SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * .. Scalar Arguments .. INTEGER INCX,LDA,N CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. DOUBLE PRECISION A(LDA,*),X(*) * .. * * Purpose * ======= * * DTRSV solves one of the systems of equations * * A*x = b, or 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' 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 .. DOUBLE PRECISION ZERO PARAMETER (ZERO=0.0D+0) * .. * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I,INFO,IX,J,JX,KX LOGICAL NOUNIT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC 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('DTRSV ',INFO) RETURN END IF * * Quick return if possible. * IF (N.EQ.0) RETURN * 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. * IF (LSAME(UPLO,'U')) THEN IF (INCX.EQ.1) THEN DO 100 J = 1,N TEMP = X(J) DO 90 I = 1,J - 1 TEMP = TEMP - A(I,J)*X(I) 90 CONTINUE IF (NOUNIT) TEMP = TEMP/A(J,J) X(J) = TEMP 100 CONTINUE ELSE JX = KX DO 120 J = 1,N TEMP = X(JX) IX = KX DO 110 I = 1,J - 1 TEMP = TEMP - A(I,J)*X(IX) IX = IX + INCX 110 CONTINUE IF (NOUNIT) TEMP = TEMP/A(J,J) X(JX) = TEMP JX = JX + INCX 120 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 140 J = N,1,-1 TEMP = X(J) DO 130 I = N,J + 1,-1 TEMP = TEMP - A(I,J)*X(I) 130 CONTINUE IF (NOUNIT) TEMP = TEMP/A(J,J) X(J) = TEMP 140 CONTINUE ELSE KX = KX + (N-1)*INCX JX = KX DO 160 J = N,1,-1 TEMP = X(JX) IX = KX DO 150 I = N,J + 1,-1 TEMP = TEMP - A(I,J)*X(IX) IX = IX - INCX 150 CONTINUE IF (NOUNIT) TEMP = TEMP/A(J,J) X(JX) = TEMP JX = JX - INCX 160 CONTINUE END IF END IF END IF * RETURN * * End of DTRSV . * END