Chris@202: /* dtrtri.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: /* Table of constant values */
Chris@202: 
Chris@202: static integer c__1 = 1;
Chris@202: static integer c_n1 = -1;
Chris@202: static integer c__2 = 2;
Chris@202: static doublereal c_b18 = 1.;
Chris@202: static doublereal c_b22 = -1.;
Chris@202: 
Chris@202: /* Subroutine */ int dtrtri_(char *uplo, char *diag, integer *n, doublereal *
Chris@202: 	a, integer *lda, integer *info)
Chris@202: {
Chris@202:     /* System generated locals */
Chris@202:     address a__1[2];
Chris@202:     integer a_dim1, a_offset, i__1, i__2[2], i__3, i__4, i__5;
Chris@202:     char ch__1[2];
Chris@202: 
Chris@202:     /* Builtin functions */
Chris@202:     /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
Chris@202: 
Chris@202:     /* Local variables */
Chris@202:     integer j, jb, nb, nn;
Chris@202:     extern logical lsame_(char *, char *);
Chris@202:     extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, 
Chris@202: 	    integer *, integer *, doublereal *, doublereal *, integer *, 
Chris@202: 	    doublereal *, integer *), dtrsm_(
Chris@202: 	    char *, char *, char *, char *, integer *, integer *, doublereal *
Chris@202: , doublereal *, integer *, doublereal *, integer *);
Chris@202:     logical upper;
Chris@202:     extern /* Subroutine */ int dtrti2_(char *, char *, integer *, doublereal 
Chris@202: 	    *, integer *, integer *), xerbla_(char *, integer 
Chris@202: 	    *);
Chris@202:     extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
Chris@202: 	    integer *, integer *);
Chris@202:     logical nounit;
Chris@202: 
Chris@202: 
Chris@202: /*  -- LAPACK routine (version 3.2) -- */
Chris@202: /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
Chris@202: /*     November 2006 */
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: /*  DTRTRI computes the inverse of a real upper or lower triangular */
Chris@202: /*  matrix A. */
Chris@202: 
Chris@202: /*  This is the Level 3 BLAS version of the algorithm. */
Chris@202: 
Chris@202: /*  Arguments */
Chris@202: /*  ========= */
Chris@202: 
Chris@202: /*  UPLO    (input) CHARACTER*1 */
Chris@202: /*          = 'U':  A is upper triangular; */
Chris@202: /*          = 'L':  A is lower triangular. */
Chris@202: 
Chris@202: /*  DIAG    (input) CHARACTER*1 */
Chris@202: /*          = 'N':  A is non-unit triangular; */
Chris@202: /*          = 'U':  A is unit triangular. */
Chris@202: 
Chris@202: /*  N       (input) INTEGER */
Chris@202: /*          The order of the matrix A.  N >= 0. */
Chris@202: 
Chris@202: /*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
Chris@202: /*          On entry, the triangular matrix A.  If UPLO = 'U', the */
Chris@202: /*          leading N-by-N upper triangular part of the array A contains */
Chris@202: /*          the upper triangular matrix, and the strictly lower */
Chris@202: /*          triangular part of A is not referenced.  If UPLO = 'L', the */
Chris@202: /*          leading N-by-N lower triangular part of the array A contains */
Chris@202: /*          the lower triangular matrix, and the strictly upper */
Chris@202: /*          triangular part of A is not referenced.  If DIAG = 'U', the */
Chris@202: /*          diagonal elements of A are also not referenced and are */
Chris@202: /*          assumed to be 1. */
Chris@202: /*          On exit, the (triangular) inverse of the original matrix, in */
Chris@202: /*          the same storage format. */
Chris@202: 
Chris@202: /*  LDA     (input) INTEGER */
Chris@202: /*          The leading dimension of the array A.  LDA >= max(1,N). */
Chris@202: 
Chris@202: /*  INFO    (output) INTEGER */
Chris@202: /*          = 0: successful exit */
Chris@202: /*          < 0: if INFO = -i, the i-th argument had an illegal value */
Chris@202: /*          > 0: if INFO = i, A(i,i) is exactly zero.  The triangular */
Chris@202: /*               matrix is singular and its inverse can not be computed. */
Chris@202: 
Chris@202: /*  ===================================================================== */
Chris@202: 
Chris@202: /*     .. Parameters .. */
Chris@202: /*     .. */
Chris@202: /*     .. Local Scalars .. */
Chris@202: /*     .. */
Chris@202: /*     .. External Functions .. */
Chris@202: /*     .. */
Chris@202: /*     .. External Subroutines .. */
Chris@202: /*     .. */
Chris@202: /*     .. Intrinsic Functions .. */
Chris@202: /*     .. */
Chris@202: /*     .. Executable Statements .. */
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: 
Chris@202:     /* Function Body */
Chris@202:     *info = 0;
Chris@202:     upper = lsame_(uplo, "U");
Chris@202:     nounit = lsame_(diag, "N");
Chris@202:     if (! upper && ! lsame_(uplo, "L")) {
Chris@202: 	*info = -1;
Chris@202:     } else if (! nounit && ! lsame_(diag, "U")) {
Chris@202: 	*info = -2;
Chris@202:     } else if (*n < 0) {
Chris@202: 	*info = -3;
Chris@202:     } else if (*lda < max(1,*n)) {
Chris@202: 	*info = -5;
Chris@202:     }
Chris@202:     if (*info != 0) {
Chris@202: 	i__1 = -(*info);
Chris@202: 	xerbla_("DTRTRI", &i__1);
Chris@202: 	return 0;
Chris@202:     }
Chris@202: 
Chris@202: /*     Quick return if possible */
Chris@202: 
Chris@202:     if (*n == 0) {
Chris@202: 	return 0;
Chris@202:     }
Chris@202: 
Chris@202: /*     Check for singularity if non-unit. */
Chris@202: 
Chris@202:     if (nounit) {
Chris@202: 	i__1 = *n;
Chris@202: 	for (*info = 1; *info <= i__1; ++(*info)) {
Chris@202: 	    if (a[*info + *info * a_dim1] == 0.) {
Chris@202: 		return 0;
Chris@202: 	    }
Chris@202: /* L10: */
Chris@202: 	}
Chris@202: 	*info = 0;
Chris@202:     }
Chris@202: 
Chris@202: /*     Determine the block size for this environment. */
Chris@202: 
Chris@202: /* Writing concatenation */
Chris@202:     i__2[0] = 1, a__1[0] = uplo;
Chris@202:     i__2[1] = 1, a__1[1] = diag;
Chris@202:     s_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2);
Chris@202:     nb = ilaenv_(&c__1, "DTRTRI", ch__1, n, &c_n1, &c_n1, &c_n1);
Chris@202:     if (nb <= 1 || nb >= *n) {
Chris@202: 
Chris@202: /*        Use unblocked code */
Chris@202: 
Chris@202: 	dtrti2_(uplo, diag, n, &a[a_offset], lda, info);
Chris@202:     } else {
Chris@202: 
Chris@202: /*        Use blocked code */
Chris@202: 
Chris@202: 	if (upper) {
Chris@202: 
Chris@202: /*           Compute inverse of upper triangular matrix */
Chris@202: 
Chris@202: 	    i__1 = *n;
Chris@202: 	    i__3 = nb;
Chris@202: 	    for (j = 1; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) {
Chris@202: /* Computing MIN */
Chris@202: 		i__4 = nb, i__5 = *n - j + 1;
Chris@202: 		jb = min(i__4,i__5);
Chris@202: 
Chris@202: /*              Compute rows 1:j-1 of current block column */
Chris@202: 
Chris@202: 		i__4 = j - 1;
Chris@202: 		dtrmm_("Left", "Upper", "No transpose", diag, &i__4, &jb, &
Chris@202: 			c_b18, &a[a_offset], lda, &a[j * a_dim1 + 1], lda);
Chris@202: 		i__4 = j - 1;
Chris@202: 		dtrsm_("Right", "Upper", "No transpose", diag, &i__4, &jb, &
Chris@202: 			c_b22, &a[j + j * a_dim1], lda, &a[j * a_dim1 + 1], 
Chris@202: 			lda);
Chris@202: 
Chris@202: /*              Compute inverse of current diagonal block */
Chris@202: 
Chris@202: 		dtrti2_("Upper", diag, &jb, &a[j + j * a_dim1], lda, info);
Chris@202: /* L20: */
Chris@202: 	    }
Chris@202: 	} else {
Chris@202: 
Chris@202: /*           Compute inverse of lower triangular matrix */
Chris@202: 
Chris@202: 	    nn = (*n - 1) / nb * nb + 1;
Chris@202: 	    i__3 = -nb;
Chris@202: 	    for (j = nn; i__3 < 0 ? j >= 1 : j <= 1; j += i__3) {
Chris@202: /* Computing MIN */
Chris@202: 		i__1 = nb, i__4 = *n - j + 1;
Chris@202: 		jb = min(i__1,i__4);
Chris@202: 		if (j + jb <= *n) {
Chris@202: 
Chris@202: /*                 Compute rows j+jb:n of current block column */
Chris@202: 
Chris@202: 		    i__1 = *n - j - jb + 1;
Chris@202: 		    dtrmm_("Left", "Lower", "No transpose", diag, &i__1, &jb, 
Chris@202: 			    &c_b18, &a[j + jb + (j + jb) * a_dim1], lda, &a[j 
Chris@202: 			    + jb + j * a_dim1], lda);
Chris@202: 		    i__1 = *n - j - jb + 1;
Chris@202: 		    dtrsm_("Right", "Lower", "No transpose", diag, &i__1, &jb, 
Chris@202: 			     &c_b22, &a[j + j * a_dim1], lda, &a[j + jb + j * 
Chris@202: 			    a_dim1], lda);
Chris@202: 		}
Chris@202: 
Chris@202: /*              Compute inverse of current diagonal block */
Chris@202: 
Chris@202: 		dtrti2_("Lower", diag, &jb, &a[j + j * a_dim1], lda, info);
Chris@202: /* L30: */
Chris@202: 	    }
Chris@202: 	}
Chris@202:     }
Chris@202: 
Chris@202:     return 0;
Chris@202: 
Chris@202: /*     End of DTRTRI */
Chris@202: 
Chris@202: } /* dtrtri_ */