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189 lines
5.5 KiB
189 lines
5.5 KiB
/* dlasd5.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 dlasd5_(integer *i__, doublereal *d__, doublereal *z__, |
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doublereal *delta, doublereal *rho, doublereal *dsigma, doublereal * |
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work) |
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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 b, c__, w, del, tau, delsq; |
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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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/* .. Array Arguments .. */ |
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/* .. */ |
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/* Purpose */ |
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/* ======= */ |
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/* This subroutine computes the square root of the I-th eigenvalue */ |
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/* of a positive symmetric rank-one modification of a 2-by-2 diagonal */ |
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/* matrix */ |
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/* diag( D ) * diag( D ) + RHO * Z * transpose(Z) . */ |
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/* The diagonal entries in the array D are assumed to satisfy */ |
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/* 0 <= D(i) < D(j) for i < j . */ |
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/* We also assume RHO > 0 and that the Euclidean norm of the vector */ |
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/* Z is one. */ |
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/* Arguments */ |
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/* ========= */ |
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/* I (input) INTEGER */ |
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/* The index of the eigenvalue to be computed. I = 1 or I = 2. */ |
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/* D (input) DOUBLE PRECISION array, dimension ( 2 ) */ |
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/* The original eigenvalues. We assume 0 <= D(1) < D(2). */ |
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/* Z (input) DOUBLE PRECISION array, dimension ( 2 ) */ |
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/* The components of the updating vector. */ |
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/* DELTA (output) DOUBLE PRECISION array, dimension ( 2 ) */ |
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/* Contains (D(j) - sigma_I) in its j-th component. */ |
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/* The vector DELTA contains the information necessary */ |
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/* to construct the eigenvectors. */ |
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/* RHO (input) DOUBLE PRECISION */ |
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/* The scalar in the symmetric updating formula. */ |
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/* DSIGMA (output) DOUBLE PRECISION */ |
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/* The computed sigma_I, the I-th updated eigenvalue. */ |
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/* WORK (workspace) DOUBLE PRECISION array, dimension ( 2 ) */ |
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/* WORK contains (D(j) + sigma_I) in its j-th component. */ |
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/* Further Details */ |
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/* =============== */ |
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/* Based on contributions by */ |
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/* Ren-Cang Li, Computer Science Division, University of California */ |
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/* at Berkeley, USA */ |
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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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/* Parameter adjustments */ |
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--work; |
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--delta; |
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--z__; |
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--d__; |
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/* Function Body */ |
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del = d__[2] - d__[1]; |
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delsq = del * (d__[2] + d__[1]); |
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if (*i__ == 1) { |
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w = *rho * 4. * (z__[2] * z__[2] / (d__[1] + d__[2] * 3.) - z__[1] * |
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z__[1] / (d__[1] * 3. + d__[2])) / del + 1.; |
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if (w > 0.) { |
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b = delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); |
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c__ = *rho * z__[1] * z__[1] * delsq; |
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/* B > ZERO, always */ |
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/* The following TAU is DSIGMA * DSIGMA - D( 1 ) * D( 1 ) */ |
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tau = c__ * 2. / (b + sqrt((d__1 = b * b - c__ * 4., abs(d__1)))); |
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/* The following TAU is DSIGMA - D( 1 ) */ |
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tau /= d__[1] + sqrt(d__[1] * d__[1] + tau); |
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*dsigma = d__[1] + tau; |
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delta[1] = -tau; |
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delta[2] = del - tau; |
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work[1] = d__[1] * 2. + tau; |
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work[2] = d__[1] + tau + d__[2]; |
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/* DELTA( 1 ) = -Z( 1 ) / TAU */ |
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/* DELTA( 2 ) = Z( 2 ) / ( DEL-TAU ) */ |
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} else { |
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b = -delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); |
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c__ = *rho * z__[2] * z__[2] * delsq; |
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/* The following TAU is DSIGMA * DSIGMA - D( 2 ) * D( 2 ) */ |
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if (b > 0.) { |
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tau = c__ * -2. / (b + sqrt(b * b + c__ * 4.)); |
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} else { |
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tau = (b - sqrt(b * b + c__ * 4.)) / 2.; |
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} |
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/* The following TAU is DSIGMA - D( 2 ) */ |
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tau /= d__[2] + sqrt((d__1 = d__[2] * d__[2] + tau, abs(d__1))); |
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*dsigma = d__[2] + tau; |
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delta[1] = -(del + tau); |
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delta[2] = -tau; |
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work[1] = d__[1] + tau + d__[2]; |
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work[2] = d__[2] * 2. + tau; |
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/* DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU ) */ |
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/* DELTA( 2 ) = -Z( 2 ) / TAU */ |
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} |
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/* TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) ) */ |
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/* DELTA( 1 ) = DELTA( 1 ) / TEMP */ |
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/* DELTA( 2 ) = DELTA( 2 ) / TEMP */ |
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} else { |
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/* Now I=2 */ |
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b = -delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); |
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c__ = *rho * z__[2] * z__[2] * delsq; |
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/* The following TAU is DSIGMA * DSIGMA - D( 2 ) * D( 2 ) */ |
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if (b > 0.) { |
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tau = (b + sqrt(b * b + c__ * 4.)) / 2.; |
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} else { |
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tau = c__ * 2. / (-b + sqrt(b * b + c__ * 4.)); |
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} |
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/* The following TAU is DSIGMA - D( 2 ) */ |
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tau /= d__[2] + sqrt(d__[2] * d__[2] + tau); |
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*dsigma = d__[2] + tau; |
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delta[1] = -(del + tau); |
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delta[2] = -tau; |
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work[1] = d__[1] + tau + d__[2]; |
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work[2] = d__[2] * 2. + tau; |
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/* DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU ) */ |
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/* DELTA( 2 ) = -Z( 2 ) / TAU */ |
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/* TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) ) */ |
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/* DELTA( 1 ) = DELTA( 1 ) / TEMP */ |
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/* DELTA( 2 ) = DELTA( 2 ) / TEMP */ |
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} |
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return 0; |
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/* End of DLASD5 */ |
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} /* dlasd5_ */
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