zlags2.f.html
来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 331 行 · 第 1/2 页
HTML
331 行
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<title>zlags2.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.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="ZLAGS2.1"></a><a href="zlags2.f.html#ZLAGS2.1">ZLAGS2</a>( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV,
$ SNV, CSQ, SNQ )
<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> LOGICAL UPPER
DOUBLE PRECISION A1, A3, B1, B3, CSQ, CSU, CSV
COMPLEX*16 A2, B2, SNQ, SNU, SNV
<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="ZLAGS2.17"></a><a href="zlags2.f.html#ZLAGS2.1">ZLAGS2</a> computes 2-by-2 unitary matrices U, V and Q, such
</span><span class="comment">*</span><span class="comment"> that if ( UPPER ) then
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> U'*A*Q = U'*( A1 A2 )*Q = ( x 0 )
</span><span class="comment">*</span><span class="comment"> ( 0 A3 ) ( x x )
</span><span class="comment">*</span><span class="comment"> and
</span><span class="comment">*</span><span class="comment"> V'*B*Q = V'*( B1 B2 )*Q = ( x 0 )
</span><span class="comment">*</span><span class="comment"> ( 0 B3 ) ( x x )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> or if ( .NOT.UPPER ) then
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> U'*A*Q = U'*( A1 0 )*Q = ( x x )
</span><span class="comment">*</span><span class="comment"> ( A2 A3 ) ( 0 x )
</span><span class="comment">*</span><span class="comment"> and
</span><span class="comment">*</span><span class="comment"> V'*B*Q = V'*( B1 0 )*Q = ( x x )
</span><span class="comment">*</span><span class="comment"> ( B2 B3 ) ( 0 x )
</span><span class="comment">*</span><span class="comment"> where
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> U = ( CSU SNU ), V = ( CSV SNV ),
</span><span class="comment">*</span><span class="comment"> ( -CONJG(SNU) CSU ) ( -CONJG(SNV) CSV )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q = ( CSQ SNQ )
</span><span class="comment">*</span><span class="comment"> ( -CONJG(SNQ) CSQ )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Z' denotes the conjugate transpose of Z.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The rows of the transformed A and B are parallel. Moreover, if the
</span><span class="comment">*</span><span class="comment"> input 2-by-2 matrix A is not zero, then the transformed (1,1) entry
</span><span class="comment">*</span><span class="comment"> of A is not zero. If the input matrices A and B are both not zero,
</span><span class="comment">*</span><span class="comment"> then the transformed (2,2) element of B is not zero, except when the
</span><span class="comment">*</span><span class="comment"> first rows of input A and B are parallel and the second rows are
</span><span class="comment">*</span><span class="comment"> zero.
</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"> UPPER (input) LOGICAL
</span><span class="comment">*</span><span class="comment"> = .TRUE.: the input matrices A and B are upper triangular.
</span><span class="comment">*</span><span class="comment"> = .FALSE.: the input matrices A and B are lower triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A1 (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> A2 (input) COMPLEX*16
</span><span class="comment">*</span><span class="comment"> A3 (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> On entry, A1, A2 and A3 are elements of the input 2-by-2
</span><span class="comment">*</span><span class="comment"> upper (lower) triangular matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> B1 (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> B2 (input) COMPLEX*16
</span><span class="comment">*</span><span class="comment"> B3 (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> On entry, B1, B2 and B3 are elements of the input 2-by-2
</span><span class="comment">*</span><span class="comment"> upper (lower) triangular matrix B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> CSU (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> SNU (output) COMPLEX*16
</span><span class="comment">*</span><span class="comment"> The desired unitary matrix U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> CSV (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> SNV (output) COMPLEX*16
</span><span class="comment">*</span><span class="comment"> The desired unitary matrix V.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> CSQ (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> SNQ (output) COMPLEX*16
</span><span class="comment">*</span><span class="comment"> The desired unitary matrix Q.
</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> DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> DOUBLE PRECISION A, AUA11, AUA12, AUA21, AUA22, AVB12, AVB11,
$ AVB21, AVB22, CSL, CSR, D, FB, FC, S1, S2,
$ SNL, SNR, UA11R, UA22R, VB11R, VB22R
COMPLEX*16 B, C, D1, R, T, UA11, UA12, UA21, UA22, VB11,
$ VB12, VB21, VB22
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="DLASV2.95"></a><a href="dlasv2.f.html#DLASV2.1">DLASV2</a>, <a name="ZLARTG.95"></a><a href="zlartg.f.html#ZLARTG.1">ZLARTG</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Statement Functions ..
</span> DOUBLE PRECISION ABS1
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Statement Function definitions ..
</span> ABS1( T ) = ABS( DBLE( T ) ) + ABS( DIMAG( T ) )
<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> IF( UPPER ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Input matrices A and B are upper triangular matrices
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Form matrix C = A*adj(B) = ( a b )
</span><span class="comment">*</span><span class="comment"> ( 0 d )
</span><span class="comment">*</span><span class="comment">
</span> A = A1*B3
D = A3*B1
B = A2*B1 - A1*B2
FB = ABS( B )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Transform complex 2-by-2 matrix C to real matrix by unitary
</span><span class="comment">*</span><span class="comment"> diagonal matrix diag(1,D1).
</span><span class="comment">*</span><span class="comment">
</span> D1 = ONE
IF( FB.NE.ZERO )
$ D1 = B / FB
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The SVD of real 2 by 2 triangular C
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ( CSL -SNL )*( A B )*( CSR SNR ) = ( R 0 )
</span><span class="comment">*</span><span class="comment"> ( SNL CSL ) ( 0 D ) ( -SNR CSR ) ( 0 T )
</span><span class="comment">*</span><span class="comment">
</span> CALL <a name="DLASV2.132"></a><a href="dlasv2.f.html#DLASV2.1">DLASV2</a>( A, FB, D, S1, S2, SNR, CSR, SNL, CSL )
<span class="comment">*</span><span class="comment">
</span> IF( ABS( CSL ).GE.ABS( SNL ) .OR. ABS( CSR ).GE.ABS( SNR ) )
$ THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Compute the (1,1) and (1,2) elements of U'*A and V'*B,
</span><span class="comment">*</span><span class="comment"> and (1,2) element of |U|'*|A| and |V|'*|B|.
</span><span class="comment">*</span><span class="comment">
</span> UA11R = CSL*A1
UA12 = CSL*A2 + D1*SNL*A3
<span class="comment">*</span><span class="comment">
</span> VB11R = CSR*B1
VB12 = CSR*B2 + D1*SNR*B3
<span class="comment">*</span><span class="comment">
</span> AUA12 = ABS( CSL )*ABS1( A2 ) + ABS( SNL )*ABS( A3 )
AVB12 = ABS( CSR )*ABS1( B2 ) + ABS( SNR )*ABS( B3 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> zero (1,2) elements of U'*A and V'*B
⌨️ 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?