MAGMA  2.3.0 Matrix Algebra for GPU and Multicore Architectures
or/unmtr: Multiply by Q from tridiagonal reduction

## 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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

## Function Documentation

 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] side magma_side_t = MagmaLeft: apply Q or Q**H from the Left; = MagmaRight: apply Q or Q**H from the Right. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A contains elementary reflectors from CHETRD; = MagmaLower: Lower triangle of A contains elementary reflectors from CHETRD. [in] trans magma_trans_t = MagmaNoTrans: No transpose, apply Q; = Magma_ConjTrans: Conjugate transpose, apply Q**H. [in] m INTEGER The number of rows of the matrix C. M >= 0. [in] n INTEGER The number of columns of the matrix C. N >= 0. [in] A COMPLEX array, dimension (LDA,M) if SIDE = MagmaLeft (LDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by CHETRD. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight. [in] tau COMPLEX 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] C COMPLEX 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] ldc INTEGER 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] lwork INTEGER 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] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 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] side magma_side_t = MagmaLeft: apply Q or Q**H from the Left; = MagmaRight: apply Q or Q**H from the Right. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A contains elementary reflectors from CHETRD; = MagmaLower: Lower triangle of A contains elementary reflectors from CHETRD. [in] trans magma_trans_t = MagmaNoTrans: No transpose, apply Q; = Magma_ConjTrans: Conjugate transpose, apply Q**H. [in] m INTEGER The number of rows of the matrix C. M >= 0. [in] n INTEGER The number of columns of the matrix C. N >= 0. [in,out] dA COMPLEX 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] ldda INTEGER The leading dimension of the array dA. If SIDE = MagmaLeft, LDDA >= max(1,M); if SIDE = MagmaRight, LDDA >= max(1,N). [in] tau COMPLEX 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] dC COMPLEX 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] lddc INTEGER The leading dimension of the array C. LDDC >= max(1,M). [in] wA COMPLEX 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] ldwa INTEGER The leading dimension of the array wA. If SIDE = MagmaLeft, LDWA >= max(1,M); if SIDE = MagmaRight, LDWA >= max(1,N). [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 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] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] side magma_side_t = MagmaLeft: apply Q or Q**H from the Left; = MagmaRight: apply Q or Q**H from the Right. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A contains elementary reflectors from CHETRD; = MagmaLower: Lower triangle of A contains elementary reflectors from CHETRD. [in] trans magma_trans_t = MagmaNoTrans: No transpose, apply Q; = Magma_ConjTrans: Conjugate transpose, apply Q**H. [in] m INTEGER The number of rows of the matrix C. M >= 0. [in] n INTEGER The number of columns of the matrix C. N >= 0. [in] A COMPLEX array, dimension (LDA,M) if SIDE = MagmaLeft (LDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by CHETRD. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight. [in] tau COMPLEX 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] C COMPLEX 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] ldc INTEGER 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] lwork INTEGER 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] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 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] side magma_side_t = MagmaLeft: apply Q or Q**H from the Left; = MagmaRight: apply Q or Q**H from the Right. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A contains elementary reflectors from DSYTRD; = MagmaLower: Lower triangle of A contains elementary reflectors from DSYTRD. [in] trans magma_trans_t = MagmaNoTrans: No transpose, apply Q; = MagmaTrans: Conjugate transpose, apply Q**H. [in] m INTEGER The number of rows of the matrix C. M >= 0. [in] n INTEGER The number of columns of the matrix C. N >= 0. [in] A DOUBLE 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] lda INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight. [in] tau DOUBLE 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] C DOUBLE 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] ldc INTEGER 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] lwork INTEGER 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] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 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] side magma_side_t = MagmaLeft: apply Q or Q**H from the Left; = MagmaRight: apply Q or Q**H from the Right. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A contains elementary reflectors from DSYTRD; = MagmaLower: Lower triangle of A contains elementary reflectors from DSYTRD. [in] trans magma_trans_t = MagmaNoTrans: No transpose, apply Q; = MagmaTrans: Conjugate transpose, apply Q**H. [in] m INTEGER The number of rows of the matrix C. M >= 0. [in] n INTEGER The number of columns of the matrix C. N >= 0. [in,out] dA DOUBLE 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] ldda INTEGER The leading dimension of the array dA. If SIDE = MagmaLeft, LDDA >= max(1,M); if SIDE = MagmaRight, LDDA >= max(1,N). [in] tau DOUBLE 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] dC DOUBLE 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] lddc INTEGER The leading dimension of the array C. LDDC >= max(1,M). [in] wA DOUBLE 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] ldwa INTEGER The leading dimension of the array wA. If SIDE = MagmaLeft, LDWA >= max(1,M); if SIDE = MagmaRight, LDWA >= max(1,N). [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 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] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] side magma_side_t = MagmaLeft: apply Q or Q**H from the Left; = MagmaRight: apply Q or Q**H from the Right. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A contains elementary reflectors from DSYTRD; = MagmaLower: Lower triangle of A contains elementary reflectors from DSYTRD. [in] trans magma_trans_t = MagmaNoTrans: No transpose, apply Q; = MagmaTrans: Conjugate transpose, apply Q**H. [in] m INTEGER The number of rows of the matrix C. M >= 0. [in] n INTEGER The number of columns of the matrix C. N >= 0. [in] A DOUBLE 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] lda INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight. [in] tau DOUBLE 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] C DOUBLE 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] ldc INTEGER 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] lwork INTEGER 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] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 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] side magma_side_t = MagmaLeft: apply Q or Q**H from the Left; = MagmaRight: apply Q or Q**H from the Right. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A contains elementary reflectors from SSYTRD; = MagmaLower: Lower triangle of A contains elementary reflectors from SSYTRD. [in] trans magma_trans_t = MagmaNoTrans: No transpose, apply Q; = MagmaTrans: Conjugate transpose, apply Q**H. [in] m INTEGER The number of rows of the matrix C. M >= 0. [in] n INTEGER The number of columns of the matrix C. N >= 0. [in] A REAL array, dimension (LDA,M) if SIDE = MagmaLeft (LDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by SSYTRD. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight. [in] tau REAL 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] C REAL 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] ldc INTEGER 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] lwork INTEGER 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] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 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] side magma_side_t = MagmaLeft: apply Q or Q**H from the Left; = MagmaRight: apply Q or Q**H from the Right. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A contains elementary reflectors from SSYTRD; = MagmaLower: Lower triangle of A contains elementary reflectors from SSYTRD. [in] trans magma_trans_t = MagmaNoTrans: No transpose, apply Q; = MagmaTrans: Conjugate transpose, apply Q**H. [in] m INTEGER The number of rows of the matrix C. M >= 0. [in] n INTEGER The number of columns of the matrix C. N >= 0. [in,out] dA REAL 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] ldda INTEGER The leading dimension of the array dA. If SIDE = MagmaLeft, LDDA >= max(1,M); if SIDE = MagmaRight, LDDA >= max(1,N). [in] tau REAL 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] dC REAL 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] lddc INTEGER The leading dimension of the array C. LDDC >= max(1,M). [in] wA REAL 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] ldwa INTEGER The leading dimension of the array wA. If SIDE = MagmaLeft, LDWA >= max(1,M); if SIDE = MagmaRight, LDWA >= max(1,N). [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 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] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] side magma_side_t = MagmaLeft: apply Q or Q**H from the Left; = MagmaRight: apply Q or Q**H from the Right. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A contains elementary reflectors from SSYTRD; = MagmaLower: Lower triangle of A contains elementary reflectors from SSYTRD. [in] trans magma_trans_t = MagmaNoTrans: No transpose, apply Q; = MagmaTrans: Conjugate transpose, apply Q**H. [in] m INTEGER The number of rows of the matrix C. M >= 0. [in] n INTEGER The number of columns of the matrix C. N >= 0. [in] A REAL array, dimension (LDA,M) if SIDE = MagmaLeft (LDA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by SSYTRD. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight. [in] tau REAL 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] C REAL 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] ldc INTEGER 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] lwork INTEGER 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] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 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] side magma_side_t = MagmaLeft: apply Q or Q**H from the Left; = MagmaRight: apply Q or Q**H from the Right. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A contains elementary reflectors from ZHETRD; = MagmaLower: Lower triangle of A contains elementary reflectors from ZHETRD. [in] trans magma_trans_t = MagmaNoTrans: No transpose, apply Q; = Magma_ConjTrans: Conjugate transpose, apply Q**H. [in] m INTEGER The number of rows of the matrix C. M >= 0. [in] n INTEGER The number of columns of the matrix C. N >= 0. [in] A COMPLEX_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] lda INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight. [in] tau COMPLEX_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] C COMPLEX_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] ldc INTEGER 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] lwork INTEGER 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] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 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] side magma_side_t = MagmaLeft: apply Q or Q**H from the Left; = MagmaRight: apply Q or Q**H from the Right. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A contains elementary reflectors from ZHETRD; = MagmaLower: Lower triangle of A contains elementary reflectors from ZHETRD. [in] trans magma_trans_t = MagmaNoTrans: No transpose, apply Q; = Magma_ConjTrans: Conjugate transpose, apply Q**H. [in] m INTEGER The number of rows of the matrix C. M >= 0. [in] n INTEGER The number of columns of the matrix C. N >= 0. [in,out] dA COMPLEX_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] ldda INTEGER The leading dimension of the array dA. If SIDE = MagmaLeft, LDDA >= max(1,M); if SIDE = MagmaRight, LDDA >= max(1,N). [in] tau COMPLEX_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] dC COMPLEX_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] lddc INTEGER The leading dimension of the array C. LDDC >= max(1,M). [in] wA COMPLEX_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] ldwa INTEGER The leading dimension of the array wA. If SIDE = MagmaLeft, LDWA >= max(1,M); if SIDE = MagmaRight, LDWA >= max(1,N). [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 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] ngpu INTEGER Number of GPUs to use. ngpu > 0. [in] side magma_side_t = MagmaLeft: apply Q or Q**H from the Left; = MagmaRight: apply Q or Q**H from the Right. [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A contains elementary reflectors from ZHETRD; = MagmaLower: Lower triangle of A contains elementary reflectors from ZHETRD. [in] trans magma_trans_t = MagmaNoTrans: No transpose, apply Q; = Magma_ConjTrans: Conjugate transpose, apply Q**H. [in] m INTEGER The number of rows of the matrix C. M >= 0. [in] n INTEGER The number of columns of the matrix C. N >= 0. [in] A COMPLEX_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] lda INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = MagmaLeft; LDA >= max(1,N) if SIDE = MagmaRight. [in] tau COMPLEX_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] C COMPLEX_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] ldc INTEGER 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] lwork INTEGER 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] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value