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336 lines
10 KiB
336 lines
10 KiB
/* slaed3.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__1 = 1; |
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static real c_b22 = 1.f; |
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static real c_b23 = 0.f; |
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/* Subroutine */ int slaed3_(integer *k, integer *n, integer *n1, real *d__, |
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real *q, integer *ldq, real *rho, real *dlamda, real *q2, integer * |
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indx, integer *ctot, real *w, real *s, integer *info) |
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{ |
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/* System generated locals */ |
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integer q_dim1, q_offset, i__1, i__2; |
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real r__1; |
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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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integer i__, j, n2, n12, ii, n23, iq2; |
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real temp; |
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extern doublereal snrm2_(integer *, real *, integer *); |
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extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, |
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integer *, real *, real *, integer *, real *, integer *, real *, |
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real *, integer *), scopy_(integer *, real *, |
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integer *, real *, integer *), slaed4_(integer *, integer *, real |
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*, real *, real *, real *, real *, integer *); |
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extern doublereal slamc3_(real *, real *); |
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extern /* Subroutine */ int xerbla_(char *, integer *), slacpy_( |
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char *, integer *, integer *, real *, integer *, real *, integer * |
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), slaset_(char *, integer *, integer *, real *, real *, |
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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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/* SLAED3 finds the roots of the secular equation, as defined by the */ |
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/* values in D, W, and RHO, between 1 and K. It makes the */ |
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/* appropriate calls to SLAED4 and then updates the eigenvectors by */ |
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/* multiplying the matrix of eigenvectors of the pair of eigensystems */ |
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/* being combined by the matrix of eigenvectors of the K-by-K system */ |
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/* which is solved here. */ |
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/* This code makes very mild assumptions about floating point */ |
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/* arithmetic. It will work on machines with a guard digit in */ |
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/* add/subtract, or on those binary machines without guard digits */ |
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/* which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */ |
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/* It could conceivably fail on hexadecimal or decimal machines */ |
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/* without guard digits, but we know of none. */ |
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/* Arguments */ |
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/* ========= */ |
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/* K (input) INTEGER */ |
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/* The number of terms in the rational function to be solved by */ |
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/* SLAED4. K >= 0. */ |
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/* N (input) INTEGER */ |
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/* The number of rows and columns in the Q matrix. */ |
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/* N >= K (deflation may result in N>K). */ |
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/* N1 (input) INTEGER */ |
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/* The location of the last eigenvalue in the leading submatrix. */ |
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/* min(1,N) <= N1 <= N/2. */ |
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/* D (output) REAL array, dimension (N) */ |
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/* D(I) contains the updated eigenvalues for */ |
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/* 1 <= I <= K. */ |
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/* Q (output) REAL array, dimension (LDQ,N) */ |
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/* Initially the first K columns are used as workspace. */ |
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/* On output the columns 1 to K contain */ |
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/* the updated eigenvectors. */ |
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/* LDQ (input) INTEGER */ |
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/* The leading dimension of the array Q. LDQ >= max(1,N). */ |
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/* RHO (input) REAL */ |
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/* The value of the parameter in the rank one update equation. */ |
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/* RHO >= 0 required. */ |
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/* DLAMDA (input/output) REAL array, dimension (K) */ |
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/* The first K elements of this array contain the old roots */ |
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/* of the deflated updating problem. These are the poles */ |
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/* of the secular equation. May be changed on output by */ |
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/* having lowest order bit set to zero on Cray X-MP, Cray Y-MP, */ |
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/* Cray-2, or Cray C-90, as described above. */ |
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/* Q2 (input) REAL array, dimension (LDQ2, N) */ |
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/* The first K columns of this matrix contain the non-deflated */ |
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/* eigenvectors for the split problem. */ |
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/* INDX (input) INTEGER array, dimension (N) */ |
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/* The permutation used to arrange the columns of the deflated */ |
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/* Q matrix into three groups (see SLAED2). */ |
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/* The rows of the eigenvectors found by SLAED4 must be likewise */ |
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/* permuted before the matrix multiply can take place. */ |
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/* CTOT (input) INTEGER array, dimension (4) */ |
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/* A count of the total number of the various types of columns */ |
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/* in Q, as described in INDX. The fourth column type is any */ |
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/* column which has been deflated. */ |
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/* W (input/output) REAL array, dimension (K) */ |
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/* The first K elements of this array contain the components */ |
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/* of the deflation-adjusted updating vector. Destroyed on */ |
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/* output. */ |
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/* S (workspace) REAL array, dimension (N1 + 1)*K */ |
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/* Will contain the eigenvectors of the repaired matrix which */ |
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/* will be multiplied by the previously accumulated eigenvectors */ |
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/* to update the system. */ |
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/* LDS (input) INTEGER */ |
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/* The leading dimension of S. LDS >= max(1,K). */ |
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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: if INFO = 1, an eigenvalue did not converge */ |
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/* Further Details */ |
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/* =============== */ |
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/* Based on contributions by */ |
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/* Jeff Rutter, Computer Science Division, University of California */ |
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/* at Berkeley, USA */ |
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/* Modified by Francoise Tisseur, University of Tennessee. */ |
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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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--d__; |
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q_dim1 = *ldq; |
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q_offset = 1 + q_dim1; |
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q -= q_offset; |
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--dlamda; |
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--q2; |
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--indx; |
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--ctot; |
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--w; |
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--s; |
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/* Function Body */ |
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*info = 0; |
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if (*k < 0) { |
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*info = -1; |
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} else if (*n < *k) { |
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*info = -2; |
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} else if (*ldq < max(1,*n)) { |
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*info = -6; |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("SLAED3", &i__1); |
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return 0; |
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} |
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/* Quick return if possible */ |
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if (*k == 0) { |
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return 0; |
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} |
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/* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */ |
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/* be computed with high relative accuracy (barring over/underflow). */ |
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/* This is a problem on machines without a guard digit in */ |
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/* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */ |
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/* The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), */ |
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/* which on any of these machines zeros out the bottommost */ |
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/* bit of DLAMDA(I) if it is 1; this makes the subsequent */ |
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/* subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation */ |
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/* occurs. On binary machines with a guard digit (almost all */ |
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/* machines) it does not change DLAMDA(I) at all. On hexadecimal */ |
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/* and decimal machines with a guard digit, it slightly */ |
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/* changes the bottommost bits of DLAMDA(I). It does not account */ |
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/* for hexadecimal or decimal machines without guard digits */ |
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/* (we know of none). We use a subroutine call to compute */ |
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/* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */ |
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/* this code. */ |
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i__1 = *k; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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dlamda[i__] = slamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__]; |
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/* L10: */ |
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} |
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i__1 = *k; |
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for (j = 1; j <= i__1; ++j) { |
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slaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j], |
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info); |
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/* If the zero finder fails, the computation is terminated. */ |
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if (*info != 0) { |
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goto L120; |
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} |
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/* L20: */ |
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} |
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if (*k == 1) { |
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goto L110; |
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} |
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if (*k == 2) { |
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i__1 = *k; |
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for (j = 1; j <= i__1; ++j) { |
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w[1] = q[j * q_dim1 + 1]; |
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w[2] = q[j * q_dim1 + 2]; |
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ii = indx[1]; |
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q[j * q_dim1 + 1] = w[ii]; |
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ii = indx[2]; |
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q[j * q_dim1 + 2] = w[ii]; |
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/* L30: */ |
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} |
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goto L110; |
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} |
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/* Compute updated W. */ |
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scopy_(k, &w[1], &c__1, &s[1], &c__1); |
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/* Initialize W(I) = Q(I,I) */ |
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i__1 = *ldq + 1; |
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scopy_(k, &q[q_offset], &i__1, &w[1], &c__1); |
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i__1 = *k; |
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for (j = 1; j <= i__1; ++j) { |
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i__2 = j - 1; |
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for (i__ = 1; i__ <= i__2; ++i__) { |
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w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); |
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/* L40: */ |
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} |
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i__2 = *k; |
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for (i__ = j + 1; i__ <= i__2; ++i__) { |
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w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); |
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/* L50: */ |
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} |
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/* L60: */ |
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} |
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i__1 = *k; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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r__1 = sqrt(-w[i__]); |
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w[i__] = r_sign(&r__1, &s[i__]); |
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/* L70: */ |
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} |
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/* Compute eigenvectors of the modified rank-1 modification. */ |
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i__1 = *k; |
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for (j = 1; j <= i__1; ++j) { |
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i__2 = *k; |
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for (i__ = 1; i__ <= i__2; ++i__) { |
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s[i__] = w[i__] / q[i__ + j * q_dim1]; |
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/* L80: */ |
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} |
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temp = snrm2_(k, &s[1], &c__1); |
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i__2 = *k; |
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for (i__ = 1; i__ <= i__2; ++i__) { |
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ii = indx[i__]; |
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q[i__ + j * q_dim1] = s[ii] / temp; |
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/* L90: */ |
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} |
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/* L100: */ |
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} |
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/* Compute the updated eigenvectors. */ |
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L110: |
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n2 = *n - *n1; |
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n12 = ctot[1] + ctot[2]; |
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n23 = ctot[2] + ctot[3]; |
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slacpy_("A", &n23, k, &q[ctot[1] + 1 + q_dim1], ldq, &s[1], &n23); |
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iq2 = *n1 * n12 + 1; |
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if (n23 != 0) { |
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sgemm_("N", "N", &n2, k, &n23, &c_b22, &q2[iq2], &n2, &s[1], &n23, & |
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c_b23, &q[*n1 + 1 + q_dim1], ldq); |
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} else { |
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slaset_("A", &n2, k, &c_b23, &c_b23, &q[*n1 + 1 + q_dim1], ldq); |
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} |
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slacpy_("A", &n12, k, &q[q_offset], ldq, &s[1], &n12); |
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if (n12 != 0) { |
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sgemm_("N", "N", n1, k, &n12, &c_b22, &q2[1], n1, &s[1], &n12, &c_b23, |
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&q[q_offset], ldq); |
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} else { |
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slaset_("A", n1, k, &c_b23, &c_b23, &q[q_dim1 + 1], ldq); |
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} |
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L120: |
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return 0; |
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/* End of SLAED3 */ |
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} /* slaed3_ */
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