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SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) |
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* .. Scalar Arguments .. |
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DOUBLE PRECISION ALPHA |
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INTEGER LDA,LDB,M,N |
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CHARACTER DIAG,SIDE,TRANSA,UPLO |
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* .. |
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* .. Array Arguments .. |
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DOUBLE PRECISION A(LDA,*),B(LDB,*) |
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* .. |
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* |
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* Purpose |
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* ======= |
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* |
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* DTRSM solves one of the matrix equations |
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* |
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* op( A )*X = alpha*B, or X*op( A ) = alpha*B, |
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* |
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* where alpha is a scalar, X and B are m by n matrices, A is a unit, or |
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* non-unit, upper or lower triangular matrix and op( A ) is one of |
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* |
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* op( A ) = A or op( A ) = A'. |
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* |
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* The matrix X is overwritten on B. |
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* |
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* Arguments |
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* ========== |
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* |
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* SIDE - CHARACTER*1. |
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* On entry, SIDE specifies whether op( A ) appears on the left |
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* or right of X as follows: |
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* |
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* SIDE = 'L' or 'l' op( A )*X = alpha*B. |
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* |
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* SIDE = 'R' or 'r' X*op( A ) = alpha*B. |
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* |
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* Unchanged on exit. |
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* |
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* UPLO - CHARACTER*1. |
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* On entry, UPLO specifies whether the matrix A is an upper or |
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* lower triangular matrix as follows: |
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* |
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* UPLO = 'U' or 'u' A is an upper triangular matrix. |
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* |
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* UPLO = 'L' or 'l' A is a lower triangular matrix. |
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* |
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* Unchanged on exit. |
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* |
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* TRANSA - CHARACTER*1. |
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* On entry, TRANSA specifies the form of op( A ) to be used in |
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* the matrix multiplication as follows: |
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* |
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* TRANSA = 'N' or 'n' op( A ) = A. |
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* |
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* TRANSA = 'T' or 't' op( A ) = A'. |
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* |
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* TRANSA = 'C' or 'c' op( A ) = A'. |
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* |
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* Unchanged on exit. |
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* |
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* DIAG - CHARACTER*1. |
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* On entry, DIAG specifies whether or not A is unit triangular |
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* as follows: |
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* |
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* DIAG = 'U' or 'u' A is assumed to be unit triangular. |
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* |
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* DIAG = 'N' or 'n' A is not assumed to be unit |
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* triangular. |
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* |
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* Unchanged on exit. |
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* |
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* M - INTEGER. |
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* On entry, M specifies the number of rows of B. M must be at |
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* least zero. |
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* Unchanged on exit. |
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* |
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* N - INTEGER. |
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* On entry, N specifies the number of columns of B. N must be |
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* at least zero. |
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* Unchanged on exit. |
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* |
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* ALPHA - DOUBLE PRECISION. |
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* On entry, ALPHA specifies the scalar alpha. When alpha is |
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* zero then A is not referenced and B need not be set before |
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* entry. |
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* Unchanged on exit. |
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* |
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* A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m |
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* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. |
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* Before entry with UPLO = 'U' or 'u', the leading k by k |
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* upper triangular part of the array A must contain the upper |
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* triangular matrix and the strictly lower triangular part of |
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* A is not referenced. |
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* Before entry with UPLO = 'L' or 'l', the leading k by k |
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* lower triangular part of the array A must contain the lower |
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* triangular matrix and the strictly upper triangular part of |
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* A is not referenced. |
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* Note that when DIAG = 'U' or 'u', the diagonal elements of |
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* A are not referenced either, but are assumed to be unity. |
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* Unchanged on exit. |
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* |
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* LDA - INTEGER. |
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* On entry, LDA specifies the first dimension of A as declared |
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* in the calling (sub) program. When SIDE = 'L' or 'l' then |
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* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' |
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* then LDA must be at least max( 1, n ). |
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* Unchanged on exit. |
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* |
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* B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). |
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* Before entry, the leading m by n part of the array B must |
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* contain the right-hand side matrix B, and on exit is |
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* overwritten by the solution matrix X. |
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* |
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* LDB - INTEGER. |
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* On entry, LDB specifies the first dimension of B as declared |
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* in the calling (sub) program. LDB must be at least |
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* max( 1, m ). |
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* Unchanged on exit. |
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* |
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* |
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* Level 3 Blas routine. |
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* |
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* |
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* -- Written on 8-February-1989. |
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* Jack Dongarra, Argonne National Laboratory. |
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* Iain Duff, AERE Harwell. |
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* Jeremy Du Croz, Numerical Algorithms Group Ltd. |
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* Sven Hammarling, Numerical Algorithms Group Ltd. |
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* |
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* |
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* .. External Functions .. |
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LOGICAL LSAME |
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EXTERNAL LSAME |
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* .. |
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* .. External Subroutines .. |
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EXTERNAL XERBLA |
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* .. |
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* .. Intrinsic Functions .. |
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INTRINSIC MAX |
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* .. |
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* .. Local Scalars .. |
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DOUBLE PRECISION TEMP |
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INTEGER I,INFO,J,K,NROWA |
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LOGICAL LSIDE,NOUNIT,UPPER |
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* .. |
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* .. Parameters .. |
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DOUBLE PRECISION ONE,ZERO |
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PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) |
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* .. |
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* |
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* Test the input parameters. |
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* |
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LSIDE = LSAME(SIDE,'L') |
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IF (LSIDE) THEN |
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NROWA = M |
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ELSE |
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NROWA = N |
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END IF |
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NOUNIT = LSAME(DIAG,'N') |
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UPPER = LSAME(UPLO,'U') |
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* |
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INFO = 0 |
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IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN |
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INFO = 1 |
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ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN |
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INFO = 2 |
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ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND. |
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+ (.NOT.LSAME(TRANSA,'T')) .AND. |
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+ (.NOT.LSAME(TRANSA,'C'))) THEN |
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INFO = 3 |
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ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN |
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INFO = 4 |
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ELSE IF (M.LT.0) THEN |
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INFO = 5 |
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ELSE IF (N.LT.0) THEN |
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INFO = 6 |
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ELSE IF (LDA.LT.MAX(1,NROWA)) THEN |
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INFO = 9 |
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ELSE IF (LDB.LT.MAX(1,M)) THEN |
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INFO = 11 |
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END IF |
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IF (INFO.NE.0) THEN |
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CALL XERBLA('DTRSM ',INFO)
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RETURN |
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END IF |
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* |
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* Quick return if possible. |
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* |
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IF (M.EQ.0 .OR. N.EQ.0) RETURN |
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* |
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* And when alpha.eq.zero. |
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* |
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IF (ALPHA.EQ.ZERO) THEN |
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DO 20 J = 1,N |
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DO 10 I = 1,M |
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B(I,J) = ZERO |
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10 CONTINUE |
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20 CONTINUE |
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RETURN |
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END IF |
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* |
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* Start the operations. |
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* |
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IF (LSIDE) THEN |
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IF (LSAME(TRANSA,'N')) THEN |
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* |
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* Form B := alpha*inv( A )*B. |
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* |
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IF (UPPER) THEN |
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DO 60 J = 1,N |
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IF (ALPHA.NE.ONE) THEN |
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DO 30 I = 1,M |
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B(I,J) = ALPHA*B(I,J) |
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30 CONTINUE |
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END IF |
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DO 50 K = M,1,-1 |
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IF (B(K,J).NE.ZERO) THEN |
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IF (NOUNIT) B(K,J) = B(K,J)/A(K,K) |
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DO 40 I = 1,K - 1 |
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B(I,J) = B(I,J) - B(K,J)*A(I,K) |
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40 CONTINUE |
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END IF |
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50 CONTINUE |
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60 CONTINUE |
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ELSE |
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DO 100 J = 1,N |
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IF (ALPHA.NE.ONE) THEN |
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DO 70 I = 1,M |
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B(I,J) = ALPHA*B(I,J) |
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70 CONTINUE |
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END IF |
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DO 90 K = 1,M |
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IF (B(K,J).NE.ZERO) THEN |
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IF (NOUNIT) B(K,J) = B(K,J)/A(K,K) |
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DO 80 I = K + 1,M |
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B(I,J) = B(I,J) - B(K,J)*A(I,K) |
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80 CONTINUE |
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END IF |
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90 CONTINUE |
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100 CONTINUE |
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END IF |
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ELSE |
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* |
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* Form B := alpha*inv( A' )*B. |
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* |
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IF (UPPER) THEN |
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DO 130 J = 1,N |
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DO 120 I = 1,M |
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TEMP = ALPHA*B(I,J) |
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DO 110 K = 1,I - 1 |
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TEMP = TEMP - A(K,I)*B(K,J) |
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110 CONTINUE |
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IF (NOUNIT) TEMP = TEMP/A(I,I) |
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B(I,J) = TEMP |
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120 CONTINUE |
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130 CONTINUE |
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ELSE |
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DO 160 J = 1,N |
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DO 150 I = M,1,-1 |
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TEMP = ALPHA*B(I,J) |
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DO 140 K = I + 1,M |
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TEMP = TEMP - A(K,I)*B(K,J) |
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140 CONTINUE |
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IF (NOUNIT) TEMP = TEMP/A(I,I) |
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B(I,J) = TEMP |
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150 CONTINUE |
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160 CONTINUE |
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END IF |
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END IF |
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ELSE |
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IF (LSAME(TRANSA,'N')) THEN |
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* |
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* Form B := alpha*B*inv( A ). |
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* |
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IF (UPPER) THEN |
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DO 210 J = 1,N |
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IF (ALPHA.NE.ONE) THEN |
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DO 170 I = 1,M |
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B(I,J) = ALPHA*B(I,J) |
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170 CONTINUE |
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END IF |
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DO 190 K = 1,J - 1 |
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IF (A(K,J).NE.ZERO) THEN |
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DO 180 I = 1,M |
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B(I,J) = B(I,J) - A(K,J)*B(I,K) |
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180 CONTINUE |
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END IF |
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190 CONTINUE |
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IF (NOUNIT) THEN |
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TEMP = ONE/A(J,J) |
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DO 200 I = 1,M |
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B(I,J) = TEMP*B(I,J) |
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200 CONTINUE |
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END IF |
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210 CONTINUE |
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ELSE |
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DO 260 J = N,1,-1 |
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IF (ALPHA.NE.ONE) THEN |
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DO 220 I = 1,M |
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B(I,J) = ALPHA*B(I,J) |
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220 CONTINUE |
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END IF |
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DO 240 K = J + 1,N |
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IF (A(K,J).NE.ZERO) THEN |
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DO 230 I = 1,M |
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B(I,J) = B(I,J) - A(K,J)*B(I,K) |
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230 CONTINUE |
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END IF |
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240 CONTINUE |
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IF (NOUNIT) THEN |
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TEMP = ONE/A(J,J) |
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DO 250 I = 1,M |
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B(I,J) = TEMP*B(I,J) |
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250 CONTINUE |
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END IF |
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260 CONTINUE |
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END IF |
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ELSE |
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* |
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* Form B := alpha*B*inv( A' ). |
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* |
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IF (UPPER) THEN |
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DO 310 K = N,1,-1 |
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IF (NOUNIT) THEN |
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TEMP = ONE/A(K,K) |
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DO 270 I = 1,M |
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B(I,K) = TEMP*B(I,K) |
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270 CONTINUE |
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END IF |
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DO 290 J = 1,K - 1 |
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IF (A(J,K).NE.ZERO) THEN |
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TEMP = A(J,K) |
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DO 280 I = 1,M |
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B(I,J) = B(I,J) - TEMP*B(I,K) |
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280 CONTINUE |
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END IF |
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290 CONTINUE |
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IF (ALPHA.NE.ONE) THEN |
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DO 300 I = 1,M |
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B(I,K) = ALPHA*B(I,K) |
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300 CONTINUE |
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END IF |
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310 CONTINUE |
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ELSE |
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DO 360 K = 1,N |
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IF (NOUNIT) THEN |
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TEMP = ONE/A(K,K) |
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DO 320 I = 1,M |
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B(I,K) = TEMP*B(I,K) |
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320 CONTINUE |
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END IF |
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DO 340 J = K + 1,N |
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IF (A(J,K).NE.ZERO) THEN |
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TEMP = A(J,K) |
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DO 330 I = 1,M |
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B(I,J) = B(I,J) - TEMP*B(I,K) |
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330 CONTINUE |
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END IF |
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340 CONTINUE |
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IF (ALPHA.NE.ONE) THEN |
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DO 350 I = 1,M |
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B(I,K) = ALPHA*B(I,K) |
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350 CONTINUE |
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END IF |
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360 CONTINUE |
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END IF |
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END IF |
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END IF |
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* |
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RETURN |
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* |
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* End of DTRSM . |
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* |
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END |