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188 lines
4.6 KiB
188 lines
4.6 KiB
/* slaev2.f -- translated by f2c (version 20061008). |
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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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#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 3.2) -- */ |
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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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