| SUBROUTINE DTRSMF ( 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 |
