slasdq.f.html
来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 341 行 · 第 1/2 页
HTML
341 行
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<title>slasdq.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="SLASDQ.1"></a><a href="slasdq.f.html#SLASDQ.1">SLASDQ</a>( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT,
$ U, LDU, C, LDC, WORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary 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> CHARACTER UPLO
INTEGER INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU, SQRE
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL C( LDC, * ), D( * ), E( * ), U( LDU, * ),
$ VT( LDVT, * ), WORK( * )
<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="SLASDQ.20"></a><a href="slasdq.f.html#SLASDQ.1">SLASDQ</a> computes the singular value decomposition (SVD) of a real
</span><span class="comment">*</span><span class="comment"> (upper or lower) bidiagonal matrix with diagonal D and offdiagonal
</span><span class="comment">*</span><span class="comment"> E, accumulating the transformations if desired. Letting B denote
</span><span class="comment">*</span><span class="comment"> the input bidiagonal matrix, the algorithm computes orthogonal
</span><span class="comment">*</span><span class="comment"> matrices Q and P such that B = Q * S * P' (P' denotes the transpose
</span><span class="comment">*</span><span class="comment"> of P). The singular values S are overwritten on D.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The input matrix U is changed to U * Q if desired.
</span><span class="comment">*</span><span class="comment"> The input matrix VT is changed to P' * VT if desired.
</span><span class="comment">*</span><span class="comment"> The input matrix C is changed to Q' * C if desired.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> See "Computing Small Singular Values of Bidiagonal Matrices With
</span><span class="comment">*</span><span class="comment"> Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan,
</span><span class="comment">*</span><span class="comment"> LAPACK Working Note #3, for a detailed description of the algorithm.
</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"> UPLO (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> On entry, UPLO specifies whether the input bidiagonal matrix
</span><span class="comment">*</span><span class="comment"> is upper or lower bidiagonal, and wether it is square are
</span><span class="comment">*</span><span class="comment"> not.
</span><span class="comment">*</span><span class="comment"> UPLO = 'U' or 'u' B is upper bidiagonal.
</span><span class="comment">*</span><span class="comment"> UPLO = 'L' or 'l' B is lower bidiagonal.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> SQRE (input) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: then the input matrix is N-by-N.
</span><span class="comment">*</span><span class="comment"> = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and
</span><span class="comment">*</span><span class="comment"> (N+1)-by-N if UPLU = 'L'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The bidiagonal matrix has
</span><span class="comment">*</span><span class="comment"> N = NL + NR + 1 rows and
</span><span class="comment">*</span><span class="comment"> M = N + SQRE >= N columns.
</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"> On entry, N specifies the number of rows and columns
</span><span class="comment">*</span><span class="comment"> in the matrix. N must be at least 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> NCVT (input) INTEGER
</span><span class="comment">*</span><span class="comment"> On entry, NCVT specifies the number of columns of
</span><span class="comment">*</span><span class="comment"> the matrix VT. NCVT must be at least 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> NRU (input) INTEGER
</span><span class="comment">*</span><span class="comment"> On entry, NRU specifies the number of rows of
</span><span class="comment">*</span><span class="comment"> the matrix U. NRU must be at least 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> NCC (input) INTEGER
</span><span class="comment">*</span><span class="comment"> On entry, NCC specifies the number of columns of
</span><span class="comment">*</span><span class="comment"> the matrix C. NCC must be at least 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> D (input/output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> On entry, D contains the diagonal entries of the
</span><span class="comment">*</span><span class="comment"> bidiagonal matrix whose SVD is desired. On normal exit,
</span><span class="comment">*</span><span class="comment"> D contains the singular values in ascending order.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> E (input/output) REAL array.
</span><span class="comment">*</span><span class="comment"> dimension is (N-1) if SQRE = 0 and N if SQRE = 1.
</span><span class="comment">*</span><span class="comment"> On entry, the entries of E contain the offdiagonal entries
</span><span class="comment">*</span><span class="comment"> of the bidiagonal matrix whose SVD is desired. On normal
</span><span class="comment">*</span><span class="comment"> exit, E will contain 0. If the algorithm does not converge,
</span><span class="comment">*</span><span class="comment"> D and E will contain the diagonal and superdiagonal entries
</span><span class="comment">*</span><span class="comment"> of a bidiagonal matrix orthogonally equivalent to the one
</span><span class="comment">*</span><span class="comment"> given as input.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> VT (input/output) REAL array, dimension (LDVT, NCVT)
</span><span class="comment">*</span><span class="comment"> On entry, contains a matrix which on exit has been
</span><span class="comment">*</span><span class="comment"> premultiplied by P', dimension N-by-NCVT if SQRE = 0
</span><span class="comment">*</span><span class="comment"> and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDVT (input) INTEGER
</span><span class="comment">*</span><span class="comment"> On entry, LDVT specifies the leading dimension of VT as
</span><span class="comment">*</span><span class="comment"> declared in the calling (sub) program. LDVT must be at
</span><span class="comment">*</span><span class="comment"> least 1. If NCVT is nonzero LDVT must also be at least N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> U (input/output) REAL array, dimension (LDU, N)
</span><span class="comment">*</span><span class="comment"> On entry, contains a matrix which on exit has been
</span><span class="comment">*</span><span class="comment"> postmultiplied by Q, dimension NRU-by-N if SQRE = 0
</span><span class="comment">*</span><span class="comment"> and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDU (input) INTEGER
</span><span class="comment">*</span><span class="comment"> On entry, LDU specifies the leading dimension of U as
</span><span class="comment">*</span><span class="comment"> declared in the calling (sub) program. LDU must be at
</span><span class="comment">*</span><span class="comment"> least max( 1, NRU ) .
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C (input/output) REAL array, dimension (LDC, NCC)
</span><span class="comment">*</span><span class="comment"> On entry, contains an N-by-NCC matrix which on exit
</span><span class="comment">*</span><span class="comment"> has been premultiplied by Q' dimension N-by-NCC if SQRE = 0
</span><span class="comment">*</span><span class="comment"> and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDC (input) INTEGER
</span><span class="comment">*</span><span class="comment"> On entry, LDC specifies the leading dimension of C as
</span><span class="comment">*</span><span class="comment"> declared in the calling (sub) program. LDC must be at
</span><span class="comment">*</span><span class="comment"> least 1. If NCC is nonzero, LDC must also be at least N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace) REAL array, dimension (4*N)
</span><span class="comment">*</span><span class="comment"> Workspace. Only referenced if one of NCVT, NRU, or NCC is
</span><span class="comment">*</span><span class="comment"> nonzero, and if N is at least 2.
</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"> On exit, a value of 0 indicates a successful exit.
</span><span class="comment">*</span><span class="comment"> If INFO < 0, argument number -INFO is illegal.
</span><span class="comment">*</span><span class="comment"> If INFO > 0, the algorithm did not converge, and INFO
</span><span class="comment">*</span><span class="comment"> specifies how many superdiagonals did not converge.
</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 Huan Ren, 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">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> REAL ZERO
PARAMETER ( ZERO = 0.0E+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL ROTATE
INTEGER I, ISUB, IUPLO, J, NP1, SQRE1
REAL CS, R, SMIN, SN
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="SBDSQR.143"></a><a href="sbdsqr.f.html#SBDSQR.1">SBDSQR</a>, <a name="SLARTG.143"></a><a href="slartg.f.html#SLARTG.1">SLARTG</a>, <a name="SLASR.143"></a><a href="slasr.f.html#SLASR.1">SLASR</a>, SSWAP, <a name="XERBLA.143"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.146"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.147"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC MAX
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
⌨️ 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?