strrfs.f.html

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      SUBROUTINE <a name="STRRFS.1"></a><a href="strrfs.f.html#STRRFS.1">STRRFS</a>( UPLO, TRANS, DIAG, N, NRHS, A, LDA, 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>, 7 Feb 03, SJH.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          DIAG, TRANS, UPLO
      INTEGER            INFO, LDA, LDB, LDX, N, NRHS
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            IWORK( * )
      REAL               A( LDA, * ), 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="STRRFS.23"></a><a href="strrfs.f.html#STRRFS.1">STRRFS</a> provides error bounds and backward error estimates for the
</span><span class="comment">*</span><span class="comment">  solution to a system of linear equations with a triangular
</span><span class="comment">*</span><span class="comment">  coefficient matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The solution matrix X must be computed by <a name="STRTRS.27"></a><a href="strtrs.f.html#STRTRS.1">STRTRS</a> or some other
</span><span class="comment">*</span><span class="comment">  means before entering this routine.  <a name="STRRFS.28"></a><a href="strrfs.f.html#STRRFS.1">STRRFS</a> does not do iterative
</span><span class="comment">*</span><span class="comment">  refinement because doing so cannot improve the backward error.
</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':  A is upper triangular;
</span><span class="comment">*</span><span class="comment">          = 'L':  A is lower triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TRANS   (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies the form of the system of equations:
</span><span class="comment">*</span><span class="comment">          = 'N':  A * X = B  (No transpose)
</span><span class="comment">*</span><span class="comment">          = 'T':  A**T * X = B  (Transpose)
</span><span class="comment">*</span><span class="comment">          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DIAG    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N':  A is non-unit triangular;
</span><span class="comment">*</span><span class="comment">          = 'U':  A is unit 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 &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 columns
</span><span class="comment">*</span><span class="comment">          of the 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) REAL array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          The triangular matrix A.  If UPLO = 'U', the leading N-by-N
</span><span class="comment">*</span><span class="comment">          upper triangular part of the array A contains the upper
</span><span class="comment">*</span><span class="comment">          triangular matrix, and the strictly lower triangular part of
</span><span class="comment">*</span><span class="comment">          A is not referenced.  If UPLO = 'L', the leading N-by-N lower
</span><span class="comment">*</span><span class="comment">          triangular part of the array A contains the lower triangular
</span><span class="comment">*</span><span class="comment">          matrix, and the strictly upper triangular part of A is not
</span><span class="comment">*</span><span class="comment">          referenced.  If DIAG = 'U', the diagonal elements of A are
</span><span class="comment">*</span><span class="comment">          also not referenced and are assumed to be 1.
</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,N).
</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 &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  X       (input) REAL array, dimension (LDX,NRHS)
</span><span class="comment">*</span><span class="comment">          The 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 &gt;= 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">          &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>      REAL               ZERO
      PARAMETER          ( ZERO = 0.0E+0 )
      REAL               ONE
      PARAMETER          ( ONE = 1.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            NOTRAN, NOUNIT, UPPER
      CHARACTER          TRANST
      INTEGER            I, J, K, KASE, 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="SLACN2.121"></a><a href="slacn2.f.html#SLACN2.1">SLACN2</a>, STRMV, STRSV, <a name="XERBLA.121"></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.127"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      REAL               <a name="SLAMCH.128"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
      EXTERNAL           <a name="LSAME.129"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="SLAMCH.129"></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.136"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      NOTRAN = <a name="LSAME.137"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'N'</span> )
      NOUNIT = <a name="LSAME.138"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( DIAG, <span class="string">'N'</span> )
<span class="comment">*</span><span class="comment">
</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( .NOT.NOTRAN .AND. .NOT.<a name="LSAME.142"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'T'</span> ) .AND. .NOT.
     $         <a name="LSAME.143"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'C'</span> ) ) THEN
         INFO = -2
      ELSE IF( .NOT.NOUNIT .AND. .NOT.<a name="LSAME.145"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( DIAG, <span class="string">'U'</span> ) ) THEN
         INFO = -3
      ELSE IF( N.LT.0 ) THEN
         INFO = -4
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -5
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -7
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -9
      ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
         INFO = -11
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.159"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="STRRFS.159"></a><a href="strrfs.f.html#STRRFS.1">STRRFS</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
   10    CONTINUE
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( NOTRAN ) THEN
         TRANST = <span class="string">'T'</span>
      ELSE
         TRANST = <span class="string">'N'</span>
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     NZ = maximum number of nonzero elements in each row of A, plus 1
</span><span class="comment">*</span><span class="comment">
</span>      NZ = N + 1
12

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