gemlq

sgemlq

Functions

void sgemlq(
    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 T,
    const INT            tsize,
          f32*  restrict C,
    const INT            ldc,
          f32*  restrict work,
    const INT            lwork,
          INT*           info
);

void sgemlq(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 T, const INT tsize, f32 *restrict C, const INT ldc, f32 *restrict work, const INT lwork, INT *info)

SGEMLQ 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 defined as the product of blocked elementary reflectors computed by short wide LQ factorization (SGELQ)

Parameters

in

side

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

in

trans

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

in

m

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

in

n

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

in

k

The number of elementary reflectors whose product defines the matrix Q. If SIDE = ‘L’, m >= k >= 0; if SIDE = ‘R’, n >= k >= 0.

in

A

Double precision array, dimension (lda, m) if SIDE=’L’, (lda, n) if SIDE=’R’. Part of the data structure to represent Q as returned by SGELQ.

in

lda

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

in

T

Double precision array, dimension (max(5, tsize)). Part of the data structure to represent Q as returned by SGELQ.

in

tsize

The dimension of the array T. tsize >= 5.

inout

C

Double precision array, dimension (ldc, n). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C, Q^T*C, C*Q^T, or C*Q.

in

ldc

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

out

work

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

in

lwork

The dimension of the array work. lwork >= 1. 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.

dgemlq

Functions

void dgemlq(
    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 T,
    const INT            tsize,
          f64*  restrict C,
    const INT            ldc,
          f64*  restrict work,
    const INT            lwork,
          INT*           info
);

void dgemlq(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 T, const INT tsize, f64 *restrict C, const INT ldc, f64 *restrict work, const INT lwork, INT *info)

DGEMLQ 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 defined as the product of blocked elementary reflectors computed by short wide LQ factorization (DGELQ)

Parameters

in

side

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

in

trans

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

in

m

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

in

n

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

in

k

The number of elementary reflectors whose product defines the matrix Q. If SIDE = ‘L’, m >= k >= 0; if SIDE = ‘R’, n >= k >= 0.

in

A

Double precision array, dimension (lda, m) if SIDE=’L’, (lda, n) if SIDE=’R’. Part of the data structure to represent Q as returned by DGELQ.

in

lda

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

in

T

Double precision array, dimension (max(5, tsize)). Part of the data structure to represent Q as returned by DGELQ.

in

tsize

The dimension of the array T. tsize >= 5.

inout

C

Double precision array, dimension (ldc, n). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C, Q^T*C, C*Q^T, or C*Q.

in

ldc

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

out

work

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

in

lwork

The dimension of the array work. lwork >= 1. 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.

cgemlq

Functions

void cgemlq(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const c64*  restrict A,
    const INT            lda,
    const c64*  restrict T,
    const INT            tsize,
          c64*  restrict C,
    const INT            ldc,
          c64*  restrict work,
    const INT            lwork,
          INT*           info
);

void cgemlq(const char *side, const char *trans, const INT m, const INT n, const INT k, const c64 *restrict A, const INT lda, const c64 *restrict T, const INT tsize, c64 *restrict C, const INT ldc, c64 *restrict work, const INT lwork, INT *info)

CGEMLQ overwrites the general complex M-by-N matrix C with.

         SIDE = 'L'     SIDE = 'R'

TRANS = ‘N’: Q * C C * Q TRANS = ‘C’: Q^H * C C * Q^H

where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (CGELQ)

Parameters

in

side

‘L’: apply Q or Q^H from the Left; ‘R’: apply Q or Q^H from the Right.

in

trans

‘N’: No transpose, apply Q; ‘C’: Conjugate transpose, apply Q^H.

in

m

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

in

n

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

in

k

The number of elementary reflectors whose product defines the matrix Q. If SIDE = ‘L’, m >= k >= 0; if SIDE = ‘R’, n >= k >= 0.

in

A

Complex*16 array, dimension (lda, m) if SIDE=’L’, (lda, n) if SIDE=’R’. Part of the data structure to represent Q as returned by CGELQ.

in

lda

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

in

T

Complex*16 array, dimension (max(5, tsize)). Part of the data structure to represent Q as returned by CGELQ.

in

tsize

The dimension of the array T. tsize >= 5.

inout

C

Complex*16 array, dimension (ldc, n). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C, Q^H*C, C*Q^H, or C*Q.

in

ldc

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

out

work

Complex*16 workspace array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the minimal lwork.

in

lwork

The dimension of the array work. lwork >= 1. 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.

zgemlq

Functions

void zgemlq(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const c128* restrict A,
    const INT            lda,
    const c128* restrict T,
    const INT            tsize,
          c128* restrict C,
    const INT            ldc,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);

void zgemlq(const char *side, const char *trans, const INT m, const INT n, const INT k, const c128 *restrict A, const INT lda, const c128 *restrict T, const INT tsize, c128 *restrict C, const INT ldc, c128 *restrict work, const INT lwork, INT *info)

ZGEMLQ overwrites the general complex M-by-N matrix C with.

         SIDE = 'L'     SIDE = 'R'

TRANS = ‘N’: Q * C C * Q TRANS = ‘C’: Q^H * C C * Q^H

where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (ZGELQ)

Parameters

in

side

‘L’: apply Q or Q^H from the Left; ‘R’: apply Q or Q^H from the Right.

in

trans

‘N’: No transpose, apply Q; ‘C’: Conjugate transpose, apply Q^H.

in

m

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

in

n

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

in

k

The number of elementary reflectors whose product defines the matrix Q. If SIDE = ‘L’, m >= k >= 0; if SIDE = ‘R’, n >= k >= 0.

in

A

Complex*16 array, dimension (lda, m) if SIDE=’L’, (lda, n) if SIDE=’R’. Part of the data structure to represent Q as returned by ZGELQ.

in

lda

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

in

T

Complex*16 array, dimension (max(5, tsize)). Part of the data structure to represent Q as returned by ZGELQ.

in

tsize

The dimension of the array T. tsize >= 5.

inout

C

Complex*16 array, dimension (ldc, n). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C, Q^H*C, C*Q^H, or C*Q.

in

ldc

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

out

work

Complex*16 workspace array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the minimal lwork.

in

lwork

The dimension of the array work. lwork >= 1. 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.