comparison ext/clapack/src/dtrtri.c @ 430:335af74a25b6

Merge from branch clapack-included

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