cpbtrf.f.html
来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 396 行 · 第 1/2 页
HTML
396 行
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<title>cpbtrf.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="CPBTRF.1"></a><a href="cpbtrf.f.html#CPBTRF.1">CPBTRF</a>( UPLO, N, KD, AB, LDAB, 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, KD, LDAB, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> COMPLEX AB( LDAB, * )
<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="CPBTRF.18"></a><a href="cpbtrf.f.html#CPBTRF.1">CPBTRF</a> computes the Cholesky factorization of a complex Hermitian
</span><span class="comment">*</span><span class="comment"> positive definite band matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The factorization has the form
</span><span class="comment">*</span><span class="comment"> A = U**H * U, if UPLO = 'U', or
</span><span class="comment">*</span><span class="comment"> A = L * L**H, if UPLO = 'L',
</span><span class="comment">*</span><span class="comment"> where U is an upper triangular matrix and L is lower triangular.
</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"> KD (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of superdiagonals of the matrix A if UPLO = 'U',
</span><span class="comment">*</span><span class="comment"> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AB (input/output) COMPLEX array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment"> On entry, the upper or lower triangle of the Hermitian band
</span><span class="comment">*</span><span class="comment"> matrix A, stored in the first KD+1 rows of the array. The
</span><span class="comment">*</span><span class="comment"> j-th column of A is stored in the j-th column of the array AB
</span><span class="comment">*</span><span class="comment"> as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, the triangular factor U or L from the
</span><span class="comment">*</span><span class="comment"> Cholesky factorization A = U**H*U or A = L*L**H of the band
</span><span class="comment">*</span><span class="comment"> matrix A, in the same storage format as A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDAB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array AB. LDAB >= KD+1.
</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, the leading minor of order i is not
</span><span class="comment">*</span><span class="comment"> positive definite, and the factorization could not be
</span><span class="comment">*</span><span class="comment"> completed.
</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 band storage scheme is illustrated by the following example, when
</span><span class="comment">*</span><span class="comment"> N = 6, KD = 2, and UPLO = 'U':
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On entry: On exit:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> * * a13 a24 a35 a46 * * u13 u24 u35 u46
</span><span class="comment">*</span><span class="comment"> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
</span><span class="comment">*</span><span class="comment"> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Similarly, if UPLO = 'L' the format of A is as follows:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On entry: On exit:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
</span><span class="comment">*</span><span class="comment"> a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
</span><span class="comment">*</span><span class="comment"> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Array elements marked * are not used by the routine.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Contributed by
</span><span class="comment">*</span><span class="comment"> Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989
</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> REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
COMPLEX CONE
PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
INTEGER NBMAX, LDWORK
PARAMETER ( NBMAX = 32, LDWORK = NBMAX+1 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> INTEGER I, I2, I3, IB, II, J, JJ, NB
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Arrays ..
</span> COMPLEX WORK( LDWORK, NBMAX )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.104"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
INTEGER <a name="ILAENV.105"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
EXTERNAL <a name="LSAME.106"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.106"></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 CGEMM, CHERK, <a name="CPBTF2.109"></a><a href="cpbtf2.f.html#CPBTF2.1">CPBTF2</a>, <a name="CPOTF2.109"></a><a href="cpotf2.f.html#CPOTF2.1">CPOTF2</a>, CTRSM, <a name="XERBLA.109"></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 MIN
<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
IF( ( .NOT.<a name="LSAME.119"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) .AND.
$ ( .NOT.<a name="LSAME.120"></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( KD.LT.0 ) THEN
INFO = -3
ELSE IF( LDAB.LT.KD+1 ) THEN
INFO = -5
END IF
IF( INFO.NE.0 ) THEN
CALL <a name="XERBLA.130"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CPBTRF.130"></a><a href="cpbtrf.f.html#CPBTRF.1">CPBTRF</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 )
$ RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Determine the block size for this environment
</span><span class="comment">*</span><span class="comment">
</span> NB = <a name="ILAENV.141"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="CPBTRF.141"></a><a href="cpbtrf.f.html#CPBTRF.1">CPBTRF</a>'</span>, UPLO, N, KD, -1, -1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The block size must not exceed the semi-bandwidth KD, and must not
</span><span class="comment">*</span><span class="comment"> exceed the limit set by the size of the local array WORK.
</span><span class="comment">*</span><span class="comment">
</span> NB = MIN( NB, NBMAX )
<span class="comment">*</span><span class="comment">
</span> IF( NB.LE.1 .OR. NB.GT.KD ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Use unblocked code
</span><span class="comment">*</span><span class="comment">
</span> CALL <a name="CPBTF2.152"></a><a href="cpbtf2.f.html#CPBTF2.1">CPBTF2</a>( UPLO, N, KD, AB, LDAB, INFO )
ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Use blocked code
</span><span class="comment">*</span><span class="comment">
</span> IF( <a name="LSAME.157"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Compute the Cholesky factorization of a Hermitian band
</span><span class="comment">*</span><span class="comment"> matrix, given the upper triangle of the matrix in band
</span><span class="comment">*</span><span class="comment"> storage.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Zero the upper triangle of the work array.
</span><span class="comment">*</span><span class="comment">
</span> DO 20 J = 1, NB
DO 10 I = 1, J - 1
WORK( I, J ) = ZERO
10 CONTINUE
20 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Process the band matrix one diagonal block at a time.
</span><span class="comment">*</span><span class="comment">
</span> DO 70 I = 1, N, NB
IB = MIN( NB, N-I+1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Factorize the diagonal block
</span><span class="comment">*</span><span class="comment">
</span> CALL <a name="CPOTF2.178"></a><a href="cpotf2.f.html#CPOTF2.1">CPOTF2</a>( UPLO, IB, AB( KD+1, I ), LDAB-1, II )
IF( II.NE.0 ) THEN
⌨️ 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?