211 lines
5.5 KiB
C++
211 lines
5.5 KiB
C++
/* fortran/dlae2.f -- translated by f2c (version 20200916).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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/* > \brief \b DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download DLAE2 + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlae2.f
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"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlae2.f
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"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlae2.f
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"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE DLAE2( A, B, C, RT1, RT2 ) */
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/* .. Scalar Arguments .. */
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/* DOUBLE PRECISION A, B, C, RT1, RT2 */
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/* .. */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > DLAE2 computes the eigenvalues 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, and RT2 */
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/* > is the eigenvalue of smaller absolute value. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] A */
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/* > \verbatim */
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/* > A is DOUBLE PRECISION */
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/* > The (1,1) element of the 2-by-2 matrix. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] B */
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/* > \verbatim */
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/* > B is DOUBLE PRECISION */
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/* > The (1,2) and (2,1) elements of the 2-by-2 matrix. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] C */
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/* > \verbatim */
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/* > C is DOUBLE PRECISION */
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/* > The (2,2) element of the 2-by-2 matrix. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] RT1 */
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/* > \verbatim */
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/* > RT1 is DOUBLE PRECISION */
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/* > The eigenvalue of larger absolute value. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] RT2 */
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/* > \verbatim */
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/* > RT2 is DOUBLE PRECISION */
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/* > The eigenvalue of smaller absolute value. */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \ingroup OTHERauxiliary */
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/* > \par Further Details: */
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/* ===================== */
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/* > */
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/* > \verbatim */
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/* > */
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/* > RT1 is accurate to a few ulps barring over/underflow. */
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/* > */
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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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/* > */
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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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/* > \endverbatim */
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/* > */
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/* ===================================================================== */
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/* Subroutine */ int dlae2_(doublereal *a, doublereal *b, doublereal *c__,
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doublereal *rt1, doublereal *rt2)
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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);
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/* Local variables */
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doublereal ab, df, tb, sm, rt, adf, acmn, acmx;
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/* -- LAPACK auxiliary routine -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* .. Scalar Arguments .. */
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/* .. */
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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 = abs(df);
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tb = *b + *b;
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ab = abs(tb);
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if (abs(*a) > abs(*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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d__1 = ab / adf;
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rt = adf * sqrt(d__1 * d__1 + 1.);
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} else if (adf < ab) {
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/* Computing 2nd power */
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d__1 = adf / ab;
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rt = ab * sqrt(d__1 * d__1 + 1.);
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} else {
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/* Includes case AB=ADF=0 */
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rt = ab * sqrt(2.);
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}
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if (sm < 0.) {
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*rt1 = (sm - rt) * .5;
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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.) {
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*rt1 = (sm + rt) * .5;
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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 * .5;
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*rt2 = rt * -.5;
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}
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return 0;
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/* End of DLAE2 */
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} /* dlae2_ */
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#ifdef __cplusplus
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}
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#endif
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