clalsa.f.html
来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 528 行 · 第 1/3 页
HTML
528 行
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<title>clalsa.f</title>
<meta name="generator" content="emacs 21.3.1; htmlfontify 0.20">
<style type="text/css"><!--
body { background: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-weight: 500; font-stretch: normal; font-family: adobe-courier; font-size: 11pt; text-decoration: none; }
span.default { background: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-weight: 500; font-stretch: normal; font-family: adobe-courier; font-size: 11pt; text-decoration: none; }
span.default a { background: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-weight: 500; font-stretch: normal; font-family: adobe-courier; font-size: 11pt; text-decoration: underline; }
span.string { color: rgb(188, 143, 143); background: rgb(255, 255, 255); font-style: normal; font-weight: 500; font-stretch: normal; font-family: adobe-courier; font-size: 11pt; text-decoration: none; }
span.string a { color: rgb(188, 143, 143); background: rgb(255, 255, 255); font-style: normal; font-weight: 500; font-stretch: normal; font-family: adobe-courier; font-size: 11pt; text-decoration: underline; }
span.comment { color: rgb(178, 34, 34); background: rgb(255, 255, 255); font-style: normal; font-weight: 500; font-stretch: normal; font-family: adobe-courier; font-size: 11pt; text-decoration: none; }
span.comment a { color: rgb(178, 34, 34); background: rgb(255, 255, 255); font-style: normal; font-weight: 500; font-stretch: normal; font-family: adobe-courier; font-size: 11pt; text-decoration: underline; }
--></style>
</head>
<body>
<pre>
SUBROUTINE <a name="CLALSA.1"></a><a href="clalsa.f.html#CLALSA.1">CLALSA</a>( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U,
$ LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR,
$ GIVCOL, LDGCOL, PERM, GIVNUM, C, S, RWORK,
$ IWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS,
$ SMLSIZ
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ),
$ K( * ), PERM( LDGCOL, * )
REAL C( * ), DIFL( LDU, * ), DIFR( LDU, * ),
$ GIVNUM( LDU, * ), POLES( LDU, * ), RWORK( * ),
$ S( * ), U( LDU, * ), VT( LDU, * ), Z( LDU, * )
COMPLEX B( LDB, * ), BX( LDBX, * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="CLALSA.26"></a><a href="clalsa.f.html#CLALSA.1">CLALSA</a> is an itermediate step in solving the least squares problem
</span><span class="comment">*</span><span class="comment"> by computing the SVD of the coefficient matrix in compact form (The
</span><span class="comment">*</span><span class="comment"> singular vectors are computed as products of simple orthorgonal
</span><span class="comment">*</span><span class="comment"> matrices.).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If ICOMPQ = 0, <a name="CLALSA.31"></a><a href="clalsa.f.html#CLALSA.1">CLALSA</a> applies the inverse of the left singular vector
</span><span class="comment">*</span><span class="comment"> matrix of an upper bidiagonal matrix to the right hand side; and if
</span><span class="comment">*</span><span class="comment"> ICOMPQ = 1, <a name="CLALSA.33"></a><a href="clalsa.f.html#CLALSA.1">CLALSA</a> applies the right singular vector matrix to the
</span><span class="comment">*</span><span class="comment"> right hand side. The singular vector matrices were generated in
</span><span class="comment">*</span><span class="comment"> compact form by <a name="CLALSA.35"></a><a href="clalsa.f.html#CLALSA.1">CLALSA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ICOMPQ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> Specifies whether the left or the right singular vector
</span><span class="comment">*</span><span class="comment"> matrix is involved.
</span><span class="comment">*</span><span class="comment"> = 0: Left singular vector matrix
</span><span class="comment">*</span><span class="comment"> = 1: Right singular vector matrix
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> SMLSIZ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The maximum size of the subproblems at the bottom of the
</span><span class="comment">*</span><span class="comment"> computation tree.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The row and column dimensions of the upper bidiagonal matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> NRHS (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of columns of B and BX. NRHS must be at least 1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> B (input/output) COMPLEX array, dimension ( LDB, NRHS )
</span><span class="comment">*</span><span class="comment"> On input, B contains the right hand sides of the least
</span><span class="comment">*</span><span class="comment"> squares problem in rows 1 through M.
</span><span class="comment">*</span><span class="comment"> On output, B contains the solution X in rows 1 through N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of B in the calling subprogram.
</span><span class="comment">*</span><span class="comment"> LDB must be at least max(1,MAX( M, N ) ).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> BX (output) COMPLEX array, dimension ( LDBX, NRHS )
</span><span class="comment">*</span><span class="comment"> On exit, the result of applying the left or right singular
</span><span class="comment">*</span><span class="comment"> vector matrix to B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDBX (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of BX.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> U (input) REAL array, dimension ( LDU, SMLSIZ ).
</span><span class="comment">*</span><span class="comment"> On entry, U contains the left singular vector matrices of all
</span><span class="comment">*</span><span class="comment"> subproblems at the bottom level.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDU (input) INTEGER, LDU = > N.
</span><span class="comment">*</span><span class="comment"> The leading dimension of arrays U, VT, DIFL, DIFR,
</span><span class="comment">*</span><span class="comment"> POLES, GIVNUM, and Z.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> VT (input) REAL array, dimension ( LDU, SMLSIZ+1 ).
</span><span class="comment">*</span><span class="comment"> On entry, VT' contains the right singular vector matrices of
</span><span class="comment">*</span><span class="comment"> all subproblems at the bottom level.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> K (input) INTEGER array, dimension ( N ).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DIFL (input) REAL array, dimension ( LDU, NLVL ).
</span><span class="comment">*</span><span class="comment"> where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DIFR (input) REAL array, dimension ( LDU, 2 * NLVL ).
</span><span class="comment">*</span><span class="comment"> On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record
</span><span class="comment">*</span><span class="comment"> distances between singular values on the I-th level and
</span><span class="comment">*</span><span class="comment"> singular values on the (I -1)-th level, and DIFR(*, 2 * I)
</span><span class="comment">*</span><span class="comment"> record the normalizing factors of the right singular vectors
</span><span class="comment">*</span><span class="comment"> matrices of subproblems on I-th level.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Z (input) REAL array, dimension ( LDU, NLVL ).
</span><span class="comment">*</span><span class="comment"> On entry, Z(1, I) contains the components of the deflation-
</span><span class="comment">*</span><span class="comment"> adjusted updating row vector for subproblems on the I-th
</span><span class="comment">*</span><span class="comment"> level.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> POLES (input) REAL array, dimension ( LDU, 2 * NLVL ).
</span><span class="comment">*</span><span class="comment"> On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old
</span><span class="comment">*</span><span class="comment"> singular values involved in the secular equations on the I-th
</span><span class="comment">*</span><span class="comment"> level.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> GIVPTR (input) INTEGER array, dimension ( N ).
</span><span class="comment">*</span><span class="comment"> On entry, GIVPTR( I ) records the number of Givens
</span><span class="comment">*</span><span class="comment"> rotations performed on the I-th problem on the computation
</span><span class="comment">*</span><span class="comment"> tree.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ).
</span><span class="comment">*</span><span class="comment"> On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the
</span><span class="comment">*</span><span class="comment"> locations of Givens rotations performed on the I-th level on
</span><span class="comment">*</span><span class="comment"> the computation tree.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDGCOL (input) INTEGER, LDGCOL = > N.
</span><span class="comment">*</span><span class="comment"> The leading dimension of arrays GIVCOL and PERM.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> PERM (input) INTEGER array, dimension ( LDGCOL, NLVL ).
</span><span class="comment">*</span><span class="comment"> On entry, PERM(*, I) records permutations done on the I-th
</span><span class="comment">*</span><span class="comment"> level of the computation tree.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> GIVNUM (input) REAL array, dimension ( LDU, 2 * NLVL ).
</span><span class="comment">*</span><span class="comment"> On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S-
</span><span class="comment">*</span><span class="comment"> values of Givens rotations performed on the I-th level on the
</span><span class="comment">*</span><span class="comment"> computation tree.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C (input) REAL array, dimension ( N ).
</span><span class="comment">*</span><span class="comment"> On entry, if the I-th subproblem is not square,
</span><span class="comment">*</span><span class="comment"> C( I ) contains the C-value of a Givens rotation related to
</span><span class="comment">*</span><span class="comment"> the right null space of the I-th subproblem.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> S (input) REAL array, dimension ( N ).
</span><span class="comment">*</span><span class="comment"> On entry, if the I-th subproblem is not square,
</span><span class="comment">*</span><span class="comment"> S( I ) contains the S-value of a Givens rotation related to
</span><span class="comment">*</span><span class="comment"> the right null space of the I-th subproblem.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RWORK (workspace) REAL array, dimension at least
</span><span class="comment">*</span><span class="comment"> max ( N, (SMLSZ+1)*NRHS*3 ).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IWORK (workspace) INTEGER array.
</span><span class="comment">*</span><span class="comment"> The dimension must be at least 3 * N
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit.
</span><span class="comment">*</span><span class="comment"> < 0: if INFO = -i, the i-th argument had an illegal value.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Further Details
</span><span class="comment">*</span><span class="comment"> ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Based on contributions by
</span><span class="comment">*</span><span class="comment"> Ming Gu and Ren-Cang Li, Computer Science Division, University of
</span><span class="comment">*</span><span class="comment"> California at Berkeley, USA
</span><span class="comment">*</span><span class="comment"> Osni Marques, LBNL/NERSC, USA
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
⌨️ 快捷键说明
复制代码Ctrl + C
搜索代码Ctrl + F
全屏模式F11
增大字号Ctrl + =
减小字号Ctrl + -
显示快捷键?