sgelsx.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 374 行 · 第 1/2 页

HTML
374 行
字号
12
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
 <head>
  <title>sgelsx.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="SGELSX.1"></a><a href="sgelsx.f.html#SGELSX.1">SGELSX</a>( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
     $                   WORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK driver 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>      INTEGER            INFO, LDA, LDB, M, N, NRHS, RANK
      REAL               RCOND
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            JPVT( * )
      REAL               A( LDA, * ), B( LDB, * ), 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">  This routine is deprecated and has been replaced by routine <a name="SGELSY.20"></a><a href="sgelsy.f.html#SGELSY.1">SGELSY</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="SGELSX.22"></a><a href="sgelsx.f.html#SGELSX.1">SGELSX</a> computes the minimum-norm solution to a real linear least
</span><span class="comment">*</span><span class="comment">  squares problem:
</span><span class="comment">*</span><span class="comment">      minimize || A * X - B ||
</span><span class="comment">*</span><span class="comment">  using a complete orthogonal factorization of A.  A is an M-by-N
</span><span class="comment">*</span><span class="comment">  matrix which may be rank-deficient.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Several right hand side vectors b and solution vectors x can be 
</span><span class="comment">*</span><span class="comment">  handled in a single call; they are stored as the columns of the
</span><span class="comment">*</span><span class="comment">  M-by-NRHS right hand side matrix B and the N-by-NRHS solution
</span><span class="comment">*</span><span class="comment">  matrix X.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The routine first computes a QR factorization with column pivoting:
</span><span class="comment">*</span><span class="comment">      A * P = Q * [ R11 R12 ]
</span><span class="comment">*</span><span class="comment">                  [  0  R22 ]
</span><span class="comment">*</span><span class="comment">  with R11 defined as the largest leading submatrix whose estimated
</span><span class="comment">*</span><span class="comment">  condition number is less than 1/RCOND.  The order of R11, RANK,
</span><span class="comment">*</span><span class="comment">  is the effective rank of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Then, R22 is considered to be negligible, and R12 is annihilated
</span><span class="comment">*</span><span class="comment">  by orthogonal transformations from the right, arriving at the
</span><span class="comment">*</span><span class="comment">  complete orthogonal factorization:
</span><span class="comment">*</span><span class="comment">     A * P = Q * [ T11 0 ] * Z
</span><span class="comment">*</span><span class="comment">                 [  0  0 ]
</span><span class="comment">*</span><span class="comment">  The minimum-norm solution is then
</span><span class="comment">*</span><span class="comment">     X = P * Z' [ inv(T11)*Q1'*B ]
</span><span class="comment">*</span><span class="comment">                [        0       ]
</span><span class="comment">*</span><span class="comment">  where Q1 consists of the first RANK columns of Q.
</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">  M       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of rows of the matrix A.  M &gt;= 0.
</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 number of columns of the matrix A.  N &gt;= 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
</span><span class="comment">*</span><span class="comment">          columns of matrices B and X. NRHS &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input/output) REAL array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          On entry, the M-by-N matrix A.
</span><span class="comment">*</span><span class="comment">          On exit, A has been overwritten by details of its
</span><span class="comment">*</span><span class="comment">          complete orthogonal factorization.
</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 &gt;= max(1,M).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input/output) REAL array, dimension (LDB,NRHS)
</span><span class="comment">*</span><span class="comment">          On entry, the M-by-NRHS right hand side matrix B.
</span><span class="comment">*</span><span class="comment">          On exit, the N-by-NRHS solution matrix X.
</span><span class="comment">*</span><span class="comment">          If m &gt;= n and RANK = n, the residual sum-of-squares for
</span><span class="comment">*</span><span class="comment">          the solution in the i-th column is given by the sum of
</span><span class="comment">*</span><span class="comment">          squares of elements N+1:M in that column.
</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 &gt;= max(1,M,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  JPVT    (input/output) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment">          On entry, if JPVT(i) .ne. 0, the i-th column of A is an
</span><span class="comment">*</span><span class="comment">          initial column, otherwise it is a free column.  Before
</span><span class="comment">*</span><span class="comment">          the QR factorization of A, all initial columns are
</span><span class="comment">*</span><span class="comment">          permuted to the leading positions; only the remaining
</span><span class="comment">*</span><span class="comment">          free columns are moved as a result of column pivoting
</span><span class="comment">*</span><span class="comment">          during the factorization.
</span><span class="comment">*</span><span class="comment">          On exit, if JPVT(i) = k, then the i-th column of A*P
</span><span class="comment">*</span><span class="comment">          was the k-th column of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RCOND   (input) REAL
</span><span class="comment">*</span><span class="comment">          RCOND is used to determine the effective rank of A, which
</span><span class="comment">*</span><span class="comment">          is defined as the order of the largest leading triangular
</span><span class="comment">*</span><span class="comment">          submatrix R11 in the QR factorization with pivoting of A,
</span><span class="comment">*</span><span class="comment">          whose estimated condition number &lt; 1/RCOND.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RANK    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          The effective rank of A, i.e., the order of the submatrix
</span><span class="comment">*</span><span class="comment">          R11.  This is the same as the order of the submatrix T11
</span><span class="comment">*</span><span class="comment">          in the complete orthogonal factorization of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) REAL array, dimension
</span><span class="comment">*</span><span class="comment">                      (max( min(M,N)+3*N, 2*min(M,N)+NRHS )),
</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">          &lt; 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">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      INTEGER            IMAX, IMIN
      PARAMETER          ( IMAX = 1, IMIN = 2 )
      REAL               ZERO, ONE, DONE, NTDONE
      PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0, DONE = ZERO,
     $                   NTDONE = ONE )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, IASCL, IBSCL, ISMAX, ISMIN, J, K, MN
      REAL               ANRM, BIGNUM, BNRM, C1, C2, S1, S2, SMAX,
     $                   SMAXPR, SMIN, SMINPR, SMLNUM, T1, T2
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      REAL               <a name="SLAMCH.124"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANGE.124"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>
      EXTERNAL           <a name="SLAMCH.125"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANGE.125"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="SGEQPF.128"></a><a href="sgeqpf.f.html#SGEQPF.1">SGEQPF</a>, <a name="SLABAD.128"></a><a href="slabad.f.html#SLABAD.1">SLABAD</a>, <a name="SLAIC1.128"></a><a href="slaic1.f.html#SLAIC1.1">SLAIC1</a>, <a name="SLASCL.128"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>, <a name="SLASET.128"></a><a href="slaset.f.html#SLASET.1">SLASET</a>, <a name="SLATZM.128"></a><a href="slatzm.f.html#SLATZM.1">SLATZM</a>,
     $                   <a name="SORM2R.129"></a><a href="sorm2r.f.html#SORM2R.1">SORM2R</a>, STRSM, <a name="STZRQF.129"></a><a href="stzrqf.f.html#STZRQF.1">STZRQF</a>, <a name="XERBLA.129"></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, 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>      MN = MIN( M, N )
      ISMIN = MN + 1
      ISMAX = 2*MN + 1
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input arguments.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( M.LT.0 ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -5
      ELSE IF( LDB.LT.MAX( 1, M, N ) ) THEN
         INFO = -7
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.156"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SGELSX.156"></a><a href="sgelsx.f.html#SGELSX.1">SGELSX</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( MIN( M, N, NRHS ).EQ.0 ) THEN
         RANK = 0
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Get machine parameters
</span><span class="comment">*</span><span class="comment">
12

sgelsx.f.html - 源码说明

本页面展示了「famous linear algebra library (LAPACK) ports to windows」中的 sgelsx.f.html 源码文件，采用 HTML 编程语言编写，共 374 行代码。您可以在线阅读完整代码内容，也可以返回资源详情页下载完整源码包进行本地学习和开发。

虫虫下载站收录了大量与algebra相关的技术资源，包括源代码、技术文档、电路图等，是电子工程师和嵌入式开发者的专业学习平台。

⌨️ 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?