# cungbr.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **cungbr** (VECT, M, **N**, K, A, **LDA**, TAU, WORK, LWORK, INFO)**CUNGBR**

## Function/Subroutine Documentation

### subroutine cungbr (character VECT, integer M, integer N, integer K, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( * ) WORK, integer LWORK, integer INFO)

**CUNGBR**

**Purpose:**

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.

**Parameters:***VECT*VECT is CHARACTER*1 Specifies whether the matrix Q or the matrix P**H is required, as defined in the transformation applied by CGEBRD: = 'Q': generate Q; = 'P': generate P**H.

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

*N*N is INTEGER 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).

*K*K is INTEGER 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.

*A*A is 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.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= M.

*TAU*TAU is 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.

*WORK*WORK is COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*LWORK*LWORK is INTEGER 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. 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.

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**April 2012

Definition at line 159 of file cungbr.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cungbr(3) is an alias of cungbr.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK