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693 lines
22 KiB
693 lines
22 KiB
/* dgelsd.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__6 = 6; |
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static integer c_n1 = -1; |
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static integer c__9 = 9; |
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static integer c__0 = 0; |
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static integer c__1 = 1; |
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static doublereal c_b82 = 0.; |
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|
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/* Subroutine */ int dgelsd_(integer *m, integer *n, integer *nrhs, |
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doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * |
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s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork, |
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integer *iwork, integer *info) |
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{ |
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/* System generated locals */ |
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integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4; |
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/* Builtin functions */ |
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double log(doublereal); |
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/* Local variables */ |
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integer ie, il, mm; |
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doublereal eps, anrm, bnrm; |
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integer itau, nlvl, iascl, ibscl; |
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doublereal sfmin; |
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integer minmn, maxmn, itaup, itauq, mnthr, nwork; |
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extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), dgebrd_( |
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integer *, integer *, doublereal *, integer *, doublereal *, |
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doublereal *, doublereal *, doublereal *, doublereal *, integer *, |
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integer *); |
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extern doublereal dlamch_(char *), dlange_(char *, integer *, |
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integer *, doublereal *, integer *, doublereal *); |
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extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, |
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integer *, doublereal *, doublereal *, integer *, integer *), |
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dlalsd_(char *, integer *, integer *, integer *, doublereal *, |
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doublereal *, doublereal *, integer *, doublereal *, integer *, |
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doublereal *, integer *, integer *), dlascl_(char *, |
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integer *, integer *, doublereal *, doublereal *, integer *, |
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integer *, doublereal *, integer *, integer *), dgeqrf_( |
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integer *, integer *, doublereal *, integer *, doublereal *, |
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doublereal *, integer *, integer *), dlacpy_(char *, integer *, |
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integer *, doublereal *, integer *, doublereal *, integer *), dlaset_(char *, integer *, integer *, doublereal *, |
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doublereal *, doublereal *, integer *), xerbla_(char *, |
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integer *); |
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *, |
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integer *, integer *); |
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doublereal bignum; |
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extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, |
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integer *, integer *, doublereal *, integer *, doublereal *, |
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doublereal *, integer *, doublereal *, integer *, integer *); |
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integer wlalsd; |
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extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *, |
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integer *, doublereal *, integer *, doublereal *, doublereal *, |
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integer *, doublereal *, integer *, integer *); |
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integer ldwork; |
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extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, |
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integer *, doublereal *, integer *, doublereal *, doublereal *, |
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integer *, doublereal *, integer *, integer *); |
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integer minwrk, maxwrk; |
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doublereal smlnum; |
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logical lquery; |
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integer smlsiz; |
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/* -- LAPACK driver 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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|
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/* .. Scalar Arguments .. */ |
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/* .. */ |
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/* .. Array Arguments .. */ |
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/* .. */ |
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|
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/* Purpose */ |
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/* ======= */ |
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/* DGELSD computes the minimum-norm solution to a real linear least */ |
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/* squares problem: */ |
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/* minimize 2-norm(| b - A*x |) */ |
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/* using the singular value decomposition (SVD) of A. A is an M-by-N */ |
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/* matrix which may be rank-deficient. */ |
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/* Several right hand side vectors b and solution vectors x can be */ |
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/* handled in a single call; they are stored as the columns of the */ |
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/* M-by-NRHS right hand side matrix B and the N-by-NRHS solution */ |
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/* matrix X. */ |
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/* The problem is solved in three steps: */ |
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/* (1) Reduce the coefficient matrix A to bidiagonal form with */ |
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/* Householder transformations, reducing the original problem */ |
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/* into a "bidiagonal least squares problem" (BLS) */ |
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/* (2) Solve the BLS using a divide and conquer approach. */ |
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/* (3) Apply back all the Householder tranformations to solve */ |
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/* the original least squares problem. */ |
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/* The effective rank of A is determined by treating as zero those */ |
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/* singular values which are less than RCOND times the largest singular */ |
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/* value. */ |
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/* The divide and conquer algorithm makes very mild assumptions about */ |
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/* floating point arithmetic. It will work on machines with a guard */ |
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/* digit in add/subtract, or on those binary machines without guard */ |
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/* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ |
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/* Cray-2. 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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/* M (input) INTEGER */ |
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/* The number of rows of A. M >= 0. */ |
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/* N (input) INTEGER */ |
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/* The number of columns of A. N >= 0. */ |
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/* NRHS (input) INTEGER */ |
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/* The number of right hand sides, i.e., the number of columns */ |
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/* of the matrices B and X. NRHS >= 0. */ |
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/* A (input) DOUBLE PRECISION array, dimension (LDA,N) */ |
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/* On entry, the M-by-N matrix A. */ |
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/* On exit, A has been destroyed. */ |
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/* LDA (input) INTEGER */ |
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/* The leading dimension of the array A. LDA >= max(1,M). */ |
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/* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */ |
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/* On entry, the M-by-NRHS right hand side matrix B. */ |
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/* On exit, B is overwritten by the N-by-NRHS solution */ |
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/* matrix X. If m >= n and RANK = n, the residual */ |
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/* sum-of-squares for the solution in the i-th column is given */ |
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/* by the sum of squares of elements n+1:m in that column. */ |
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/* LDB (input) INTEGER */ |
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/* The leading dimension of the array B. LDB >= max(1,max(M,N)). */ |
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/* S (output) DOUBLE PRECISION array, dimension (min(M,N)) */ |
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/* The singular values of A in decreasing order. */ |
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/* The condition number of A in the 2-norm = S(1)/S(min(m,n)). */ |
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/* RCOND (input) DOUBLE PRECISION */ |
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/* RCOND is used to determine the effective rank of A. */ |
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/* Singular values S(i) <= RCOND*S(1) are treated as zero. */ |
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/* If RCOND < 0, machine precision is used instead. */ |
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/* RANK (output) INTEGER */ |
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/* The effective rank of A, i.e., the number of singular values */ |
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/* which are greater than RCOND*S(1). */ |
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/* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ |
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/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ |
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/* LWORK (input) INTEGER */ |
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/* The dimension of the array WORK. LWORK must be at least 1. */ |
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/* The exact minimum amount of workspace needed depends on M, */ |
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/* N and NRHS. As long as LWORK is at least */ |
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/* 12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2, */ |
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/* if M is greater than or equal to N or */ |
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/* 12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2, */ |
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/* if M is less than N, the code will execute correctly. */ |
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/* SMLSIZ is returned by ILAENV and is equal to the maximum */ |
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/* size of the subproblems at the bottom of the computation */ |
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/* tree (usually about 25), and */ |
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/* NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 ) */ |
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/* For good performance, LWORK should generally be larger. */ |
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/* If LWORK = -1, then a workspace query is assumed; the routine */ |
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/* only calculates the optimal size of the WORK array, returns */ |
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/* this value as the first entry of the WORK array, and no error */ |
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/* message related to LWORK is issued by XERBLA. */ |
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/* IWORK (workspace) INTEGER array, dimension (MAX(1,LIWORK)) */ |
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/* LIWORK >= 3 * MINMN * NLVL + 11 * MINMN, */ |
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/* where MINMN = MIN( M,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: the algorithm for computing the SVD failed to converge; */ |
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/* if INFO = i, i off-diagonal elements of an intermediate */ |
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/* bidiagonal form did not converge to zero. */ |
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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 Ren-Cang Li, Computer Science Division, University of */ |
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/* California at Berkeley, USA */ |
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/* Osni Marques, LBNL/NERSC, 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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/* .. External Functions .. */ |
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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 arguments. */ |
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/* Parameter adjustments */ |
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a_dim1 = *lda; |
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a_offset = 1 + a_dim1; |
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a -= a_offset; |
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b_dim1 = *ldb; |
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b_offset = 1 + b_dim1; |
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b -= b_offset; |
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--s; |
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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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minmn = min(*m,*n); |
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maxmn = max(*m,*n); |
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mnthr = ilaenv_(&c__6, "DGELSD", " ", m, n, nrhs, &c_n1); |
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lquery = *lwork == -1; |
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if (*m < 0) { |
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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 (*nrhs < 0) { |
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*info = -3; |
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} else if (*lda < max(1,*m)) { |
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*info = -5; |
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} else if (*ldb < max(1,maxmn)) { |
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*info = -7; |
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} |
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smlsiz = ilaenv_(&c__9, "DGELSD", " ", &c__0, &c__0, &c__0, &c__0); |
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/* Compute workspace. */ |
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/* (Note: Comments in the code beginning "Workspace:" describe the */ |
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/* minimal amount of workspace needed at that point in the code, */ |
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/* as well as the preferred amount for good performance. */ |
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/* NB refers to the optimal block size for the immediately */ |
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/* following subroutine, as returned by ILAENV.) */ |
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minwrk = 1; |
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minmn = max(1,minmn); |
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/* Computing MAX */ |
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i__1 = (integer) (log((doublereal) minmn / (doublereal) (smlsiz + 1)) / |
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log(2.)) + 1; |
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nlvl = max(i__1,0); |
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if (*info == 0) { |
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maxwrk = 0; |
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mm = *m; |
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if (*m >= *n && *m >= mnthr) { |
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/* Path 1a - overdetermined, with many more rows than columns. */ |
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mm = *n; |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "DGEQRF", " ", m, |
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n, &c_n1, &c_n1); |
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maxwrk = max(i__1,i__2); |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, "DORMQR", "LT", |
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m, nrhs, n, &c_n1); |
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maxwrk = max(i__1,i__2); |
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} |
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if (*m >= *n) { |
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/* Path 1 - overdetermined or exactly determined. */ |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, "DGEBRD" |
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, " ", &mm, n, &c_n1, &c_n1); |
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maxwrk = max(i__1,i__2); |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, "DORMBR", |
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"QLT", &mm, nrhs, n, &c_n1); |
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maxwrk = max(i__1,i__2); |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, "DORMBR", |
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"PLN", n, nrhs, n, &c_n1); |
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maxwrk = max(i__1,i__2); |
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/* Computing 2nd power */ |
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i__1 = smlsiz + 1; |
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wlalsd = *n * 9 + (*n << 1) * smlsiz + (*n << 3) * nlvl + *n * * |
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nrhs + i__1 * i__1; |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *n * 3 + wlalsd; |
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maxwrk = max(i__1,i__2); |
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/* Computing MAX */ |
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i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1,i__2), |
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i__2 = *n * 3 + wlalsd; |
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minwrk = max(i__1,i__2); |
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} |
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if (*n > *m) { |
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/* Computing 2nd power */ |
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i__1 = smlsiz + 1; |
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wlalsd = *m * 9 + (*m << 1) * smlsiz + (*m << 3) * nlvl + *m * * |
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nrhs + i__1 * i__1; |
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if (*n >= mnthr) { |
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/* Path 2a - underdetermined, with many more columns */ |
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/* than rows. */ |
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maxwrk = *m + *m * ilaenv_(&c__1, "DGELQF", " ", m, n, &c_n1, |
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&c_n1); |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) * |
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ilaenv_(&c__1, "DGEBRD", " ", m, m, &c_n1, &c_n1); |
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maxwrk = max(i__1,i__2); |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * ilaenv_(& |
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c__1, "DORMBR", "QLT", m, nrhs, m, &c_n1); |
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maxwrk = max(i__1,i__2); |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) * |
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ilaenv_(&c__1, "DORMBR", "PLN", m, nrhs, m, &c_n1); |
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maxwrk = max(i__1,i__2); |
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if (*nrhs > 1) { |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs; |
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maxwrk = max(i__1,i__2); |
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} else { |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *m * *m + (*m << 1); |
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maxwrk = max(i__1,i__2); |
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} |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *m + *nrhs * ilaenv_(&c__1, "DORMLQ", |
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"LT", n, nrhs, m, &c_n1); |
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maxwrk = max(i__1,i__2); |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + wlalsd; |
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maxwrk = max(i__1,i__2); |
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/* XXX: Ensure the Path 2a case below is triggered. The workspace */ |
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/* calculation should use queries for all routines eventually. */ |
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/* Computing MAX */ |
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/* Computing MAX */ |
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i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = |
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max(i__3,*nrhs), i__4 = *n - *m * 3; |
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i__1 = maxwrk, i__2 = (*m << 2) + *m * *m + max(i__3,i__4); |
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maxwrk = max(i__1,i__2); |
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} else { |
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/* Path 2 - remaining underdetermined cases. */ |
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maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, "DGEBRD", " ", m, |
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n, &c_n1, &c_n1); |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, "DORMBR" |
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, "QLT", m, nrhs, n, &c_n1); |
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maxwrk = max(i__1,i__2); |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORMBR", |
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"PLN", n, nrhs, m, &c_n1); |
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maxwrk = max(i__1,i__2); |
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/* Computing MAX */ |
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i__1 = maxwrk, i__2 = *m * 3 + wlalsd; |
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maxwrk = max(i__1,i__2); |
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} |
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/* Computing MAX */ |
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i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *m, i__1 = max(i__1,i__2), |
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i__2 = *m * 3 + wlalsd; |
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minwrk = max(i__1,i__2); |
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} |
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minwrk = min(minwrk,maxwrk); |
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work[1] = (doublereal) maxwrk; |
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if (*lwork < minwrk && ! lquery) { |
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*info = -12; |
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} |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("DGELSD", &i__1); |
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return 0; |
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} else if (lquery) { |
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goto L10; |
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} |
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/* Quick return if possible. */ |
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if (*m == 0 || *n == 0) { |
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*rank = 0; |
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return 0; |
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} |
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/* Get machine parameters. */ |
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eps = dlamch_("P"); |
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sfmin = dlamch_("S"); |
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smlnum = sfmin / eps; |
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bignum = 1. / smlnum; |
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dlabad_(&smlnum, &bignum); |
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/* Scale A if max entry outside range [SMLNUM,BIGNUM]. */ |
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anrm = dlange_("M", m, n, &a[a_offset], lda, &work[1]); |
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iascl = 0; |
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if (anrm > 0. && anrm < smlnum) { |
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/* Scale matrix norm up to SMLNUM. */ |
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dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, |
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info); |
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iascl = 1; |
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} else if (anrm > bignum) { |
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/* Scale matrix norm down to BIGNUM. */ |
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dlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, |
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info); |
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iascl = 2; |
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} else if (anrm == 0.) { |
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/* Matrix all zero. Return zero solution. */ |
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i__1 = max(*m,*n); |
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dlaset_("F", &i__1, nrhs, &c_b82, &c_b82, &b[b_offset], ldb); |
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dlaset_("F", &minmn, &c__1, &c_b82, &c_b82, &s[1], &c__1); |
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*rank = 0; |
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goto L10; |
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} |
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/* Scale B if max entry outside range [SMLNUM,BIGNUM]. */ |
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bnrm = dlange_("M", m, nrhs, &b[b_offset], ldb, &work[1]); |
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ibscl = 0; |
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if (bnrm > 0. && bnrm < smlnum) { |
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/* Scale matrix norm up to SMLNUM. */ |
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dlascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb, |
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info); |
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ibscl = 1; |
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} else if (bnrm > bignum) { |
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/* Scale matrix norm down to BIGNUM. */ |
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dlascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, |
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info); |
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ibscl = 2; |
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} |
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/* If M < N make sure certain entries of B are zero. */ |
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if (*m < *n) { |
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i__1 = *n - *m; |
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dlaset_("F", &i__1, nrhs, &c_b82, &c_b82, &b[*m + 1 + b_dim1], ldb); |
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} |
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/* Overdetermined case. */ |
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if (*m >= *n) { |
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/* Path 1 - overdetermined or exactly determined. */ |
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mm = *m; |
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if (*m >= mnthr) { |
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|
|
/* Path 1a - overdetermined, with many more rows than columns. */ |
|
|
|
mm = *n; |
|
itau = 1; |
|
nwork = itau + *n; |
|
|
|
/* Compute A=Q*R. */ |
|
/* (Workspace: need 2*N, prefer N+N*NB) */ |
|
|
|
i__1 = *lwork - nwork + 1; |
|
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, |
|
info); |
|
|
|
/* Multiply B by transpose(Q). */ |
|
/* (Workspace: need N+NRHS, prefer N+NRHS*NB) */ |
|
|
|
i__1 = *lwork - nwork + 1; |
|
dormqr_("L", "T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[ |
|
b_offset], ldb, &work[nwork], &i__1, info); |
|
|
|
/* Zero out below R. */ |
|
|
|
if (*n > 1) { |
|
i__1 = *n - 1; |
|
i__2 = *n - 1; |
|
dlaset_("L", &i__1, &i__2, &c_b82, &c_b82, &a[a_dim1 + 2], |
|
lda); |
|
} |
|
} |
|
|
|
ie = 1; |
|
itauq = ie + *n; |
|
itaup = itauq + *n; |
|
nwork = itaup + *n; |
|
|
|
/* Bidiagonalize R in A. */ |
|
/* (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */ |
|
|
|
i__1 = *lwork - nwork + 1; |
|
dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & |
|
work[itaup], &work[nwork], &i__1, info); |
|
|
|
/* Multiply B by transpose of left bidiagonalizing vectors of R. */ |
|
/* (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */ |
|
|
|
i__1 = *lwork - nwork + 1; |
|
dormbr_("Q", "L", "T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], |
|
&b[b_offset], ldb, &work[nwork], &i__1, info); |
|
|
|
/* Solve the bidiagonal least squares problem. */ |
|
|
|
dlalsd_("U", &smlsiz, n, nrhs, &s[1], &work[ie], &b[b_offset], ldb, |
|
rcond, rank, &work[nwork], &iwork[1], info); |
|
if (*info != 0) { |
|
goto L10; |
|
} |
|
|
|
/* Multiply B by right bidiagonalizing vectors of R. */ |
|
|
|
i__1 = *lwork - nwork + 1; |
|
dormbr_("P", "L", "N", n, nrhs, n, &a[a_offset], lda, &work[itaup], & |
|
b[b_offset], ldb, &work[nwork], &i__1, info); |
|
|
|
} else /* if(complicated condition) */ { |
|
/* Computing MAX */ |
|
i__1 = *m, i__2 = (*m << 1) - 4, i__1 = max(i__1,i__2), i__1 = max( |
|
i__1,*nrhs), i__2 = *n - *m * 3, i__1 = max(i__1,i__2); |
|
if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__1,wlalsd)) { |
|
|
|
/* Path 2a - underdetermined, with many more columns than rows */ |
|
/* and sufficient workspace for an efficient algorithm. */ |
|
|
|
ldwork = *m; |
|
/* Computing MAX */ |
|
/* Computing MAX */ |
|
i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = |
|
max(i__3,*nrhs), i__4 = *n - *m * 3; |
|
i__1 = (*m << 2) + *m * *lda + max(i__3,i__4), i__2 = *m * *lda + |
|
*m + *m * *nrhs, i__1 = max(i__1,i__2), i__2 = (*m << 2) |
|
+ *m * *lda + wlalsd; |
|
if (*lwork >= max(i__1,i__2)) { |
|
ldwork = *lda; |
|
} |
|
itau = 1; |
|
nwork = *m + 1; |
|
|
|
/* Compute A=L*Q. */ |
|
/* (Workspace: need 2*M, prefer M+M*NB) */ |
|
|
|
i__1 = *lwork - nwork + 1; |
|
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, |
|
info); |
|
il = nwork; |
|
|
|
/* Copy L to WORK(IL), zeroing out above its diagonal. */ |
|
|
|
dlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork); |
|
i__1 = *m - 1; |
|
i__2 = *m - 1; |
|
dlaset_("U", &i__1, &i__2, &c_b82, &c_b82, &work[il + ldwork], & |
|
ldwork); |
|
ie = il + ldwork * *m; |
|
itauq = ie + *m; |
|
itaup = itauq + *m; |
|
nwork = itaup + *m; |
|
|
|
/* Bidiagonalize L in WORK(IL). */ |
|
/* (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */ |
|
|
|
i__1 = *lwork - nwork + 1; |
|
dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], |
|
&work[itaup], &work[nwork], &i__1, info); |
|
|
|
/* Multiply B by transpose of left bidiagonalizing vectors of L. */ |
|
/* (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */ |
|
|
|
i__1 = *lwork - nwork + 1; |
|
dormbr_("Q", "L", "T", m, nrhs, m, &work[il], &ldwork, &work[ |
|
itauq], &b[b_offset], ldb, &work[nwork], &i__1, info); |
|
|
|
/* Solve the bidiagonal least squares problem. */ |
|
|
|
dlalsd_("U", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], |
|
ldb, rcond, rank, &work[nwork], &iwork[1], info); |
|
if (*info != 0) { |
|
goto L10; |
|
} |
|
|
|
/* Multiply B by right bidiagonalizing vectors of L. */ |
|
|
|
i__1 = *lwork - nwork + 1; |
|
dormbr_("P", "L", "N", m, nrhs, m, &work[il], &ldwork, &work[ |
|
itaup], &b[b_offset], ldb, &work[nwork], &i__1, info); |
|
|
|
/* Zero out below first M rows of B. */ |
|
|
|
i__1 = *n - *m; |
|
dlaset_("F", &i__1, nrhs, &c_b82, &c_b82, &b[*m + 1 + b_dim1], |
|
ldb); |
|
nwork = itau + *m; |
|
|
|
/* Multiply transpose(Q) by B. */ |
|
/* (Workspace: need M+NRHS, prefer M+NRHS*NB) */ |
|
|
|
i__1 = *lwork - nwork + 1; |
|
dormlq_("L", "T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[ |
|
b_offset], ldb, &work[nwork], &i__1, info); |
|
|
|
} else { |
|
|
|
/* Path 2 - remaining underdetermined cases. */ |
|
|
|
ie = 1; |
|
itauq = ie + *m; |
|
itaup = itauq + *m; |
|
nwork = itaup + *m; |
|
|
|
/* Bidiagonalize A. */ |
|
/* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */ |
|
|
|
i__1 = *lwork - nwork + 1; |
|
dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & |
|
work[itaup], &work[nwork], &i__1, info); |
|
|
|
/* Multiply B by transpose of left bidiagonalizing vectors. */ |
|
/* (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */ |
|
|
|
i__1 = *lwork - nwork + 1; |
|
dormbr_("Q", "L", "T", m, nrhs, n, &a[a_offset], lda, &work[itauq] |
|
, &b[b_offset], ldb, &work[nwork], &i__1, info); |
|
|
|
/* Solve the bidiagonal least squares problem. */ |
|
|
|
dlalsd_("L", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], |
|
ldb, rcond, rank, &work[nwork], &iwork[1], info); |
|
if (*info != 0) { |
|
goto L10; |
|
} |
|
|
|
/* Multiply B by right bidiagonalizing vectors of A. */ |
|
|
|
i__1 = *lwork - nwork + 1; |
|
dormbr_("P", "L", "N", n, nrhs, m, &a[a_offset], lda, &work[itaup] |
|
, &b[b_offset], ldb, &work[nwork], &i__1, info); |
|
|
|
} |
|
} |
|
|
|
/* Undo scaling. */ |
|
|
|
if (iascl == 1) { |
|
dlascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, |
|
info); |
|
dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & |
|
minmn, info); |
|
} else if (iascl == 2) { |
|
dlascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, |
|
info); |
|
dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & |
|
minmn, info); |
|
} |
|
if (ibscl == 1) { |
|
dlascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, |
|
info); |
|
} else if (ibscl == 2) { |
|
dlascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, |
|
info); |
|
} |
|
|
|
L10: |
|
work[1] = (doublereal) maxwrk; |
|
return 0; |
|
|
|
/* End of DGELSD */ |
|
|
|
} /* dgelsd_ */
|
|
|