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176 lines
4.1 KiB
C
176 lines
4.1 KiB
C
#include "clapack.h"
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/* Subroutine */ int slaev2_(real *a, real *b, real *c__, real *rt1, real *
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rt2, real *cs1, real *sn1)
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{
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/* System generated locals */
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real r__1;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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real ab, df, cs, ct, tb, sm, tn, rt, adf, acs;
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integer sgn1, sgn2;
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real acmn, acmx;
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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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/* SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix */
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/* [ A B ] */
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/* [ B C ]. */
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/* On return, RT1 is the eigenvalue of larger absolute value, RT2 is the */
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/* eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right */
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/* eigenvector for RT1, giving the decomposition */
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/* [ CS1 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ] */
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/* [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]. */
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/* Arguments */
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/* ========= */
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/* A (input) REAL */
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/* The (1,1) element of the 2-by-2 matrix. */
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/* B (input) REAL */
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/* The (1,2) element and the conjugate of the (2,1) element of */
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/* the 2-by-2 matrix. */
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/* C (input) REAL */
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/* The (2,2) element of the 2-by-2 matrix. */
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/* RT1 (output) REAL */
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/* The eigenvalue of larger absolute value. */
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/* RT2 (output) REAL */
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/* The eigenvalue of smaller absolute value. */
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/* CS1 (output) REAL */
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/* SN1 (output) REAL */
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/* The vector (CS1, SN1) is a unit right eigenvector for RT1. */
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/* Further Details */
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/* =============== */
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/* RT1 is accurate to a few ulps barring over/underflow. */
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/* RT2 may be inaccurate if there is massive cancellation in the */
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/* determinant A*C-B*B; higher precision or correctly rounded or */
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/* correctly truncated arithmetic would be needed to compute RT2 */
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/* accurately in all cases. */
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/* CS1 and SN1 are accurate to a few ulps barring over/underflow. */
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/* Overflow is possible only if RT1 is within a factor of 5 of overflow. */
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/* Underflow is harmless if the input data is 0 or exceeds */
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/* underflow_threshold / macheps. */
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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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/* Compute the eigenvalues */
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sm = *a + *c__;
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df = *a - *c__;
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adf = dabs(df);
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tb = *b + *b;
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ab = dabs(tb);
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if (dabs(*a) > dabs(*c__)) {
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acmx = *a;
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acmn = *c__;
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} else {
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acmx = *c__;
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acmn = *a;
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}
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if (adf > ab) {
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/* Computing 2nd power */
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r__1 = ab / adf;
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rt = adf * sqrt(r__1 * r__1 + 1.f);
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} else if (adf < ab) {
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/* Computing 2nd power */
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r__1 = adf / ab;
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rt = ab * sqrt(r__1 * r__1 + 1.f);
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} else {
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/* Includes case AB=ADF=0 */
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rt = ab * sqrt(2.f);
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}
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if (sm < 0.f) {
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*rt1 = (sm - rt) * .5f;
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sgn1 = -1;
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/* Order of execution important. */
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/* To get fully accurate smaller eigenvalue, */
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/* next line needs to be executed in higher precision. */
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*rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
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} else if (sm > 0.f) {
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*rt1 = (sm + rt) * .5f;
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sgn1 = 1;
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/* Order of execution important. */
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/* To get fully accurate smaller eigenvalue, */
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/* next line needs to be executed in higher precision. */
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*rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
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} else {
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/* Includes case RT1 = RT2 = 0 */
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*rt1 = rt * .5f;
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*rt2 = rt * -.5f;
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sgn1 = 1;
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}
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/* Compute the eigenvector */
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if (df >= 0.f) {
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cs = df + rt;
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sgn2 = 1;
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} else {
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cs = df - rt;
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sgn2 = -1;
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}
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acs = dabs(cs);
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if (acs > ab) {
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ct = -tb / cs;
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*sn1 = 1.f / sqrt(ct * ct + 1.f);
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*cs1 = ct * *sn1;
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} else {
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if (ab == 0.f) {
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*cs1 = 1.f;
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*sn1 = 0.f;
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} else {
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tn = -cs / tb;
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*cs1 = 1.f / sqrt(tn * tn + 1.f);
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*sn1 = tn * *cs1;
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}
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}
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if (sgn1 == sgn2) {
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tn = *cs1;
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*cs1 = -(*sn1);
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*sn1 = tn;
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}
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return 0;
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/* End of SLAEV2 */
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} /* slaev2_ */
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