dsyrfs.f.html

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      SUBROUTINE <a name="DSYRFS.1"></a><a href="dsyrfs.f.html#DSYRFS.1">DSYRFS</a>( UPLO, N, NRHS, A, LDA, AF, LDAF, 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="DLACN2.8"></a><a href="dlacn2.f.html#DLACN2.1">DLACN2</a> in place of <a name="DLACON.8"></a><a href="dlacon.f.html#DLACON.1">DLACON</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, LDA, LDAF, 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( * )
      DOUBLE PRECISION   A( LDA, * ), AF( LDAF, * ), 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="DSYRFS.23"></a><a href="dsyrfs.f.html#DSYRFS.1">DSYRFS</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, and
</span><span class="comment">*</span><span class="comment">  provides error bounds and backward error estimates 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 &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) DOUBLE PRECISION array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          The symmetric matrix A.  If UPLO = 'U', the leading N-by-N
</span><span class="comment">*</span><span class="comment">          upper triangular part of A contains the upper triangular part
</span><span class="comment">*</span><span class="comment">          of the matrix A, and the strictly lower triangular part of A
</span><span class="comment">*</span><span class="comment">          is not referenced.  If UPLO = 'L', the leading N-by-N lower
</span><span class="comment">*</span><span class="comment">          triangular part of A contains the lower triangular part of
</span><span class="comment">*</span><span class="comment">          the matrix A, and the strictly upper triangular part of A is
</span><span class="comment">*</span><span class="comment">          not referenced.
</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">  AF      (input) DOUBLE PRECISION array, dimension (LDAF,N)
</span><span class="comment">*</span><span class="comment">          The factored form of the matrix A.  AF 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="DSYTRF.57"></a><a href="dsytrf.f.html#DSYTRF.1">DSYTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDAF    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array AF.  LDAF &gt;= max(1,N).
</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="DSYTRF.64"></a><a href="dsytrf.f.html#DSYTRF.1">DSYTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input) DOUBLE PRECISION 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/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
</span><span class="comment">*</span><span class="comment">          On entry, the solution matrix X, as computed by <a name="DSYTRS.73"></a><a href="dsytrs.f.html#DSYTRS.1">DSYTRS</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 &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  FERR    (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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">  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 )
      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0D+0 )
      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0D+0 )
      DOUBLE PRECISION   TWO
      PARAMETER          ( TWO = 2.0D+0 )
      DOUBLE PRECISION   THREE
      PARAMETER          ( THREE = 3.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            UPPER
      INTEGER            COUNT, I, J, K, KASE, NZ
      DOUBLE PRECISION   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           DAXPY, DCOPY, <a name="DLACN2.130"></a><a href="dlacn2.f.html#DLACN2.1">DLACN2</a>, DSYMV, <a name="DSYTRS.130"></a><a href="dsytrs.f.html#DSYTRS.1">DSYTRS</a>, <a name="XERBLA.130"></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.136"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      DOUBLE PRECISION   <a name="DLAMCH.137"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
      EXTERNAL           <a name="LSAME.138"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="DLAMCH.138"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</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.145"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.146"></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( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -5
      ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
         INFO = -7
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -10
      ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
         INFO = -12
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.162"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DSYRFS.162"></a><a href="dsyrfs.f.html#DSYRFS.1">DSYRFS</a>'</span>, -INFO )
         RETURN
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