ormtr#

Functions

void sormtr(
    const char*          side,
    const char*          uplo,
    const char*          trans,
    const INT            m,
    const INT            n,
    const f32*  restrict A,
    const INT            lda,
    const f32*  restrict tau,
          f32*  restrict C,
    const INT            ldc,
          f32*  restrict work,
    const INT            lwork,
          INT*           info
);
void sormtr(const char *side, const char *uplo, const char *trans, const INT m, const INT n, const f32 *restrict A, const INT lda, const f32 *restrict tau, f32 *restrict C, const INT ldc, f32 *restrict work, const INT lwork, INT *info)#

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

            SIDE = 'L'     SIDE = 'R'
TRANS = ‘N’: Q * C C * Q TRANS = ‘T’: Q^T * C C * Q^T

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

if UPLO = ‘U’, Q = H(nq-1) … H(2) H(1);

if UPLO = ‘L’, Q = H(1) H(2) … H(nq-1).

Parameters

in
side

= ‘L’: apply Q or Q^T from the Left; = ‘R’: apply Q or Q^T from the Right.

in
uplo

= ‘U’: Upper triangle of A contains elementary reflectors from SSYTRD; = ‘L’: Lower triangle of A contains elementary reflectors from SSYTRD.

in
trans

= ‘N’: No transpose, apply Q; = ‘T’: Transpose, apply Q^T.

in
m

The number of rows of C. m >= 0.

in
n

The number of columns of C. n >= 0.

in
A

Double precision array, dimension (lda, m) if SIDE = ‘L’, (lda, n) if SIDE = ‘R’. The vectors which define the elementary reflectors, as returned by SSYTRD.

in
lda

The leading dimension of A. lda >= max(1, m) if SIDE = ‘L’; lda >= max(1, n) if SIDE = ‘R’.

in
tau

Double precision array, dimension (m-1) if SIDE = ‘L’, (n-1) if SIDE = ‘R’. TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSYTRD.

inout
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^T*C or C*Q^T or C*Q.

in
ldc

The leading dimension of C. ldc >= max(1, m).

out
work

Double precision array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The dimension of the array work. If SIDE = ‘L’, lwork >= max(1, n); if SIDE = ‘R’, lwork >= max(1, m). For optimum performance lwork >= n*nb if SIDE = ‘L’, and lwork >= m*nb if SIDE = ‘R’, where nb is the optimal blocksize. If lwork = -1, then a workspace query is assumed.

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value.

Functions

void dormtr(
    const char*          side,
    const char*          uplo,
    const char*          trans,
    const INT            m,
    const INT            n,
    const f64*  restrict A,
    const INT            lda,
    const f64*  restrict tau,
          f64*  restrict C,
    const INT            ldc,
          f64*  restrict work,
    const INT            lwork,
          INT*           info
);
void dormtr(const char *side, const char *uplo, const char *trans, const INT m, const INT n, const f64 *restrict A, const INT lda, const f64 *restrict tau, f64 *restrict C, const INT ldc, f64 *restrict work, const INT lwork, INT *info)#

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

            SIDE = 'L'     SIDE = 'R'
TRANS = ‘N’: Q * C C * Q TRANS = ‘T’: Q^T * C C * Q^T

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

if UPLO = ‘U’, Q = H(nq-1) … H(2) H(1);

if UPLO = ‘L’, Q = H(1) H(2) … H(nq-1).

Parameters

in
side

= ‘L’: apply Q or Q^T from the Left; = ‘R’: apply Q or Q^T from the Right.

in
uplo

= ‘U’: Upper triangle of A contains elementary reflectors from DSYTRD; = ‘L’: Lower triangle of A contains elementary reflectors from DSYTRD.

in
trans

= ‘N’: No transpose, apply Q; = ‘T’: Transpose, apply Q^T.

in
m

The number of rows of C. m >= 0.

in
n

The number of columns of C. n >= 0.

in
A

Double precision array, dimension (lda, m) if SIDE = ‘L’, (lda, n) if SIDE = ‘R’. The vectors which define the elementary reflectors, as returned by DSYTRD.

in
lda

The leading dimension of A. lda >= max(1, m) if SIDE = ‘L’; lda >= max(1, n) if SIDE = ‘R’.

in
tau

Double precision array, dimension (m-1) if SIDE = ‘L’, (n-1) if SIDE = ‘R’. TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DSYTRD.

inout
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^T*C or C*Q^T or C*Q.

in
ldc

The leading dimension of C. ldc >= max(1, m).

out
work

Double precision array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The dimension of the array work. If SIDE = ‘L’, lwork >= max(1, n); if SIDE = ‘R’, lwork >= max(1, m). For optimum performance lwork >= n*nb if SIDE = ‘L’, and lwork >= m*nb if SIDE = ‘R’, where nb is the optimal blocksize. If lwork = -1, then a workspace query is assumed.

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value.

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