orgql#

Functions

void sorgql(
    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 sorgql(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)#

SORGQL generates an M-by-N real matrix Q with orthonormal columns, which is defined as the last N columns of a product of K elementary reflectors of order M.

Q = H(k-1) … H(1) H(0)

as returned by SGEQLF.

This is the blocked Level 3 BLAS version of the algorithm.

Parameters

in
m

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

in
n

The number of columns of Q. m >= n >= 0.

in
k

The number of elementary reflectors whose product defines Q. n >= k >= 0.

inout
A

On entry, the (n-k+i)-th column must contain the vector which defines the elementary reflector H(i), for i = 0,…,k-1, as returned by SGEQLF. On exit, the m-by-n matrix Q.

in
lda

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

in
tau

Array of dimension (k). TAU(i) is the scalar factor of H(i), as returned by SGEQLF.

out
work

Workspace, dimension (max(1, lwork)). On exit, work[0] contains the optimal lwork.

in
lwork

Dimension of work. lwork >= max(1, n). For optimal performance, lwork >= n*nb. If lwork == -1, workspace query only.

out
info

  • = 0: successful exit

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

Functions

void dorgql(
    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 dorgql(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)#

DORGQL generates an M-by-N real matrix Q with orthonormal columns, which is defined as the last N columns of a product of K elementary reflectors of order M.

Q = H(k-1) … H(1) H(0)

as returned by DGEQLF.

This is the blocked Level 3 BLAS version of the algorithm.

Parameters

in
m

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

in
n

The number of columns of Q. m >= n >= 0.

in
k

The number of elementary reflectors whose product defines Q. n >= k >= 0.

inout
A

On entry, the (n-k+i)-th column must contain the vector which defines the elementary reflector H(i), for i = 0,…,k-1, as returned by DGEQLF. On exit, the m-by-n matrix Q.

in
lda

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

in
tau

Array of dimension (k). TAU(i) is the scalar factor of H(i), as returned by DGEQLF.

out
work

Workspace, dimension (max(1, lwork)). On exit, work[0] contains the optimal lwork.

in
lwork

Dimension of work. lwork >= max(1, n). For optimal performance, lwork >= n*nb. If lwork == -1, workspace query only.

out
info

  • = 0: successful exit

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

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