julie
be91086043
Those are just cosmetic changes to update version number and various other minor change.
185 lines
5.2 KiB
FortranFixed
185 lines
5.2 KiB
FortranFixed
SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
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*
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* -- LAPACK routine (version 3.2) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER INFO, LDA, LWORK, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* DORGTR generates a real orthogonal matrix Q which is defined as the
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* product of n-1 elementary reflectors of order N, as returned by
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* DSYTRD:
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*
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* if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
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*
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* if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
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*
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* Arguments
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* =========
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*
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* UPLO (input) CHARACTER*1
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* = 'U': Upper triangle of A contains elementary reflectors
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* from DSYTRD;
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* = 'L': Lower triangle of A contains elementary reflectors
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* from DSYTRD.
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*
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* N (input) INTEGER
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* The order of the matrix Q. N >= 0.
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*
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* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
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* On entry, the vectors which define the elementary reflectors,
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* as returned by DSYTRD.
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* On exit, the N-by-N orthogonal matrix Q.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,N).
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*
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* TAU (input) DOUBLE PRECISION array, dimension (N-1)
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* TAU(i) must contain the scalar factor of the elementary
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* reflector H(i), as returned by DSYTRD.
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*
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* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
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* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*
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* LWORK (input) INTEGER
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* The dimension of the array WORK. LWORK >= max(1,N-1).
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* For optimum performance LWORK >= (N-1)*NB, where NB is
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* the optimal blocksize.
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*
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* If LWORK = -1, then a workspace query is assumed; the routine
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* only calculates the optimal size of the WORK array, returns
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* this value as the first entry of the WORK array, and no error
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* message related to LWORK is issued by XERBLA.
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY, UPPER
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INTEGER I, IINFO, J, LWKOPT, NB
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ILAENV
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EXTERNAL LSAME, ILAENV
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* ..
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* .. External Subroutines ..
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EXTERNAL DORGQL, DORGQR, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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INFO = 0
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LQUERY = ( LWORK.EQ.-1 )
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UPPER = LSAME( UPLO, 'U' )
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IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -4
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ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
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INFO = -7
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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IF( UPPER ) THEN
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NB = ILAENV( 1, 'DORGQL', ' ', N-1, N-1, N-1, -1 )
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ELSE
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NB = ILAENV( 1, 'DORGQR', ' ', N-1, N-1, N-1, -1 )
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END IF
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LWKOPT = MAX( 1, N-1 )*NB
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WORK( 1 ) = LWKOPT
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DORGTR', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 ) THEN
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WORK( 1 ) = 1
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RETURN
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END IF
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*
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IF( UPPER ) THEN
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*
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* Q was determined by a call to DSYTRD with UPLO = 'U'
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*
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* Shift the vectors which define the elementary reflectors one
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* column to the left, and set the last row and column of Q to
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* those of the unit matrix
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*
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DO 20 J = 1, N - 1
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DO 10 I = 1, J - 1
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A( I, J ) = A( I, J+1 )
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10 CONTINUE
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A( N, J ) = ZERO
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20 CONTINUE
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DO 30 I = 1, N - 1
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A( I, N ) = ZERO
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30 CONTINUE
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A( N, N ) = ONE
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*
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* Generate Q(1:n-1,1:n-1)
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*
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CALL DORGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
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*
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ELSE
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*
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* Q was determined by a call to DSYTRD with UPLO = 'L'.
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*
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* Shift the vectors which define the elementary reflectors one
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* column to the right, and set the first row and column of Q to
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* those of the unit matrix
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*
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DO 50 J = N, 2, -1
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A( 1, J ) = ZERO
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DO 40 I = J + 1, N
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A( I, J ) = A( I, J-1 )
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40 CONTINUE
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50 CONTINUE
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A( 1, 1 ) = ONE
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DO 60 I = 2, N
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A( I, 1 ) = ZERO
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60 CONTINUE
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IF( N.GT.1 ) THEN
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*
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* Generate Q(2:n,2:n)
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*
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CALL DORGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
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$ LWORK, IINFO )
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END IF
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END IF
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WORK( 1 ) = LWKOPT
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RETURN
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*
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* End of DORGTR
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*
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END
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