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SUBROUTINE DATRMV( UPLO, TRANS, DIAG, N, ALPHA, A, LDA, X, INCX,
$ BETA, Y, INCY )
*
* -- PBLAS auxiliary routine (version 2.0) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* April 1, 1998
*
* .. Scalar Arguments ..
CHARACTER*1 DIAG, TRANS, UPLO
INTEGER INCX, INCY, LDA, N
DOUBLE PRECISION ALPHA, BETA
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )
* ..
*
* Purpose
* =======
*
* DATRMV performs one of the matrix-vector operations
*
* y := abs( alpha )*abs( A )*abs( x )+ abs( beta*y ),
*
* or
*
* y := abs( alpha )*abs( A' )*abs( x ) + abs( beta*y ),
*
* where alpha and beta are real scalars, y is a real vector, x is a
* vector and A is an n by n unit or non-unit, upper or lower triangular
* matrix.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* On entry, UPLO specifies whether the matrix is an upper or
* lower triangular matrix as follows:
*
* UPLO = 'U' or 'u' A is an upper triangular matrix.
*
* UPLO = 'L' or 'l' A is a lower triangular matrix.
*
* TRANS (input) CHARACTER*1
* On entry, TRANS specifies the operation to be performed as
* follows:
*
* TRANS = 'N' or 'n':
* y := abs( alpha )*abs( A )*abs( x )+ abs( beta*y )
*
* TRANS = 'T' or 't':
* y := abs( alpha )*abs( A' )*abs( x ) + abs( beta*y )
*
* TRANS = 'C' or 'c':
* y := abs( alpha )*abs( A' )*abs( x ) + abs( beta*y )
*
* DIAG (input) CHARACTER*1
* On entry, DIAG specifies whether or not A is unit triangular
* as follows:
*
* DIAG = 'U' or 'u' A is assumed to be unit triangular.
*
* DIAG = 'N' or 'n' A is not assumed to be unit triangular.
*
* N (input) INTEGER
* On entry, N specifies the order of the matrix A. N must be at
* least zero.
*
* ALPHA (input) DOUBLE PRECISION
* On entry, ALPHA specifies the real scalar alpha.
*
* A (input) DOUBLE PRECISION array
* On entry, A is an array of dimension (LDA,N). Before entry
* with UPLO = 'U' or 'u', the leading n by n part of the array
* A must contain the upper triangular part of the matrix A and
* the strictly lower triangular part of A is not referenced.
* When UPLO = 'L' or 'l', the leading n by n part of the array
* A must contain the lower triangular part of the matrix A and
* the strictly upper trapezoidal part of A is not referenced.
* Note that when DIAG = 'U' or 'u', the diagonal elements of A
* are not referenced either, but are assumed to be unity.
*
* LDA (input) INTEGER
* On entry, LDA specifies the leading dimension of the array A.
* LDA must be at least max( 1, N ).
*
* X (input) DOUBLE PRECISION array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented
* array X must contain the vector x.
*
* INCX (input) INTEGER
* On entry, INCX specifies the increment for the elements of X.
* INCX must not be zero.
*
* BETA (input) DOUBLE PRECISION
* On entry, BETA specifies the real scalar beta. When BETA is
* supplied as zero then Y need not be set on input.
*
* Y (input/output) DOUBLE PRECISION array of dimension at least
* ( 1 + ( n - 1 )*abs( INCY ) ). Before entry with BETA non-
* zero, the incremented array Y must contain the vector y. On
* exit, the incremented array Y is overwritten by the updated
* vector y.
*
* INCY (input) INTEGER
* On entry, INCY specifies the increment for the elements of Y.
* INCY must not be zero.
*
* -- Written on April 1, 1998 by
* Antoine Petitet, University of Tennessee, Knoxville 37996, USA.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY
LOGICAL NOUNIT
DOUBLE PRECISION ABSX, TALPHA, TEMP
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF ( .NOT.LSAME( UPLO , 'U' ).AND.
$ .NOT.LSAME( UPLO , 'L' ) )THEN
INFO = 1
ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
$ .NOT.LSAME( TRANS, 'T' ).AND.
$ .NOT.LSAME( TRANS, 'C' ) )THEN
INFO = 2
ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND.
$ .NOT.LSAME( DIAG , 'N' ) )THEN
INFO = 3
ELSE IF( N.LT.0 )THEN
INFO = 4
ELSE IF( LDA.LT.MAX( 1, N ) )THEN
INFO = 7
ELSE IF( INCX.EQ.0 )THEN
INFO = 9
ELSE IF( INCY.EQ.0 ) THEN
INFO = 12
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'DATRMV', INFO )
RETURN
END IF
*
* Quick return if possible.
*
IF( ( N.EQ.0 ).OR.
$ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
$ RETURN
*
NOUNIT = LSAME( DIAG , 'N' )
*
* Set up the start points in X and Y.
*
IF( INCX.GT.0 ) THEN
KX = 1
ELSE
KX = 1 - ( N - 1 ) * INCX
END IF
IF( INCY.GT.0 ) THEN
KY = 1
ELSE
KY = 1 - ( N - 1 ) * INCY
END IF
*
* Start the operations. In this version the elements of A are
* accessed sequentially with one pass through A.
*
* First form y := abs( beta*y ).
*
IF( INCY.EQ.1 ) THEN
IF( BETA.EQ.ZERO ) THEN
DO 10, I = 1, N
Y( I ) = ZERO
10 CONTINUE
ELSE IF( BETA.EQ.ONE ) THEN
DO 20, I = 1, N
Y( I ) = ABS( Y( I ) )
20 CONTINUE
ELSE
DO 30, I = 1, N
Y( I ) = ABS( BETA * Y( I ) )
30 CONTINUE
END IF
ELSE
IY = KY
IF( BETA.EQ.ZERO ) THEN
DO 40, I = 1, N
Y( IY ) = ZERO
IY = IY + INCY
40 CONTINUE
ELSE IF( BETA.EQ.ONE ) THEN
DO 50, I = 1, N
Y( IY ) = ABS( Y( IY ) )
IY = IY + INCY
50 CONTINUE
ELSE
DO 60, I = 1, N
Y( IY ) = ABS( BETA * Y( IY ) )
IY = IY + INCY
60 CONTINUE
END IF
END IF
*
IF( ALPHA.EQ.ZERO )
$ RETURN
*
TALPHA = ABS( ALPHA )
*
IF( LSAME( TRANS, 'N' ) )THEN
*
* Form y := abs( alpha ) * abs( A ) * abs( x ) + y.
*
IF( LSAME( UPLO, 'U' ) )THEN
JX = KX
IF( INCY.EQ.1 ) THEN
DO 80, J = 1, N
ABSX = ABS( X( JX ) )
IF( ABSX.NE.ZERO ) THEN
TEMP = TALPHA * ABSX
DO 70, I = 1, J - 1
Y( I ) = Y( I ) + TEMP * ABS( A( I, J ) )
70 CONTINUE
*
IF( NOUNIT ) THEN
Y( J ) = Y( J ) + TEMP * ABS( A( J, J ) )
ELSE
Y( J ) = Y( J ) + TEMP
END IF
END IF
JX = JX + INCX
80 CONTINUE
*
ELSE
*
DO 100, J = 1, N
ABSX = ABS( X( JX ) )
IF( ABSX.NE.ZERO ) THEN
TEMP = TALPHA * ABSX
IY = KY
DO 90, I = 1, J - 1
Y( IY ) = Y( IY ) + TEMP * ABS( A( I, J ) )
IY = IY + INCY
90 CONTINUE
*
IF( NOUNIT ) THEN
Y( IY ) = Y( IY ) + TEMP * ABS( A( J, J ) )
ELSE
Y( IY ) = Y( IY ) + TEMP
END IF
END IF
JX = JX + INCX
100 CONTINUE
*
END IF
*
ELSE
*
JX = KX
IF( INCY.EQ.1 ) THEN
DO 120, J = 1, N
ABSX = ABS( X( JX ) )
IF( ABSX.NE.ZERO ) THEN
*
TEMP = TALPHA * ABSX
*
IF( NOUNIT ) THEN
Y( J ) = Y( J ) + TEMP * ABS( A( J, J ) )
ELSE
Y( J ) = Y( J ) + TEMP
END IF
*
DO 110, I = J + 1, N
Y( I ) = Y( I ) + TEMP * ABS( A( I, J ) )
110 CONTINUE
END IF
JX = JX + INCX
120 CONTINUE
*
ELSE
*
DO 140, J = 1, N
ABSX = ABS( X( JX ) )
IF( ABSX.NE.ZERO ) THEN
TEMP = TALPHA * ABSX
IY = KY + ( J - 1 ) * INCY
*
IF( NOUNIT ) THEN
Y( IY ) = Y( IY ) + TEMP * ABS( A( J, J ) )
ELSE
Y( IY ) = Y( IY ) + TEMP
END IF
*
DO 130, I = J + 1, N
IY = IY + INCY
Y( IY ) = Y( IY ) + TEMP * ABS( A( I, J ) )
130 CONTINUE
END IF
JX = JX + INCX
140 CONTINUE
*
END IF
*
END IF
*
ELSE
*
* Form y := abs( alpha ) * abs( A' ) * abs( x ) + y.
*
IF( LSAME( UPLO, 'U' ) )THEN
JY = KY
IF( INCX.EQ.1 ) THEN
DO 160, J = 1, N
*
TEMP = ZERO
*
DO 150, I = 1, J - 1
TEMP = TEMP + ABS( A( I, J ) * X( I ) )
150 CONTINUE
*
IF( NOUNIT ) THEN
TEMP = TEMP + ABS( A( J, J ) * X( J ) )
ELSE
TEMP = TEMP + ABS( X( J ) )
END IF
*
Y( JY ) = Y( JY ) + TALPHA * TEMP
JY = JY + INCY
*
160 CONTINUE
*
ELSE
*
DO 180, J = 1, N
TEMP = ZERO
IX = KX
DO 170, I = 1, J - 1
TEMP = TEMP + ABS( A( I, J ) * X( IX ) )
IX = IX + INCX
170 CONTINUE
*
IF( NOUNIT ) THEN
TEMP = TEMP + ABS( A( J, J ) * X( IX ) )
ELSE
TEMP = TEMP + ABS( X( IX ) )
END IF
*
Y( JY ) = Y( JY ) + TALPHA * TEMP
JY = JY + INCY
*
180 CONTINUE
*
END IF
*
ELSE
*
JY = KY
IF( INCX.EQ.1 ) THEN
*
DO 200, J = 1, N
*
IF( NOUNIT ) THEN
TEMP = ABS( A( J, J ) * X( J ) )
ELSE
TEMP = ABS( X( J ) )
END IF
*
DO 190, I = J + 1, N
TEMP = TEMP + ABS( A( I, J ) * X( I ) )
190 CONTINUE
*
Y( JY ) = Y( JY ) + TALPHA * TEMP
JY = JY + INCY
*
200 CONTINUE
*
ELSE
*
DO 220, J = 1, N
*
IX = KX + ( J - 1 ) * INCX
*
IF( NOUNIT ) THEN
TEMP = ABS( A( J, J ) * X( IX ) )
ELSE
TEMP = ABS( X( IX ) )
END IF
*
DO 210, I = J + 1, N
IX = IX + INCX
TEMP = TEMP + ABS( A( I, J ) * X( IX ) )
210 CONTINUE
Y( JY ) = Y( JY ) + TALPHA * TEMP
JY = JY + INCY
220 CONTINUE
END IF
END IF
*
END IF
*
RETURN
*
* End of DATRMV
*
END
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