chetd2.f.html
来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 283 行 · 第 1/2 页
HTML
283 行
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<title>chetd2.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="CHETD2.1"></a><a href="chetd2.f.html#CHETD2.1">CHETD2</a>( UPLO, N, A, LDA, D, E, TAU, 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, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL D( * ), E( * )
COMPLEX A( LDA, * ), TAU( * )
<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="CHETD2.19"></a><a href="chetd2.f.html#CHETD2.1">CHETD2</a> reduces a complex Hermitian matrix A to real symmetric
</span><span class="comment">*</span><span class="comment"> tridiagonal form T by a unitary similarity transformation:
</span><span class="comment">*</span><span class="comment"> Q' * A * Q = T.
</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"> Specifies whether the upper or lower triangular part of the
</span><span class="comment">*</span><span class="comment"> Hermitian matrix A is stored:
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangular
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangular
</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 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"> On exit, if UPLO = 'U', the diagonal and first superdiagonal
</span><span class="comment">*</span><span class="comment"> of A are overwritten by the corresponding elements of the
</span><span class="comment">*</span><span class="comment"> tridiagonal matrix T, and the elements above the first
</span><span class="comment">*</span><span class="comment"> superdiagonal, with the array TAU, represent the unitary
</span><span class="comment">*</span><span class="comment"> matrix Q as a product of elementary reflectors; if UPLO
</span><span class="comment">*</span><span class="comment"> = 'L', the diagonal and first subdiagonal of A are over-
</span><span class="comment">*</span><span class="comment"> written by the corresponding elements of the tridiagonal
</span><span class="comment">*</span><span class="comment"> matrix T, and the elements below the first subdiagonal, with
</span><span class="comment">*</span><span class="comment"> the array TAU, represent the unitary matrix Q as a product
</span><span class="comment">*</span><span class="comment"> of elementary reflectors. 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,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> D (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> The diagonal elements of the tridiagonal matrix T:
</span><span class="comment">*</span><span class="comment"> D(i) = A(i,i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> E (output) REAL array, dimension (N-1)
</span><span class="comment">*</span><span class="comment"> The off-diagonal elements of the tridiagonal matrix T:
</span><span class="comment">*</span><span class="comment"> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TAU (output) COMPLEX array, dimension (N-1)
</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"> 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"> If UPLO = 'U', the matrix Q is represented as a product of elementary
</span><span class="comment">*</span><span class="comment"> reflectors
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q = H(n-1) . . . H(2) H(1).
</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 complex scalar, and v is a complex vector with
</span><span class="comment">*</span><span class="comment"> v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
</span><span class="comment">*</span><span class="comment"> A(1:i-1,i+1), and tau in TAU(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If UPLO = 'L', the matrix Q is represented as a product of elementary
</span><span class="comment">*</span><span class="comment"> reflectors
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q = H(1) H(2) . . . H(n-1).
</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 complex scalar, and v is a complex vector with
</span><span class="comment">*</span><span class="comment"> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
</span><span class="comment">*</span><span class="comment"> and tau in TAU(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The contents of A on exit are illustrated by the following examples
</span><span class="comment">*</span><span class="comment"> with n = 5:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U': if UPLO = 'L':
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ( d e v2 v3 v4 ) ( d )
</span><span class="comment">*</span><span class="comment"> ( d e v3 v4 ) ( e d )
</span><span class="comment">*</span><span class="comment"> ( d e v4 ) ( v1 e d )
</span><span class="comment">*</span><span class="comment"> ( d e ) ( v1 v2 e d )
</span><span class="comment">*</span><span class="comment"> ( d ) ( v1 v2 v3 e d )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where d and e denote diagonal and off-diagonal elements of T, and vi
</span><span class="comment">*</span><span class="comment"> denotes an element of the vector defining H(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"> .. Parameters ..
</span> COMPLEX ONE, ZERO, HALF
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
$ ZERO = ( 0.0E+0, 0.0E+0 ),
$ HALF = ( 0.5E+0, 0.0E+0 ) )
<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?