Chris@202: /* dtrsm.f -- translated by f2c (version 20061008).
Chris@202:    You must link the resulting object file with libf2c:
Chris@202: 	on Microsoft Windows system, link with libf2c.lib;
Chris@202: 	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
Chris@202: 	or, if you install libf2c.a in a standard place, with -lf2c -lm
Chris@202: 	-- in that order, at the end of the command line, as in
Chris@202: 		cc *.o -lf2c -lm
Chris@202: 	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
Chris@202: 
Chris@202: 		http://www.netlib.org/f2c/libf2c.zip
Chris@202: */
Chris@202: 
Chris@202: #include "f2c.h"
Chris@202: #include "blaswrap.h"
Chris@202: 
Chris@202: /* Subroutine */ int dtrsm_(char *side, char *uplo, char *transa, char *diag, 
Chris@202: 	integer *m, integer *n, doublereal *alpha, doublereal *a, integer *
Chris@202: 	lda, doublereal *b, integer *ldb)
Chris@202: {
Chris@202:     /* System generated locals */
Chris@202:     integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
Chris@202: 
Chris@202:     /* Local variables */
Chris@202:     integer i__, j, k, info;
Chris@202:     doublereal temp;
Chris@202:     logical lside;
Chris@202:     extern logical lsame_(char *, char *);
Chris@202:     integer nrowa;
Chris@202:     logical upper;
Chris@202:     extern /* Subroutine */ int xerbla_(char *, integer *);
Chris@202:     logical nounit;
Chris@202: 
Chris@202: /*     .. Scalar Arguments .. */
Chris@202: /*     .. */
Chris@202: /*     .. Array Arguments .. */
Chris@202: /*     .. */
Chris@202: 
Chris@202: /*  Purpose */
Chris@202: /*  ======= */
Chris@202: 
Chris@202: /*  DTRSM  solves one of the matrix equations */
Chris@202: 
Chris@202: /*     op( A )*X = alpha*B,   or   X*op( A ) = alpha*B, */
Chris@202: 
Chris@202: /*  where alpha is a scalar, X and B are m by n matrices, A is a unit, or */
Chris@202: /*  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of */
Chris@202: 
Chris@202: /*     op( A ) = A   or   op( A ) = A'. */
Chris@202: 
Chris@202: /*  The matrix X is overwritten on B. */
Chris@202: 
Chris@202: /*  Arguments */
Chris@202: /*  ========== */
Chris@202: 
Chris@202: /*  SIDE   - CHARACTER*1. */
Chris@202: /*           On entry, SIDE specifies whether op( A ) appears on the left */
Chris@202: /*           or right of X as follows: */
Chris@202: 
Chris@202: /*              SIDE = 'L' or 'l'   op( A )*X = alpha*B. */
Chris@202: 
Chris@202: /*              SIDE = 'R' or 'r'   X*op( A ) = alpha*B. */
Chris@202: 
Chris@202: /*           Unchanged on exit. */
Chris@202: 
Chris@202: /*  UPLO   - CHARACTER*1. */
Chris@202: /*           On entry, UPLO specifies whether the matrix A is an upper or */
Chris@202: /*           lower triangular matrix as follows: */
Chris@202: 
Chris@202: /*              UPLO = 'U' or 'u'   A is an upper triangular matrix. */
Chris@202: 
Chris@202: /*              UPLO = 'L' or 'l'   A is a lower triangular matrix. */
Chris@202: 
Chris@202: /*           Unchanged on exit. */
Chris@202: 
Chris@202: /*  TRANSA - CHARACTER*1. */
Chris@202: /*           On entry, TRANSA specifies the form of op( A ) to be used in */
Chris@202: /*           the matrix multiplication as follows: */
Chris@202: 
Chris@202: /*              TRANSA = 'N' or 'n'   op( A ) = A. */
Chris@202: 
Chris@202: /*              TRANSA = 'T' or 't'   op( A ) = A'. */
Chris@202: 
Chris@202: /*              TRANSA = 'C' or 'c'   op( A ) = A'. */
Chris@202: 
Chris@202: /*           Unchanged on exit. */
Chris@202: 
Chris@202: /*  DIAG   - CHARACTER*1. */
Chris@202: /*           On entry, DIAG specifies whether or not A is unit triangular */
Chris@202: /*           as follows: */
Chris@202: 
Chris@202: /*              DIAG = 'U' or 'u'   A is assumed to be unit triangular. */
Chris@202: 
Chris@202: /*              DIAG = 'N' or 'n'   A is not assumed to be unit */
Chris@202: /*                                  triangular. */
Chris@202: 
Chris@202: /*           Unchanged on exit. */
Chris@202: 
Chris@202: /*  M      - INTEGER. */
Chris@202: /*           On entry, M specifies the number of rows of B. M must be at */
Chris@202: /*           least zero. */
Chris@202: /*           Unchanged on exit. */
Chris@202: 
Chris@202: /*  N      - INTEGER. */
Chris@202: /*           On entry, N specifies the number of columns of B.  N must be */
Chris@202: /*           at least zero. */
Chris@202: /*           Unchanged on exit. */
Chris@202: 
Chris@202: /*  ALPHA  - DOUBLE PRECISION. */
Chris@202: /*           On entry,  ALPHA specifies the scalar  alpha. When  alpha is */
Chris@202: /*           zero then  A is not referenced and  B need not be set before */
Chris@202: /*           entry. */
Chris@202: /*           Unchanged on exit. */
Chris@202: 
Chris@202: /*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m */
Chris@202: /*           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'. */
Chris@202: /*           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k */
Chris@202: /*           upper triangular part of the array  A must contain the upper */
Chris@202: /*           triangular matrix  and the strictly lower triangular part of */
Chris@202: /*           A is not referenced. */
Chris@202: /*           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k */
Chris@202: /*           lower triangular part of the array  A must contain the lower */
Chris@202: /*           triangular matrix  and the strictly upper triangular part of */
Chris@202: /*           A is not referenced. */
Chris@202: /*           Note that when  DIAG = 'U' or 'u',  the diagonal elements of */
Chris@202: /*           A  are not referenced either,  but are assumed to be  unity. */
Chris@202: /*           Unchanged on exit. */
Chris@202: 
Chris@202: /*  LDA    - INTEGER. */
Chris@202: /*           On entry, LDA specifies the first dimension of A as declared */
Chris@202: /*           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then */
Chris@202: /*           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r' */
Chris@202: /*           then LDA must be at least max( 1, n ). */
Chris@202: /*           Unchanged on exit. */
Chris@202: 
Chris@202: /*  B      - DOUBLE PRECISION array of DIMENSION ( LDB, n ). */
Chris@202: /*           Before entry,  the leading  m by n part of the array  B must */
Chris@202: /*           contain  the  right-hand  side  matrix  B,  and  on exit  is */
Chris@202: /*           overwritten by the solution matrix  X. */
Chris@202: 
Chris@202: /*  LDB    - INTEGER. */
Chris@202: /*           On entry, LDB specifies the first dimension of B as declared */
Chris@202: /*           in  the  calling  (sub)  program.   LDB  must  be  at  least */
Chris@202: /*           max( 1, m ). */
Chris@202: /*           Unchanged on exit. */
Chris@202: 
Chris@202: 
Chris@202: /*  Level 3 Blas routine. */
Chris@202: 
Chris@202: 
Chris@202: /*  -- Written on 8-February-1989. */
Chris@202: /*     Jack Dongarra, Argonne National Laboratory. */
Chris@202: /*     Iain Duff, AERE Harwell. */
Chris@202: /*     Jeremy Du Croz, Numerical Algorithms Group Ltd. */
Chris@202: /*     Sven Hammarling, Numerical Algorithms Group Ltd. */
Chris@202: 
Chris@202: 
Chris@202: /*     .. External Functions .. */
Chris@202: /*     .. */
Chris@202: /*     .. External Subroutines .. */
Chris@202: /*     .. */
Chris@202: /*     .. Intrinsic Functions .. */
Chris@202: /*     .. */
Chris@202: /*     .. Local Scalars .. */
Chris@202: /*     .. */
Chris@202: /*     .. Parameters .. */
Chris@202: /*     .. */
Chris@202: 
Chris@202: /*     Test the input parameters. */
Chris@202: 
Chris@202:     /* Parameter adjustments */
Chris@202:     a_dim1 = *lda;
Chris@202:     a_offset = 1 + a_dim1;
Chris@202:     a -= a_offset;
Chris@202:     b_dim1 = *ldb;
Chris@202:     b_offset = 1 + b_dim1;
Chris@202:     b -= b_offset;
Chris@202: 
Chris@202:     /* Function Body */
Chris@202:     lside = lsame_(side, "L");
Chris@202:     if (lside) {
Chris@202: 	nrowa = *m;
Chris@202:     } else {
Chris@202: 	nrowa = *n;
Chris@202:     }
Chris@202:     nounit = lsame_(diag, "N");
Chris@202:     upper = lsame_(uplo, "U");
Chris@202: 
Chris@202:     info = 0;
Chris@202:     if (! lside && ! lsame_(side, "R")) {
Chris@202: 	info = 1;
Chris@202:     } else if (! upper && ! lsame_(uplo, "L")) {
Chris@202: 	info = 2;
Chris@202:     } else if (! lsame_(transa, "N") && ! lsame_(transa, 
Chris@202: 	     "T") && ! lsame_(transa, "C")) {
Chris@202: 	info = 3;
Chris@202:     } else if (! lsame_(diag, "U") && ! lsame_(diag, 
Chris@202: 	    "N")) {
Chris@202: 	info = 4;
Chris@202:     } else if (*m < 0) {
Chris@202: 	info = 5;
Chris@202:     } else if (*n < 0) {
Chris@202: 	info = 6;
Chris@202:     } else if (*lda < max(1,nrowa)) {
Chris@202: 	info = 9;
Chris@202:     } else if (*ldb < max(1,*m)) {
Chris@202: 	info = 11;
Chris@202:     }
Chris@202:     if (info != 0) {
Chris@202: 	xerbla_("DTRSM ", &info);
Chris@202: 	return 0;
Chris@202:     }
Chris@202: 
Chris@202: /*     Quick return if possible. */
Chris@202: 
Chris@202:     if (*m == 0 || *n == 0) {
Chris@202: 	return 0;
Chris@202:     }
Chris@202: 
Chris@202: /*     And when  alpha.eq.zero. */
Chris@202: 
Chris@202:     if (*alpha == 0.) {
Chris@202: 	i__1 = *n;
Chris@202: 	for (j = 1; j <= i__1; ++j) {
Chris@202: 	    i__2 = *m;
Chris@202: 	    for (i__ = 1; i__ <= i__2; ++i__) {
Chris@202: 		b[i__ + j * b_dim1] = 0.;
Chris@202: /* L10: */
Chris@202: 	    }
Chris@202: /* L20: */
Chris@202: 	}
Chris@202: 	return 0;
Chris@202:     }
Chris@202: 
Chris@202: /*     Start the operations. */
Chris@202: 
Chris@202:     if (lside) {
Chris@202: 	if (lsame_(transa, "N")) {
Chris@202: 
Chris@202: /*           Form  B := alpha*inv( A )*B. */
Chris@202: 
Chris@202: 	    if (upper) {
Chris@202: 		i__1 = *n;
Chris@202: 		for (j = 1; j <= i__1; ++j) {
Chris@202: 		    if (*alpha != 1.) {
Chris@202: 			i__2 = *m;
Chris@202: 			for (i__ = 1; i__ <= i__2; ++i__) {
Chris@202: 			    b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
Chris@202: 				    ;
Chris@202: /* L30: */
Chris@202: 			}
Chris@202: 		    }
Chris@202: 		    for (k = *m; k >= 1; --k) {
Chris@202: 			if (b[k + j * b_dim1] != 0.) {
Chris@202: 			    if (nounit) {
Chris@202: 				b[k + j * b_dim1] /= a[k + k * a_dim1];
Chris@202: 			    }
Chris@202: 			    i__2 = k - 1;
Chris@202: 			    for (i__ = 1; i__ <= i__2; ++i__) {
Chris@202: 				b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
Chris@202: 					i__ + k * a_dim1];
Chris@202: /* L40: */
Chris@202: 			    }
Chris@202: 			}
Chris@202: /* L50: */
Chris@202: 		    }
Chris@202: /* L60: */
Chris@202: 		}
Chris@202: 	    } else {
Chris@202: 		i__1 = *n;
Chris@202: 		for (j = 1; j <= i__1; ++j) {
Chris@202: 		    if (*alpha != 1.) {
Chris@202: 			i__2 = *m;
Chris@202: 			for (i__ = 1; i__ <= i__2; ++i__) {
Chris@202: 			    b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
Chris@202: 				    ;
Chris@202: /* L70: */
Chris@202: 			}
Chris@202: 		    }
Chris@202: 		    i__2 = *m;
Chris@202: 		    for (k = 1; k <= i__2; ++k) {
Chris@202: 			if (b[k + j * b_dim1] != 0.) {
Chris@202: 			    if (nounit) {
Chris@202: 				b[k + j * b_dim1] /= a[k + k * a_dim1];
Chris@202: 			    }
Chris@202: 			    i__3 = *m;
Chris@202: 			    for (i__ = k + 1; i__ <= i__3; ++i__) {
Chris@202: 				b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
Chris@202: 					i__ + k * a_dim1];
Chris@202: /* L80: */
Chris@202: 			    }
Chris@202: 			}
Chris@202: /* L90: */
Chris@202: 		    }
Chris@202: /* L100: */
Chris@202: 		}
Chris@202: 	    }
Chris@202: 	} else {
Chris@202: 
Chris@202: /*           Form  B := alpha*inv( A' )*B. */
Chris@202: 
Chris@202: 	    if (upper) {
Chris@202: 		i__1 = *n;
Chris@202: 		for (j = 1; j <= i__1; ++j) {
Chris@202: 		    i__2 = *m;
Chris@202: 		    for (i__ = 1; i__ <= i__2; ++i__) {
Chris@202: 			temp = *alpha * b[i__ + j * b_dim1];
Chris@202: 			i__3 = i__ - 1;
Chris@202: 			for (k = 1; k <= i__3; ++k) {
Chris@202: 			    temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
Chris@202: /* L110: */
Chris@202: 			}
Chris@202: 			if (nounit) {
Chris@202: 			    temp /= a[i__ + i__ * a_dim1];
Chris@202: 			}
Chris@202: 			b[i__ + j * b_dim1] = temp;
Chris@202: /* L120: */
Chris@202: 		    }
Chris@202: /* L130: */
Chris@202: 		}
Chris@202: 	    } else {
Chris@202: 		i__1 = *n;
Chris@202: 		for (j = 1; j <= i__1; ++j) {
Chris@202: 		    for (i__ = *m; i__ >= 1; --i__) {
Chris@202: 			temp = *alpha * b[i__ + j * b_dim1];
Chris@202: 			i__2 = *m;
Chris@202: 			for (k = i__ + 1; k <= i__2; ++k) {
Chris@202: 			    temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
Chris@202: /* L140: */
Chris@202: 			}
Chris@202: 			if (nounit) {
Chris@202: 			    temp /= a[i__ + i__ * a_dim1];
Chris@202: 			}
Chris@202: 			b[i__ + j * b_dim1] = temp;
Chris@202: /* L150: */
Chris@202: 		    }
Chris@202: /* L160: */
Chris@202: 		}
Chris@202: 	    }
Chris@202: 	}
Chris@202:     } else {
Chris@202: 	if (lsame_(transa, "N")) {
Chris@202: 
Chris@202: /*           Form  B := alpha*B*inv( A ). */
Chris@202: 
Chris@202: 	    if (upper) {
Chris@202: 		i__1 = *n;
Chris@202: 		for (j = 1; j <= i__1; ++j) {
Chris@202: 		    if (*alpha != 1.) {
Chris@202: 			i__2 = *m;
Chris@202: 			for (i__ = 1; i__ <= i__2; ++i__) {
Chris@202: 			    b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
Chris@202: 				    ;
Chris@202: /* L170: */
Chris@202: 			}
Chris@202: 		    }
Chris@202: 		    i__2 = j - 1;
Chris@202: 		    for (k = 1; k <= i__2; ++k) {
Chris@202: 			if (a[k + j * a_dim1] != 0.) {
Chris@202: 			    i__3 = *m;
Chris@202: 			    for (i__ = 1; i__ <= i__3; ++i__) {
Chris@202: 				b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
Chris@202: 					i__ + k * b_dim1];
Chris@202: /* L180: */
Chris@202: 			    }
Chris@202: 			}
Chris@202: /* L190: */
Chris@202: 		    }
Chris@202: 		    if (nounit) {
Chris@202: 			temp = 1. / a[j + j * a_dim1];
Chris@202: 			i__2 = *m;
Chris@202: 			for (i__ = 1; i__ <= i__2; ++i__) {
Chris@202: 			    b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
Chris@202: /* L200: */
Chris@202: 			}
Chris@202: 		    }
Chris@202: /* L210: */
Chris@202: 		}
Chris@202: 	    } else {
Chris@202: 		for (j = *n; j >= 1; --j) {
Chris@202: 		    if (*alpha != 1.) {
Chris@202: 			i__1 = *m;
Chris@202: 			for (i__ = 1; i__ <= i__1; ++i__) {
Chris@202: 			    b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
Chris@202: 				    ;
Chris@202: /* L220: */
Chris@202: 			}
Chris@202: 		    }
Chris@202: 		    i__1 = *n;
Chris@202: 		    for (k = j + 1; k <= i__1; ++k) {
Chris@202: 			if (a[k + j * a_dim1] != 0.) {
Chris@202: 			    i__2 = *m;
Chris@202: 			    for (i__ = 1; i__ <= i__2; ++i__) {
Chris@202: 				b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
Chris@202: 					i__ + k * b_dim1];
Chris@202: /* L230: */
Chris@202: 			    }
Chris@202: 			}
Chris@202: /* L240: */
Chris@202: 		    }
Chris@202: 		    if (nounit) {
Chris@202: 			temp = 1. / a[j + j * a_dim1];
Chris@202: 			i__1 = *m;
Chris@202: 			for (i__ = 1; i__ <= i__1; ++i__) {
Chris@202: 			    b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
Chris@202: /* L250: */
Chris@202: 			}
Chris@202: 		    }
Chris@202: /* L260: */
Chris@202: 		}
Chris@202: 	    }
Chris@202: 	} else {
Chris@202: 
Chris@202: /*           Form  B := alpha*B*inv( A' ). */
Chris@202: 
Chris@202: 	    if (upper) {
Chris@202: 		for (k = *n; k >= 1; --k) {
Chris@202: 		    if (nounit) {
Chris@202: 			temp = 1. / a[k + k * a_dim1];
Chris@202: 			i__1 = *m;
Chris@202: 			for (i__ = 1; i__ <= i__1; ++i__) {
Chris@202: 			    b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
Chris@202: /* L270: */
Chris@202: 			}
Chris@202: 		    }
Chris@202: 		    i__1 = k - 1;
Chris@202: 		    for (j = 1; j <= i__1; ++j) {
Chris@202: 			if (a[j + k * a_dim1] != 0.) {
Chris@202: 			    temp = a[j + k * a_dim1];
Chris@202: 			    i__2 = *m;
Chris@202: 			    for (i__ = 1; i__ <= i__2; ++i__) {
Chris@202: 				b[i__ + j * b_dim1] -= temp * b[i__ + k * 
Chris@202: 					b_dim1];
Chris@202: /* L280: */
Chris@202: 			    }
Chris@202: 			}
Chris@202: /* L290: */
Chris@202: 		    }
Chris@202: 		    if (*alpha != 1.) {
Chris@202: 			i__1 = *m;
Chris@202: 			for (i__ = 1; i__ <= i__1; ++i__) {
Chris@202: 			    b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1]
Chris@202: 				    ;
Chris@202: /* L300: */
Chris@202: 			}
Chris@202: 		    }
Chris@202: /* L310: */
Chris@202: 		}
Chris@202: 	    } else {
Chris@202: 		i__1 = *n;
Chris@202: 		for (k = 1; k <= i__1; ++k) {
Chris@202: 		    if (nounit) {
Chris@202: 			temp = 1. / a[k + k * a_dim1];
Chris@202: 			i__2 = *m;
Chris@202: 			for (i__ = 1; i__ <= i__2; ++i__) {
Chris@202: 			    b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
Chris@202: /* L320: */
Chris@202: 			}
Chris@202: 		    }
Chris@202: 		    i__2 = *n;
Chris@202: 		    for (j = k + 1; j <= i__2; ++j) {
Chris@202: 			if (a[j + k * a_dim1] != 0.) {
Chris@202: 			    temp = a[j + k * a_dim1];
Chris@202: 			    i__3 = *m;
Chris@202: 			    for (i__ = 1; i__ <= i__3; ++i__) {
Chris@202: 				b[i__ + j * b_dim1] -= temp * b[i__ + k * 
Chris@202: 					b_dim1];
Chris@202: /* L330: */
Chris@202: 			    }
Chris@202: 			}
Chris@202: /* L340: */
Chris@202: 		    }
Chris@202: 		    if (*alpha != 1.) {
Chris@202: 			i__2 = *m;
Chris@202: 			for (i__ = 1; i__ <= i__2; ++i__) {
Chris@202: 			    b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1]
Chris@202: 				    ;
Chris@202: /* L350: */
Chris@202: 			}
Chris@202: 		    }
Chris@202: /* L360: */
Chris@202: 		}
Chris@202: 	    }
Chris@202: 	}
Chris@202:     }
Chris@202: 
Chris@202:     return 0;
Chris@202: 
Chris@202: /*     End of DTRSM . */
Chris@202: 
Chris@202: } /* dtrsm_ */