dtrtri.c

#include "clapack.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 3.1) -- */
/*     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_ */