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288 lines
9.5 KiB
288 lines
9.5 KiB
/* dlasd1.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 doublereal c_b7 = 1.; |
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static integer c__1 = 1; |
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static integer c_n1 = -1; |
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/* Subroutine */ int dlasd1_(integer *nl, integer *nr, integer *sqre, |
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doublereal *d__, doublereal *alpha, doublereal *beta, doublereal *u, |
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integer *ldu, doublereal *vt, integer *ldvt, integer *idxq, integer * |
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iwork, doublereal *work, integer *info) |
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{ |
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/* System generated locals */ |
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integer u_dim1, u_offset, vt_dim1, vt_offset, i__1; |
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doublereal d__1, d__2; |
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/* Local variables */ |
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integer i__, k, m, n, n1, n2, iq, iz, iu2, ldq, idx, ldu2, ivt2, idxc, |
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idxp, ldvt2; |
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extern /* Subroutine */ int dlasd2_(integer *, integer *, integer *, |
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integer *, doublereal *, doublereal *, doublereal *, doublereal *, |
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doublereal *, integer *, doublereal *, integer *, doublereal *, |
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doublereal *, integer *, doublereal *, integer *, integer *, |
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integer *, integer *, integer *, integer *, integer *), dlasd3_( |
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integer *, integer *, integer *, integer *, doublereal *, |
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doublereal *, integer *, doublereal *, doublereal *, integer *, |
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doublereal *, integer *, doublereal *, integer *, doublereal *, |
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integer *, integer *, integer *, doublereal *, integer *), |
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dlascl_(char *, integer *, integer *, doublereal *, doublereal *, |
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integer *, integer *, doublereal *, integer *, integer *), |
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dlamrg_(integer *, integer *, doublereal *, integer *, integer *, |
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integer *); |
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integer isigma; |
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extern /* Subroutine */ int xerbla_(char *, integer *); |
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doublereal orgnrm; |
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integer coltyp; |
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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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/* DLASD1 computes the SVD of an upper bidiagonal N-by-M matrix B, */ |
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/* where N = NL + NR + 1 and M = N + SQRE. DLASD1 is called from DLASD0. */ |
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/* A related subroutine DLASD7 handles the case in which the singular */ |
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/* values (and the singular vectors in factored form) are desired. */ |
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/* DLASD1 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 left singular vectors of the original matrix are stored in U, and */ |
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/* the transpose of the right singular vectors are stored in VT, and the */ |
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/* singular values 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 singular values or when there are zeros 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 DLASD2. */ |
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/* The second stage consists of calculating the updated */ |
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/* singular values. This is done by finding the square roots of the */ |
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/* roots of the secular equation via the routine DLASD4 (as called */ |
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/* by DLASD3). This routine also calculates the singular vectors of */ |
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/* the current problem. */ |
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/* The final stage consists of computing the updated singular vectors */ |
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/* directly using the updated singular values. The singular vectors */ |
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/* for the current problem are multiplied with the singular vectors */ |
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/* from the overall problem. */ |
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/* Arguments */ |
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/* ========= */ |
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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) DOUBLE PRECISION array, */ |
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/* dimension (N = 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 of */ |
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/* the lower block. On exit D(1:N) contains the singular values */ |
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/* of the modified matrix. */ |
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/* ALPHA (input/output) DOUBLE PRECISION */ |
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/* Contains the diagonal element associated with the added row. */ |
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/* BETA (input/output) DOUBLE PRECISION */ |
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/* Contains the off-diagonal element associated with the added */ |
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/* row. */ |
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/* U (input/output) DOUBLE PRECISION array, dimension(LDU,N) */ |
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/* On entry U(1:NL, 1:NL) contains the left singular vectors of */ |
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/* the upper block; U(NL+2:N, NL+2:N) contains the left singular */ |
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/* vectors of the lower block. On exit U contains the left */ |
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/* singular vectors of the bidiagonal matrix. */ |
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/* LDU (input) INTEGER */ |
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/* The leading dimension of the array U. LDU >= max( 1, N ). */ |
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/* VT (input/output) DOUBLE PRECISION array, dimension(LDVT,M) */ |
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/* where M = N + SQRE. */ |
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/* On entry VT(1:NL+1, 1:NL+1)' contains the right singular */ |
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/* vectors of the upper block; VT(NL+2:M, NL+2:M)' contains */ |
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/* the right singular vectors of the lower block. On exit */ |
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/* VT' contains the right singular vectors of the */ |
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/* bidiagonal matrix. */ |
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/* LDVT (input) INTEGER */ |
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/* The leading dimension of the array VT. LDVT >= max( 1, M ). */ |
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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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/* IWORK (workspace) INTEGER array, dimension( 4 * N ) */ |
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/* WORK (workspace) DOUBLE PRECISION array, dimension( 3*M**2 + 2*M ) */ |
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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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u_dim1 = *ldu; |
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u_offset = 1 + u_dim1; |
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u -= u_offset; |
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vt_dim1 = *ldvt; |
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vt_offset = 1 + vt_dim1; |
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vt -= vt_offset; |
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--idxq; |
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--iwork; |
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--work; |
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/* Function Body */ |
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*info = 0; |
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if (*nl < 1) { |
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*info = -1; |
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} else if (*nr < 1) { |
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*info = -2; |
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} else if (*sqre < 0 || *sqre > 1) { |
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*info = -3; |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("DLASD1", &i__1); |
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return 0; |
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} |
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n = *nl + *nr + 1; |
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m = n + *sqre; |
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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 DLASD2 and DLASD3. */ |
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ldu2 = n; |
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ldvt2 = m; |
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iz = 1; |
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isigma = iz + m; |
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iu2 = isigma + n; |
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ivt2 = iu2 + ldu2 * n; |
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iq = ivt2 + ldvt2 * m; |
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idx = 1; |
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idxc = idx + n; |
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coltyp = idxc + n; |
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idxp = coltyp + n; |
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/* Scale. */ |
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/* Computing MAX */ |
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d__1 = abs(*alpha), d__2 = abs(*beta); |
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orgnrm = max(d__1,d__2); |
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d__[*nl + 1] = 0.; |
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i__1 = n; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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if ((d__1 = d__[i__], abs(d__1)) > orgnrm) { |
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orgnrm = (d__1 = d__[i__], abs(d__1)); |
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} |
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/* L10: */ |
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} |
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dlascl_("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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/* Deflate singular values. */ |
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dlasd2_(nl, nr, sqre, &k, &d__[1], &work[iz], alpha, beta, &u[u_offset], |
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ldu, &vt[vt_offset], ldvt, &work[isigma], &work[iu2], &ldu2, & |
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work[ivt2], &ldvt2, &iwork[idxp], &iwork[idx], &iwork[idxc], & |
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idxq[1], &iwork[coltyp], info); |
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/* Solve Secular Equation and update singular vectors. */ |
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ldq = k; |
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dlasd3_(nl, nr, sqre, &k, &d__[1], &work[iq], &ldq, &work[isigma], &u[ |
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u_offset], ldu, &work[iu2], &ldu2, &vt[vt_offset], ldvt, &work[ |
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ivt2], &ldvt2, &iwork[idxc], &iwork[coltyp], &work[iz], info); |
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if (*info != 0) { |
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return 0; |
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} |
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/* Unscale. */ |
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dlascl_("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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dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]); |
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return 0; |
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/* End of DLASD1 */ |
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} /* dlasd1_ */
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