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/* dlaev2.f -- translated by f2c (version 20060506).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/*< SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) >*/
/* Subroutine */ int dlaev2_(doublereal *a, doublereal *b, doublereal *c__,
doublereal *rt1, doublereal *rt2, doublereal *cs1, doublereal *sn1)
{
/* System generated locals */
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal ab, df, cs, ct, tb, sm, tn, rt, adf, acs;
integer sgn1, sgn2;
doublereal acmn, acmx;
/* -- LAPACK auxiliary routine (version 2.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* October 31, 1992 */
/* .. Scalar Arguments .. */
/*< DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1 >*/
/* .. */
/* Purpose */
/* ======= */
/* DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix */
/* [ A B ] */
/* [ B C ]. */
/* On return, RT1 is the eigenvalue of larger absolute value, RT2 is the */
/* eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right */
/* eigenvector for RT1, giving the decomposition */
/* [ CS1 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ] */
/* [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]. */
/* Arguments */
/* ========= */
/* A (input) DOUBLE PRECISION */
/* The (1,1) element of the 2-by-2 matrix. */
/* B (input) DOUBLE PRECISION */
/* The (1,2) element and the conjugate of the (2,1) element of */
/* the 2-by-2 matrix. */
/* C (input) DOUBLE PRECISION */
/* The (2,2) element of the 2-by-2 matrix. */
/* RT1 (output) DOUBLE PRECISION */
/* The eigenvalue of larger absolute value. */
/* RT2 (output) DOUBLE PRECISION */
/* The eigenvalue of smaller absolute value. */
/* CS1 (output) DOUBLE PRECISION */
/* SN1 (output) DOUBLE PRECISION */
/* The vector (CS1, SN1) is a unit right eigenvector for RT1. */
/* Further Details */
/* =============== */
/* RT1 is accurate to a few ulps barring over/underflow. */
/* RT2 may be inaccurate if there is massive cancellation in the */
/* determinant A*C-B*B; higher precision or correctly rounded or */
/* correctly truncated arithmetic would be needed to compute RT2 */
/* accurately in all cases. */
/* CS1 and SN1 are accurate to a few ulps barring over/underflow. */
/* Overflow is possible only if RT1 is within a factor of 5 of overflow. */
/* Underflow is harmless if the input data is 0 or exceeds */
/* underflow_threshold / macheps. */
/* ===================================================================== */
/* .. Parameters .. */
/*< DOUBLE PRECISION ONE >*/
/*< PARAMETER ( ONE = 1.0D0 ) >*/
/*< DOUBLE PRECISION TWO >*/
/*< PARAMETER ( TWO = 2.0D0 ) >*/
/*< DOUBLE PRECISION ZERO >*/
/*< PARAMETER ( ZERO = 0.0D0 ) >*/
/*< DOUBLE PRECISION HALF >*/
/*< PARAMETER ( HALF = 0.5D0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< INTEGER SGN1, SGN2 >*/
/*< >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, SQRT >*/
/* .. */
/* .. Executable Statements .. */
/* Compute the eigenvalues */
/*< SM = A + C >*/
sm = *a + *c__;
/*< DF = A - C >*/
df = *a - *c__;
/*< ADF = ABS( DF ) >*/
adf = abs(df);
/*< TB = B + B >*/
tb = *b + *b;
/*< AB = ABS( TB ) >*/
ab = abs(tb);
/*< IF( ABS( A ).GT.ABS( C ) ) THEN >*/
if (abs(*a) > abs(*c__)) {
/*< ACMX = A >*/
acmx = *a;
/*< ACMN = C >*/
acmn = *c__;
/*< ELSE >*/
} else {
/*< ACMX = C >*/
acmx = *c__;
/*< ACMN = A >*/
acmn = *a;
/*< END IF >*/
}
/*< IF( ADF.GT.AB ) THEN >*/
if (adf > ab) {
/*< RT = ADF*SQRT( ONE+( AB / ADF )**2 ) >*/
/* Computing 2nd power */
d__1 = ab / adf;
rt = adf * sqrt(d__1 * d__1 + 1.);
/*< ELSE IF( ADF.LT.AB ) THEN >*/
} else if (adf < ab) {
/*< RT = AB*SQRT( ONE+( ADF / AB )**2 ) >*/
/* Computing 2nd power */
d__1 = adf / ab;
rt = ab * sqrt(d__1 * d__1 + 1.);
/*< ELSE >*/
} else {
/* Includes case AB=ADF=0 */
/*< RT = AB*SQRT( TWO ) >*/
rt = ab * sqrt(2.);
/*< END IF >*/
}
/*< IF( SM.LT.ZERO ) THEN >*/
if (sm < 0.) {
/*< RT1 = HALF*( SM-RT ) >*/
*rt1 = (sm - rt) * .5;
/*< SGN1 = -1 >*/
sgn1 = -1;
/* Order of execution important. */
/* To get fully accurate smaller eigenvalue, */
/* next line needs to be executed in higher precision. */
/*< RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B >*/
*rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
/*< ELSE IF( SM.GT.ZERO ) THEN >*/
} else if (sm > 0.) {
/*< RT1 = HALF*( SM+RT ) >*/
*rt1 = (sm + rt) * .5;
/*< SGN1 = 1 >*/
sgn1 = 1;
/* Order of execution important. */
/* To get fully accurate smaller eigenvalue, */
/* next line needs to be executed in higher precision. */
/*< RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B >*/
*rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
/*< ELSE >*/
} else {
/* Includes case RT1 = RT2 = 0 */
/*< RT1 = HALF*RT >*/
*rt1 = rt * .5;
/*< RT2 = -HALF*RT >*/
*rt2 = rt * -.5;
/*< SGN1 = 1 >*/
sgn1 = 1;
/*< END IF >*/
}
/* Compute the eigenvector */
/*< IF( DF.GE.ZERO ) THEN >*/
if (df >= 0.) {
/*< CS = DF + RT >*/
cs = df + rt;
/*< SGN2 = 1 >*/
sgn2 = 1;
/*< ELSE >*/
} else {
/*< CS = DF - RT >*/
cs = df - rt;
/*< SGN2 = -1 >*/
sgn2 = -1;
/*< END IF >*/
}
/*< ACS = ABS( CS ) >*/
acs = abs(cs);
/*< IF( ACS.GT.AB ) THEN >*/
if (acs > ab) {
/*< CT = -TB / CS >*/
ct = -tb / cs;
/*< SN1 = ONE / SQRT( ONE+CT*CT ) >*/
*sn1 = 1. / sqrt(ct * ct + 1.);
/*< CS1 = CT*SN1 >*/
*cs1 = ct * *sn1;
/*< ELSE >*/
} else {
/*< IF( AB.EQ.ZERO ) THEN >*/
if (ab == 0.) {
/*< CS1 = ONE >*/
*cs1 = 1.;
/*< SN1 = ZERO >*/
*sn1 = 0.;
/*< ELSE >*/
} else {
/*< TN = -CS / TB >*/
tn = -cs / tb;
/*< CS1 = ONE / SQRT( ONE+TN*TN ) >*/
*cs1 = 1. / sqrt(tn * tn + 1.);
/*< SN1 = TN*CS1 >*/
*sn1 = tn * *cs1;
/*< END IF >*/
}
/*< END IF >*/
}
/*< IF( SGN1.EQ.SGN2 ) THEN >*/
if (sgn1 == sgn2) {
/*< TN = CS1 >*/
tn = *cs1;
/*< CS1 = -SN1 >*/
*cs1 = -(*sn1);
/*< SN1 = TN >*/
*sn1 = tn;
/*< END IF >*/
}
/*< RETURN >*/
return 0;
/* End of DLAEV2 */
/*< END >*/
} /* dlaev2_ */
#ifdef __cplusplus
}
#endif
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