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352 lines
12 KiB
352 lines
12 KiB
/* slaed7.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__2 = 2; |
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static integer c__1 = 1; |
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static real c_b10 = 1.f; |
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static real c_b11 = 0.f; |
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static integer c_n1 = -1; |
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/* Subroutine */ int slaed7_(integer *icompq, integer *n, integer *qsiz, |
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integer *tlvls, integer *curlvl, integer *curpbm, real *d__, real *q, |
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integer *ldq, integer *indxq, real *rho, integer *cutpnt, real * |
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qstore, integer *qptr, integer *prmptr, integer *perm, integer * |
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givptr, integer *givcol, real *givnum, real *work, integer *iwork, |
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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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/* Builtin functions */ |
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integer pow_ii(integer *, integer *); |
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/* Local variables */ |
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integer i__, k, n1, n2, is, iw, iz, iq2, ptr, ldq2, indx, curr, indxc; |
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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 *); |
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integer indxp; |
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extern /* Subroutine */ int slaed8_(integer *, integer *, integer *, |
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integer *, real *, real *, integer *, integer *, real *, integer * |
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, real *, real *, real *, integer *, real *, integer *, integer *, |
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integer *, real *, integer *, integer *, integer *), slaed9_( |
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integer *, integer *, integer *, integer *, real *, real *, |
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integer *, real *, real *, real *, real *, integer *, integer *), |
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slaeda_(integer *, integer *, integer *, integer *, integer *, |
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integer *, integer *, integer *, real *, real *, integer *, real * |
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, real *, integer *); |
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integer idlmda; |
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extern /* Subroutine */ int xerbla_(char *, integer *), slamrg_( |
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integer *, integer *, real *, integer *, integer *, integer *); |
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integer coltyp; |
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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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/* SLAED7 computes the updated eigensystem of a diagonal */ |
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/* matrix after modification by a rank-one symmetric matrix. This */ |
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/* routine is used only for the eigenproblem which requires all */ |
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/* eigenvalues and optionally eigenvectors of a dense symmetric matrix */ |
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/* that has been reduced to tridiagonal form. SLAED1 handles */ |
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/* the case in which all eigenvalues and eigenvectors of a symmetric */ |
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/* tridiagonal matrix are desired. */ |
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/* T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out) */ |
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/* where Z = Q'u, u is a vector of length N with ones in the */ |
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/* CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */ |
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/* The eigenvectors of the original matrix are stored in Q, and the */ |
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/* eigenvalues are in D. The algorithm consists of three stages: */ |
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/* The first stage consists of deflating the size of the problem */ |
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/* when there are multiple eigenvalues or if there is a zero in */ |
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/* the Z vector. For each such occurence the dimension of the */ |
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/* secular equation problem is reduced by one. This stage is */ |
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/* performed by the routine SLAED8. */ |
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/* The second stage consists of calculating the updated */ |
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/* eigenvalues. This is done by finding the roots of the secular */ |
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/* equation via the routine SLAED4 (as called by SLAED9). */ |
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/* This routine also calculates the eigenvectors of the current */ |
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/* problem. */ |
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/* The final stage consists of computing the updated eigenvectors */ |
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/* directly using the updated eigenvalues. The eigenvectors for */ |
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/* the current problem are multiplied with the eigenvectors from */ |
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/* the overall problem. */ |
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/* Arguments */ |
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/* ========= */ |
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/* ICOMPQ (input) INTEGER */ |
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/* = 0: Compute eigenvalues only. */ |
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/* = 1: Compute eigenvectors of original dense symmetric matrix */ |
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/* also. On entry, Q contains the orthogonal matrix used */ |
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/* to reduce the original matrix to tridiagonal form. */ |
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/* N (input) INTEGER */ |
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/* The dimension of the symmetric tridiagonal matrix. N >= 0. */ |
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/* QSIZ (input) INTEGER */ |
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/* The dimension of the orthogonal matrix used to reduce */ |
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/* the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */ |
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/* TLVLS (input) INTEGER */ |
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/* The total number of merging levels in the overall divide and */ |
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/* conquer tree. */ |
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/* CURLVL (input) INTEGER */ |
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/* The current level in the overall merge routine, */ |
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/* 0 <= CURLVL <= TLVLS. */ |
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/* CURPBM (input) INTEGER */ |
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/* The current problem in the current level in the overall */ |
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/* merge routine (counting from upper left to lower right). */ |
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/* D (input/output) REAL array, dimension (N) */ |
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/* On entry, the eigenvalues of the rank-1-perturbed matrix. */ |
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/* On exit, the eigenvalues of the repaired matrix. */ |
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/* Q (input/output) REAL array, dimension (LDQ, N) */ |
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/* On entry, the eigenvectors of the rank-1-perturbed matrix. */ |
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/* On exit, the eigenvectors of the repaired tridiagonal matrix. */ |
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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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/* INDXQ (output) INTEGER array, dimension (N) */ |
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/* The permutation which will reintegrate the subproblem just */ |
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/* solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) */ |
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/* will be in ascending order. */ |
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/* RHO (input) REAL */ |
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/* The subdiagonal element used to create the rank-1 */ |
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/* modification. */ |
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/* CUTPNT (input) INTEGER */ |
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/* Contains the location of the last eigenvalue in the leading */ |
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/* sub-matrix. min(1,N) <= CUTPNT <= N. */ |
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/* QSTORE (input/output) REAL array, dimension (N**2+1) */ |
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/* Stores eigenvectors of submatrices encountered during */ |
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/* divide and conquer, packed together. QPTR points to */ |
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/* beginning of the submatrices. */ |
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/* QPTR (input/output) INTEGER array, dimension (N+2) */ |
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/* List of indices pointing to beginning of submatrices stored */ |
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/* in QSTORE. The submatrices are numbered starting at the */ |
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/* bottom left of the divide and conquer tree, from left to */ |
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/* right and bottom to top. */ |
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/* PRMPTR (input) INTEGER array, dimension (N lg N) */ |
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/* Contains a list of pointers which indicate where in PERM a */ |
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/* level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) */ |
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/* indicates the size of the permutation and also the size of */ |
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/* the full, non-deflated problem. */ |
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/* PERM (input) INTEGER array, dimension (N lg N) */ |
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/* Contains the permutations (from deflation and sorting) to be */ |
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/* applied to each eigenblock. */ |
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/* GIVPTR (input) INTEGER array, dimension (N lg N) */ |
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/* Contains a list of pointers which indicate where in GIVCOL a */ |
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/* level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) */ |
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/* indicates the number of Givens rotations. */ |
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/* GIVCOL (input) INTEGER array, dimension (2, N lg N) */ |
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/* Each pair of numbers indicates a pair of columns to take place */ |
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/* in a Givens rotation. */ |
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/* GIVNUM (input) REAL array, dimension (2, N lg N) */ |
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/* Each number indicates the S value to be used in the */ |
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/* corresponding Givens rotation. */ |
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/* WORK (workspace) REAL array, dimension (3*N+QSIZ*N) */ |
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/* IWORK (workspace) INTEGER array, dimension (4*N) */ |
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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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/* ===================================================================== */ |
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/* .. Parameters .. */ |
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/* .. */ |
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/* .. Local Scalars .. */ |
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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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--indxq; |
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--qstore; |
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--qptr; |
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--prmptr; |
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--perm; |
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--givptr; |
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givcol -= 3; |
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givnum -= 3; |
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--work; |
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--iwork; |
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/* Function Body */ |
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*info = 0; |
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if (*icompq < 0 || *icompq > 1) { |
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*info = -1; |
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} else if (*n < 0) { |
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*info = -2; |
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} else if (*icompq == 1 && *qsiz < *n) { |
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*info = -4; |
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} else if (*ldq < max(1,*n)) { |
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*info = -9; |
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} else if (min(1,*n) > *cutpnt || *n < *cutpnt) { |
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*info = -12; |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("SLAED7", &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 (*n == 0) { |
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return 0; |
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} |
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/* The following values are for bookkeeping purposes only. They are */ |
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/* integer pointers which indicate the portion of the workspace */ |
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/* used by a particular array in SLAED8 and SLAED9. */ |
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if (*icompq == 1) { |
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ldq2 = *qsiz; |
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} else { |
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ldq2 = *n; |
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} |
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iz = 1; |
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idlmda = iz + *n; |
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iw = idlmda + *n; |
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iq2 = iw + *n; |
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is = iq2 + *n * ldq2; |
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indx = 1; |
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indxc = indx + *n; |
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coltyp = indxc + *n; |
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indxp = coltyp + *n; |
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/* Form the z-vector which consists of the last row of Q_1 and the */ |
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/* first row of Q_2. */ |
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ptr = pow_ii(&c__2, tlvls) + 1; |
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i__1 = *curlvl - 1; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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i__2 = *tlvls - i__; |
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ptr += pow_ii(&c__2, &i__2); |
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/* L10: */ |
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} |
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curr = ptr + *curpbm; |
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slaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], & |
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givcol[3], &givnum[3], &qstore[1], &qptr[1], &work[iz], &work[iz |
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+ *n], info); |
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/* When solving the final problem, we no longer need the stored data, */ |
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/* so we will overwrite the data from this level onto the previously */ |
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/* used storage space. */ |
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if (*curlvl == *tlvls) { |
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qptr[curr] = 1; |
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prmptr[curr] = 1; |
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givptr[curr] = 1; |
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} |
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/* Sort and Deflate eigenvalues. */ |
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slaed8_(icompq, &k, n, qsiz, &d__[1], &q[q_offset], ldq, &indxq[1], rho, |
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cutpnt, &work[iz], &work[idlmda], &work[iq2], &ldq2, &work[iw], & |
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perm[prmptr[curr]], &givptr[curr + 1], &givcol[(givptr[curr] << 1) |
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+ 1], &givnum[(givptr[curr] << 1) + 1], &iwork[indxp], &iwork[ |
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indx], info); |
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prmptr[curr + 1] = prmptr[curr] + *n; |
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givptr[curr + 1] += givptr[curr]; |
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/* Solve Secular Equation. */ |
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if (k != 0) { |
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slaed9_(&k, &c__1, &k, n, &d__[1], &work[is], &k, rho, &work[idlmda], |
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&work[iw], &qstore[qptr[curr]], &k, info); |
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if (*info != 0) { |
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goto L30; |
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} |
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if (*icompq == 1) { |
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sgemm_("N", "N", qsiz, &k, &k, &c_b10, &work[iq2], &ldq2, &qstore[ |
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qptr[curr]], &k, &c_b11, &q[q_offset], ldq); |
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} |
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/* Computing 2nd power */ |
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i__1 = k; |
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qptr[curr + 1] = qptr[curr] + i__1 * i__1; |
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/* Prepare the INDXQ sorting permutation. */ |
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n1 = k; |
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n2 = *n - k; |
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slamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]); |
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} else { |
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qptr[curr + 1] = qptr[curr]; |
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i__1 = *n; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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indxq[i__] = i__; |
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/* L20: */ |
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} |
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} |
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L30: |
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return 0; |
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/* End of SLAED7 */ |
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} /* slaed7_ */
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