unmrq#

Functions

void cunmrq(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
          c64*  restrict A,
    const INT            lda,
    const c64*  restrict tau,
          c64*  restrict C,
    const INT            ldc,
          c64*  restrict work,
    const INT            lwork,
          INT*           info
);
void cunmrq(const char *side, const char *trans, const INT m, const INT n, const INT k, c64 *restrict A, const INT lda, const c64 *restrict tau, c64 *restrict C, const INT ldc, c64 *restrict work, const INT lwork, INT *info)#

CUNMRQ 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 k elementary reflectors 

  Q = H(1)**H H(2)**H . . . H(k)**H
as returned by CGERQF. Q is of order M if SIDE = ‘L’ and of order N if SIDE = ‘R’.

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.

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 C. 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

Single complex array, dimension (lda, m) if SIDE = ‘L’, (lda, n) if SIDE = ‘R’ The i-th row must contain the vector which defines the elementary reflector H(i), for i = 0,1,…,k-1, as returned by CGERQF in the last k rows of its array argument A.

in
lda

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

in
tau

Single complex array, dimension (k). tau[i] must contain the scalar factor of the elementary reflector H(i), as returned by CGERQF.

inout
C

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

in
ldc

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

out
work

Single complex 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 good performance, lwork should generally be larger.

out
info

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

Functions

void zunmrq(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
          c128* restrict A,
    const INT            lda,
    const c128* restrict tau,
          c128* restrict C,
    const INT            ldc,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);
void zunmrq(const char *side, const char *trans, const INT m, const INT n, const INT k, c128 *restrict A, const INT lda, const c128 *restrict tau, c128 *restrict C, const INT ldc, c128 *restrict work, const INT lwork, INT *info)#

ZUNMRQ 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 k elementary reflectors 

  Q = H(1)**H H(2)**H . . . H(k)**H
as returned by ZGERQF. Q is of order M if SIDE = ‘L’ and of order N if SIDE = ‘R’.

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.

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 C. 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 complex array, dimension (lda, m) if SIDE = ‘L’, (lda, n) if SIDE = ‘R’ The i-th row must contain the vector which defines the elementary reflector H(i), for i = 0,1,…,k-1, as returned by ZGERQF in the last k rows of its array argument A.

in
lda

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

in
tau

Double complex array, dimension (k). tau[i] must contain the scalar factor of the elementary reflector H(i), as returned by ZGERQF.

inout
C

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

in
ldc

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

out
work

Double complex 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 good performance, lwork should generally be larger.

out
info

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

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