orgbr#

Functions

void sorgbr(
    const char*          vect,
    const INT            m,
    const INT            n,
    const INT            k,
          f32*  restrict A,
    const INT            lda,
    const f32*  restrict tau,
          f32*  restrict work,
    const INT            lwork,
          INT*           info
);
void sorgbr(const char *vect, const INT m, const INT n, const INT k, f32 *restrict A, const INT lda, const f32 *restrict tau, f32 *restrict work, const INT lwork, INT *info)#

SORGBR generates one of the real orthogonal matrices Q or P**T 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) or G(i) respectively.

If VECT = ‘Q’, A is assumed to have been an M-by-K matrix, and Q is of order M: if m >= k, Q = H(1) H(2) … H(k) and SORGBR returns the first n columns of Q, where m >= n >= k; if m < k, Q = H(1) H(2) … H(m-1) and SORGBR returns Q as an M-by-M matrix.

If VECT = ‘P’, A is assumed to have been a K-by-N matrix, and P**T is of order N: if k < n, P**T = G(k) … G(2) G(1) and SORGBR returns the first m rows of P**T, where n >= m >= k; if k >= n, P**T = G(n-1) … G(2) G(1) and SORGBR returns P**T as an N-by-N matrix.

Parameters

in
vect

Specifies whether the matrix Q or the matrix P**T is required, as defined in the transformation applied by SGEBRD: = ‘Q’: generate Q; = ‘P’: generate P**T.

in
m

The number of rows of the matrix Q or P**T to be returned. m >= 0.

in
n

The number of columns of the matrix Q or P**T to be returned. n >= 0. If vect = ‘Q’, m >= n >= min(m,k); if vect = ‘P’, n >= m >= min(n,k).

in
k

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

inout
A

Double precision array, dimension (lda, n). On entry, the vectors which define the elementary reflectors, as returned by SGEBRD. On exit, the M-by-N matrix Q or P**T.

in
lda

The leading dimension of the array A. lda >= max(1,m).

in
tau

Double precision array, dimension (min(m,k)) if vect = ‘Q’ (min(n,k)) if vect = ‘P’ tau[i] must contain the scalar factor of the elementary reflector H(i) or G(i), which determines Q or P**T, as returned by SGEBRD in its array argument TAUQ or TAUP.

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. lwork >= max(1,min(m,n)). For optimum performance lwork >= min(m,n)*NB, 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 dorgbr(
    const char*          vect,
    const INT            m,
    const INT            n,
    const INT            k,
          f64*  restrict A,
    const INT            lda,
    const f64*  restrict tau,
          f64*  restrict work,
    const INT            lwork,
          INT*           info
);
void dorgbr(const char *vect, const INT m, const INT n, const INT k, f64 *restrict A, const INT lda, const f64 *restrict tau, f64 *restrict work, const INT lwork, INT *info)#

DORGBR generates one of the real orthogonal matrices Q or P**T 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) or G(i) respectively.

If VECT = ‘Q’, A is assumed to have been an M-by-K matrix, and Q is of order M: if m >= k, Q = H(1) H(2) … H(k) and DORGBR returns the first n columns of Q, where m >= n >= k; if m < k, Q = H(1) H(2) … H(m-1) and DORGBR returns Q as an M-by-M matrix.

If VECT = ‘P’, A is assumed to have been a K-by-N matrix, and P**T is of order N: if k < n, P**T = G(k) … G(2) G(1) and DORGBR returns the first m rows of P**T, where n >= m >= k; if k >= n, P**T = G(n-1) … G(2) G(1) and DORGBR returns P**T as an N-by-N matrix.

Parameters

in
vect

Specifies whether the matrix Q or the matrix P**T is required, as defined in the transformation applied by DGEBRD: = ‘Q’: generate Q; = ‘P’: generate P**T.

in
m

The number of rows of the matrix Q or P**T to be returned. m >= 0.

in
n

The number of columns of the matrix Q or P**T to be returned. n >= 0. If vect = ‘Q’, m >= n >= min(m,k); if vect = ‘P’, n >= m >= min(n,k).

in
k

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

inout
A

Double precision array, dimension (lda, n). On entry, the vectors which define the elementary reflectors, as returned by DGEBRD. On exit, the M-by-N matrix Q or P**T.

in
lda

The leading dimension of the array A. lda >= max(1,m).

in
tau

Double precision array, dimension (min(m,k)) if vect = ‘Q’ (min(n,k)) if vect = ‘P’ tau[i] must contain the scalar factor of the elementary reflector H(i) or G(i), which determines Q or P**T, as returned by DGEBRD in its array argument TAUQ or TAUP.

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. lwork >= max(1,min(m,n)). For optimum performance lwork >= min(m,n)*NB, 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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