262 lines
6.1 KiB
C
262 lines
6.1 KiB
C
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#include "clapack.h"
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/* Table of constant values */
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static doublereal c_b3 = 2.;
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static doublereal c_b4 = 1.;
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/* Subroutine */ int dlasv2_(doublereal *f, doublereal *g, doublereal *h__,
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doublereal *ssmin, doublereal *ssmax, doublereal *snr, doublereal *
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csr, doublereal *snl, doublereal *csl)
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{
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/* System generated locals */
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doublereal d__1;
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/* Builtin functions */
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double sqrt(doublereal), d_sign(doublereal *, doublereal *);
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/* Local variables */
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doublereal a, d__, l, m, r__, s, t, fa, ga, ha, ft, gt, ht, mm, tt, clt,
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crt, slt, srt;
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integer pmax;
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doublereal temp;
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logical swap;
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doublereal tsign;
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extern doublereal dlamch_(char *);
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logical gasmal;
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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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/* Purpose */
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/* ======= */
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/* DLASV2 computes the singular value decomposition of a 2-by-2 */
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/* triangular matrix */
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/* [ F G ] */
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/* [ 0 H ]. */
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/* On return, abs(SSMAX) is the larger singular value, abs(SSMIN) is the */
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/* smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and */
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/* right singular vectors for abs(SSMAX), giving the decomposition */
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/* [ CSL SNL ] [ F G ] [ CSR -SNR ] = [ SSMAX 0 ] */
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/* [-SNL CSL ] [ 0 H ] [ SNR CSR ] [ 0 SSMIN ]. */
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/* Arguments */
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/* ========= */
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/* F (input) DOUBLE PRECISION */
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/* The (1,1) element of the 2-by-2 matrix. */
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/* G (input) DOUBLE PRECISION */
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/* The (1,2) element of the 2-by-2 matrix. */
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/* H (input) DOUBLE PRECISION */
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/* The (2,2) element of the 2-by-2 matrix. */
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/* SSMIN (output) DOUBLE PRECISION */
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/* abs(SSMIN) is the smaller singular value. */
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/* SSMAX (output) DOUBLE PRECISION */
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/* abs(SSMAX) is the larger singular value. */
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/* SNL (output) DOUBLE PRECISION */
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/* CSL (output) DOUBLE PRECISION */
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/* The vector (CSL, SNL) is a unit left singular vector for the */
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/* singular value abs(SSMAX). */
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/* SNR (output) DOUBLE PRECISION */
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/* CSR (output) DOUBLE PRECISION */
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/* The vector (CSR, SNR) is a unit right singular vector for the */
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/* singular value abs(SSMAX). */
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/* Further Details */
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/* =============== */
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/* Any input parameter may be aliased with any output parameter. */
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/* Barring over/underflow and assuming a guard digit in subtraction, all */
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/* output quantities are correct to within a few units in the last */
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/* place (ulps). */
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/* In IEEE arithmetic, the code works correctly if one matrix element is */
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/* infinite. */
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/* Overflow will not occur unless the largest singular value itself */
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/* overflows or is within a few ulps of overflow. (On machines with */
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/* partial overflow, like the Cray, overflow may occur if the largest */
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/* singular value is within a factor of 2 of overflow.) */
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/* Underflow is harmless if underflow is gradual. Otherwise, results */
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/* may correspond to a matrix modified by perturbations of size near */
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/* the underflow threshold. */
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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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/* .. Executable Statements .. */
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ft = *f;
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fa = abs(ft);
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ht = *h__;
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ha = abs(*h__);
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/* PMAX points to the maximum absolute element of matrix */
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/* PMAX = 1 if F largest in absolute values */
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/* PMAX = 2 if G largest in absolute values */
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/* PMAX = 3 if H largest in absolute values */
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pmax = 1;
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swap = ha > fa;
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if (swap) {
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pmax = 3;
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temp = ft;
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ft = ht;
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ht = temp;
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temp = fa;
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fa = ha;
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ha = temp;
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/* Now FA .ge. HA */
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}
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gt = *g;
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ga = abs(gt);
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if (ga == 0.) {
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/* Diagonal matrix */
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*ssmin = ha;
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*ssmax = fa;
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clt = 1.;
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crt = 1.;
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slt = 0.;
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srt = 0.;
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} else {
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gasmal = TRUE_;
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if (ga > fa) {
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pmax = 2;
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if (fa / ga < dlamch_("EPS")) {
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/* Case of very large GA */
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gasmal = FALSE_;
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*ssmax = ga;
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if (ha > 1.) {
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*ssmin = fa / (ga / ha);
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} else {
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*ssmin = fa / ga * ha;
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}
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clt = 1.;
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slt = ht / gt;
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srt = 1.;
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crt = ft / gt;
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}
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}
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if (gasmal) {
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/* Normal case */
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d__ = fa - ha;
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if (d__ == fa) {
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/* Copes with infinite F or H */
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l = 1.;
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} else {
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l = d__ / fa;
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}
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/* Note that 0 .le. L .le. 1 */
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m = gt / ft;
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/* Note that abs(M) .le. 1/macheps */
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t = 2. - l;
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/* Note that T .ge. 1 */
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mm = m * m;
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tt = t * t;
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s = sqrt(tt + mm);
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/* Note that 1 .le. S .le. 1 + 1/macheps */
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if (l == 0.) {
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r__ = abs(m);
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} else {
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r__ = sqrt(l * l + mm);
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}
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/* Note that 0 .le. R .le. 1 + 1/macheps */
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a = (s + r__) * .5;
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/* Note that 1 .le. A .le. 1 + abs(M) */
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*ssmin = ha / a;
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*ssmax = fa * a;
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if (mm == 0.) {
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/* Note that M is very tiny */
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if (l == 0.) {
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t = d_sign(&c_b3, &ft) * d_sign(&c_b4, >);
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} else {
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t = gt / d_sign(&d__, &ft) + m / t;
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}
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} else {
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t = (m / (s + t) + m / (r__ + l)) * (a + 1.);
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}
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l = sqrt(t * t + 4.);
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crt = 2. / l;
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srt = t / l;
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clt = (crt + srt * m) / a;
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slt = ht / ft * srt / a;
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}
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}
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if (swap) {
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*csl = srt;
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*snl = crt;
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*csr = slt;
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*snr = clt;
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} else {
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*csl = clt;
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*snl = slt;
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*csr = crt;
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*snr = srt;
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}
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/* Correct signs of SSMAX and SSMIN */
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if (pmax == 1) {
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tsign = d_sign(&c_b4, csr) * d_sign(&c_b4, csl) * d_sign(&c_b4, f);
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}
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if (pmax == 2) {
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tsign = d_sign(&c_b4, snr) * d_sign(&c_b4, csl) * d_sign(&c_b4, g);
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}
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if (pmax == 3) {
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tsign = d_sign(&c_b4, snr) * d_sign(&c_b4, snl) * d_sign(&c_b4, h__);
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}
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*ssmax = d_sign(ssmax, &tsign);
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d__1 = tsign * d_sign(&c_b4, f) * d_sign(&c_b4, h__);
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*ssmin = d_sign(ssmin, &d__1);
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return 0;
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/* End of DLASV2 */
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} /* dlasv2_ */
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