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460 lines
9.4 KiB
460 lines
9.4 KiB
/* ssterf.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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/* Table of constant values */ |
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static integer c__0 = 0; |
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static integer c__1 = 1; |
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static real c_b32 = 1.f; |
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/* Subroutine */ int ssterf_(integer *n, real *d__, real *e, integer *info) |
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{ |
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/* System generated locals */ |
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integer i__1; |
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real r__1, r__2, r__3; |
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/* Builtin functions */ |
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double sqrt(doublereal), r_sign(real *, real *); |
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/* Local variables */ |
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real c__; |
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integer i__, l, m; |
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real p, r__, s; |
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integer l1; |
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real bb, rt1, rt2, eps, rte; |
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integer lsv; |
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real eps2, oldc; |
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integer lend, jtot; |
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extern /* Subroutine */ int slae2_(real *, real *, real *, real *, real *) |
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; |
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real gamma, alpha, sigma, anorm; |
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extern doublereal slapy2_(real *, real *); |
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integer iscale; |
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real oldgam; |
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extern doublereal slamch_(char *); |
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real safmin; |
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extern /* Subroutine */ int xerbla_(char *, integer *); |
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real safmax; |
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extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, |
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real *, integer *, integer *, real *, integer *, integer *); |
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integer lendsv; |
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real ssfmin; |
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integer nmaxit; |
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real ssfmax; |
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extern doublereal slanst_(char *, integer *, real *, real *); |
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extern /* Subroutine */ int slasrt_(char *, integer *, real *, integer *); |
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/* -- LAPACK 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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/* SSTERF computes all eigenvalues of a symmetric tridiagonal matrix */ |
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/* using the Pal-Walker-Kahan variant of the QL or QR algorithm. */ |
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/* Arguments */ |
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/* ========= */ |
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/* N (input) INTEGER */ |
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/* The order of the matrix. N >= 0. */ |
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/* D (input/output) REAL array, dimension (N) */ |
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/* On entry, the n diagonal elements of the tridiagonal matrix. */ |
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/* On exit, if INFO = 0, the eigenvalues in ascending order. */ |
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/* E (input/output) REAL array, dimension (N-1) */ |
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/* On entry, the (n-1) subdiagonal elements of the tridiagonal */ |
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/* matrix. */ |
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/* On exit, E has been destroyed. */ |
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/* INFO (output) INTEGER */ |
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/* = 0: successful exit */ |
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/* < 0: if INFO = -i, the i-th argument had an illegal value */ |
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/* > 0: the algorithm failed to find all of the eigenvalues in */ |
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/* a total of 30*N iterations; if INFO = i, then i */ |
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/* elements of E have not converged to zero. */ |
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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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/* .. External Functions .. */ |
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/* .. */ |
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/* .. External Subroutines .. */ |
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/* .. */ |
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/* .. Intrinsic Functions .. */ |
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/* .. */ |
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/* .. Executable Statements .. */ |
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/* Test the input parameters. */ |
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/* Parameter adjustments */ |
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--e; |
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--d__; |
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/* Function Body */ |
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*info = 0; |
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/* Quick return if possible */ |
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if (*n < 0) { |
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*info = -1; |
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i__1 = -(*info); |
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xerbla_("SSTERF", &i__1); |
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return 0; |
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} |
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if (*n <= 1) { |
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return 0; |
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} |
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/* Determine the unit roundoff for this environment. */ |
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eps = slamch_("E"); |
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/* Computing 2nd power */ |
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r__1 = eps; |
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eps2 = r__1 * r__1; |
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safmin = slamch_("S"); |
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safmax = 1.f / safmin; |
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ssfmax = sqrt(safmax) / 3.f; |
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ssfmin = sqrt(safmin) / eps2; |
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/* Compute the eigenvalues of the tridiagonal matrix. */ |
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nmaxit = *n * 30; |
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sigma = 0.f; |
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jtot = 0; |
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/* Determine where the matrix splits and choose QL or QR iteration */ |
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/* for each block, according to whether top or bottom diagonal */ |
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/* element is smaller. */ |
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l1 = 1; |
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L10: |
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if (l1 > *n) { |
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goto L170; |
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} |
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if (l1 > 1) { |
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e[l1 - 1] = 0.f; |
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} |
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i__1 = *n - 1; |
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for (m = l1; m <= i__1; ++m) { |
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if ((r__3 = e[m], dabs(r__3)) <= sqrt((r__1 = d__[m], dabs(r__1))) * |
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sqrt((r__2 = d__[m + 1], dabs(r__2))) * eps) { |
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e[m] = 0.f; |
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goto L30; |
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} |
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/* L20: */ |
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} |
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m = *n; |
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L30: |
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l = l1; |
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lsv = l; |
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lend = m; |
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lendsv = lend; |
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l1 = m + 1; |
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if (lend == l) { |
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goto L10; |
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} |
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/* Scale submatrix in rows and columns L to LEND */ |
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i__1 = lend - l + 1; |
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anorm = slanst_("I", &i__1, &d__[l], &e[l]); |
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iscale = 0; |
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if (anorm > ssfmax) { |
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iscale = 1; |
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i__1 = lend - l + 1; |
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slascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, |
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info); |
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i__1 = lend - l; |
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slascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, |
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info); |
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} else if (anorm < ssfmin) { |
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iscale = 2; |
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i__1 = lend - l + 1; |
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slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, |
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info); |
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i__1 = lend - l; |
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slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, |
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info); |
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} |
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i__1 = lend - 1; |
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for (i__ = l; i__ <= i__1; ++i__) { |
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/* Computing 2nd power */ |
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r__1 = e[i__]; |
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e[i__] = r__1 * r__1; |
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/* L40: */ |
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} |
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/* Choose between QL and QR iteration */ |
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if ((r__1 = d__[lend], dabs(r__1)) < (r__2 = d__[l], dabs(r__2))) { |
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lend = lsv; |
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l = lendsv; |
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} |
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if (lend >= l) { |
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/* QL Iteration */ |
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/* Look for small subdiagonal element. */ |
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L50: |
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if (l != lend) { |
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i__1 = lend - 1; |
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for (m = l; m <= i__1; ++m) { |
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if ((r__2 = e[m], dabs(r__2)) <= eps2 * (r__1 = d__[m] * d__[ |
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m + 1], dabs(r__1))) { |
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goto L70; |
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} |
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/* L60: */ |
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} |
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} |
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m = lend; |
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L70: |
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if (m < lend) { |
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e[m] = 0.f; |
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} |
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p = d__[l]; |
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if (m == l) { |
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goto L90; |
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} |
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/* If remaining matrix is 2 by 2, use SLAE2 to compute its */ |
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/* eigenvalues. */ |
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if (m == l + 1) { |
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rte = sqrt(e[l]); |
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slae2_(&d__[l], &rte, &d__[l + 1], &rt1, &rt2); |
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d__[l] = rt1; |
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d__[l + 1] = rt2; |
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e[l] = 0.f; |
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l += 2; |
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if (l <= lend) { |
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goto L50; |
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} |
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goto L150; |
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} |
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if (jtot == nmaxit) { |
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goto L150; |
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} |
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++jtot; |
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/* Form shift. */ |
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rte = sqrt(e[l]); |
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sigma = (d__[l + 1] - p) / (rte * 2.f); |
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r__ = slapy2_(&sigma, &c_b32); |
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sigma = p - rte / (sigma + r_sign(&r__, &sigma)); |
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c__ = 1.f; |
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s = 0.f; |
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gamma = d__[m] - sigma; |
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p = gamma * gamma; |
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/* Inner loop */ |
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i__1 = l; |
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for (i__ = m - 1; i__ >= i__1; --i__) { |
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bb = e[i__]; |
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r__ = p + bb; |
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if (i__ != m - 1) { |
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e[i__ + 1] = s * r__; |
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} |
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oldc = c__; |
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c__ = p / r__; |
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s = bb / r__; |
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oldgam = gamma; |
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alpha = d__[i__]; |
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gamma = c__ * (alpha - sigma) - s * oldgam; |
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d__[i__ + 1] = oldgam + (alpha - gamma); |
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if (c__ != 0.f) { |
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p = gamma * gamma / c__; |
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} else { |
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p = oldc * bb; |
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} |
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/* L80: */ |
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} |
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e[l] = s * p; |
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d__[l] = sigma + gamma; |
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goto L50; |
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/* Eigenvalue found. */ |
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L90: |
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d__[l] = p; |
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++l; |
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if (l <= lend) { |
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goto L50; |
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} |
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goto L150; |
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} else { |
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/* QR Iteration */ |
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/* Look for small superdiagonal element. */ |
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L100: |
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i__1 = lend + 1; |
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for (m = l; m >= i__1; --m) { |
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if ((r__2 = e[m - 1], dabs(r__2)) <= eps2 * (r__1 = d__[m] * d__[ |
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m - 1], dabs(r__1))) { |
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goto L120; |
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} |
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/* L110: */ |
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} |
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m = lend; |
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L120: |
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if (m > lend) { |
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e[m - 1] = 0.f; |
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} |
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p = d__[l]; |
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if (m == l) { |
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goto L140; |
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} |
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/* If remaining matrix is 2 by 2, use SLAE2 to compute its */ |
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/* eigenvalues. */ |
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if (m == l - 1) { |
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rte = sqrt(e[l - 1]); |
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slae2_(&d__[l], &rte, &d__[l - 1], &rt1, &rt2); |
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d__[l] = rt1; |
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d__[l - 1] = rt2; |
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e[l - 1] = 0.f; |
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l += -2; |
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if (l >= lend) { |
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goto L100; |
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} |
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goto L150; |
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} |
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if (jtot == nmaxit) { |
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goto L150; |
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} |
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++jtot; |
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/* Form shift. */ |
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rte = sqrt(e[l - 1]); |
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sigma = (d__[l - 1] - p) / (rte * 2.f); |
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r__ = slapy2_(&sigma, &c_b32); |
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sigma = p - rte / (sigma + r_sign(&r__, &sigma)); |
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c__ = 1.f; |
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s = 0.f; |
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gamma = d__[m] - sigma; |
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p = gamma * gamma; |
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/* Inner loop */ |
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i__1 = l - 1; |
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for (i__ = m; i__ <= i__1; ++i__) { |
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bb = e[i__]; |
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r__ = p + bb; |
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if (i__ != m) { |
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e[i__ - 1] = s * r__; |
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} |
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oldc = c__; |
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c__ = p / r__; |
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s = bb / r__; |
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oldgam = gamma; |
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alpha = d__[i__ + 1]; |
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gamma = c__ * (alpha - sigma) - s * oldgam; |
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d__[i__] = oldgam + (alpha - gamma); |
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if (c__ != 0.f) { |
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p = gamma * gamma / c__; |
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} else { |
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p = oldc * bb; |
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} |
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/* L130: */ |
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} |
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e[l - 1] = s * p; |
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d__[l] = sigma + gamma; |
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goto L100; |
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/* Eigenvalue found. */ |
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L140: |
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d__[l] = p; |
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--l; |
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if (l >= lend) { |
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goto L100; |
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} |
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goto L150; |
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} |
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/* Undo scaling if necessary */ |
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L150: |
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if (iscale == 1) { |
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i__1 = lendsv - lsv + 1; |
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slascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], |
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n, info); |
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} |
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if (iscale == 2) { |
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i__1 = lendsv - lsv + 1; |
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slascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], |
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n, info); |
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} |
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/* Check for no convergence to an eigenvalue after a total */ |
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/* of N*MAXIT iterations. */ |
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if (jtot < nmaxit) { |
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goto L10; |
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} |
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i__1 = *n - 1; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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if (e[i__] != 0.f) { |
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++(*info); |
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} |
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/* L160: */ |
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} |
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goto L180; |
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/* Sort eigenvalues in increasing order. */ |
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L170: |
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slasrt_("I", n, &d__[1], info); |
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L180: |
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return 0; |
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/* End of SSTERF */ |
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} /* ssterf_ */
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