unmbr

cunmbr

Functions

void cunmbr(
    const char*          vect,
    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 cunmbr(const char *vect, 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)

If VECT = ‘Q’, CUNMBR 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.

If VECT = ‘P’, CUNMBR overwrites the general complex M-by-N matrix C with SIDE = ‘L’ SIDE = ‘R’ TRANS = ‘N’: P * C C * P TRANS = ‘C’: P**H * C C * P**H

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

Let nq = m if SIDE = ‘L’ and nq = n if SIDE = ‘R’. Thus nq is the order of the unitary matrix Q or P**H that is applied.

If VECT = ‘Q’, A is assumed to have been an NQ-by-K matrix: if nq >= k, Q = H(1) H(2) … H(k); if nq < k, Q = H(1) H(2) … H(nq-1).

If VECT = ‘P’, A is assumed to have been a K-by-NQ matrix: if k < nq, P = G(1) G(2) … G(k); if k >= nq, P = G(1) G(2) … G(nq-1).

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

vect

‘Q’: apply Q or Q**H; ‘P’: apply P or P**H.

in

side

‘L’: apply Q, Q**H, P or P**H from the Left; ‘R’: apply Q, Q**H, P or P**H from the Right.

in

trans

‘N’: No transpose, apply Q or P; ‘C’: Conjugate transpose, apply Q**H or P**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

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

in

A

Single complex 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 CGEBRD.

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

Single complex 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 CGEBRD in the array argument TAUQ or TAUP.

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 or P*C or P**H*C or C*P or C*P**H.

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); if n = 0 or m = 0, lwork >= 1. For optimum performance lwork >= max(1, n*NB) if SIDE = ‘L’, and lwork >= max(1, m*NB) if SIDE = ‘R’, where NB is the optimal blocksize. (NB = 0 if M = 0 or N = 0.)

out

info

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

zunmbr

Functions

void zunmbr(
    const char*          vect,
    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 zunmbr(const char *vect, 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)

If VECT = ‘Q’, ZUNMBR 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.

If VECT = ‘P’, ZUNMBR overwrites the general complex M-by-N matrix C with SIDE = ‘L’ SIDE = ‘R’ TRANS = ‘N’: P * C C * P TRANS = ‘C’: P**H * C C * P**H

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

Let nq = m if SIDE = ‘L’ and nq = n if SIDE = ‘R’. Thus nq is the order of the unitary matrix Q or P**H that is applied.

If VECT = ‘Q’, A is assumed to have been an NQ-by-K matrix: if nq >= k, Q = H(1) H(2) … H(k); if nq < k, Q = H(1) H(2) … H(nq-1).

If VECT = ‘P’, A is assumed to have been a K-by-NQ matrix: if k < nq, P = G(1) G(2) … G(k); if k >= nq, P = G(1) G(2) … G(nq-1).

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

vect

‘Q’: apply Q or Q**H; ‘P’: apply P or P**H.

in

side

‘L’: apply Q, Q**H, P or P**H from the Left; ‘R’: apply Q, Q**H, P or P**H from the Right.

in

trans

‘N’: No transpose, apply Q or P; ‘C’: Conjugate transpose, apply Q**H or P**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

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

in

A

Double complex 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 ZGEBRD.

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 complex 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 ZGEBRD in the array argument TAUQ or TAUP.

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 or P*C or P**H*C or C*P or C*P**H.

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); if n = 0 or m = 0, lwork >= 1. For optimum performance lwork >= max(1, n*NB) if SIDE = ‘L’, and lwork >= max(1, m*NB) if SIDE = ‘R’, where NB is the optimal blocksize. (NB = 0 if M = 0 or N = 0.)

out

info

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