zhetrf.f.html
来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 306 行 · 第 1/2 页
HTML
306 行
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<title>zhetrf.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="ZHETRF.1"></a><a href="zhetrf.f.html#ZHETRF.1">ZHETRF</a>( UPLO, N, A, LDA, IPIV, 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> CHARACTER UPLO
INTEGER INFO, LDA, LWORK, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IPIV( * )
COMPLEX*16 A( LDA, * ), 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="ZHETRF.19"></a><a href="zhetrf.f.html#ZHETRF.1">ZHETRF</a> computes the factorization of a complex Hermitian matrix A
</span><span class="comment">*</span><span class="comment"> using the Bunch-Kaufman diagonal pivoting method. The form of the
</span><span class="comment">*</span><span class="comment"> factorization is
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A = U*D*U**H or A = L*D*L**H
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where U (or L) is a product of permutation and unit upper (lower)
</span><span class="comment">*</span><span class="comment"> triangular matrices, and D is Hermitian and block diagonal with
</span><span class="comment">*</span><span class="comment"> 1-by-1 and 2-by-2 diagonal blocks.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> This is the blocked version of the algorithm, calling Level 3 BLAS.
</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"> = 'U': Upper triangle of A is stored;
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangle of A is stored.
</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 order 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) COMPLEX*16 array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment"> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
</span><span class="comment">*</span><span class="comment"> N-by-N upper triangular part of A contains the upper
</span><span class="comment">*</span><span class="comment"> triangular part of the matrix A, and the strictly lower
</span><span class="comment">*</span><span class="comment"> triangular part of A is not referenced. If UPLO = 'L', the
</span><span class="comment">*</span><span class="comment"> leading N-by-N lower triangular part of A contains the lower
</span><span class="comment">*</span><span class="comment"> triangular part of the matrix A, and the strictly upper
</span><span class="comment">*</span><span class="comment"> triangular part of A is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, the block diagonal matrix D and the multipliers used
</span><span class="comment">*</span><span class="comment"> to obtain the factor U or L (see below for 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,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IPIV (output) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment"> Details of the interchanges and the block structure of D.
</span><span class="comment">*</span><span class="comment"> If IPIV(k) > 0, then rows and columns k and IPIV(k) were
</span><span class="comment">*</span><span class="comment"> interchanged and D(k,k) is a 1-by-1 diagonal block.
</span><span class="comment">*</span><span class="comment"> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
</span><span class="comment">*</span><span class="comment"> columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
</span><span class="comment">*</span><span class="comment"> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) =
</span><span class="comment">*</span><span class="comment"> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
</span><span class="comment">*</span><span class="comment"> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace/output) COMPLEX*16 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 length of WORK. LWORK >=1. For best performance
</span><span class="comment">*</span><span class="comment"> LWORK >= N*NB, where NB is the block size returned by <a name="ILAENV.71"></a><a href="hfy-index.html#ILAENV">ILAENV</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"> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
</span><span class="comment">*</span><span class="comment"> has been completed, but the block diagonal matrix D is
</span><span class="comment">*</span><span class="comment"> exactly singular, and division by zero will occur if it
</span><span class="comment">*</span><span class="comment"> is used to solve a system of equations.
</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"> If UPLO = 'U', then A = U*D*U', where
</span><span class="comment">*</span><span class="comment"> U = P(n)*U(n)* ... *P(k)U(k)* ...,
</span><span class="comment">*</span><span class="comment"> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
</span><span class="comment">*</span><span class="comment"> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
</span><span class="comment">*</span><span class="comment"> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
</span><span class="comment">*</span><span class="comment"> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
</span><span class="comment">*</span><span class="comment"> that if the diagonal block D(k) is of order s (s = 1 or 2), then
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ( I v 0 ) k-s
</span><span class="comment">*</span><span class="comment"> U(k) = ( 0 I 0 ) s
</span><span class="comment">*</span><span class="comment"> ( 0 0 I ) n-k
</span><span class="comment">*</span><span class="comment"> k-s s n-k
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
</span><span class="comment">*</span><span class="comment"> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
</span><span class="comment">*</span><span class="comment"> and A(k,k), and v overwrites A(1:k-2,k-1:k).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If UPLO = 'L', then A = L*D*L', where
</span><span class="comment">*</span><span class="comment"> L = P(1)*L(1)* ... *P(k)*L(k)* ...,
</span><span class="comment">*</span><span class="comment"> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
</span><span class="comment">*</span><span class="comment"> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
</span><span class="comment">*</span><span class="comment"> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
</span><span class="comment">*</span><span class="comment"> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
</span><span class="comment">*</span><span class="comment"> that if the diagonal block D(k) is of order s (s = 1 or 2), then
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ( I 0 0 ) k-1
</span><span class="comment">*</span><span class="comment"> L(k) = ( 0 I 0 ) s
</span><span class="comment">*</span><span class="comment"> ( 0 v I ) n-k-s+1
</span><span class="comment">*</span><span class="comment"> k-1 s n-k-s+1
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
</span><span class="comment">*</span><span class="comment"> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
</span><span class="comment">*</span><span class="comment"> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
</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, UPPER
INTEGER IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.125"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
INTEGER <a name="ILAENV.126"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
EXTERNAL <a name="LSAME.127"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.127"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="XERBLA.130"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>, <a name="ZHETF2.130"></a><a href="zhetf2.f.html#ZHETF2.1">ZHETF2</a>, <a name="ZLAHEF.130"></a><a href="zlahef.f.html#ZLAHEF.1">ZLAHEF</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"> ..
⌨️ 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?