ormbr#

Functions

void sormbr(
    const char*          vect,
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    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 sormbr(const char *vect, const char *side, const char *trans, const INT m, const INT n, const INT k, 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)#

If VECT = ‘Q’, SORMBR 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.

If VECT = ‘P’, SORMBR overwrites the general real M-by-N matrix C with SIDE = ‘L’ SIDE = ‘R’ TRANS = ‘N’: P * C C * P TRANS = ‘T’: P**T * C C * P**T

Here Q and P**T are the orthogonal matrices determined by SGEBRD when reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and P**T are defined as products of elementary reflectors H(i) and G(i) respectively.

Parameters

in
vect

= ‘Q’: apply Q or Q**T; = ‘P’: apply P or P**T.

in
side

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

in
trans

= ‘N’: No transpose, apply Q or P; = ‘T’: Transpose, apply Q**T or P**T.

in
m

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

in
n

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

in
k

If vect = ‘Q’, the number of columns in the original matrix reduced by SGEBRD. If vect = ‘P’, the number of rows in the original matrix reduced by SGEBRD. k >= 0.

in
A

Double precision array, dimension (lda, min(nq,k)) if vect = ‘Q’ (lda, nq) if vect = ‘P’ The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by SGEBRD.

in
lda

The leading dimension of the array A. If vect = ‘Q’, lda >= max(1,nq); if vect = ‘P’, lda >= max(1,min(nq,k)).

in
tau

Double precision array, dimension (min(nq,k)). tau[i] must contain the scalar factor of the elementary reflector H(i) or G(i) which determines Q or P, as returned by SGEBRD in the array argument TAUQ or TAUP.

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 or P*C or P**T*C or C*P or C*P**T.

in
ldc

The leading dimension of the array 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; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla.

out
info

  • = 0: successful exit

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

Functions

void dormbr(
    const char*          vect,
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    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 dormbr(const char *vect, const char *side, const char *trans, const INT m, const INT n, const INT k, 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)#

If VECT = ‘Q’, DORMBR 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.

If VECT = ‘P’, DORMBR overwrites the general real M-by-N matrix C with SIDE = ‘L’ SIDE = ‘R’ TRANS = ‘N’: P * C C * P TRANS = ‘T’: P**T * C C * P**T

Here Q and P**T are the orthogonal matrices determined by DGEBRD when reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and P**T are defined as products of elementary reflectors H(i) and G(i) respectively.

Parameters

in
vect

= ‘Q’: apply Q or Q**T; = ‘P’: apply P or P**T.

in
side

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

in
trans

= ‘N’: No transpose, apply Q or P; = ‘T’: Transpose, apply Q**T or P**T.

in
m

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

in
n

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

in
k

If vect = ‘Q’, the number of columns in the original matrix reduced by DGEBRD. If vect = ‘P’, the number of rows in the original matrix reduced by DGEBRD. k >= 0.

in
A

Double precision array, dimension (lda, min(nq,k)) if vect = ‘Q’ (lda, nq) if vect = ‘P’ The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by DGEBRD.

in
lda

The leading dimension of the array A. If vect = ‘Q’, lda >= max(1,nq); if vect = ‘P’, lda >= max(1,min(nq,k)).

in
tau

Double precision array, dimension (min(nq,k)). tau[i] must contain the scalar factor of the elementary reflector H(i) or G(i) which determines Q or P, as returned by DGEBRD in the array argument TAUQ or TAUP.

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 or P*C or P**T*C or C*P or C*P**T.

in
ldc

The leading dimension of the array 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; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla.

out
info

  • = 0: successful exit

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

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