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364 lines
13 KiB
364 lines
13 KiB
/* slasd6.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 real c_b7 = 1.f; |
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static integer c__1 = 1; |
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static integer c_n1 = -1; |
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/* Subroutine */ int slasd6_(integer *icompq, integer *nl, integer *nr, |
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integer *sqre, real *d__, real *vf, real *vl, real *alpha, real *beta, |
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integer *idxq, integer *perm, integer *givptr, integer *givcol, |
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integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real * |
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difl, real *difr, real *z__, integer *k, real *c__, real *s, real * |
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work, integer *iwork, integer *info) |
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{ |
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/* System generated locals */ |
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integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, |
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poles_dim1, poles_offset, i__1; |
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real r__1, r__2; |
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/* Local variables */ |
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integer i__, m, n, n1, n2, iw, idx, idxc, idxp, ivfw, ivlw; |
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extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, |
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integer *), slasd7_(integer *, integer *, integer *, integer *, |
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integer *, real *, real *, real *, real *, real *, real *, real *, |
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real *, real *, real *, integer *, integer *, integer *, integer |
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*, integer *, integer *, integer *, real *, integer *, real *, |
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real *, integer *), slasd8_(integer *, integer *, real *, real *, |
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real *, real *, real *, real *, integer *, real *, real *, |
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integer *); |
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integer isigma; |
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extern /* Subroutine */ int xerbla_(char *, integer *), slascl_( |
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char *, integer *, integer *, real *, real *, integer *, integer * |
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, real *, integer *, integer *), slamrg_(integer *, |
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integer *, real *, integer *, integer *, integer *); |
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real orgnrm; |
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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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/* SLASD6 computes the SVD of an updated upper bidiagonal matrix B */ |
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/* obtained by merging two smaller ones by appending a row. This */ |
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/* routine is used only for the problem which requires all singular */ |
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/* values and optionally singular vector matrices in factored form. */ |
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/* B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE. */ |
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/* A related subroutine, SLASD1, handles the case in which all singular */ |
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/* values and singular vectors of the bidiagonal matrix are desired. */ |
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/* SLASD6 computes the SVD as follows: */ |
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/* ( D1(in) 0 0 0 ) */ |
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/* B = U(in) * ( Z1' a Z2' b ) * VT(in) */ |
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/* ( 0 0 D2(in) 0 ) */ |
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/* = U(out) * ( D(out) 0) * VT(out) */ |
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/* where Z' = (Z1' a Z2' b) = u' VT', and u is a vector of dimension M */ |
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/* with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros */ |
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/* elsewhere; and the entry b is empty if SQRE = 0. */ |
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/* The singular values of B can be computed using D1, D2, the first */ |
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/* components of all the right singular vectors of the lower block, and */ |
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/* the last components of all the right singular vectors of the upper */ |
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/* block. These components are stored and updated in VF and VL, */ |
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/* respectively, in SLASD6. Hence U and VT are not explicitly */ |
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/* referenced. */ |
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/* The singular values are stored in D. The algorithm consists of two */ |
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/* stages: */ |
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/* The first stage consists of deflating the size of the problem */ |
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/* when there are multiple singular values or if there is a zero */ |
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/* in 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 SLASD7. */ |
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/* The second stage consists of calculating the updated */ |
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/* singular values. This is done by finding the roots of the */ |
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/* secular equation via the routine SLASD4 (as called by SLASD8). */ |
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/* This routine also updates VF and VL and computes the distances */ |
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/* between the updated singular values and the old singular */ |
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/* values. */ |
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/* SLASD6 is called from SLASDA. */ |
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/* Arguments */ |
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/* ========= */ |
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/* ICOMPQ (input) INTEGER */ |
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/* Specifies whether singular vectors are to be computed in */ |
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/* factored form: */ |
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/* = 0: Compute singular values only. */ |
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/* = 1: Compute singular vectors in factored form as well. */ |
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/* NL (input) INTEGER */ |
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/* The row dimension of the upper block. NL >= 1. */ |
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/* NR (input) INTEGER */ |
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/* The row dimension of the lower block. NR >= 1. */ |
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/* SQRE (input) INTEGER */ |
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/* = 0: the lower block is an NR-by-NR square matrix. */ |
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/* = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */ |
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/* The bidiagonal matrix has row dimension N = NL + NR + 1, */ |
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/* and column dimension M = N + SQRE. */ |
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/* D (input/output) REAL array, dimension (NL+NR+1). */ |
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/* On entry D(1:NL,1:NL) contains the singular values of the */ |
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/* upper block, and D(NL+2:N) contains the singular values */ |
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/* of the lower block. On exit D(1:N) contains the singular */ |
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/* values of the modified matrix. */ |
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/* VF (input/output) REAL array, dimension (M) */ |
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/* On entry, VF(1:NL+1) contains the first components of all */ |
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/* right singular vectors of the upper block; and VF(NL+2:M) */ |
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/* contains the first components of all right singular vectors */ |
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/* of the lower block. On exit, VF contains the first components */ |
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/* of all right singular vectors of the bidiagonal matrix. */ |
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/* VL (input/output) REAL array, dimension (M) */ |
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/* On entry, VL(1:NL+1) contains the last components of all */ |
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/* right singular vectors of the upper block; and VL(NL+2:M) */ |
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/* contains the last components of all right singular vectors of */ |
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/* the lower block. On exit, VL contains the last components of */ |
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/* all right singular vectors of the bidiagonal matrix. */ |
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/* ALPHA (input/output) REAL */ |
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/* Contains the diagonal element associated with the added row. */ |
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/* BETA (input/output) REAL */ |
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/* Contains the off-diagonal element associated with the added */ |
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/* row. */ |
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/* IDXQ (output) INTEGER array, dimension (N) */ |
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/* This contains the permutation which will reintegrate the */ |
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/* subproblem just solved back into sorted order, i.e. */ |
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/* D( IDXQ( I = 1, N ) ) will be in ascending order. */ |
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/* PERM (output) INTEGER array, dimension ( N ) */ |
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/* The permutations (from deflation and sorting) to be applied */ |
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/* to each block. Not referenced if ICOMPQ = 0. */ |
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/* GIVPTR (output) INTEGER */ |
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/* The number of Givens rotations which took place in this */ |
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/* subproblem. Not referenced if ICOMPQ = 0. */ |
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/* GIVCOL (output) INTEGER array, dimension ( LDGCOL, 2 ) */ |
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/* Each pair of numbers indicates a pair of columns to take place */ |
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/* in a Givens rotation. Not referenced if ICOMPQ = 0. */ |
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/* LDGCOL (input) INTEGER */ |
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/* leading dimension of GIVCOL, must be at least N. */ |
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/* GIVNUM (output) REAL array, dimension ( LDGNUM, 2 ) */ |
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/* Each number indicates the C or S value to be used in the */ |
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/* corresponding Givens rotation. Not referenced if ICOMPQ = 0. */ |
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/* LDGNUM (input) INTEGER */ |
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/* The leading dimension of GIVNUM and POLES, must be at least N. */ |
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/* POLES (output) REAL array, dimension ( LDGNUM, 2 ) */ |
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/* On exit, POLES(1,*) is an array containing the new singular */ |
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/* values obtained from solving the secular equation, and */ |
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/* POLES(2,*) is an array containing the poles in the secular */ |
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/* equation. Not referenced if ICOMPQ = 0. */ |
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/* DIFL (output) REAL array, dimension ( N ) */ |
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/* On exit, DIFL(I) is the distance between I-th updated */ |
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/* (undeflated) singular value and the I-th (undeflated) old */ |
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/* singular value. */ |
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/* DIFR (output) REAL array, */ |
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/* dimension ( LDGNUM, 2 ) if ICOMPQ = 1 and */ |
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/* dimension ( N ) if ICOMPQ = 0. */ |
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/* On exit, DIFR(I, 1) is the distance between I-th updated */ |
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/* (undeflated) singular value and the I+1-th (undeflated) old */ |
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/* singular value. */ |
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/* If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */ |
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/* normalizing factors for the right singular vector matrix. */ |
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/* See SLASD8 for details on DIFL and DIFR. */ |
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/* Z (output) REAL array, dimension ( M ) */ |
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/* The first elements of this array contain the components */ |
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/* of the deflation-adjusted updating row vector. */ |
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/* K (output) INTEGER */ |
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/* Contains the dimension of the non-deflated matrix, */ |
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/* This is the order of the related secular equation. 1 <= K <=N. */ |
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/* C (output) REAL */ |
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/* C contains garbage if SQRE =0 and the C-value of a Givens */ |
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/* rotation related to the right null space if SQRE = 1. */ |
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/* S (output) REAL */ |
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/* S contains garbage if SQRE =0 and the S-value of a Givens */ |
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/* rotation related to the right null space if SQRE = 1. */ |
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/* WORK (workspace) REAL array, dimension ( 4 * M ) */ |
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/* IWORK (workspace) INTEGER array, dimension ( 3 * 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 singular value 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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/* Ming Gu and Huan Ren, Computer Science Division, University of */ |
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/* California 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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--vf; |
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--vl; |
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--idxq; |
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--perm; |
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givcol_dim1 = *ldgcol; |
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givcol_offset = 1 + givcol_dim1; |
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givcol -= givcol_offset; |
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poles_dim1 = *ldgnum; |
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poles_offset = 1 + poles_dim1; |
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poles -= poles_offset; |
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givnum_dim1 = *ldgnum; |
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givnum_offset = 1 + givnum_dim1; |
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givnum -= givnum_offset; |
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--difl; |
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--difr; |
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--z__; |
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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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n = *nl + *nr + 1; |
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m = n + *sqre; |
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if (*icompq < 0 || *icompq > 1) { |
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*info = -1; |
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} else if (*nl < 1) { |
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*info = -2; |
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} else if (*nr < 1) { |
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*info = -3; |
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} else if (*sqre < 0 || *sqre > 1) { |
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*info = -4; |
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} else if (*ldgcol < n) { |
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*info = -14; |
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} else if (*ldgnum < n) { |
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*info = -16; |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("SLASD6", &i__1); |
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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 SLASD7 and SLASD8. */ |
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isigma = 1; |
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iw = isigma + n; |
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ivfw = iw + m; |
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ivlw = ivfw + m; |
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idx = 1; |
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idxc = idx + n; |
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idxp = idxc + n; |
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/* Scale. */ |
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/* Computing MAX */ |
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r__1 = dabs(*alpha), r__2 = dabs(*beta); |
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orgnrm = dmax(r__1,r__2); |
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d__[*nl + 1] = 0.f; |
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i__1 = n; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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if ((r__1 = d__[i__], dabs(r__1)) > orgnrm) { |
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orgnrm = (r__1 = d__[i__], dabs(r__1)); |
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} |
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/* L10: */ |
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} |
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slascl_("G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info); |
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*alpha /= orgnrm; |
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*beta /= orgnrm; |
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/* Sort and Deflate singular values. */ |
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slasd7_(icompq, nl, nr, sqre, k, &d__[1], &z__[1], &work[iw], &vf[1], & |
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work[ivfw], &vl[1], &work[ivlw], alpha, beta, &work[isigma], & |
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iwork[idx], &iwork[idxp], &idxq[1], &perm[1], givptr, &givcol[ |
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givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s, |
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info); |
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/* Solve Secular Equation, compute DIFL, DIFR, and update VF, VL. */ |
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slasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1], |
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ldgnum, &work[isigma], &work[iw], info); |
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/* Save the poles if ICOMPQ = 1. */ |
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if (*icompq == 1) { |
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scopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1); |
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scopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1); |
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} |
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/* Unscale. */ |
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slascl_("G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info); |
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/* Prepare the IDXQ 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, &idxq[1]); |
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return 0; |
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/* End of SLASD6 */ |
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} /* slasd6_ */
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