"atomic bomb" commit. Reorganized OpenCV directory structure
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Vadim Pisarevsky
211
3rdparty/lapack/dlagtf.c
vendored
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211
3rdparty/lapack/dlagtf.c
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#include "clapack.h"
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/* Subroutine */ int dlagtf_(integer *n, doublereal *a, doublereal *lambda,
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doublereal *b, doublereal *c__, doublereal *tol, doublereal *d__,
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integer *in, integer *info)
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{
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/* System generated locals */
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integer i__1;
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doublereal d__1, d__2;
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/* Local variables */
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integer k;
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doublereal tl, eps, piv1, piv2, temp, mult, scale1, scale2;
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extern doublereal dlamch_(char *);
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extern /* Subroutine */ int xerbla_(char *, integer *);
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/* -- LAPACK routine (version 3.1) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* DLAGTF factorizes the matrix (T - lambda*I), where T is an n by n */
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/* tridiagonal matrix and lambda is a scalar, as */
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/* T - lambda*I = PLU, */
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/* where P is a permutation matrix, L is a unit lower tridiagonal matrix */
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/* with at most one non-zero sub-diagonal elements per column and U is */
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/* an upper triangular matrix with at most two non-zero super-diagonal */
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/* elements per column. */
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/* The factorization is obtained by Gaussian elimination with partial */
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/* pivoting and implicit row scaling. */
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/* The parameter LAMBDA is included in the routine so that DLAGTF may */
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/* be used, in conjunction with DLAGTS, to obtain eigenvectors of T by */
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/* inverse iteration. */
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/* Arguments */
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/* ========= */
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/* N (input) INTEGER */
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/* The order of the matrix T. */
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/* A (input/output) DOUBLE PRECISION array, dimension (N) */
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/* On entry, A must contain the diagonal elements of T. */
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/* On exit, A is overwritten by the n diagonal elements of the */
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/* upper triangular matrix U of the factorization of T. */
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/* LAMBDA (input) DOUBLE PRECISION */
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/* On entry, the scalar lambda. */
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/* B (input/output) DOUBLE PRECISION array, dimension (N-1) */
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/* On entry, B must contain the (n-1) super-diagonal elements of */
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/* T. */
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/* On exit, B is overwritten by the (n-1) super-diagonal */
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/* elements of the matrix U of the factorization of T. */
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/* C (input/output) DOUBLE PRECISION array, dimension (N-1) */
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/* On entry, C must contain the (n-1) sub-diagonal elements of */
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/* T. */
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/* On exit, C is overwritten by the (n-1) sub-diagonal elements */
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/* of the matrix L of the factorization of T. */
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/* TOL (input) DOUBLE PRECISION */
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/* On entry, a relative tolerance used to indicate whether or */
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/* not the matrix (T - lambda*I) is nearly singular. TOL should */
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/* normally be chose as approximately the largest relative error */
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/* in the elements of T. For example, if the elements of T are */
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/* correct to about 4 significant figures, then TOL should be */
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/* set to about 5*10**(-4). If TOL is supplied as less than eps, */
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/* where eps is the relative machine precision, then the value */
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/* eps is used in place of TOL. */
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/* D (output) DOUBLE PRECISION array, dimension (N-2) */
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/* On exit, D is overwritten by the (n-2) second super-diagonal */
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/* elements of the matrix U of the factorization of T. */
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/* IN (output) INTEGER array, dimension (N) */
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/* On exit, IN contains details of the permutation matrix P. If */
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/* an interchange occurred at the kth step of the elimination, */
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/* then IN(k) = 1, otherwise IN(k) = 0. The element IN(n) */
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/* returns the smallest positive integer j such that */
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/* abs( u(j,j) ).le. norm( (T - lambda*I)(j) )*TOL, */
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/* where norm( A(j) ) denotes the sum of the absolute values of */
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/* the jth row of the matrix A. If no such j exists then IN(n) */
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/* is returned as zero. If IN(n) is returned as positive, then a */
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/* diagonal element of U is small, indicating that */
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/* (T - lambda*I) is singular or nearly singular, */
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/* INFO (output) INTEGER */
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/* = 0 : successful exit */
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/* .lt. 0: if INFO = -k, the kth argument had an illegal value */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Parameter adjustments */
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--in;
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--d__;
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--c__;
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--b;
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--a;
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/* Function Body */
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*info = 0;
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if (*n < 0) {
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*info = -1;
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i__1 = -(*info);
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xerbla_("DLAGTF", &i__1);
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return 0;
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}
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if (*n == 0) {
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return 0;
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}
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a[1] -= *lambda;
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in[*n] = 0;
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if (*n == 1) {
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if (a[1] == 0.) {
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in[1] = 1;
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}
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return 0;
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}
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eps = dlamch_("Epsilon");
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tl = max(*tol,eps);
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scale1 = abs(a[1]) + abs(b[1]);
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i__1 = *n - 1;
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for (k = 1; k <= i__1; ++k) {
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a[k + 1] -= *lambda;
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scale2 = (d__1 = c__[k], abs(d__1)) + (d__2 = a[k + 1], abs(d__2));
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if (k < *n - 1) {
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scale2 += (d__1 = b[k + 1], abs(d__1));
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}
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if (a[k] == 0.) {
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piv1 = 0.;
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} else {
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piv1 = (d__1 = a[k], abs(d__1)) / scale1;
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}
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if (c__[k] == 0.) {
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in[k] = 0;
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piv2 = 0.;
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scale1 = scale2;
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if (k < *n - 1) {
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d__[k] = 0.;
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}
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} else {
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piv2 = (d__1 = c__[k], abs(d__1)) / scale2;
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if (piv2 <= piv1) {
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in[k] = 0;
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scale1 = scale2;
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c__[k] /= a[k];
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a[k + 1] -= c__[k] * b[k];
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if (k < *n - 1) {
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d__[k] = 0.;
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}
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} else {
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in[k] = 1;
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mult = a[k] / c__[k];
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a[k] = c__[k];
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temp = a[k + 1];
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a[k + 1] = b[k] - mult * temp;
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if (k < *n - 1) {
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d__[k] = b[k + 1];
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b[k + 1] = -mult * d__[k];
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}
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b[k] = temp;
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c__[k] = mult;
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}
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}
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if (max(piv1,piv2) <= tl && in[*n] == 0) {
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in[*n] = k;
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}
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/* L10: */
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}
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if ((d__1 = a[*n], abs(d__1)) <= scale1 * tl && in[*n] == 0) {
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in[*n] = *n;
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}
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return 0;
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/* End of DLAGTF */
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} /* dlagtf_ */
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