dorgtr(l) [redhat man page]

DORGTR(l)								 )								 DORGTR(l)

NAME

       DORGTR - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by DSYTRD

SYNOPSIS

       SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDA, LWORK, N

	   DOUBLE	  PRECISION A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

       DORGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by DSYTRD:
       if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

       if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).

ARGUMENTS

       UPLO    (input) CHARACTER*1
	       = 'U': Upper triangle of A contains elementary reflectors from DSYTRD; = 'L': Lower triangle of A  contains  elementary	reflectors
	       from DSYTRD.

       N       (input) INTEGER
	       The order of the matrix Q. N >= 0.

       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
	       On entry, the vectors which define the elementary reflectors, as returned by DSYTRD.  On exit, the N-by-N orthogonal matrix Q.

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

       TAU     (input) DOUBLE PRECISION array, dimension (N-1)
	       TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DSYTRD.

       WORK    (workspace/output) DOUBLE PRECISION 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,N-1).  For optimum performance LWORK >= (N-1)*NB, where NB is the optimal block-
	       size.

	       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 							 DORGTR(l)

DORMTR(l)								 )								 DORMTR(l)

NAME

       DORMTR - overwrite the general real M-by-N matrix C with  SIDE = 'L' SIDE = 'R' TRANS = 'N'

SYNOPSIS

       SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

	   CHARACTER	  SIDE, TRANS, UPLO

	   INTEGER	  INFO, LDA, LDC, LWORK, M, N

	   DOUBLE	  PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )

PURPOSE

       DORMTR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T':	Q**T * C       C *
       Q**T

       where Q is a real orthogonal matrix of order nq, with nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the  product  of  nq-1
       elementary reflectors, as returned by DSYTRD:

       if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);

       if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

ARGUMENTS

       SIDE    (input) CHARACTER*1
	       = 'L': apply Q or Q**T from the Left;
	       = 'R': apply Q or Q**T from the Right.

       UPLO    (input) CHARACTER*1
	       =  'U':	Upper  triangle of A contains elementary reflectors from DSYTRD; = 'L': Lower triangle of A contains elementary reflectors
	       from DSYTRD.

       TRANS   (input) CHARACTER*1
	       = 'N':  No transpose, apply Q;
	       = 'T':  Transpose, apply Q**T.

       M       (input) INTEGER
	       The number of rows of the matrix C. M >= 0.

       N       (input) INTEGER
	       The number of columns of the matrix C. N >= 0.

       A       (input) DOUBLE PRECISION array, dimension
	       (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by DSYTRD.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.

       TAU     (input) DOUBLE PRECISION array, dimension
	       (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain the scalar factor of the elementary	reflector  H(i),  as  returned	by
	       DSYTRD.

       C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
	       On entry, the M-by-N matrix C.  On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

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

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

       LWORK   (input) INTEGER
	       The  dimension  of  the	array  WORK.  If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M).  For optimum performance
	       LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', 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 							 DORMTR(l)