ngpu, magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_int_t m, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex *tau, magmaDoubleComplex *C, magma_int_t ldc, magmaDoubleComplex *work, magma_int_t lwork, magma_int_t *info)
 ZUNMTR overwrites the general complex M-by-N matrix C with.
 

Detailed Description

Function Documentation

◆ magma_cunmtr()

magma_int_t magma_cunmtr ( magma_side_t side,
magma_uplo_t uplo,
magma_trans_t trans,
magma_int_t m,
magma_int_t n,
magmaFloatComplex * A,
magma_int_t lda,
magmaFloatComplex * tau,
magmaFloatComplex * C,
magma_int_t ldc,
magmaFloatComplex * work,
magma_int_t lwork,
magma_int_t * info )

CUNMTR overwrites the general complex M-by-N matrix C with. 

                        SIDE = MagmaLeft    SIDE = MagmaRight

TRANS = MagmaNoTrans: Q * C C * Q TRANS = Magma_ConjTrans: Q**H * C C * Q**H

where Q is a complex unitary matrix of order nq, with nq = m if SIDE = MagmaLeft and nq = n if SIDE = MagmaRight. Q is defined as the product of nq-1 elementary reflectors, as returned by CHETRD:

if UPLO = MagmaUpper, Q = H(nq-1) . . . H(2) H(1);

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(nq-1).

Parameters
[in]sidemagma_side_t
  • = MagmaLeft: apply Q or Q**H from the Left;
  • = MagmaRight: apply Q or Q**H from the Right.
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from CHETRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from CHETRD.
[in]transmagma_trans_t
  • = MagmaNoTrans: No transpose, apply Q;
  • = Magma_ConjTrans: Conjugate transpose, apply Q**H.
[in]mINTEGER The number of rows of the matrix C. M >= 0.
[in]nINTEGER The number of columns of the matrix C. N >= 0.
[in]ACOMPLEX array, dimension (LDA,M) if SIDE = MagmaLeft (LDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by CHETRD.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight.
[in]tauCOMPLEX array, dimension (M-1) if SIDE = MagmaLeft (N-1) if SIDE = MagmaRight TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CHETRD.
[in,out]CCOMPLEX array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H * C or C * Q**H or C*Q.
[in]ldcINTEGER The leading dimension of the array C. LDC >= max(1,M).
[out]work(workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. If SIDE = MagmaLeft, LWORK >= max(1,N); if SIDE = MagmaRight, LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = MagmaLeft, and LWORK >= M*NB if SIDE = MagmaRight, where NB is the optimal blocksize.
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.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

◆ magma_cunmtr_gpu()

magma_int_t magma_cunmtr_gpu ( magma_side_t side,
magma_uplo_t uplo,
magma_trans_t trans,
magma_int_t m,
magma_int_t n,
magmaFloatComplex_ptr dA,
magma_int_t ldda,
magmaFloatComplex * tau,
magmaFloatComplex_ptr dC,
magma_int_t lddc,
const magmaFloatComplex * wA,
magma_int_t ldwa,
magma_int_t * info )

CUNMTR overwrites the general complex M-by-N matrix C with. 

                        SIDE = MagmaLeft    SIDE = MagmaRight

TRANS = MagmaNoTrans: Q * C C * Q TRANS = Magma_ConjTrans: Q**H * C C * Q**H

where Q is a complex unitary matrix of order nq, with nq = m if SIDE = MagmaLeft and nq = n if SIDE = MagmaRight. Q is defined as the product of nq-1 elementary reflectors, as returned by CHETRD:

if UPLO = MagmaUpper, Q = H(nq-1) . . . H(2) H(1);

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(nq-1).

Parameters
[in]sidemagma_side_t
  • = MagmaLeft: apply Q or Q**H from the Left;
  • = MagmaRight: apply Q or Q**H from the Right.
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from CHETRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from CHETRD.
[in]transmagma_trans_t
  • = MagmaNoTrans: No transpose, apply Q;
  • = Magma_ConjTrans: Conjugate transpose, apply Q**H.
[in]mINTEGER The number of rows of the matrix C. M >= 0.
[in]nINTEGER The number of columns of the matrix C. N >= 0.
[in,out]dACOMPLEX array, dimension (LDDA,M) if SIDE = MagmaLeft (LDDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by CHETRD_GPU. On output the diagonal, the subdiagonal and the upper part (UPLO=MagmaLower) or lower part (UPLO=MagmaUpper) are destroyed.
[in]lddaINTEGER The leading dimension of the array dA. If SIDE = MagmaLeft, LDDA >= max(1,M); if SIDE = MagmaRight, LDDA >= max(1,N).
[in]tauCOMPLEX array, dimension (M-1) if SIDE = MagmaLeft (N-1) if SIDE = MagmaRight TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CHETRD.
[in,out]dCCOMPLEX array, dimension (LDDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by (Q*C) or (Q**H * C) or (C * Q**H) or (C*Q).
[in]lddcINTEGER The leading dimension of the array C. LDDC >= max(1,M).
[in]wACOMPLEX array, dimension (LDWA,M) if SIDE = MagmaLeft (LDWA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by CHETRD_GPU. (A copy of the upper or lower part of dA, on the host.)
[in]ldwaINTEGER The leading dimension of the array wA. If SIDE = MagmaLeft, LDWA >= max(1,M); if SIDE = MagmaRight, LDWA >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

◆ magma_cunmtr_m()

magma_int_t magma_cunmtr_m ( magma_int_t ngpu,
magma_side_t side,
magma_uplo_t uplo,
magma_trans_t trans,
magma_int_t m,
magma_int_t n,
magmaFloatComplex * A,
magma_int_t lda,
magmaFloatComplex * tau,
magmaFloatComplex * C,
magma_int_t ldc,
magmaFloatComplex * work,
magma_int_t lwork,
magma_int_t * info )

CUNMTR overwrites the general complex M-by-N matrix C with. 

                        SIDE = MagmaLeft    SIDE = MagmaRight

TRANS = MagmaNoTrans: Q * C C * Q TRANS = Magma_ConjTrans: Q**H * C C * Q**H

where Q is a complex unitary matrix of order nq, with nq = m if SIDE = MagmaLeft and nq = n if SIDE = MagmaRight. Q is defined as the product of nq-1 elementary reflectors, as returned by CHETRD:

if UPLO = MagmaUpper, Q = H(nq-1) . . . H(2) H(1);

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(nq-1).

Parameters
[in]ngpuINTEGER Number of GPUs to use. ngpu > 0.
[in]sidemagma_side_t
  • = MagmaLeft: apply Q or Q**H from the Left;
  • = MagmaRight: apply Q or Q**H from the Right.
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from CHETRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from CHETRD.
[in]transmagma_trans_t
  • = MagmaNoTrans: No transpose, apply Q;
  • = Magma_ConjTrans: Conjugate transpose, apply Q**H.
[in]mINTEGER The number of rows of the matrix C. M >= 0.
[in]nINTEGER The number of columns of the matrix C. N >= 0.
[in]ACOMPLEX array, dimension (LDA,M) if SIDE = MagmaLeft (LDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by CHETRD.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight.
[in]tauCOMPLEX array, dimension (M-1) if SIDE = MagmaLeft (N-1) if SIDE = MagmaRight TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CHETRD.
[in,out]CCOMPLEX array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
[in]ldcINTEGER The leading dimension of the array C. LDC >= max(1,M).
[out]work(workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. If SIDE = MagmaLeft, LWORK >= max(1,N); if SIDE = MagmaRight, LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = MagmaLeft, and LWORK >= M*NB if SIDE = MagmaRight, where NB is the optimal blocksize.
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.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

◆ magma_dormtr()

magma_int_t magma_dormtr ( magma_side_t side,
magma_uplo_t uplo,
magma_trans_t trans,
magma_int_t m,
magma_int_t n,
double * A,
magma_int_t lda,
double * tau,
double * C,
magma_int_t ldc,
double * work,
magma_int_t lwork,
magma_int_t * info )

DORMTR overwrites the general real M-by-N matrix C with. 

                        SIDE = MagmaLeft    SIDE = MagmaRight

TRANS = MagmaNoTrans: Q * C C * Q TRANS = MagmaTrans: Q**H * C C * Q**H

where Q is a real orthogonal matrix of order nq, with nq = m if SIDE = MagmaLeft and nq = n if SIDE = MagmaRight. Q is defined as the product of nq-1 elementary reflectors, as returned by DSYTRD:

if UPLO = MagmaUpper, Q = H(nq-1) . . . H(2) H(1);

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(nq-1).

Parameters
[in]sidemagma_side_t
  • = MagmaLeft: apply Q or Q**H from the Left;
  • = MagmaRight: apply Q or Q**H from the Right.
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from DSYTRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from DSYTRD.
[in]transmagma_trans_t
  • = MagmaNoTrans: No transpose, apply Q;
  • = MagmaTrans: Conjugate transpose, apply Q**H.
[in]mINTEGER The number of rows of the matrix C. M >= 0.
[in]nINTEGER The number of columns of the matrix C. N >= 0.
[in]ADOUBLE PRECISION array, dimension (LDA,M) if SIDE = MagmaLeft (LDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by DSYTRD.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight.
[in]tauDOUBLE PRECISION array, dimension (M-1) if SIDE = MagmaLeft (N-1) if SIDE = MagmaRight TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DSYTRD.
[in,out]CDOUBLE PRECISION array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H * C or C * Q**H or C*Q.
[in]ldcINTEGER The leading dimension of the array C. LDC >= max(1,M).
[out]work(workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. If SIDE = MagmaLeft, LWORK >= max(1,N); if SIDE = MagmaRight, LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = MagmaLeft, and LWORK >= M*NB if SIDE = MagmaRight, where NB is the optimal blocksize.
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.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

◆ magma_dormtr_gpu()

magma_int_t magma_dormtr_gpu ( magma_side_t side,
magma_uplo_t uplo,
magma_trans_t trans,
magma_int_t m,
magma_int_t n,
magmaDouble_ptr dA,
magma_int_t ldda,
double * tau,
magmaDouble_ptr dC,
magma_int_t lddc,
const double * wA,
magma_int_t ldwa,
magma_int_t * info )

DORMTR overwrites the general real M-by-N matrix C with. 

                        SIDE = MagmaLeft    SIDE = MagmaRight

TRANS = MagmaNoTrans: Q * C C * Q TRANS = MagmaTrans: Q**H * C C * Q**H

where Q is a real orthogonal matrix of order nq, with nq = m if SIDE = MagmaLeft and nq = n if SIDE = MagmaRight. Q is defined as the product of nq-1 elementary reflectors, as returned by DSYTRD:

if UPLO = MagmaUpper, Q = H(nq-1) . . . H(2) H(1);

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(nq-1).

Parameters
[in]sidemagma_side_t
  • = MagmaLeft: apply Q or Q**H from the Left;
  • = MagmaRight: apply Q or Q**H from the Right.
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from DSYTRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from DSYTRD.
[in]transmagma_trans_t
  • = MagmaNoTrans: No transpose, apply Q;
  • = MagmaTrans: Conjugate transpose, apply Q**H.
[in]mINTEGER The number of rows of the matrix C. M >= 0.
[in]nINTEGER The number of columns of the matrix C. N >= 0.
[in,out]dADOUBLE PRECISION array, dimension (LDDA,M) if SIDE = MagmaLeft (LDDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by DSYTRD_GPU. On output the diagonal, the subdiagonal and the upper part (UPLO=MagmaLower) or lower part (UPLO=MagmaUpper) are destroyed.
[in]lddaINTEGER The leading dimension of the array dA. If SIDE = MagmaLeft, LDDA >= max(1,M); if SIDE = MagmaRight, LDDA >= max(1,N).
[in]tauDOUBLE PRECISION array, dimension (M-1) if SIDE = MagmaLeft (N-1) if SIDE = MagmaRight TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DSYTRD.
[in,out]dCDOUBLE PRECISION array, dimension (LDDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by (Q*C) or (Q**H * C) or (C * Q**H) or (C*Q).
[in]lddcINTEGER The leading dimension of the array C. LDDC >= max(1,M).
[in]wADOUBLE PRECISION array, dimension (LDWA,M) if SIDE = MagmaLeft (LDWA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by DSYTRD_GPU. (A copy of the upper or lower part of dA, on the host.)
[in]ldwaINTEGER The leading dimension of the array wA. If SIDE = MagmaLeft, LDWA >= max(1,M); if SIDE = MagmaRight, LDWA >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

◆ magma_dormtr_m()

magma_int_t magma_dormtr_m ( magma_int_t ngpu,
magma_side_t side,
magma_uplo_t uplo,
magma_trans_t trans,
magma_int_t m,
magma_int_t n,
double * A,
magma_int_t lda,
double * tau,
double * C,
magma_int_t ldc,
double * work,
magma_int_t lwork,
magma_int_t * info )

DORMTR overwrites the general real M-by-N matrix C with. 

                        SIDE = MagmaLeft    SIDE = MagmaRight

TRANS = MagmaNoTrans: Q * C C * Q TRANS = MagmaTrans: Q**H * C C * Q**H

where Q is a real orthogonal matrix of order nq, with nq = m if SIDE = MagmaLeft and nq = n if SIDE = MagmaRight. Q is defined as the product of nq-1 elementary reflectors, as returned by DSYTRD:

if UPLO = MagmaUpper, Q = H(nq-1) . . . H(2) H(1);

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(nq-1).

Parameters
[in]ngpuINTEGER Number of GPUs to use. ngpu > 0.
[in]sidemagma_side_t
  • = MagmaLeft: apply Q or Q**H from the Left;
  • = MagmaRight: apply Q or Q**H from the Right.
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from DSYTRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from DSYTRD.
[in]transmagma_trans_t
  • = MagmaNoTrans: No transpose, apply Q;
  • = MagmaTrans: Conjugate transpose, apply Q**H.
[in]mINTEGER The number of rows of the matrix C. M >= 0.
[in]nINTEGER The number of columns of the matrix C. N >= 0.
[in]ADOUBLE PRECISION array, dimension (LDA,M) if SIDE = MagmaLeft (LDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by DSYTRD.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight.
[in]tauDOUBLE PRECISION array, dimension (M-1) if SIDE = MagmaLeft (N-1) if SIDE = MagmaRight TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DSYTRD.
[in,out]CDOUBLE PRECISION array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
[in]ldcINTEGER The leading dimension of the array C. LDC >= max(1,M).
[out]work(workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. If SIDE = MagmaLeft, LWORK >= max(1,N); if SIDE = MagmaRight, LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = MagmaLeft, and LWORK >= M*NB if SIDE = MagmaRight, where NB is the optimal blocksize.
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.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

◆ magma_sormtr()

magma_int_t magma_sormtr ( magma_side_t side,
magma_uplo_t uplo,
magma_trans_t trans,
magma_int_t m,
magma_int_t n,
float * A,
magma_int_t lda,
float * tau,
float * C,
magma_int_t ldc,
float * work,
magma_int_t lwork,
magma_int_t * info )

SORMTR overwrites the general real M-by-N matrix C with. 

                        SIDE = MagmaLeft    SIDE = MagmaRight

TRANS = MagmaNoTrans: Q * C C * Q TRANS = MagmaTrans: Q**H * C C * Q**H

where Q is a real orthogonal matrix of order nq, with nq = m if SIDE = MagmaLeft and nq = n if SIDE = MagmaRight. Q is defined as the product of nq-1 elementary reflectors, as returned by SSYTRD:

if UPLO = MagmaUpper, Q = H(nq-1) . . . H(2) H(1);

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(nq-1).

Parameters
[in]sidemagma_side_t
  • = MagmaLeft: apply Q or Q**H from the Left;
  • = MagmaRight: apply Q or Q**H from the Right.
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from SSYTRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from SSYTRD.
[in]transmagma_trans_t
  • = MagmaNoTrans: No transpose, apply Q;
  • = MagmaTrans: Conjugate transpose, apply Q**H.
[in]mINTEGER The number of rows of the matrix C. M >= 0.
[in]nINTEGER The number of columns of the matrix C. N >= 0.
[in]AREAL array, dimension (LDA,M) if SIDE = MagmaLeft (LDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by SSYTRD.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight.
[in]tauREAL array, dimension (M-1) if SIDE = MagmaLeft (N-1) if SIDE = MagmaRight TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSYTRD.
[in,out]CREAL array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H * C or C * Q**H or C*Q.
[in]ldcINTEGER The leading dimension of the array C. LDC >= max(1,M).
[out]work(workspace) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. If SIDE = MagmaLeft, LWORK >= max(1,N); if SIDE = MagmaRight, LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = MagmaLeft, and LWORK >= M*NB if SIDE = MagmaRight, where NB is the optimal blocksize.
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.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

◆ magma_sormtr_gpu()

magma_int_t magma_sormtr_gpu ( magma_side_t side,
magma_uplo_t uplo,
magma_trans_t trans,
magma_int_t m,
magma_int_t n,
magmaFloat_ptr dA,
magma_int_t ldda,
float * tau,
magmaFloat_ptr dC,
magma_int_t lddc,
const float * wA,
magma_int_t ldwa,
magma_int_t * info )

SORMTR overwrites the general real M-by-N matrix C with. 

                        SIDE = MagmaLeft    SIDE = MagmaRight

TRANS = MagmaNoTrans: Q * C C * Q TRANS = MagmaTrans: Q**H * C C * Q**H

where Q is a real orthogonal matrix of order nq, with nq = m if SIDE = MagmaLeft and nq = n if SIDE = MagmaRight. Q is defined as the product of nq-1 elementary reflectors, as returned by SSYTRD:

if UPLO = MagmaUpper, Q = H(nq-1) . . . H(2) H(1);

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(nq-1).

Parameters
[in]sidemagma_side_t
  • = MagmaLeft: apply Q or Q**H from the Left;
  • = MagmaRight: apply Q or Q**H from the Right.
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from SSYTRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from SSYTRD.
[in]transmagma_trans_t
  • = MagmaNoTrans: No transpose, apply Q;
  • = MagmaTrans: Conjugate transpose, apply Q**H.
[in]mINTEGER The number of rows of the matrix C. M >= 0.
[in]nINTEGER The number of columns of the matrix C. N >= 0.
[in,out]dAREAL array, dimension (LDDA,M) if SIDE = MagmaLeft (LDDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by SSYTRD_GPU. On output the diagonal, the subdiagonal and the upper part (UPLO=MagmaLower) or lower part (UPLO=MagmaUpper) are destroyed.
[in]lddaINTEGER The leading dimension of the array dA. If SIDE = MagmaLeft, LDDA >= max(1,M); if SIDE = MagmaRight, LDDA >= max(1,N).
[in]tauREAL array, dimension (M-1) if SIDE = MagmaLeft (N-1) if SIDE = MagmaRight TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSYTRD.
[in,out]dCREAL array, dimension (LDDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by (Q*C) or (Q**H * C) or (C * Q**H) or (C*Q).
[in]lddcINTEGER The leading dimension of the array C. LDDC >= max(1,M).
[in]wAREAL array, dimension (LDWA,M) if SIDE = MagmaLeft (LDWA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by SSYTRD_GPU. (A copy of the upper or lower part of dA, on the host.)
[in]ldwaINTEGER The leading dimension of the array wA. If SIDE = MagmaLeft, LDWA >= max(1,M); if SIDE = MagmaRight, LDWA >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

◆ magma_sormtr_m()

magma_int_t magma_sormtr_m ( magma_int_t ngpu,
magma_side_t side,
magma_uplo_t uplo,
magma_trans_t trans,
magma_int_t m,
magma_int_t n,
float * A,
magma_int_t lda,
float * tau,
float * C,
magma_int_t ldc,
float * work,
magma_int_t lwork,
magma_int_t * info )

SORMTR overwrites the general real M-by-N matrix C with. 

                        SIDE = MagmaLeft    SIDE = MagmaRight

TRANS = MagmaNoTrans: Q * C C * Q TRANS = MagmaTrans: Q**H * C C * Q**H

where Q is a real orthogonal matrix of order nq, with nq = m if SIDE = MagmaLeft and nq = n if SIDE = MagmaRight. Q is defined as the product of nq-1 elementary reflectors, as returned by SSYTRD:

if UPLO = MagmaUpper, Q = H(nq-1) . . . H(2) H(1);

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(nq-1).

Parameters
[in]ngpuINTEGER Number of GPUs to use. ngpu > 0.
[in]sidemagma_side_t
  • = MagmaLeft: apply Q or Q**H from the Left;
  • = MagmaRight: apply Q or Q**H from the Right.
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from SSYTRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from SSYTRD.
[in]transmagma_trans_t
  • = MagmaNoTrans: No transpose, apply Q;
  • = MagmaTrans: Conjugate transpose, apply Q**H.
[in]mINTEGER The number of rows of the matrix C. M >= 0.
[in]nINTEGER The number of columns of the matrix C. N >= 0.
[in]AREAL array, dimension (LDA,M) if SIDE = MagmaLeft (LDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by SSYTRD.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight.
[in]tauREAL array, dimension (M-1) if SIDE = MagmaLeft (N-1) if SIDE = MagmaRight TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSYTRD.
[in,out]CREAL array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
[in]ldcINTEGER The leading dimension of the array C. LDC >= max(1,M).
[out]work(workspace) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. If SIDE = MagmaLeft, LWORK >= max(1,N); if SIDE = MagmaRight, LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = MagmaLeft, and LWORK >= M*NB if SIDE = MagmaRight, where NB is the optimal blocksize.
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.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

◆ magma_zunmtr()

magma_int_t magma_zunmtr ( magma_side_t side,
magma_uplo_t uplo,
magma_trans_t trans,
magma_int_t m,
magma_int_t n,
magmaDoubleComplex * A,
magma_int_t lda,
magmaDoubleComplex * tau,
magmaDoubleComplex * C,
magma_int_t ldc,
magmaDoubleComplex * work,
magma_int_t lwork,
magma_int_t * info )

ZUNMTR overwrites the general complex M-by-N matrix C with. 

                        SIDE = MagmaLeft    SIDE = MagmaRight

TRANS = MagmaNoTrans: Q * C C * Q TRANS = Magma_ConjTrans: Q**H * C C * Q**H

where Q is a complex unitary matrix of order nq, with nq = m if SIDE = MagmaLeft and nq = n if SIDE = MagmaRight. Q is defined as the product of nq-1 elementary reflectors, as returned by ZHETRD:

if UPLO = MagmaUpper, Q = H(nq-1) . . . H(2) H(1);

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(nq-1).

Parameters
[in]sidemagma_side_t
  • = MagmaLeft: apply Q or Q**H from the Left;
  • = MagmaRight: apply Q or Q**H from the Right.
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from ZHETRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from ZHETRD.
[in]transmagma_trans_t
  • = MagmaNoTrans: No transpose, apply Q;
  • = Magma_ConjTrans: Conjugate transpose, apply Q**H.
[in]mINTEGER The number of rows of the matrix C. M >= 0.
[in]nINTEGER The number of columns of the matrix C. N >= 0.
[in]ACOMPLEX_16 array, dimension (LDA,M) if SIDE = MagmaLeft (LDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by ZHETRD.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight.
[in]tauCOMPLEX_16 array, dimension (M-1) if SIDE = MagmaLeft (N-1) if SIDE = MagmaRight TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZHETRD.
[in,out]CCOMPLEX_16 array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H * C or C * Q**H or C*Q.
[in]ldcINTEGER The leading dimension of the array C. LDC >= max(1,M).
[out]work(workspace) COMPLEX_16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. If SIDE = MagmaLeft, LWORK >= max(1,N); if SIDE = MagmaRight, LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = MagmaLeft, and LWORK >= M*NB if SIDE = MagmaRight, where NB is the optimal blocksize.
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.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

◆ magma_zunmtr_gpu()

magma_int_t magma_zunmtr_gpu ( magma_side_t side,
magma_uplo_t uplo,
magma_trans_t trans,
magma_int_t m,
magma_int_t n,
magmaDoubleComplex_ptr dA,
magma_int_t ldda,
magmaDoubleComplex * tau,
magmaDoubleComplex_ptr dC,
magma_int_t lddc,
const magmaDoubleComplex * wA,
magma_int_t ldwa,
magma_int_t * info )

ZUNMTR overwrites the general complex M-by-N matrix C with. 

                        SIDE = MagmaLeft    SIDE = MagmaRight

TRANS = MagmaNoTrans: Q * C C * Q TRANS = Magma_ConjTrans: Q**H * C C * Q**H

where Q is a complex unitary matrix of order nq, with nq = m if SIDE = MagmaLeft and nq = n if SIDE = MagmaRight. Q is defined as the product of nq-1 elementary reflectors, as returned by ZHETRD:

if UPLO = MagmaUpper, Q = H(nq-1) . . . H(2) H(1);

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(nq-1).

Parameters
[in]sidemagma_side_t
  • = MagmaLeft: apply Q or Q**H from the Left;
  • = MagmaRight: apply Q or Q**H from the Right.
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from ZHETRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from ZHETRD.
[in]transmagma_trans_t
  • = MagmaNoTrans: No transpose, apply Q;
  • = Magma_ConjTrans: Conjugate transpose, apply Q**H.
[in]mINTEGER The number of rows of the matrix C. M >= 0.
[in]nINTEGER The number of columns of the matrix C. N >= 0.
[in,out]dACOMPLEX_16 array, dimension (LDDA,M) if SIDE = MagmaLeft (LDDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by ZHETRD_GPU. On output the diagonal, the subdiagonal and the upper part (UPLO=MagmaLower) or lower part (UPLO=MagmaUpper) are destroyed.
[in]lddaINTEGER The leading dimension of the array dA. If SIDE = MagmaLeft, LDDA >= max(1,M); if SIDE = MagmaRight, LDDA >= max(1,N).
[in]tauCOMPLEX_16 array, dimension (M-1) if SIDE = MagmaLeft (N-1) if SIDE = MagmaRight TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZHETRD.
[in,out]dCCOMPLEX_16 array, dimension (LDDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by (Q*C) or (Q**H * C) or (C * Q**H) or (C*Q).
[in]lddcINTEGER The leading dimension of the array C. LDDC >= max(1,M).
[in]wACOMPLEX_16 array, dimension (LDWA,M) if SIDE = MagmaLeft (LDWA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by ZHETRD_GPU. (A copy of the upper or lower part of dA, on the host.)
[in]ldwaINTEGER The leading dimension of the array wA. If SIDE = MagmaLeft, LDWA >= max(1,M); if SIDE = MagmaRight, LDWA >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

◆ magma_zunmtr_m()

magma_int_t magma_zunmtr_m ( magma_int_t ngpu,
magma_side_t side,
magma_uplo_t uplo,
magma_trans_t trans,
magma_int_t m,
magma_int_t n,
magmaDoubleComplex * A,
magma_int_t lda,
magmaDoubleComplex * tau,
magmaDoubleComplex * C,
magma_int_t ldc,
magmaDoubleComplex * work,
magma_int_t lwork,
magma_int_t * info )

ZUNMTR overwrites the general complex M-by-N matrix C with. 

                        SIDE = MagmaLeft    SIDE = MagmaRight

TRANS = MagmaNoTrans: Q * C C * Q TRANS = Magma_ConjTrans: Q**H * C C * Q**H

where Q is a complex unitary matrix of order nq, with nq = m if SIDE = MagmaLeft and nq = n if SIDE = MagmaRight. Q is defined as the product of nq-1 elementary reflectors, as returned by ZHETRD:

if UPLO = MagmaUpper, Q = H(nq-1) . . . H(2) H(1);

if UPLO = MagmaLower, Q = H(1) H(2) . . . H(nq-1).

Parameters
[in]ngpuINTEGER Number of GPUs to use. ngpu > 0.
[in]sidemagma_side_t
  • = MagmaLeft: apply Q or Q**H from the Left;
  • = MagmaRight: apply Q or Q**H from the Right.
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A contains elementary reflectors from ZHETRD;
  • = MagmaLower: Lower triangle of A contains elementary reflectors from ZHETRD.
[in]transmagma_trans_t
  • = MagmaNoTrans: No transpose, apply Q;
  • = Magma_ConjTrans: Conjugate transpose, apply Q**H.
[in]mINTEGER The number of rows of the matrix C. M >= 0.
[in]nINTEGER The number of columns of the matrix C. N >= 0.
[in]ACOMPLEX_16 array, dimension (LDA,M) if SIDE = MagmaLeft (LDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by ZHETRD.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight.
[in]tauCOMPLEX_16 array, dimension (M-1) if SIDE = MagmaLeft (N-1) if SIDE = MagmaRight TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZHETRD.
[in,out]CCOMPLEX_16 array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
[in]ldcINTEGER The leading dimension of the array C. LDC >= max(1,M).
[out]work(workspace) COMPLEX_16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. If SIDE = MagmaLeft, LWORK >= max(1,N); if SIDE = MagmaRight, LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = MagmaLeft, and LWORK >= M*NB if SIDE = MagmaRight, where NB is the optimal blocksize.
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.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value