ungbr#

Functions

void cungbr(
    const char*          vect,
    const INT            m,
    const INT            n,
    const INT            k,
          c64*  restrict A,
    const INT            lda,
    const c64*  restrict tau,
          c64*  restrict work,
    const INT            lwork,
          INT*           info
);
void cungbr(const char *vect, const INT m, const INT n, const INT k, c64 *restrict A, const INT lda, const c64 *restrict tau, c64 *restrict work, const INT lwork, INT *info)#

CUNGBR generates one of the complex unitary matrices Q or P**H 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) 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 CUNGBR returns the first n columns of Q, where m >= n >= k; if m < k, Q = H(1) H(2) … H(m-1) and CUNGBR returns Q as an M-by-M matrix.

If VECT = ‘P’, A is assumed to have been a K-by-N matrix, and P**H is of order N: if k < n, P**H = G(k) … G(2) G(1) and CUNGBR returns the first m rows of P**H, where n >= m >= k; if k >= n, P**H = G(n-1) … G(2) G(1) and CUNGBR returns P**H as an N-by-N matrix.

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

Specifies whether the matrix Q or the matrix P**H is required: = ‘Q’: generate Q; = ‘P’: generate P**H.

in
m

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

in
n

The number of columns of the matrix Q or P**H 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 CGEBRD. If VECT = ‘P’, the number of rows in the original k-by-n matrix reduced by CGEBRD. k >= 0.

inout
A

Complex array, dimension (lda, n). On entry, the vectors which define the elementary reflectors, as returned by CGEBRD. On exit, the m-by-n matrix Q or P**H.

in
lda

The leading dimension of the array A. lda >= m.

in
tau

Complex 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**H, as returned by CGEBRD in its array argument TAUQ or TAUP.

out
work

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. lwork >= max(1,min(m,n)). For optimum performance lwork >= min(m,n)*NB, where NB is the optimal blocksize.

out
info

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

Functions

void zungbr(
    const char*          vect,
    const INT            m,
    const INT            n,
    const INT            k,
          c128* restrict A,
    const INT            lda,
    const c128* restrict tau,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);
void zungbr(const char *vect, const INT m, const INT n, const INT k, c128 *restrict A, const INT lda, const c128 *restrict tau, c128 *restrict work, const INT lwork, INT *info)#

ZUNGBR generates one of the complex unitary matrices Q or P**H 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) 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 ZUNGBR returns the first n columns of Q, where m >= n >= k; if m < k, Q = H(1) H(2) … H(m-1) and ZUNGBR returns Q as an M-by-M matrix.

If VECT = ‘P’, A is assumed to have been a K-by-N matrix, and P**H is of order N: if k < n, P**H = G(k) … G(2) G(1) and ZUNGBR returns the first m rows of P**H, where n >= m >= k; if k >= n, P**H = G(n-1) … G(2) G(1) and ZUNGBR returns P**H as an N-by-N matrix.

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

Specifies whether the matrix Q or the matrix P**H is required: = ‘Q’: generate Q; = ‘P’: generate P**H.

in
m

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

in
n

The number of columns of the matrix Q or P**H 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 ZGEBRD. If VECT = ‘P’, the number of rows in the original k-by-n matrix reduced by ZGEBRD. k >= 0.

inout
A

Complex array, dimension (lda, n). On entry, the vectors which define the elementary reflectors, as returned by ZGEBRD. On exit, the m-by-n matrix Q or P**H.

in
lda

The leading dimension of the array A. lda >= m.

in
tau

Complex 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**H, as returned by ZGEBRD in its array argument TAUQ or TAUP.

out
work

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. lwork >= max(1,min(m,n)). For optimum performance lwork >= min(m,n)*NB, where NB is the optimal blocksize.

out
info

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

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