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Open Source Computer Vision Library
https://opencv.org/
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387 lines
8.2 KiB
387 lines
8.2 KiB
15 years ago
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#include "clapack.h"
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/* Subroutine */ int slazq4_(integer *i0, integer *n0, real *z__, integer *pp,
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integer *n0in, real *dmin__, real *dmin1, real *dmin2, real *dn,
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real *dn1, real *dn2, real *tau, integer *ttype, real *g)
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{
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/* System generated locals */
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integer i__1;
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real r__1, r__2;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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real s, a2, b1, b2;
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integer i4, nn, np;
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real gam, gap1, gap2;
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/* -- LAPACK auxiliary 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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/* SLAZQ4 computes an approximation TAU to the smallest eigenvalue */
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/* using values of d from the previous transform. */
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/* I0 (input) INTEGER */
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/* First index. */
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/* N0 (input) INTEGER */
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/* Last index. */
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/* Z (input) REAL array, dimension ( 4*N ) */
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/* Z holds the qd array. */
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/* PP (input) INTEGER */
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/* PP=0 for ping, PP=1 for pong. */
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/* N0IN (input) INTEGER */
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/* The value of N0 at start of EIGTEST. */
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/* DMIN (input) REAL */
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/* Minimum value of d. */
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/* DMIN1 (input) REAL */
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/* Minimum value of d, excluding D( N0 ). */
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/* DMIN2 (input) REAL */
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/* Minimum value of d, excluding D( N0 ) and D( N0-1 ). */
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/* DN (input) REAL */
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/* d(N) */
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/* DN1 (input) REAL */
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/* d(N-1) */
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/* DN2 (input) REAL */
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/* d(N-2) */
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/* TAU (output) REAL */
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/* This is the shift. */
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/* TTYPE (output) INTEGER */
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/* Shift type. */
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/* G (input/output) REAL */
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/* G is passed as an argument in order to save its value between */
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/* calls to SLAZQ4 */
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/* Further Details */
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/* =============== */
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/* CNST1 = 9/16 */
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/* This is a thread safe version of SLASQ4, which passes G through the */
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/* argument list in place of declaring G in a SAVE statment. */
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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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/* .. Executable Statements .. */
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/* A negative DMIN forces the shift to take that absolute value */
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/* TTYPE records the type of shift. */
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/* Parameter adjustments */
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--z__;
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/* Function Body */
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if (*dmin__ <= 0.f) {
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*tau = -(*dmin__);
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*ttype = -1;
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return 0;
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}
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nn = (*n0 << 2) + *pp;
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if (*n0in == *n0) {
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/* No eigenvalues deflated. */
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if (*dmin__ == *dn || *dmin__ == *dn1) {
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b1 = sqrt(z__[nn - 3]) * sqrt(z__[nn - 5]);
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b2 = sqrt(z__[nn - 7]) * sqrt(z__[nn - 9]);
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a2 = z__[nn - 7] + z__[nn - 5];
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/* Cases 2 and 3. */
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if (*dmin__ == *dn && *dmin1 == *dn1) {
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gap2 = *dmin2 - a2 - *dmin2 * .25f;
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if (gap2 > 0.f && gap2 > b2) {
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gap1 = a2 - *dn - b2 / gap2 * b2;
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} else {
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gap1 = a2 - *dn - (b1 + b2);
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}
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if (gap1 > 0.f && gap1 > b1) {
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/* Computing MAX */
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r__1 = *dn - b1 / gap1 * b1, r__2 = *dmin__ * .5f;
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s = dmax(r__1,r__2);
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*ttype = -2;
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} else {
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s = 0.f;
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if (*dn > b1) {
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s = *dn - b1;
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}
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if (a2 > b1 + b2) {
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/* Computing MIN */
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r__1 = s, r__2 = a2 - (b1 + b2);
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s = dmin(r__1,r__2);
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}
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/* Computing MAX */
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r__1 = s, r__2 = *dmin__ * .333f;
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s = dmax(r__1,r__2);
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*ttype = -3;
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}
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} else {
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/* Case 4. */
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*ttype = -4;
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s = *dmin__ * .25f;
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if (*dmin__ == *dn) {
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gam = *dn;
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a2 = 0.f;
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if (z__[nn - 5] > z__[nn - 7]) {
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return 0;
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}
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b2 = z__[nn - 5] / z__[nn - 7];
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np = nn - 9;
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} else {
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np = nn - (*pp << 1);
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b2 = z__[np - 2];
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gam = *dn1;
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if (z__[np - 4] > z__[np - 2]) {
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return 0;
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}
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a2 = z__[np - 4] / z__[np - 2];
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if (z__[nn - 9] > z__[nn - 11]) {
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return 0;
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}
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b2 = z__[nn - 9] / z__[nn - 11];
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np = nn - 13;
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}
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/* Approximate contribution to norm squared from I < NN-1. */
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a2 += b2;
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i__1 = (*i0 << 2) - 1 + *pp;
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for (i4 = np; i4 >= i__1; i4 += -4) {
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if (b2 == 0.f) {
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goto L20;
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}
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b1 = b2;
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if (z__[i4] > z__[i4 - 2]) {
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return 0;
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}
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b2 *= z__[i4] / z__[i4 - 2];
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a2 += b2;
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if (dmax(b2,b1) * 100.f < a2 || .563f < a2) {
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goto L20;
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}
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/* L10: */
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}
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L20:
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a2 *= 1.05f;
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/* Rayleigh quotient residual bound. */
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if (a2 < .563f) {
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s = gam * (1.f - sqrt(a2)) / (a2 + 1.f);
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}
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}
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} else if (*dmin__ == *dn2) {
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/* Case 5. */
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*ttype = -5;
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s = *dmin__ * .25f;
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/* Compute contribution to norm squared from I > NN-2. */
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np = nn - (*pp << 1);
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b1 = z__[np - 2];
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b2 = z__[np - 6];
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gam = *dn2;
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if (z__[np - 8] > b2 || z__[np - 4] > b1) {
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return 0;
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}
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a2 = z__[np - 8] / b2 * (z__[np - 4] / b1 + 1.f);
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/* Approximate contribution to norm squared from I < NN-2. */
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if (*n0 - *i0 > 2) {
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b2 = z__[nn - 13] / z__[nn - 15];
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a2 += b2;
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i__1 = (*i0 << 2) - 1 + *pp;
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for (i4 = nn - 17; i4 >= i__1; i4 += -4) {
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if (b2 == 0.f) {
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goto L40;
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}
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b1 = b2;
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if (z__[i4] > z__[i4 - 2]) {
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return 0;
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}
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b2 *= z__[i4] / z__[i4 - 2];
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a2 += b2;
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if (dmax(b2,b1) * 100.f < a2 || .563f < a2) {
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goto L40;
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}
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/* L30: */
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}
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L40:
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a2 *= 1.05f;
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}
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if (a2 < .563f) {
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s = gam * (1.f - sqrt(a2)) / (a2 + 1.f);
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}
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} else {
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/* Case 6, no information to guide us. */
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if (*ttype == -6) {
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*g += (1.f - *g) * .333f;
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} else if (*ttype == -18) {
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*g = .083250000000000005f;
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} else {
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*g = .25f;
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}
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s = *g * *dmin__;
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*ttype = -6;
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}
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} else if (*n0in == *n0 + 1) {
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/* One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN. */
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if (*dmin1 == *dn1 && *dmin2 == *dn2) {
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/* Cases 7 and 8. */
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*ttype = -7;
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s = *dmin1 * .333f;
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if (z__[nn - 5] > z__[nn - 7]) {
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return 0;
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}
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b1 = z__[nn - 5] / z__[nn - 7];
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b2 = b1;
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if (b2 == 0.f) {
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goto L60;
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}
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i__1 = (*i0 << 2) - 1 + *pp;
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for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) {
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a2 = b1;
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if (z__[i4] > z__[i4 - 2]) {
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return 0;
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}
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b1 *= z__[i4] / z__[i4 - 2];
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b2 += b1;
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if (dmax(b1,a2) * 100.f < b2) {
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goto L60;
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}
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/* L50: */
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}
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L60:
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b2 = sqrt(b2 * 1.05f);
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/* Computing 2nd power */
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r__1 = b2;
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a2 = *dmin1 / (r__1 * r__1 + 1.f);
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gap2 = *dmin2 * .5f - a2;
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if (gap2 > 0.f && gap2 > b2 * a2) {
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/* Computing MAX */
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r__1 = s, r__2 = a2 * (1.f - a2 * 1.01f * (b2 / gap2) * b2);
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s = dmax(r__1,r__2);
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} else {
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/* Computing MAX */
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r__1 = s, r__2 = a2 * (1.f - b2 * 1.01f);
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s = dmax(r__1,r__2);
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*ttype = -8;
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}
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} else {
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/* Case 9. */
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s = *dmin1 * .25f;
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if (*dmin1 == *dn1) {
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s = *dmin1 * .5f;
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}
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*ttype = -9;
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}
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} else if (*n0in == *n0 + 2) {
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/* Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN. */
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/* Cases 10 and 11. */
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if (*dmin2 == *dn2 && z__[nn - 5] * 2.f < z__[nn - 7]) {
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*ttype = -10;
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s = *dmin2 * .333f;
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if (z__[nn - 5] > z__[nn - 7]) {
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return 0;
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}
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b1 = z__[nn - 5] / z__[nn - 7];
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b2 = b1;
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if (b2 == 0.f) {
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goto L80;
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}
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i__1 = (*i0 << 2) - 1 + *pp;
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for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) {
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if (z__[i4] > z__[i4 - 2]) {
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return 0;
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}
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b1 *= z__[i4] / z__[i4 - 2];
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b2 += b1;
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if (b1 * 100.f < b2) {
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goto L80;
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}
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/* L70: */
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}
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L80:
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b2 = sqrt(b2 * 1.05f);
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/* Computing 2nd power */
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r__1 = b2;
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a2 = *dmin2 / (r__1 * r__1 + 1.f);
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gap2 = z__[nn - 7] + z__[nn - 9] - sqrt(z__[nn - 11]) * sqrt(z__[
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nn - 9]) - a2;
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if (gap2 > 0.f && gap2 > b2 * a2) {
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/* Computing MAX */
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r__1 = s, r__2 = a2 * (1.f - a2 * 1.01f * (b2 / gap2) * b2);
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s = dmax(r__1,r__2);
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} else {
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/* Computing MAX */
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r__1 = s, r__2 = a2 * (1.f - b2 * 1.01f);
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s = dmax(r__1,r__2);
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}
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} else {
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s = *dmin2 * .25f;
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*ttype = -11;
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}
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} else if (*n0in > *n0 + 2) {
|
||
|
|
|
||
|
|
/* Case 12, more than two eigenvalues deflated. No information. */
|
||
|
|
|
||
|
|
s = 0.f;
|
||
|
|
*ttype = -12;
|
||
|
|
}
|
||
|
|
|
||
|
|
*tau = s;
|
||
|
|
return 0;
|
||
|
|
|
||
|
|
/* End of SLAZQ4 */
|
||
|
|
|
||
|
|
} /* slazq4_ */
|