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Diffstat (limited to 'BLAS/SRC/ctrsv.f')
| -rw-r--r-- | BLAS/SRC/ctrsv.f | 312 |
1 files changed, 312 insertions, 0 deletions
diff --git a/BLAS/SRC/ctrsv.f b/BLAS/SRC/ctrsv.f new file mode 100644 index 00000000..280a7bc6 --- /dev/null +++ b/BLAS/SRC/ctrsv.f @@ -0,0 +1,312 @@ + SUBROUTINE CTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) +* .. Scalar Arguments .. + INTEGER INCX,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*) +* .. +* +* Purpose +* ======= +* +* CTRSV solves one of the systems of equations +* +* A*x = b, or A'*x = b, or conjg( A' )*x = b, +* +* where b and x are n element vectors and A is an n by n unit, or +* non-unit, upper or lower triangular matrix. +* +* No test for singularity or near-singularity is included in this +* routine. Such tests must be performed before calling this routine. +* +* Arguments +* ========== +* +* UPLO - 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. +* +* Unchanged on exit. +* +* TRANS - CHARACTER*1. +* On entry, TRANS specifies the equations to be solved as +* follows: +* +* TRANS = 'N' or 'n' A*x = b. +* +* TRANS = 'T' or 't' A'*x = b. +* +* TRANS = 'C' or 'c' conjg( A' )*x = b. +* +* 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. +* +* N - INTEGER. +* On entry, N specifies the order of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* A - COMPLEX array of DIMENSION ( LDA, n ). +* Before entry with UPLO = 'U' or 'u', the leading n by n +* 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 n by n +* 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. LDA must be at least +* max( 1, n ). +* Unchanged on exit. +* +* X - COMPLEX array of dimension at least +* ( 1 + ( n - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the n +* element right-hand side vector b. On exit, X is overwritten +* with the solution vector x. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* +* .. Parameters .. + COMPLEX ZERO + PARAMETER (ZERO= (0.0E+0,0.0E+0)) +* .. +* .. Local Scalars .. + COMPLEX TEMP + INTEGER I,INFO,IX,J,JX,KX + LOGICAL NOCONJ,NOUNIT +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC CONJG,MAX +* .. +* +* 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 = 6 + ELSE IF (INCX.EQ.0) THEN + INFO = 8 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('CTRSV ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (N.EQ.0) RETURN +* + NOCONJ = LSAME(TRANS,'T') + NOUNIT = LSAME(DIAG,'N') +* +* Set up the start point in X if the increment is not unity. This +* will be ( N - 1 )*INCX too small for descending loops. +* + IF (INCX.LE.0) THEN + KX = 1 - (N-1)*INCX + ELSE IF (INCX.NE.1) THEN + KX = 1 + END IF +* +* Start the operations. In this version the elements of A are +* accessed sequentially with one pass through A. +* + IF (LSAME(TRANS,'N')) THEN +* +* Form x := inv( A )*x. +* + IF (LSAME(UPLO,'U')) THEN + IF (INCX.EQ.1) THEN + DO 20 J = N,1,-1 + IF (X(J).NE.ZERO) THEN + IF (NOUNIT) X(J) = X(J)/A(J,J) + TEMP = X(J) + DO 10 I = J - 1,1,-1 + X(I) = X(I) - TEMP*A(I,J) + 10 CONTINUE + END IF + 20 CONTINUE + ELSE + JX = KX + (N-1)*INCX + DO 40 J = N,1,-1 + IF (X(JX).NE.ZERO) THEN + IF (NOUNIT) X(JX) = X(JX)/A(J,J) + TEMP = X(JX) + IX = JX + DO 30 I = J - 1,1,-1 + IX = IX - INCX + X(IX) = X(IX) - TEMP*A(I,J) + 30 CONTINUE + END IF + JX = JX - INCX + 40 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 60 J = 1,N + IF (X(J).NE.ZERO) THEN + IF (NOUNIT) X(J) = X(J)/A(J,J) + TEMP = X(J) + DO 50 I = J + 1,N + X(I) = X(I) - TEMP*A(I,J) + 50 CONTINUE + END IF + 60 CONTINUE + ELSE + JX = KX + DO 80 J = 1,N + IF (X(JX).NE.ZERO) THEN + IF (NOUNIT) X(JX) = X(JX)/A(J,J) + TEMP = X(JX) + IX = JX + DO 70 I = J + 1,N + IX = IX + INCX + X(IX) = X(IX) - TEMP*A(I,J) + 70 CONTINUE + END IF + JX = JX + INCX + 80 CONTINUE + END IF + END IF + ELSE +* +* Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. +* + IF (LSAME(UPLO,'U')) THEN + IF (INCX.EQ.1) THEN + DO 110 J = 1,N + TEMP = X(J) + IF (NOCONJ) THEN + DO 90 I = 1,J - 1 + TEMP = TEMP - A(I,J)*X(I) + 90 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(J,J) + ELSE + DO 100 I = 1,J - 1 + TEMP = TEMP - CONJG(A(I,J))*X(I) + 100 CONTINUE + IF (NOUNIT) TEMP = TEMP/CONJG(A(J,J)) + END IF + X(J) = TEMP + 110 CONTINUE + ELSE + JX = KX + DO 140 J = 1,N + IX = KX + TEMP = X(JX) + IF (NOCONJ) THEN + DO 120 I = 1,J - 1 + TEMP = TEMP - A(I,J)*X(IX) + IX = IX + INCX + 120 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(J,J) + ELSE + DO 130 I = 1,J - 1 + TEMP = TEMP - CONJG(A(I,J))*X(IX) + IX = IX + INCX + 130 CONTINUE + IF (NOUNIT) TEMP = TEMP/CONJG(A(J,J)) + END IF + X(JX) = TEMP + JX = JX + INCX + 140 CONTINUE + END IF + ELSE + IF (INCX.EQ.1) THEN + DO 170 J = N,1,-1 + TEMP = X(J) + IF (NOCONJ) THEN + DO 150 I = N,J + 1,-1 + TEMP = TEMP - A(I,J)*X(I) + 150 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(J,J) + ELSE + DO 160 I = N,J + 1,-1 + TEMP = TEMP - CONJG(A(I,J))*X(I) + 160 CONTINUE + IF (NOUNIT) TEMP = TEMP/CONJG(A(J,J)) + END IF + X(J) = TEMP + 170 CONTINUE + ELSE + KX = KX + (N-1)*INCX + JX = KX + DO 200 J = N,1,-1 + IX = KX + TEMP = X(JX) + IF (NOCONJ) THEN + DO 180 I = N,J + 1,-1 + TEMP = TEMP - A(I,J)*X(IX) + IX = IX - INCX + 180 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(J,J) + ELSE + DO 190 I = N,J + 1,-1 + TEMP = TEMP - CONJG(A(I,J))*X(IX) + IX = IX - INCX + 190 CONTINUE + IF (NOUNIT) TEMP = TEMP/CONJG(A(J,J)) + END IF + X(JX) = TEMP + JX = JX - INCX + 200 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of CTRSV . +* + END |