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dtrsm.f
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dtrsm.f
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SUBROUTINE DTRSM ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA,
$ B, LDB )
* .. SCALAR ARGUMENTS ..
CHARACTER*1 SIDE, UPLO, TRANSA, DIAG
INTEGER M, N, LDA, LDB
DOUBLE PRECISION ALPHA
* .. ARRAY ARGUMENTS ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * )
* ..
*
* PURPOSE
* =======
*
* DTRSM SOLVES ONE OF THE MATRIX EQUATIONS
*
* OP( A )*X = ALPHA*B, OR X*OP( A ) = ALPHA*B,
*
* WHERE ALPHA IS A SCALAR, X AND B ARE M BY N MATRICES, A IS A UNIT, OR
* NON-UNIT, UPPER OR LOWER TRIANGULAR MATRIX AND OP( A ) IS ONE OF
*
* OP( A ) = A OR OP( A ) = A'.
*
* THE MATRIX X IS OVERWRITTEN ON B.
*
* PARAMETERS
* ==========
*
* SIDE - CHARACTER*1.
* ON ENTRY, SIDE SPECIFIES WHETHER OP( A ) APPEARS ON THE LEFT
* OR RIGHT OF X AS FOLLOWS:
*
* SIDE = 'L' OR 'L' OP( A )*X = ALPHA*B.
*
* SIDE = 'R' OR 'R' X*OP( A ) = ALPHA*B.
*
* UNCHANGED ON EXIT.
*
* UPLO - CHARACTER*1.
* ON ENTRY, UPLO SPECIFIES WHETHER THE MATRIX A 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.
*
* UNCHANGED ON EXIT.
*
* TRANSA - CHARACTER*1.
* ON ENTRY, TRANSA SPECIFIES THE FORM OF OP( A ) TO BE USED IN
* THE MATRIX MULTIPLICATION AS FOLLOWS:
*
* TRANSA = 'N' OR 'N' OP( A ) = A.
*
* TRANSA = 'T' OR 'T' OP( A ) = A'.
*
* TRANSA = 'C' OR 'C' OP( A ) = A'.
*
* UNCHANGED ON EXIT.
*
* DIAG - 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.
*
* UNCHANGED ON EXIT.
*
* M - INTEGER.
* ON ENTRY, M SPECIFIES THE NUMBER OF ROWS OF B. M MUST BE AT
* LEAST ZERO.
* UNCHANGED ON EXIT.
*
* N - INTEGER.
* ON ENTRY, N SPECIFIES THE NUMBER OF COLUMNS OF B. N MUST BE
* AT LEAST ZERO.
* UNCHANGED ON EXIT.
*
* ALPHA - DOUBLE PRECISION.
* ON ENTRY, ALPHA SPECIFIES THE SCALAR ALPHA. WHEN ALPHA IS
* ZERO THEN A IS NOT REFERENCED AND B NEED NOT BE SET BEFORE
* ENTRY.
* UNCHANGED ON EXIT.
*
* A - DOUBLE PRECISION ARRAY OF DIMENSION ( LDA, K ), WHERE K IS M
* WHEN SIDE = 'L' OR 'L' AND IS N WHEN SIDE = 'R' OR 'R'.
* BEFORE ENTRY WITH UPLO = 'U' OR 'U', THE LEADING K BY K
* UPPER TRIANGULAR PART OF THE ARRAY A MUST CONTAIN THE UPPER
* TRIANGULAR MATRIX AND THE STRICTLY LOWER TRIANGULAR PART OF
* A IS NOT REFERENCED.
* BEFORE ENTRY WITH UPLO = 'L' OR 'L', THE LEADING K BY K
* LOWER TRIANGULAR PART OF THE ARRAY A MUST CONTAIN THE LOWER
* TRIANGULAR MATRIX AND THE STRICTLY UPPER TRIANGULAR 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.
* UNCHANGED ON EXIT.
*
* LDA - INTEGER.
* ON ENTRY, LDA SPECIFIES THE FIRST DIMENSION OF A AS DECLARED
* IN THE CALLING (SUB) PROGRAM. WHEN SIDE = 'L' OR 'L' THEN
* LDA MUST BE AT LEAST MAX( 1, M ), WHEN SIDE = 'R' OR 'R'
* THEN LDA MUST BE AT LEAST MAX( 1, N ).
* UNCHANGED ON EXIT.
*
* B - DOUBLE PRECISION ARRAY OF DIMENSION ( LDB, N ).
* BEFORE ENTRY, THE LEADING M BY N PART OF THE ARRAY B MUST
* CONTAIN THE RIGHT-HAND SIDE MATRIX B, AND ON EXIT IS
* OVERWRITTEN BY THE SOLUTION MATRIX X.
*
* LDB - INTEGER.
* ON ENTRY, LDB SPECIFIES THE FIRST DIMENSION OF B AS DECLARED
* IN THE CALLING (SUB) PROGRAM. LDB MUST BE AT LEAST
* MAX( 1, M ).
* UNCHANGED ON EXIT.
*
*
* LEVEL 3 BLAS ROUTINE.
*
*
* -- WRITTEN ON 8-FEBRUARY-1989.
* JACK DONGARRA, ARGONNE NATIONAL LABORATORY.
* IAIN DUFF, AERE HARWELL.
* JEREMY DU CROZ, NUMERICAL ALGORITHMS GROUP LTD.
* SVEN HAMMARLING, NUMERICAL ALGORITHMS GROUP LTD.
*
*
* .. EXTERNAL FUNCTIONS ..
LOGICAL LSAME
EXTERNAL LSAME
* .. EXTERNAL SUBROUTINES ..
EXTERNAL XERBLA
* .. INTRINSIC FUNCTIONS ..
INTRINSIC MAX
* .. LOCAL SCALARS ..
LOGICAL LSIDE, NOUNIT, UPPER
INTEGER I, INFO, J, K, NROWA
DOUBLE PRECISION TEMP
* .. PARAMETERS ..
DOUBLE PRECISION ONE , ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. EXECUTABLE STATEMENTS ..
*
* TEST THE INPUT PARAMETERS.
*
LSIDE = LSAME( SIDE , 'L' )
IF( LSIDE )THEN
NROWA = M
ELSE
NROWA = N
END IF
NOUNIT = LSAME( DIAG , 'N' )
UPPER = LSAME( UPLO , 'U' )
*
INFO = 0
IF( ( .NOT.LSIDE ).AND.
$ ( .NOT.LSAME( SIDE , 'R' ) ) )THEN
INFO = 1
ELSE IF( ( .NOT.UPPER ).AND.
$ ( .NOT.LSAME( UPLO , 'L' ) ) )THEN
INFO = 2
ELSE IF( ( .NOT.LSAME( TRANSA, 'N' ) ).AND.
$ ( .NOT.LSAME( TRANSA, 'T' ) ).AND.
$ ( .NOT.LSAME( TRANSA, 'C' ) ) )THEN
INFO = 3
ELSE IF( ( .NOT.LSAME( DIAG , 'U' ) ).AND.
$ ( .NOT.LSAME( DIAG , 'N' ) ) )THEN
INFO = 4
ELSE IF( M .LT.0 )THEN
INFO = 5
ELSE IF( N .LT.0 )THEN
INFO = 6
ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
INFO = 9
ELSE IF( LDB.LT.MAX( 1, M ) )THEN
INFO = 11
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'DTRSM ', INFO )
RETURN
END IF
*
* QUICK RETURN IF POSSIBLE.
*
IF( N.EQ.0 )
$ RETURN
*
* AND WHEN ALPHA.EQ.ZERO.
*
IF( ALPHA.EQ.ZERO )THEN
DO 20, J = 1, N
DO 10, I = 1, M
B( I, J ) = ZERO
10 CONTINUE
20 CONTINUE
RETURN
END IF
*
* START THE OPERATIONS.
*
IF( LSIDE )THEN
IF( LSAME( TRANSA, 'N' ) )THEN
*
* FORM B := ALPHA*INV( A )*B.
*
IF( UPPER )THEN
DO 60, J = 1, N
IF( ALPHA.NE.ONE )THEN
DO 30, I = 1, M
B( I, J ) = ALPHA*B( I, J )
30 CONTINUE
END IF
DO 50, K = M, 1, -1
IF( B( K, J ).NE.ZERO )THEN
IF( NOUNIT )
$ B( K, J ) = B( K, J )/A( K, K )
DO 40, I = 1, K - 1
B( I, J ) = B( I, J ) - B( K, J )*A( I, K )
40 CONTINUE
END IF
50 CONTINUE
60 CONTINUE
ELSE
DO 100, J = 1, N
IF( ALPHA.NE.ONE )THEN
DO 70, I = 1, M
B( I, J ) = ALPHA*B( I, J )
70 CONTINUE
END IF
DO 90 K = 1, M
IF( B( K, J ).NE.ZERO )THEN
IF( NOUNIT )
$ B( K, J ) = B( K, J )/A( K, K )
DO 80, I = K + 1, M
B( I, J ) = B( I, J ) - B( K, J )*A( I, K )
80 CONTINUE
END IF
90 CONTINUE
100 CONTINUE
END IF
ELSE
*
* FORM B := ALPHA*INV( A' )*B.
*
IF( UPPER )THEN
DO 130, J = 1, N
DO 120, I = 1, M
TEMP = ALPHA*B( I, J )
DO 110, K = 1, I - 1
TEMP = TEMP - A( K, I )*B( K, J )
110 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/A( I, I )
B( I, J ) = TEMP
120 CONTINUE
130 CONTINUE
ELSE
DO 160, J = 1, N
DO 150, I = M, 1, -1
TEMP = ALPHA*B( I, J )
DO 140, K = I + 1, M
TEMP = TEMP - A( K, I )*B( K, J )
140 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/A( I, I )
B( I, J ) = TEMP
150 CONTINUE
160 CONTINUE
END IF
END IF
ELSE
IF( LSAME( TRANSA, 'N' ) )THEN
*
* FORM B := ALPHA*B*INV( A ).
*
IF( UPPER )THEN
DO 210, J = 1, N
IF( ALPHA.NE.ONE )THEN
DO 170, I = 1, M
B( I, J ) = ALPHA*B( I, J )
170 CONTINUE
END IF
DO 190, K = 1, J - 1
IF( A( K, J ).NE.ZERO )THEN
DO 180, I = 1, M
B( I, J ) = B( I, J ) - A( K, J )*B( I, K )
180 CONTINUE
END IF
190 CONTINUE
IF( NOUNIT )THEN
TEMP = ONE/A( J, J )
DO 200, I = 1, M
B( I, J ) = TEMP*B( I, J )
200 CONTINUE
END IF
210 CONTINUE
ELSE
DO 260, J = N, 1, -1
IF( ALPHA.NE.ONE )THEN
DO 220, I = 1, M
B( I, J ) = ALPHA*B( I, J )
220 CONTINUE
END IF
DO 240, K = J + 1, N
IF( A( K, J ).NE.ZERO )THEN
DO 230, I = 1, M
B( I, J ) = B( I, J ) - A( K, J )*B( I, K )
230 CONTINUE
END IF
240 CONTINUE
IF( NOUNIT )THEN
TEMP = ONE/A( J, J )
DO 250, I = 1, M
B( I, J ) = TEMP*B( I, J )
250 CONTINUE
END IF
260 CONTINUE
END IF
ELSE
*
* FORM B := ALPHA*B*INV( A' ).
*
IF( UPPER )THEN
DO 310, K = N, 1, -1
IF( NOUNIT )THEN
TEMP = ONE/A( K, K )
DO 270, I = 1, M
B( I, K ) = TEMP*B( I, K )
270 CONTINUE
END IF
DO 290, J = 1, K - 1
IF( A( J, K ).NE.ZERO )THEN
TEMP = A( J, K )
DO 280, I = 1, M
B( I, J ) = B( I, J ) - TEMP*B( I, K )
280 CONTINUE
END IF
290 CONTINUE
IF( ALPHA.NE.ONE )THEN
DO 300, I = 1, M
B( I, K ) = ALPHA*B( I, K )
300 CONTINUE
END IF
310 CONTINUE
ELSE
DO 360, K = 1, N
IF( NOUNIT )THEN
TEMP = ONE/A( K, K )
DO 320, I = 1, M
B( I, K ) = TEMP*B( I, K )
320 CONTINUE
END IF
DO 340, J = K + 1, N
IF( A( J, K ).NE.ZERO )THEN
TEMP = A( J, K )
DO 330, I = 1, M
B( I, J ) = B( I, J ) - TEMP*B( I, K )
330 CONTINUE
END IF
340 CONTINUE
IF( ALPHA.NE.ONE )THEN
DO 350, I = 1, M
B( I, K ) = ALPHA*B( I, K )
350 CONTINUE
END IF
360 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* END OF DTRSM .
*
END