sorgbr(l) [redhat man page]

SORGBR(l)								 )								 SORGBR(l)

NAME

       SORGBR - generate one of the real orthogonal matrices Q or P**T determined by SGEBRD when reducing a real matrix A to bidiagonal form

SYNOPSIS

       SUBROUTINE SORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )

	   CHARACTER	  VECT

	   INTEGER	  INFO, K, LDA, LWORK, M, N

	   REAL 	  A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

       SORGBR generates one of the real orthogonal matrices Q or P**T determined by SGEBRD when reducing a real matrix A to bidiagonal form: A = Q
       * B * P**T. Q and P**T 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 SORGBR returns the first n columns of Q, where m >= n >= k;
       if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR returns Q as an M-by-M matrix.

       If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T is of order N:
       if k < n, P**T = G(k) . . . G(2) G(1) and SORGBR returns the first m rows of P**T, where n >= m >= k;
       if k >= n, P**T = G(n-1) . . . G(2) G(1) and SORGBR returns P**T as an N-by-N matrix.

ARGUMENTS

       VECT    (input) CHARACTER*1
	       Specifies whether the matrix Q or the matrix P**T is required, as defined in the transformation applied by SGEBRD:
	       = 'Q':  generate Q;
	       = 'P':  generate P**T.

       M       (input) INTEGER
	       The number of rows of the matrix Q or P**T to be returned.  M >= 0.

       N       (input) INTEGER
	       The number of columns of the matrix Q or P**T to be returned.  N >= 0.  If VECT = 'Q', M >= N >= min(M,K); if VECT = 'P', N >= M >=
	       min(N,K).

       K       (input) INTEGER
	       If  VECT  =  'Q',  the number of columns in the original M-by-K matrix reduced by SGEBRD.  If VECT = 'P', the number of rows in the
	       original K-by-N matrix reduced by SGEBRD.  K >= 0.

       A       (input/output) REAL array, dimension (LDA,N)
	       On entry, the vectors which define the elementary reflectors, as returned by SGEBRD.  On exit, the M-by-N matrix Q or P**T.

       LDA     (input) INTEGER
	       The leading dimension of the array A. LDA >= max(1,M).

       TAU     (input) REAL 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**T, as returned by SGEBRD in its array argument TAUQ or TAUP.

       WORK    (workspace/output) REAL array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) 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    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

LAPACK version 3.0						   15 June 2000 							 SORGBR(l)

CUNGBR(l)								 )								 CUNGBR(l)

NAME

       CUNGBR - generate one of the complex unitary matrices Q or P**H determined by CGEBRD when reducing a complex matrix A to bidiagonal form

SYNOPSIS

       SUBROUTINE CUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )

	   CHARACTER	  VECT

	   INTEGER	  INFO, K, LDA, LWORK, M, N

	   COMPLEX	  A( LDA, * ), TAU( * ), WORK( * )

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.

ARGUMENTS

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

       N       (input) 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       (input) 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       (input/output) 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     (input) INTEGER
	       The leading dimension of the array A. LDA >= M.

       TAU     (input) 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    (workspace/output) COMPLEX array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) 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    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

LAPACK version 3.0						   15 June 2000 							 CUNGBR(l)