--- /dev/null
+#include "clapack.h"
+
+/* Subroutine */ int slagtf_(integer *n, real *a, real *lambda, real *b, real
+ *c__, real *tol, real *d__, integer *in, integer *info)
+{
+ /* System generated locals */
+ integer i__1;
+ real r__1, r__2;
+
+ /* Local variables */
+ integer k;
+ real tl, eps, piv1, piv2, temp, mult, scale1, scale2;
+ extern doublereal slamch_(char *);
+ extern /* Subroutine */ int xerbla_(char *, integer *);
+
+
+/* -- LAPACK routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLAGTF factorizes the matrix (T - lambda*I), where T is an n by n */
+/* tridiagonal matrix and lambda is a scalar, as */
+
+/* T - lambda*I = PLU, */
+
+/* where P is a permutation matrix, L is a unit lower tridiagonal matrix */
+/* with at most one non-zero sub-diagonal elements per column and U is */
+/* an upper triangular matrix with at most two non-zero super-diagonal */
+/* elements per column. */
+
+/* The factorization is obtained by Gaussian elimination with partial */
+/* pivoting and implicit row scaling. */
+
+/* The parameter LAMBDA is included in the routine so that SLAGTF may */
+/* be used, in conjunction with SLAGTS, to obtain eigenvectors of T by */
+/* inverse iteration. */
+
+/* Arguments */
+/* ========= */
+
+/* N (input) INTEGER */
+/* The order of the matrix T. */
+
+/* A (input/output) REAL array, dimension (N) */
+/* On entry, A must contain the diagonal elements of T. */
+
+/* On exit, A is overwritten by the n diagonal elements of the */
+/* upper triangular matrix U of the factorization of T. */
+
+/* LAMBDA (input) REAL */
+/* On entry, the scalar lambda. */
+
+/* B (input/output) REAL array, dimension (N-1) */
+/* On entry, B must contain the (n-1) super-diagonal elements of */
+/* T. */
+
+/* On exit, B is overwritten by the (n-1) super-diagonal */
+/* elements of the matrix U of the factorization of T. */
+
+/* C (input/output) REAL array, dimension (N-1) */
+/* On entry, C must contain the (n-1) sub-diagonal elements of */
+/* T. */
+
+/* On exit, C is overwritten by the (n-1) sub-diagonal elements */
+/* of the matrix L of the factorization of T. */
+
+/* TOL (input) REAL */
+/* On entry, a relative tolerance used to indicate whether or */
+/* not the matrix (T - lambda*I) is nearly singular. TOL should */
+/* normally be chose as approximately the largest relative error */
+/* in the elements of T. For example, if the elements of T are */
+/* correct to about 4 significant figures, then TOL should be */
+/* set to about 5*10**(-4). If TOL is supplied as less than eps, */
+/* where eps is the relative machine precision, then the value */
+/* eps is used in place of TOL. */
+
+/* D (output) REAL array, dimension (N-2) */
+/* On exit, D is overwritten by the (n-2) second super-diagonal */
+/* elements of the matrix U of the factorization of T. */
+
+/* IN (output) INTEGER array, dimension (N) */
+/* On exit, IN contains details of the permutation matrix P. If */
+/* an interchange occurred at the kth step of the elimination, */
+/* then IN(k) = 1, otherwise IN(k) = 0. The element IN(n) */
+/* returns the smallest positive integer j such that */
+
+/* abs( u(j,j) ).le. norm( (T - lambda*I)(j) )*TOL, */
+
+/* where norm( A(j) ) denotes the sum of the absolute values of */
+/* the jth row of the matrix A. If no such j exists then IN(n) */
+/* is returned as zero. If IN(n) is returned as positive, then a */
+/* diagonal element of U is small, indicating that */
+/* (T - lambda*I) is singular or nearly singular, */
+
+/* INFO (output) INTEGER */
+/* = 0 : successful exit */
+/* .lt. 0: if INFO = -k, the kth argument had an illegal value */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ --in;
+ --d__;
+ --c__;
+ --b;
+ --a;
+
+ /* Function Body */
+ *info = 0;
+ if (*n < 0) {
+ *info = -1;
+ i__1 = -(*info);
+ xerbla_("SLAGTF", &i__1);
+ return 0;
+ }
+
+ if (*n == 0) {
+ return 0;
+ }
+
+ a[1] -= *lambda;
+ in[*n] = 0;
+ if (*n == 1) {
+ if (a[1] == 0.f) {
+ in[1] = 1;
+ }
+ return 0;
+ }
+
+ eps = slamch_("Epsilon");
+
+ tl = dmax(*tol,eps);
+ scale1 = dabs(a[1]) + dabs(b[1]);
+ i__1 = *n - 1;
+ for (k = 1; k <= i__1; ++k) {
+ a[k + 1] -= *lambda;
+ scale2 = (r__1 = c__[k], dabs(r__1)) + (r__2 = a[k + 1], dabs(r__2));
+ if (k < *n - 1) {
+ scale2 += (r__1 = b[k + 1], dabs(r__1));
+ }
+ if (a[k] == 0.f) {
+ piv1 = 0.f;
+ } else {
+ piv1 = (r__1 = a[k], dabs(r__1)) / scale1;
+ }
+ if (c__[k] == 0.f) {
+ in[k] = 0;
+ piv2 = 0.f;
+ scale1 = scale2;
+ if (k < *n - 1) {
+ d__[k] = 0.f;
+ }
+ } else {
+ piv2 = (r__1 = c__[k], dabs(r__1)) / scale2;
+ if (piv2 <= piv1) {
+ in[k] = 0;
+ scale1 = scale2;
+ c__[k] /= a[k];
+ a[k + 1] -= c__[k] * b[k];
+ if (k < *n - 1) {
+ d__[k] = 0.f;
+ }
+ } else {
+ in[k] = 1;
+ mult = a[k] / c__[k];
+ a[k] = c__[k];
+ temp = a[k + 1];
+ a[k + 1] = b[k] - mult * temp;
+ if (k < *n - 1) {
+ d__[k] = b[k + 1];
+ b[k + 1] = -mult * d__[k];
+ }
+ b[k] = temp;
+ c__[k] = mult;
+ }
+ }
+ if (dmax(piv1,piv2) <= tl && in[*n] == 0) {
+ in[*n] = k;
+ }
+/* L10: */
+ }
+ if ((r__1 = a[*n], dabs(r__1)) <= scale1 * tl && in[*n] == 0) {
+ in[*n] = *n;
+ }
+
+ return 0;
+
+/* End of SLAGTF */
+
+} /* slagtf_ */
projects / opencv / blobdiff