sgeqlf.f.html
来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 238 行 · 第 1/2 页
HTML
238 行
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<title>sgeqlf.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="SGEQLF.1"></a><a href="sgeqlf.f.html#SGEQLF.1">SGEQLF</a>( M, N, A, LDA, TAU, WORK, LWORK, 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 INFO, LDA, LWORK, M, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL A( LDA, * ), TAU( * ), 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="SGEQLF.17"></a><a href="sgeqlf.f.html#SGEQLF.1">SGEQLF</a> computes a QL factorization of a real M-by-N matrix A:
</span><span class="comment">*</span><span class="comment"> A = Q * L.
</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"> M (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of rows of the matrix A. M >= 0.
</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 number of columns of the matrix A. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input/output) REAL array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment"> On entry, the M-by-N matrix A.
</span><span class="comment">*</span><span class="comment"> On exit,
</span><span class="comment">*</span><span class="comment"> if m >= n, the lower triangle of the subarray
</span><span class="comment">*</span><span class="comment"> A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L;
</span><span class="comment">*</span><span class="comment"> if m <= n, the elements on and below the (n-m)-th
</span><span class="comment">*</span><span class="comment"> superdiagonal contain the M-by-N lower trapezoidal matrix L;
</span><span class="comment">*</span><span class="comment"> the remaining elements, with the array TAU, represent the
</span><span class="comment">*</span><span class="comment"> orthogonal matrix Q as a product of elementary reflectors
</span><span class="comment">*</span><span class="comment"> (see Further Details).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDA (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array A. LDA >= max(1,M).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TAU (output) REAL array, dimension (min(M,N))
</span><span class="comment">*</span><span class="comment"> The scalar factors of the elementary reflectors (see Further
</span><span class="comment">*</span><span class="comment"> Details).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of the array WORK. LWORK >= max(1,N).
</span><span class="comment">*</span><span class="comment"> For optimum performance LWORK >= N*NB, where NB is the
</span><span class="comment">*</span><span class="comment"> optimal blocksize.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment"> only calculates the optimal size of the WORK array, returns
</span><span class="comment">*</span><span class="comment"> this value as the first entry of the WORK array, and no error
</span><span class="comment">*</span><span class="comment"> message related to LWORK is issued by <a name="XERBLA.58"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</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"> The matrix Q is represented as a product of elementary reflectors
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q = H(k) . . . H(2) H(1), where k = min(m,n).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Each H(i) has the form
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> H(i) = I - tau * v * v'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where tau is a real scalar, and v is a real vector with
</span><span class="comment">*</span><span class="comment"> v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
</span><span class="comment">*</span><span class="comment"> A(1:m-k+i-1,n-k+i), and tau in TAU(i).
</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"> .. Local Scalars ..
</span> LOGICAL LQUERY
INTEGER I, IB, IINFO, IWS, K, KI, KK, LDWORK, LWKOPT,
$ MU, NB, NBMIN, NU, NX
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="SGEQL2.87"></a><a href="sgeql2.f.html#SGEQL2.1">SGEQL2</a>, <a name="SLARFB.87"></a><a href="slarfb.f.html#SLARFB.1">SLARFB</a>, <a name="SLARFT.87"></a><a href="slarft.f.html#SLARFT.1">SLARFT</a>, <a name="XERBLA.87"></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"> .. Intrinsic Functions ..
</span> INTRINSIC MAX, MIN
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> INTEGER <a name="ILAENV.93"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
EXTERNAL <a name="ILAENV.94"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Test the input arguments
</span><span class="comment">*</span><span class="comment">
</span> INFO = 0
⌨️ 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?