--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static integer c__0 = 0;
+static integer c__1 = 1;
+static real c_b32 = 1.f;
+
+/* Subroutine */ int ssterf_(integer *n, real *d__, real *e, integer *info)
+{
+ /* System generated locals */
+ integer i__1;
+ real r__1, r__2, r__3;
+
+ /* Builtin functions */
+ double sqrt(doublereal), r_sign(real *, real *);
+
+ /* Local variables */
+ real c__;
+ integer i__, l, m;
+ real p, r__, s;
+ integer l1;
+ real bb, rt1, rt2, eps, rte;
+ integer lsv;
+ real eps2, oldc;
+ integer lend, jtot;
+ extern /* Subroutine */ int slae2_(real *, real *, real *, real *, real *)
+ ;
+ real gamma, alpha, sigma, anorm;
+ extern doublereal slapy2_(real *, real *);
+ integer iscale;
+ real oldgam;
+ extern doublereal slamch_(char *);
+ real safmin;
+ extern /* Subroutine */ int xerbla_(char *, integer *);
+ real safmax;
+ extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
+ real *, integer *, integer *, real *, integer *, integer *);
+ integer lendsv;
+ real ssfmin;
+ integer nmaxit;
+ real ssfmax;
+ extern doublereal slanst_(char *, integer *, real *, real *);
+ extern /* Subroutine */ int slasrt_(char *, integer *, real *, integer *);
+
+
+/* -- LAPACK routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SSTERF computes all eigenvalues of a symmetric tridiagonal matrix */
+/* using the Pal-Walker-Kahan variant of the QL or QR algorithm. */
+
+/* Arguments */
+/* ========= */
+
+/* N (input) INTEGER */
+/* The order of the matrix. N >= 0. */
+
+/* D (input/output) REAL array, dimension (N) */
+/* On entry, the n diagonal elements of the tridiagonal matrix. */
+/* On exit, if INFO = 0, the eigenvalues in ascending order. */
+
+/* E (input/output) REAL array, dimension (N-1) */
+/* On entry, the (n-1) subdiagonal elements of the tridiagonal */
+/* matrix. */
+/* On exit, E has been destroyed. */
+
+/* INFO (output) INTEGER */
+/* = 0: successful exit */
+/* < 0: if INFO = -i, the i-th argument had an illegal value */
+/* > 0: the algorithm failed to find all of the eigenvalues in */
+/* a total of 30*N iterations; if INFO = i, then i */
+/* elements of E have not converged to zero. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ --e;
+ --d__;
+
+ /* Function Body */
+ *info = 0;
+
+/* Quick return if possible */
+
+ if (*n < 0) {
+ *info = -1;
+ i__1 = -(*info);
+ xerbla_("SSTERF", &i__1);
+ return 0;
+ }
+ if (*n <= 1) {
+ return 0;
+ }
+
+/* Determine the unit roundoff for this environment. */
+
+ eps = slamch_("E");
+/* Computing 2nd power */
+ r__1 = eps;
+ eps2 = r__1 * r__1;
+ safmin = slamch_("S");
+ safmax = 1.f / safmin;
+ ssfmax = sqrt(safmax) / 3.f;
+ ssfmin = sqrt(safmin) / eps2;
+
+/* Compute the eigenvalues of the tridiagonal matrix. */
+
+ nmaxit = *n * 30;
+ sigma = 0.f;
+ jtot = 0;
+
+/* Determine where the matrix splits and choose QL or QR iteration */
+/* for each block, according to whether top or bottom diagonal */
+/* element is smaller. */
+
+ l1 = 1;
+
+L10:
+ if (l1 > *n) {
+ goto L170;
+ }
+ if (l1 > 1) {
+ e[l1 - 1] = 0.f;
+ }
+ i__1 = *n - 1;
+ for (m = l1; m <= i__1; ++m) {
+ if ((r__3 = e[m], dabs(r__3)) <= sqrt((r__1 = d__[m], dabs(r__1))) *
+ sqrt((r__2 = d__[m + 1], dabs(r__2))) * eps) {
+ e[m] = 0.f;
+ goto L30;
+ }
+/* L20: */
+ }
+ m = *n;
+
+L30:
+ l = l1;
+ lsv = l;
+ lend = m;
+ lendsv = lend;
+ l1 = m + 1;
+ if (lend == l) {
+ goto L10;
+ }
+
+/* Scale submatrix in rows and columns L to LEND */
+
+ i__1 = lend - l + 1;
+ anorm = slanst_("I", &i__1, &d__[l], &e[l]);
+ iscale = 0;
+ if (anorm > ssfmax) {
+ iscale = 1;
+ i__1 = lend - l + 1;
+ slascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n,
+ info);
+ i__1 = lend - l;
+ slascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n,
+ info);
+ } else if (anorm < ssfmin) {
+ iscale = 2;
+ i__1 = lend - l + 1;
+ slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n,
+ info);
+ i__1 = lend - l;
+ slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n,
+ info);
+ }
+
+ i__1 = lend - 1;
+ for (i__ = l; i__ <= i__1; ++i__) {
+/* Computing 2nd power */
+ r__1 = e[i__];
+ e[i__] = r__1 * r__1;
+/* L40: */
+ }
+
+/* Choose between QL and QR iteration */
+
+ if ((r__1 = d__[lend], dabs(r__1)) < (r__2 = d__[l], dabs(r__2))) {
+ lend = lsv;
+ l = lendsv;
+ }
+
+ if (lend >= l) {
+
+/* QL Iteration */
+
+/* Look for small subdiagonal element. */
+
+L50:
+ if (l != lend) {
+ i__1 = lend - 1;
+ for (m = l; m <= i__1; ++m) {
+ if ((r__2 = e[m], dabs(r__2)) <= eps2 * (r__1 = d__[m] * d__[
+ m + 1], dabs(r__1))) {
+ goto L70;
+ }
+/* L60: */
+ }
+ }
+ m = lend;
+
+L70:
+ if (m < lend) {
+ e[m] = 0.f;
+ }
+ p = d__[l];
+ if (m == l) {
+ goto L90;
+ }
+
+/* If remaining matrix is 2 by 2, use SLAE2 to compute its */
+/* eigenvalues. */
+
+ if (m == l + 1) {
+ rte = sqrt(e[l]);
+ slae2_(&d__[l], &rte, &d__[l + 1], &rt1, &rt2);
+ d__[l] = rt1;
+ d__[l + 1] = rt2;
+ e[l] = 0.f;
+ l += 2;
+ if (l <= lend) {
+ goto L50;
+ }
+ goto L150;
+ }
+
+ if (jtot == nmaxit) {
+ goto L150;
+ }
+ ++jtot;
+
+/* Form shift. */
+
+ rte = sqrt(e[l]);
+ sigma = (d__[l + 1] - p) / (rte * 2.f);
+ r__ = slapy2_(&sigma, &c_b32);
+ sigma = p - rte / (sigma + r_sign(&r__, &sigma));
+
+ c__ = 1.f;
+ s = 0.f;
+ gamma = d__[m] - sigma;
+ p = gamma * gamma;
+
+/* Inner loop */
+
+ i__1 = l;
+ for (i__ = m - 1; i__ >= i__1; --i__) {
+ bb = e[i__];
+ r__ = p + bb;
+ if (i__ != m - 1) {
+ e[i__ + 1] = s * r__;
+ }
+ oldc = c__;
+ c__ = p / r__;
+ s = bb / r__;
+ oldgam = gamma;
+ alpha = d__[i__];
+ gamma = c__ * (alpha - sigma) - s * oldgam;
+ d__[i__ + 1] = oldgam + (alpha - gamma);
+ if (c__ != 0.f) {
+ p = gamma * gamma / c__;
+ } else {
+ p = oldc * bb;
+ }
+/* L80: */
+ }
+
+ e[l] = s * p;
+ d__[l] = sigma + gamma;
+ goto L50;
+
+/* Eigenvalue found. */
+
+L90:
+ d__[l] = p;
+
+ ++l;
+ if (l <= lend) {
+ goto L50;
+ }
+ goto L150;
+
+ } else {
+
+/* QR Iteration */
+
+/* Look for small superdiagonal element. */
+
+L100:
+ i__1 = lend + 1;
+ for (m = l; m >= i__1; --m) {
+ if ((r__2 = e[m - 1], dabs(r__2)) <= eps2 * (r__1 = d__[m] * d__[
+ m - 1], dabs(r__1))) {
+ goto L120;
+ }
+/* L110: */
+ }
+ m = lend;
+
+L120:
+ if (m > lend) {
+ e[m - 1] = 0.f;
+ }
+ p = d__[l];
+ if (m == l) {
+ goto L140;
+ }
+
+/* If remaining matrix is 2 by 2, use SLAE2 to compute its */
+/* eigenvalues. */
+
+ if (m == l - 1) {
+ rte = sqrt(e[l - 1]);
+ slae2_(&d__[l], &rte, &d__[l - 1], &rt1, &rt2);
+ d__[l] = rt1;
+ d__[l - 1] = rt2;
+ e[l - 1] = 0.f;
+ l += -2;
+ if (l >= lend) {
+ goto L100;
+ }
+ goto L150;
+ }
+
+ if (jtot == nmaxit) {
+ goto L150;
+ }
+ ++jtot;
+
+/* Form shift. */
+
+ rte = sqrt(e[l - 1]);
+ sigma = (d__[l - 1] - p) / (rte * 2.f);
+ r__ = slapy2_(&sigma, &c_b32);
+ sigma = p - rte / (sigma + r_sign(&r__, &sigma));
+
+ c__ = 1.f;
+ s = 0.f;
+ gamma = d__[m] - sigma;
+ p = gamma * gamma;
+
+/* Inner loop */
+
+ i__1 = l - 1;
+ for (i__ = m; i__ <= i__1; ++i__) {
+ bb = e[i__];
+ r__ = p + bb;
+ if (i__ != m) {
+ e[i__ - 1] = s * r__;
+ }
+ oldc = c__;
+ c__ = p / r__;
+ s = bb / r__;
+ oldgam = gamma;
+ alpha = d__[i__ + 1];
+ gamma = c__ * (alpha - sigma) - s * oldgam;
+ d__[i__] = oldgam + (alpha - gamma);
+ if (c__ != 0.f) {
+ p = gamma * gamma / c__;
+ } else {
+ p = oldc * bb;
+ }
+/* L130: */
+ }
+
+ e[l - 1] = s * p;
+ d__[l] = sigma + gamma;
+ goto L100;
+
+/* Eigenvalue found. */
+
+L140:
+ d__[l] = p;
+
+ --l;
+ if (l >= lend) {
+ goto L100;
+ }
+ goto L150;
+
+ }
+
+/* Undo scaling if necessary */
+
+L150:
+ if (iscale == 1) {
+ i__1 = lendsv - lsv + 1;
+ slascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv],
+ n, info);
+ }
+ if (iscale == 2) {
+ i__1 = lendsv - lsv + 1;
+ slascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv],
+ n, info);
+ }
+
+/* Check for no convergence to an eigenvalue after a total */
+/* of N*MAXIT iterations. */
+
+ if (jtot < nmaxit) {
+ goto L10;
+ }
+ i__1 = *n - 1;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ if (e[i__] != 0.f) {
+ ++(*info);
+ }
+/* L160: */
+ }
+ goto L180;
+
+/* Sort eigenvalues in increasing order. */
+
+L170:
+ slasrt_("I", n, &d__[1], info);
+
+L180:
+ return 0;
+
+/* End of SSTERF */
+
+} /* ssterf_ */
projects / opencv / blobdiff