SUBROUTINE MB01UW( SIDE, TRANS, M, N, ALPHA, H, LDH, A, LDA,
$ DWORK, LDWORK, INFO )
C
C PURPOSE
C
C To compute one of the matrix products
C
C A : = alpha*op( H ) * A, or A : = alpha*A * op( H ),
C
C where alpha is a scalar, A is an m-by-n matrix, H is an upper
C Hessenberg matrix, and op( H ) is one of
C
C op( H ) = H or op( H ) = H', the transpose of H.
C
C ARGUMENTS
C
C Mode Parameters
C
C SIDE CHARACTER*1
C Specifies whether the Hessenberg matrix H appears on the
C left or right in the matrix product as follows:
C = 'L': A := alpha*op( H ) * A;
C = 'R': A := alpha*A * op( H ).
C
C TRANS CHARACTER*1
C Specifies the form of op( H ) to be used in the matrix
C multiplication as follows:
C = 'N': op( H ) = H;
C = 'T': op( H ) = H';
C = 'C': op( H ) = H'.
C
C Input/Output Parameters
C
C M (input) INTEGER
C The number of rows of the matrix A. M >= 0.
C
C N (input) INTEGER
C The number of columns of the matrix A. N >= 0.
C
C ALPHA (input) DOUBLE PRECISION
C The scalar alpha. When alpha is zero then H is not
C referenced and A need not be set before entry.
C
C H (input) DOUBLE PRECISION array, dimension (LDH,k)
C where k is M when SIDE = 'L' and is N when SIDE = 'R'.
C On entry with SIDE = 'L', the leading M-by-M upper
C Hessenberg part of this array must contain the upper
C Hessenberg matrix H.
C On entry with SIDE = 'R', the leading N-by-N upper
C Hessenberg part of this array must contain the upper
C Hessenberg matrix H.
C The elements below the subdiagonal are not referenced,
C except possibly for those in the first column, which
C could be overwritten, but are restored on exit.
C
C LDH INTEGER
C The leading dimension of the array H. LDH >= max(1,k),
C where k is M when SIDE = 'L' and is N when SIDE = 'R'.
C
C A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
C On entry, the leading M-by-N part of this array must
C contain the matrix A.
C On exit, the leading M-by-N part of this array contains
C the computed product.
C
C LDA INTEGER
C The leading dimension of the array A. LDA >= max(1,M).
C
C Workspace
C
C DWORK DOUBLE PRECISION array, dimension (LDWORK)
C On exit, if INFO = 0, alpha <> 0, and LDWORK >= M*N > 0,
C DWORK contains a copy of the matrix A, having the leading
C dimension M.
C This array is not referenced when alpha = 0.
C
C LDWORK The length of the array DWORK.
C LDWORK >= 0, if alpha = 0 or MIN(M,N) = 0;
C LDWORK >= M-1, if SIDE = 'L';
C LDWORK >= N-1, if SIDE = 'R'.
C For maximal efficiency LDWORK should be at least M*N.
C
C Error Indicator
C
C INFO INTEGER
C = 0: successful exit;
C < 0: if INFO = -i, the i-th argument had an illegal
C value.
C
C METHOD
C
C The required matrix product is computed in two steps. In the first
C step, the upper triangle of H is used; in the second step, the
C contribution of the subdiagonal is added. If the workspace can
C accomodate a copy of A, a fast BLAS 3 DTRMM operation is used in
C the first step.
C
C CONTRIBUTOR
C
C V. Sima, Katholieke Univ. Leuven, Belgium, January 1999.
C
C REVISIONS
C
C V. Sima, Research Institute for Informatics, Bucharest, Feb. 2004.
C
C KEYWORDS
C
C Elementary matrix operations, matrix operations.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
C .. Scalar Arguments ..
CHARACTER SIDE, TRANS
INTEGER INFO, LDA, LDH, LDWORK, M, N
DOUBLE PRECISION ALPHA
C .. Array Arguments ..
DOUBLE PRECISION A(LDA,*), DWORK(*), H(LDH,*)
C .. Local Scalars ..
LOGICAL LSIDE, LTRANS
INTEGER I, J, JW
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL DAXPY, DLACPY, DLASCL, DLASET, DSCAL, DSWAP,
$ DTRMM, DTRMV, XERBLA
C .. Intrinsic Functions ..
INTRINSIC MAX, MIN
C
C .. Executable Statements ..
C
C Test the input scalar arguments.
C
INFO = 0
LSIDE = LSAME( SIDE, 'L' )
LTRANS = LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' )
C
IF( ( .NOT.LSIDE ).AND.( .NOT.LSAME( SIDE, 'R' ) ) )THEN
INFO = -1
ELSE IF( ( .NOT.LTRANS ).AND.( .NOT.LSAME( TRANS, 'N' ) ) )THEN
INFO = -2
ELSE IF( M.LT.0 ) THEN
INFO = -3
ELSE IF( N.LT.0 ) THEN
INFO = -4
ELSE IF( LDH.LT.1 .OR. ( LSIDE .AND. LDH.LT.M ) .OR.
$ ( .NOT.LSIDE .AND. LDH.LT.N ) ) THEN
INFO = -7
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -9
ELSE IF( LDWORK.LT.0 .OR.
$ ( ALPHA.NE.ZERO .AND. MIN( M, N ).GT.0 .AND.
$ ( ( LSIDE .AND. LDWORK.LT.M-1 ) .OR.
$ ( .NOT.LSIDE .AND. LDWORK.LT.N-1 ) ) ) ) THEN
INFO = -11
END IF
C
IF ( INFO.NE.0 ) THEN
C
C Error return.
C
CALL XERBLA( 'MB01UW', -INFO )
RETURN
END IF
C
C Quick return, if possible.
C
IF ( MIN( M, N ).EQ.0 ) THEN
RETURN
ELSE IF ( LSIDE ) THEN
IF ( M.EQ.1 ) THEN
CALL DSCAL( N, ALPHA*H(1,1), A, LDA )
RETURN
END IF
ELSE
IF ( N.EQ.1 ) THEN
CALL DSCAL( M, ALPHA*H(1,1), A, 1 )
RETURN
END IF
END IF
C
IF( ALPHA.EQ.ZERO ) THEN
C
C Set A to zero and return.
C
CALL DLASET( 'Full', M, N, ZERO, ZERO, A, LDA )
RETURN
END IF
C
IF( LDWORK.GE.M*N ) THEN
C
C Enough workspace for a fast BLAS 3 calculation.
C Save A in the workspace and compute one of the matrix products
C A : = alpha*op( triu( H ) ) * A, or
C A : = alpha*A * op( triu( H ) ),
C involving the upper triangle of H.
C
CALL DLACPY( 'Full', M, N, A, LDA, DWORK, M )
CALL DTRMM( SIDE, 'Upper', TRANS, 'Non-unit', M, N, ALPHA, H,
$ LDH, A, LDA )
C
C Add the contribution of the subdiagonal of H.
C If SIDE = 'L', the subdiagonal of H is swapped with the
C corresponding elements in the first column of H, and the
C calculations are organized for column operations.
C
IF( LSIDE ) THEN
IF( M.GT.2 )
$ CALL DSWAP( M-2, H( 3, 2 ), LDH+1, H( 3, 1 ), 1 )
IF( LTRANS ) THEN
JW = 1
DO 20 J = 1, N
JW = JW + 1
DO 10 I = 1, M - 1
A( I, J ) = A( I, J ) +
$ ALPHA*H( I+1, 1 )*DWORK( JW )
JW = JW + 1
10 CONTINUE
20 CONTINUE
ELSE
JW = 0
DO 40 J = 1, N
JW = JW + 1
DO 30 I = 2, M
A( I, J ) = A( I, J ) +
$ ALPHA*H( I, 1 )*DWORK( JW )
JW = JW + 1
30 CONTINUE
40 CONTINUE
END IF
IF( M.GT.2 )
$ CALL DSWAP( M-2, H( 3, 2 ), LDH+1, H( 3, 1 ), 1 )
C
ELSE
C
IF( LTRANS ) THEN
JW = 1
DO 50 J = 1, N - 1
IF ( H( J+1, J ).NE.ZERO )
$ CALL DAXPY( M, ALPHA*H( J+1, J ), DWORK( JW ), 1,
$ A( 1, J+1 ), 1 )
JW = JW + M
50 CONTINUE
ELSE
JW = M + 1
DO 60 J = 1, N - 1
IF ( H( J+1, J ).NE.ZERO )
$ CALL DAXPY( M, ALPHA*H( J+1, J ), DWORK( JW ), 1,
$ A( 1, J ), 1 )
JW = JW + M
60 CONTINUE
END IF
END IF
C
ELSE
C
C Use a BLAS 2 calculation.
C
IF( LSIDE ) THEN
IF( M.GT.2 )
$ CALL DSWAP( M-2, H( 3, 2 ), LDH+1, H( 3, 1 ), 1 )
IF( LTRANS ) THEN
DO 80 J = 1, N
C
C Compute the contribution of the subdiagonal of H to
C the j-th column of the product.
C
DO 70 I = 1, M - 1
DWORK( I ) = H( I+1, 1 )*A( I+1, J )
70 CONTINUE
C
C Multiply the upper triangle of H by the j-th column
C of A, and add to the above result.
C
CALL DTRMV( 'Upper', TRANS, 'Non-unit', M, H, LDH,
$ A( 1, J ), 1 )
CALL DAXPY( M-1, ONE, DWORK, 1, A( 1, J ), 1 )
80 CONTINUE
C
ELSE
DO 100 J = 1, N
C
C Compute the contribution of the subdiagonal of H to
C the j-th column of the product.
C
DO 90 I = 1, M - 1
DWORK( I ) = H( I+1, 1 )*A( I, J )
90 CONTINUE
C
C Multiply the upper triangle of H by the j-th column
C of A, and add to the above result.
C
CALL DTRMV( 'Upper', TRANS, 'Non-unit', M, H, LDH,
$ A( 1, J ), 1 )
CALL DAXPY( M-1, ONE, DWORK, 1, A( 2, J ), 1 )
100 CONTINUE
END IF
IF( M.GT.2 )
$ CALL DSWAP( M-2, H( 3, 2 ), LDH+1, H( 3, 1 ), 1 )
C
ELSE
C
C Below, row-wise calculations are used for A.
C
IF( N.GT.2 )
$ CALL DSWAP( N-2, H( 3, 2 ), LDH+1, H( 3, 1 ), 1 )
IF( LTRANS ) THEN
DO 120 I = 1, M
C
C Compute the contribution of the subdiagonal of H to
C the i-th row of the product.
C
DO 110 J = 1, N - 1
DWORK( J ) = A( I, J )*H( J+1, 1 )
110 CONTINUE
C
C Multiply the i-th row of A by the upper triangle of H,
C and add to the above result.
C
CALL DTRMV( 'Upper', 'NoTranspose', 'Non-unit', N, H,
$ LDH, A( I, 1 ), LDA )
CALL DAXPY( N-1, ONE, DWORK, 1, A( I, 2 ), LDA )
120 CONTINUE
C
ELSE
DO 140 I = 1, M
C
C Compute the contribution of the subdiagonal of H to
C the i-th row of the product.
C
DO 130 J = 1, N - 1
DWORK( J ) = A( I, J+1 )*H( J+1, 1 )
130 CONTINUE
C
C Multiply the i-th row of A by the upper triangle of H,
C and add to the above result.
C
CALL DTRMV( 'Upper', 'Transpose', 'Non-unit', N, H,
$ LDH, A( I, 1 ), LDA )
CALL DAXPY( N-1, ONE, DWORK, 1, A( I, 1 ), LDA )
140 CONTINUE
END IF
IF( N.GT.2 )
$ CALL DSWAP( N-2, H( 3, 2 ), LDH+1, H( 3, 1 ), 1 )
C
END IF
C
C Scale the result by alpha.
C
IF ( ALPHA.NE.ONE )
$ CALL DLASCL( 'General', 0, 0, ONE, ALPHA, M, N, A, LDA,
$ INFO )
END IF
RETURN
C *** Last line of MB01UW ***
END