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sorgbr(3) [debian man page]

sorgbr.f(3)							      LAPACK							       sorgbr.f(3)

NAME

       sorgbr.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sorgbr (VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
	   SORGBR

Function/Subroutine Documentation
   subroutine sorgbr (characterVECT, integerM, integerN, integerK, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real,
       dimension( * )WORK, integerLWORK, integerINFO)
       SORGBR

       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.

       Parameters:
	   VECT

		     VECT is 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

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

	   N

		     N is 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

		     K is 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

		     A is 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

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

	   TAU

		     TAU is 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

		     WORK is REAL 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 158 of file sorgbr.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       sorgbr.f(3)

Check Out this Related 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)
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