comparison ext/cblas/src/dtrsm.c @ 430:335af74a25b6

Merge from branch clapack-included

+/* dtrsm.f -- translated by f2c (version 20061008).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Subroutine */ int dtrsm_(char *side, char *uplo, char *transa, char *diag, 
+	integer *m, integer *n, doublereal *alpha, doublereal *a, integer *
+	lda, doublereal *b, integer *ldb)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
+
+    /* Local variables */
+    integer i__, j, k, info;
+    doublereal temp;
+    logical lside;
+    extern logical lsame_(char *, char *);
+    integer nrowa;
+    logical upper;
+    extern /* Subroutine */ int xerbla_(char *, integer *);
+    logical nounit;
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*  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. */
+
+/*  Arguments */
+/*  ========== */
+
+/*  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 .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. Parameters .. */
+/*     .. */
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1;
+    b -= b_offset;
+
+    /* Function Body */
+    lside = lsame_(side, "L");
+    if (lside) {
+	nrowa = *m;
+    } else {
+	nrowa = *n;
+    }
+    nounit = lsame_(diag, "N");
+    upper = lsame_(uplo, "U");
+
+    info = 0;
+    if (! lside && ! lsame_(side, "R")) {
+	info = 1;
+    } else if (! upper && ! lsame_(uplo, "L")) {
+	info = 2;
+    } else if (! lsame_(transa, "N") && ! lsame_(transa, 
+	     "T") && ! lsame_(transa, "C")) {
+	info = 3;
+    } else if (! lsame_(diag, "U") && ! lsame_(diag, 
+	    "N")) {
+	info = 4;
+    } else if (*m < 0) {
+	info = 5;
+    } else if (*n < 0) {
+	info = 6;
+    } else if (*lda < max(1,nrowa)) {
+	info = 9;
+    } else if (*ldb < max(1,*m)) {
+	info = 11;
+    }
+    if (info != 0) {
+	xerbla_("DTRSM ", &info);
+	return 0;
+    }
+
+/*     Quick return if possible. */
+
+    if (*m == 0 || *n == 0) {
+	return 0;
+    }
+
+/*     And when  alpha.eq.zero. */
+
+    if (*alpha == 0.) {
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = *m;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		b[i__ + j * b_dim1] = 0.;
+/* L10: */
+	    }
+/* L20: */
+	}
+	return 0;
+    }
+
+/*     Start the operations. */
+
+    if (lside) {
+	if (lsame_(transa, "N")) {
+
+/*           Form  B := alpha*inv( A )*B. */
+
+	    if (upper) {
+		i__1 = *n;
+		for (j = 1; j <= i__1; ++j) {
+		    if (*alpha != 1.) {
+			i__2 = *m;
+			for (i__ = 1; i__ <= i__2; ++i__) {
+			    b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
+				    ;
+/* L30: */
+			}
+		    }
+		    for (k = *m; k >= 1; --k) {
+			if (b[k + j * b_dim1] != 0.) {
+			    if (nounit) {
+				b[k + j * b_dim1] /= a[k + k * a_dim1];
+			    }
+			    i__2 = k - 1;
+			    for (i__ = 1; i__ <= i__2; ++i__) {
+				b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
+					i__ + k * a_dim1];
+/* L40: */
+			    }
+			}
+/* L50: */
+		    }
+/* L60: */
+		}
+	    } else {
+		i__1 = *n;
+		for (j = 1; j <= i__1; ++j) {
+		    if (*alpha != 1.) {
+			i__2 = *m;
+			for (i__ = 1; i__ <= i__2; ++i__) {
+			    b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
+				    ;
+/* L70: */
+			}
+		    }
+		    i__2 = *m;
+		    for (k = 1; k <= i__2; ++k) {
+			if (b[k + j * b_dim1] != 0.) {
+			    if (nounit) {
+				b[k + j * b_dim1] /= a[k + k * a_dim1];
+			    }
+			    i__3 = *m;
+			    for (i__ = k + 1; i__ <= i__3; ++i__) {
+				b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
+					i__ + k * a_dim1];
+/* L80: */
+			    }
+			}
+/* L90: */
+		    }
+/* L100: */
+		}
+	    }
+	} else {
+
+/*           Form  B := alpha*inv( A' )*B. */
+
+	    if (upper) {
+		i__1 = *n;
+		for (j = 1; j <= i__1; ++j) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			temp = *alpha * b[i__ + j * b_dim1];
+			i__3 = i__ - 1;
+			for (k = 1; k <= i__3; ++k) {
+			    temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
+/* L110: */
+			}
+			if (nounit) {
+			    temp /= a[i__ + i__ * a_dim1];
+			}
+			b[i__ + j * b_dim1] = temp;
+/* L120: */
+		    }
+/* L130: */
+		}
+	    } else {
+		i__1 = *n;
+		for (j = 1; j <= i__1; ++j) {
+		    for (i__ = *m; i__ >= 1; --i__) {
+			temp = *alpha * b[i__ + j * b_dim1];
+			i__2 = *m;
+			for (k = i__ + 1; k <= i__2; ++k) {
+			    temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
+/* L140: */
+			}
+			if (nounit) {
+			    temp /= a[i__ + i__ * a_dim1];
+			}
+			b[i__ + j * b_dim1] = temp;
+/* L150: */
+		    }
+/* L160: */
+		}
+	    }
+	}
+    } else {
+	if (lsame_(transa, "N")) {
+
+/*           Form  B := alpha*B*inv( A ). */
+
+	    if (upper) {
+		i__1 = *n;
+		for (j = 1; j <= i__1; ++j) {
+		    if (*alpha != 1.) {
+			i__2 = *m;
+			for (i__ = 1; i__ <= i__2; ++i__) {
+			    b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
+				    ;
+/* L170: */
+			}
+		    }
+		    i__2 = j - 1;
+		    for (k = 1; k <= i__2; ++k) {
+			if (a[k + j * a_dim1] != 0.) {
+			    i__3 = *m;
+			    for (i__ = 1; i__ <= i__3; ++i__) {
+				b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
+					i__ + k * b_dim1];
+/* L180: */
+			    }
+			}
+/* L190: */
+		    }
+		    if (nounit) {
+			temp = 1. / a[j + j * a_dim1];
+			i__2 = *m;
+			for (i__ = 1; i__ <= i__2; ++i__) {
+			    b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
+/* L200: */
+			}
+		    }
+/* L210: */
+		}
+	    } else {
+		for (j = *n; j >= 1; --j) {
+		    if (*alpha != 1.) {
+			i__1 = *m;
+			for (i__ = 1; i__ <= i__1; ++i__) {
+			    b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
+				    ;
+/* L220: */
+			}
+		    }
+		    i__1 = *n;
+		    for (k = j + 1; k <= i__1; ++k) {
+			if (a[k + j * a_dim1] != 0.) {
+			    i__2 = *m;
+			    for (i__ = 1; i__ <= i__2; ++i__) {
+				b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
+					i__ + k * b_dim1];
+/* L230: */
+			    }
+			}
+/* L240: */
+		    }
+		    if (nounit) {
+			temp = 1. / a[j + j * a_dim1];
+			i__1 = *m;
+			for (i__ = 1; i__ <= i__1; ++i__) {
+			    b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
+/* L250: */
+			}
+		    }
+/* L260: */
+		}
+	    }
+	} else {
+
+/*           Form  B := alpha*B*inv( A' ). */
+
+	    if (upper) {
+		for (k = *n; k >= 1; --k) {
+		    if (nounit) {
+			temp = 1. / a[k + k * a_dim1];
+			i__1 = *m;
+			for (i__ = 1; i__ <= i__1; ++i__) {
+			    b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
+/* L270: */
+			}
+		    }
+		    i__1 = k - 1;
+		    for (j = 1; j <= i__1; ++j) {
+			if (a[j + k * a_dim1] != 0.) {
+			    temp = a[j + k * a_dim1];
+			    i__2 = *m;
+			    for (i__ = 1; i__ <= i__2; ++i__) {
+				b[i__ + j * b_dim1] -= temp * b[i__ + k * 
+					b_dim1];
+/* L280: */
+			    }
+			}
+/* L290: */
+		    }
+		    if (*alpha != 1.) {
+			i__1 = *m;
+			for (i__ = 1; i__ <= i__1; ++i__) {
+			    b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1]
+				    ;
+/* L300: */
+			}
+		    }
+/* L310: */
+		}
+	    } else {
+		i__1 = *n;
+		for (k = 1; k <= i__1; ++k) {
+		    if (nounit) {
+			temp = 1. / a[k + k * a_dim1];
+			i__2 = *m;
+			for (i__ = 1; i__ <= i__2; ++i__) {
+			    b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
+/* L320: */
+			}
+		    }
+		    i__2 = *n;
+		    for (j = k + 1; j <= i__2; ++j) {
+			if (a[j + k * a_dim1] != 0.) {
+			    temp = a[j + k * a_dim1];
+			    i__3 = *m;
+			    for (i__ = 1; i__ <= i__3; ++i__) {
+				b[i__ + j * b_dim1] -= temp * b[i__ + k * 
+					b_dim1];
+/* L330: */
+			    }
+			}
+/* L340: */
+		    }
+		    if (*alpha != 1.) {
+			i__2 = *m;
+			for (i__ = 1; i__ <= i__2; ++i__) {
+			    b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1]
+				    ;
+/* L350: */
+			}
+		    }
+/* L360: */
+		}
+	    }
+	}
+    }
+
+    return 0;
+
+/*     End of DTRSM . */
+
+} /* dtrsm_ */