| SUBROUTINE CTRMMF ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, |
| $ B, LDB ) |
| * .. Scalar Arguments .. |
| CHARACTER*1 SIDE, UPLO, TRANSA, DIAG |
| INTEGER M, N, LDA, LDB |
| COMPLEX ALPHA |
| * .. Array Arguments .. |
| COMPLEX A( LDA, * ), B( LDB, * ) |
| * .. |
| * |
| * Purpose |
| * ======= |
| * |
| * CTRMM performs one of the matrix-matrix operations |
| * |
| * B := alpha*op( A )*B, or B := alpha*B*op( A ) |
| * |
| * where alpha is a scalar, B is an m by n matrix, 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' or op( A ) = conjg( A' ). |
| * |
| * Parameters |
| * ========== |
| * |
| * SIDE - CHARACTER*1. |
| * On entry, SIDE specifies whether op( A ) multiplies B from |
| * the left or right as follows: |
| * |
| * SIDE = 'L' or 'l' B := alpha*op( A )*B. |
| * |
| * SIDE = 'R' or 'r' B := alpha*B*op( A ). |
| * |
| * 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 ) = conjg( 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 - COMPLEX . |
| * 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 - COMPLEX 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 - COMPLEX array of DIMENSION ( LDB, n ). |
| * Before entry, the leading m by n part of the array B must |
| * contain the matrix B, and on exit is overwritten by the |
| * transformed matrix. |
| * |
| * 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 CONJG, MAX |
| * .. Local Scalars .. |
| LOGICAL LSIDE, NOCONJ, NOUNIT, UPPER |
| INTEGER I, INFO, J, K, NROWA |
| COMPLEX TEMP |
| * .. Parameters .. |
| COMPLEX ONE |
| PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) |
| COMPLEX ZERO |
| PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) |
| * .. |
| * .. Executable Statements .. |
| * |
| * Test the input parameters. |
| * |
| LSIDE = LSAME( SIDE , 'L' ) |
| IF( LSIDE )THEN |
| NROWA = M |
| ELSE |
| NROWA = N |
| END IF |
| NOCONJ = LSAME( TRANSA, 'N' ) .OR. LSAME( TRANSA, 'T' ) |
| 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, 'R' ) ).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( 'CTRMM ', 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' ) .OR. LSAME( TRANSA, 'R' ))THEN |
| * |
| * Form B := alpha*A*B. |
| * |
| IF( UPPER )THEN |
| DO 50, J = 1, N |
| DO 40, K = 1, M |
| IF( B( K, J ).NE.ZERO )THEN |
| TEMP = ALPHA*B( K, J ) |
| IF (NOCONJ) THEN |
| DO 30, I = 1, K - 1 |
| B( I, J ) = B( I, J ) + TEMP*A( I, K ) |
| 30 CONTINUE |
| IF( NOUNIT ) |
| $ TEMP = TEMP*A( K, K ) |
| B( K, J ) = TEMP |
| ELSE |
| DO 35, I = 1, K - 1 |
| B( I, J ) = B( I, J ) + TEMP*CONJG(A( I, K )) |
| 35 CONTINUE |
| IF( NOUNIT ) |
| $ TEMP = TEMP*CONJG(A( K, K )) |
| B( K, J ) = TEMP |
| ENDIF |
| END IF |
| 40 CONTINUE |
| 50 CONTINUE |
| ELSE |
| DO 80, J = 1, N |
| DO 70 K = M, 1, -1 |
| IF( B( K, J ).NE.ZERO )THEN |
| TEMP = ALPHA*B( K, J ) |
| B( K, J ) = TEMP |
| IF (NOCONJ) THEN |
| IF( NOUNIT ) |
| $ B( K, J ) = B( K, J )*A( K, K ) |
| DO 60, I = K + 1, M |
| B( I, J ) = B( I, J ) + TEMP*A( I, K ) |
| 60 CONTINUE |
| ELSE |
| IF( NOUNIT ) |
| $ B( K, J ) = B( K, J )*CONJG(A( K, K )) |
| DO 65, I = K + 1, M |
| B( I, J ) = B( I, J ) + TEMP*CONJG(A( I, K )) |
| 65 CONTINUE |
| ENDIF |
| END IF |
| 70 CONTINUE |
| 80 CONTINUE |
| END IF |
| ELSE |
| * |
| * Form B := alpha*A'*B or B := alpha*conjg( A' )*B. |
| * |
| IF( UPPER )THEN |
| DO 120, J = 1, N |
| DO 110, I = M, 1, -1 |
| TEMP = B( I, J ) |
| IF( NOCONJ )THEN |
| IF( NOUNIT ) |
| $ TEMP = TEMP*A( I, I ) |
| DO 90, K = 1, I - 1 |
| TEMP = TEMP + A( K, I )*B( K, J ) |
| 90 CONTINUE |
| ELSE |
| IF( NOUNIT ) |
| $ TEMP = TEMP*CONJG( A( I, I ) ) |
| DO 100, K = 1, I - 1 |
| TEMP = TEMP + CONJG( A( K, I ) )*B( K, J ) |
| 100 CONTINUE |
| END IF |
| B( I, J ) = ALPHA*TEMP |
| 110 CONTINUE |
| 120 CONTINUE |
| ELSE |
| DO 160, J = 1, N |
| DO 150, I = 1, M |
| TEMP = B( I, J ) |
| IF( NOCONJ )THEN |
| IF( NOUNIT ) |
| $ TEMP = TEMP*A( I, I ) |
| DO 130, K = I + 1, M |
| TEMP = TEMP + A( K, I )*B( K, J ) |
| 130 CONTINUE |
| ELSE |
| IF( NOUNIT ) |
| $ TEMP = TEMP*CONJG( A( I, I ) ) |
| DO 140, K = I + 1, M |
| TEMP = TEMP + CONJG( A( K, I ) )*B( K, J ) |
| 140 CONTINUE |
| END IF |
| B( I, J ) = ALPHA*TEMP |
| 150 CONTINUE |
| 160 CONTINUE |
| END IF |
| END IF |
| ELSE |
| IF( LSAME( TRANSA, 'N' ) .OR. LSAME( TRANSA, 'R' ))THEN |
| * |
| * Form B := alpha*B*A. |
| * |
| IF( UPPER )THEN |
| DO 200, J = N, 1, -1 |
| TEMP = ALPHA |
| IF (NOCONJ) THEN |
| IF( NOUNIT ) |
| $ TEMP = TEMP*A( J, J ) |
| ELSE |
| IF( NOUNIT ) |
| $ TEMP = TEMP*CONJG(A( J, J )) |
| ENDIF |
| DO 170, I = 1, M |
| B( I, J ) = TEMP*B( I, J ) |
| 170 CONTINUE |
| DO 190, K = 1, J - 1 |
| IF( A( K, J ).NE.ZERO )THEN |
| IF (NOCONJ) THEN |
| TEMP = ALPHA*A( K, J ) |
| ELSE |
| TEMP = ALPHA*CONJG(A( K, J )) |
| ENDIF |
| DO 180, I = 1, M |
| B( I, J ) = B( I, J ) + TEMP*B( I, K ) |
| 180 CONTINUE |
| END IF |
| 190 CONTINUE |
| 200 CONTINUE |
| ELSE |
| DO 240, J = 1, N |
| TEMP = ALPHA |
| IF (NOCONJ) THEN |
| IF( NOUNIT ) |
| $ TEMP = TEMP*A( J, J ) |
| ELSE |
| IF( NOUNIT ) |
| $ TEMP = TEMP*CONJG(A( J, J )) |
| ENDIF |
| DO 210, I = 1, M |
| B( I, J ) = TEMP*B( I, J ) |
| 210 CONTINUE |
| DO 230, K = J + 1, N |
| IF( A( K, J ).NE.ZERO )THEN |
| IF (NOCONJ) THEN |
| TEMP = ALPHA*A( K, J ) |
| ELSE |
| TEMP = ALPHA*CONJG(A( K, J )) |
| ENDIF |
| DO 220, I = 1, M |
| B( I, J ) = B( I, J ) + TEMP*B( I, K ) |
| 220 CONTINUE |
| END IF |
| 230 CONTINUE |
| 240 CONTINUE |
| END IF |
| ELSE |
| * |
| * Form B := alpha*B*A' or B := alpha*B*conjg( A' ). |
| * |
| IF( UPPER )THEN |
| DO 280, K = 1, N |
| DO 260, J = 1, K - 1 |
| IF( A( J, K ).NE.ZERO )THEN |
| IF( NOCONJ )THEN |
| TEMP = ALPHA*A( J, K ) |
| ELSE |
| TEMP = ALPHA*CONJG( A( J, K ) ) |
| END IF |
| DO 250, I = 1, M |
| B( I, J ) = B( I, J ) + TEMP*B( I, K ) |
| 250 CONTINUE |
| END IF |
| 260 CONTINUE |
| TEMP = ALPHA |
| IF( NOUNIT )THEN |
| IF( NOCONJ )THEN |
| TEMP = TEMP*A( K, K ) |
| ELSE |
| TEMP = TEMP*CONJG( A( K, K ) ) |
| END IF |
| END IF |
| IF( TEMP.NE.ONE )THEN |
| DO 270, I = 1, M |
| B( I, K ) = TEMP*B( I, K ) |
| 270 CONTINUE |
| END IF |
| 280 CONTINUE |
| ELSE |
| DO 320, K = N, 1, -1 |
| DO 300, J = K + 1, N |
| IF( A( J, K ).NE.ZERO )THEN |
| IF( NOCONJ )THEN |
| TEMP = ALPHA*A( J, K ) |
| ELSE |
| TEMP = ALPHA*CONJG( A( J, K ) ) |
| END IF |
| DO 290, I = 1, M |
| B( I, J ) = B( I, J ) + TEMP*B( I, K ) |
| 290 CONTINUE |
| END IF |
| 300 CONTINUE |
| TEMP = ALPHA |
| IF( NOUNIT )THEN |
| IF( NOCONJ )THEN |
| TEMP = TEMP*A( K, K ) |
| ELSE |
| TEMP = TEMP*CONJG( A( K, K ) ) |
| END IF |
| END IF |
| IF( TEMP.NE.ONE )THEN |
| DO 310, I = 1, M |
| B( I, K ) = TEMP*B( I, K ) |
| 310 CONTINUE |
| END IF |
| 320 CONTINUE |
| END IF |
| END IF |
| END IF |
| * |
| RETURN |
| * |
| * End of CTRMM . |
| * |
| END |
