122 lines
3.1 KiB
C
122 lines
3.1 KiB
C
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#include "hypre_lapack.h"
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#include "f2c.h"
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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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/* -- LAPACK auxiliary routine (version 3.0) --
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Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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Courant Institute, Argonne National Lab, and Rice University
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October 31, 1992
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Purpose
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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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Arguments
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=========
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A (input) DOUBLE PRECISION
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The (1,1) element of the 2-by-2 matrix.
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B (input) DOUBLE PRECISION
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The (1,2) and (2,1) elements of the 2-by-2 matrix.
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C (input) DOUBLE PRECISION
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The (2,2) element of the 2-by-2 matrix.
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RT1 (output) DOUBLE PRECISION
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The eigenvalue of larger absolute value.
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RT2 (output) DOUBLE PRECISION
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The eigenvalue of smaller absolute value.
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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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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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Compute the eigenvalues */
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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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static doublereal acmn, acmx, ab, df, tb, sm, rt, adf;
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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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