dptrfs.f.html

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      SUBROUTINE <a name="DPTRFS.1"></a><a href="dptrfs.f.html#DPTRFS.1">DPTRFS</a>( N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR,
     $                   BERR, WORK, 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>      INTEGER            INFO, LDB, LDX, N, NRHS
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   B( LDB, * ), BERR( * ), D( * ), DF( * ),
     $                   E( * ), EF( * ), 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="DPTRFS.20"></a><a href="dptrfs.f.html#DPTRFS.1">DPTRFS</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 positive definite
</span><span class="comment">*</span><span class="comment">  and tridiagonal, and provides error bounds and backward error
</span><span class="comment">*</span><span class="comment">  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">  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 matrix B.  NRHS &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  D       (input) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The n diagonal elements of the tridiagonal matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  E       (input) DOUBLE PRECISION array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          The (n-1) subdiagonal elements of the tridiagonal matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DF      (input) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The n diagonal elements of the diagonal matrix D from the
</span><span class="comment">*</span><span class="comment">          factorization computed by <a name="DPTTRF.43"></a><a href="dpttrf.f.html#DPTTRF.1">DPTTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  EF      (input) DOUBLE PRECISION array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          The (n-1) subdiagonal elements of the unit bidiagonal factor
</span><span class="comment">*</span><span class="comment">          L from the factorization computed by <a name="DPTTRF.47"></a><a href="dpttrf.f.html#DPTTRF.1">DPTTRF</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="DPTTRS.56"></a><a href="dpttrs.f.html#DPTTRS.1">DPTTRS</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 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).
</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 (2*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>      INTEGER            COUNT, I, IX, J, NZ
      DOUBLE PRECISION   BI, CX, DX, EPS, EX, LSTRES, S, SAFE1, SAFE2,
     $                   SAFMIN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           DAXPY, <a name="DPTTRS.106"></a><a href="dpttrs.f.html#DPTTRS.1">DPTTRS</a>, <a name="XERBLA.106"></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>      INTEGER            IDAMAX
      DOUBLE PRECISION   <a name="DLAMCH.113"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
      EXTERNAL           IDAMAX, <a name="DLAMCH.114"></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
      IF( N.LT.0 ) THEN
         INFO = -1
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -2
      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.131"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DPTRFS.131"></a><a href="dptrfs.f.html#DPTRFS.1">DPTRFS</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">
12

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