ssprfs.f.html
来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 360 行 · 第 1/2 页
HTML
360 行
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<title>ssprfs.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="SSPRFS.1"></a><a href="ssprfs.f.html#SSPRFS.1">SSPRFS</a>( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX,
$ FERR, BERR, WORK, IWORK, 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"> Modified to call <a name="SLACN2.8"></a><a href="slacn2.f.html#SLACN2.1">SLACN2</a> in place of <a name="SLACON.8"></a><a href="slacon.f.html#SLACON.1">SLACON</a>, 5 Feb 03, SJH.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER UPLO
INTEGER INFO, LDB, LDX, N, NRHS
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IPIV( * ), IWORK( * )
REAL AFP( * ), AP( * ), B( LDB, * ), BERR( * ),
$ FERR( * ), WORK( * ), X( LDX, * )
<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="SSPRFS.23"></a><a href="ssprfs.f.html#SSPRFS.1">SSPRFS</a> improves the computed solution to a system of linear
</span><span class="comment">*</span><span class="comment"> equations when the coefficient matrix is symmetric indefinite
</span><span class="comment">*</span><span class="comment"> and packed, and provides error bounds and backward error estimates
</span><span class="comment">*</span><span class="comment"> for the solution.
</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"> NRHS (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of right hand sides, i.e., the number of columns
</span><span class="comment">*</span><span class="comment"> of the matrices B and X. NRHS >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AP (input) REAL array, dimension (N*(N+1)/2)
</span><span class="comment">*</span><span class="comment"> The upper or lower triangle of the symmetric matrix A, packed
</span><span class="comment">*</span><span class="comment"> columnwise in a linear array. The j-th column of A is stored
</span><span class="comment">*</span><span class="comment"> in the array AP as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AFP (input) REAL array, dimension (N*(N+1)/2)
</span><span class="comment">*</span><span class="comment"> The factored form of the matrix A. AFP contains the block
</span><span class="comment">*</span><span class="comment"> diagonal matrix D and the multipliers used to obtain the
</span><span class="comment">*</span><span class="comment"> factor U or L from the factorization A = U*D*U**T or
</span><span class="comment">*</span><span class="comment"> A = L*D*L**T as computed by <a name="SSPTRF.53"></a><a href="ssptrf.f.html#SSPTRF.1">SSPTRF</a>, stored as a packed
</span><span class="comment">*</span><span class="comment"> triangular matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IPIV (input) 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"> as determined by <a name="SSPTRF.58"></a><a href="ssptrf.f.html#SSPTRF.1">SSPTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> B (input) REAL array, dimension (LDB,NRHS)
</span><span class="comment">*</span><span class="comment"> The right hand side matrix B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array B. LDB >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> X (input/output) REAL array, dimension (LDX,NRHS)
</span><span class="comment">*</span><span class="comment"> On entry, the solution matrix X, as computed by <a name="SSPTRS.67"></a><a href="ssptrs.f.html#SSPTRS.1">SSPTRS</a>.
</span><span class="comment">*</span><span class="comment"> On exit, the improved solution matrix X.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDX (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array X. LDX >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> FERR (output) REAL array, dimension (NRHS)
</span><span class="comment">*</span><span class="comment"> The estimated forward error bound for each solution vector
</span><span class="comment">*</span><span class="comment"> X(j) (the j-th column of the solution matrix X).
</span><span class="comment">*</span><span class="comment"> If XTRUE is the true solution corresponding to X(j), FERR(j)
</span><span class="comment">*</span><span class="comment"> is an estimated upper bound for the magnitude of the largest
</span><span class="comment">*</span><span class="comment"> element in (X(j) - XTRUE) divided by the magnitude of the
</span><span class="comment">*</span><span class="comment"> largest element in X(j). The estimate is as reliable as
</span><span class="comment">*</span><span class="comment"> the estimate for RCOND, and is almost always a slight
</span><span class="comment">*</span><span class="comment"> overestimate of the true error.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> BERR (output) REAL array, dimension (NRHS)
</span><span class="comment">*</span><span class="comment"> The componentwise relative backward error of each solution
</span><span class="comment">*</span><span class="comment"> vector X(j) (i.e., the smallest relative change in
</span><span class="comment">*</span><span class="comment"> any element of A or B that makes X(j) an exact solution).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace) REAL array, dimension (3*N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IWORK (workspace) INTEGER array, dimension (N)
</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"> Internal Parameters
</span><span class="comment">*</span><span class="comment"> ===================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ITMAX is the maximum number of steps of iterative refinement.
</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> INTEGER ITMAX
PARAMETER ( ITMAX = 5 )
REAL ZERO
PARAMETER ( ZERO = 0.0E+0 )
REAL ONE
PARAMETER ( ONE = 1.0E+0 )
REAL TWO
PARAMETER ( TWO = 2.0E+0 )
REAL THREE
PARAMETER ( THREE = 3.0E+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL UPPER
INTEGER COUNT, I, IK, J, K, KASE, KK, NZ
REAL EPS, LSTRES, S, SAFE1, SAFE2, SAFMIN, XK
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Arrays ..
</span> INTEGER ISAVE( 3 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL SAXPY, SCOPY, <a name="SLACN2.124"></a><a href="slacn2.f.html#SLACN2.1">SLACN2</a>, SSPMV, <a name="SSPTRS.124"></a><a href="ssptrs.f.html#SSPTRS.1">SSPTRS</a>, <a name="XERBLA.124"></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 ABS, MAX
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.130"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
REAL <a name="SLAMCH.131"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
EXTERNAL <a name="LSAME.132"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="SLAMCH.132"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</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 parameters.
</span><span class="comment">*</span><span class="comment">
</span> INFO = 0
UPPER = <a name="LSAME.139"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.140"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( NRHS.LT.0 ) THEN
INFO = -3
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -8
ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL <a name="XERBLA.152"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SSPRFS.152"></a><a href="ssprfs.f.html#SSPRFS.1">SSPRFS</a>'</span>, -INFO )
RETURN
END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span> IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN
DO 10 J = 1, NRHS
FERR( J ) = ZERO
BERR( J ) = ZERO
⌨️ 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?