dppt03.f

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      SUBROUTINE dppt03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND,
     $                   resid )
*
*  -- LAPACK test routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          uplo
      INTEGER            ldwork, n
      DOUBLE PRECISION   rcond, resid
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   a( * ), ainv( * ), rwork( * ),
     $                   work( ldwork, * )
*     ..
*
*  Purpose
*  =======
*
*  DPPT03 computes the residual for a symmetric packed matrix times its
*  inverse:
*     norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*  where EPS is the machine epsilon.
*
*  Arguments
*  ==========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the upper or lower triangular part of the
*          symmetric matrix A is stored:
*          = 'U':  Upper triangular
*          = 'L':  Lower triangular
*
*  N       (input) INTEGER
*          The number of rows and columns of the matrix A.  N >= 0.
*
*  A       (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
*          The original symmetric matrix A, stored as a packed
*          triangular matrix.
*
*  AINV    (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
*          The (symmetric) inverse of the matrix A, stored as a packed
*          triangular matrix.
*
*  WORK    (workspace) DOUBLE PRECISION array, dimension (LDWORK,N)
*
*  LDWORK  (input) INTEGER
*          The leading dimension of the array WORK.  LDWORK >= max(1,N).
*
*  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
*
*  RCOND   (output) DOUBLE PRECISION
*          The reciprocal of the condition number of A, computed as
*          ( 1/norm(A) ) / norm(AINV).
*
*  RESID   (output) DOUBLE PRECISION
*          norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   zero, one
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            i, j, jj
      DOUBLE PRECISION   ainvnm, anorm, eps
*     ..
*     .. External Functions ..
      LOGICAL            lsame
      DOUBLE PRECISION   dlamch, dlange, dlansp
      EXTERNAL           lsame, dlamch, dlange, dlansp
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble
*     ..
*     .. External Subroutines ..
      EXTERNAL           dcopy, dspmv
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0.
*
      IF( n.LE.0 ) THEN
         rcond = one
         resid = zero
         return
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
*
      eps = dlamch( 'Epsilon' )
      anorm = dlansp( '1', uplo, n, a, rwork )
      ainvnm = dlansp( '1', uplo, n, ainv, rwork )
      IF( anorm.LE.zero .OR. ainvnm.EQ.zero ) THEN
         rcond = zero
         resid = one / eps
         return
      END IF
      rcond = ( one / anorm ) / ainvnm
*
*     UPLO = 'U':
*     Copy the leading N-1 x N-1 submatrix of AINV to WORK(1:N,2:N) and
*     expand it to a full matrix, then multiply by A one column at a
*     time, moving the result one column to the left.
*
      IF( lsame( uplo, 'U' ) ) THEN
*
*        Copy AINV
*
         jj = 1
         DO 10 j = 1, n - 1
            CALL dcopy( j, ainv( jj ), 1, work( 1, j+1 ), 1 )
            CALL dcopy( j-1, ainv( jj ), 1, work( j, 2 ), ldwork )
            jj = jj + j
   10    continue
         jj = ( ( n-1 )*n ) / 2 + 1
         CALL dcopy( n-1, ainv( jj ), 1, work( n, 2 ), ldwork )
*
*        Multiply by A
*
         DO 20 j = 1, n - 1
            CALL dspmv( 'Upper', n, -one, a, work( 1, j+1 ), 1, zero,
     $                  work( 1, j ), 1 )
   20    continue
         CALL dspmv( 'Upper', n, -one, a, ainv( jj ), 1, zero,
     $               work( 1, n ), 1 )
*
*     UPLO = 'L':
*     Copy the trailing N-1 x N-1 submatrix of AINV to WORK(1:N,1:N-1)
*     and multiply by A, moving each column to the right.
*
      ELSE
*
*        Copy AINV
*
         CALL dcopy( n-1, ainv( 2 ), 1, work( 1, 1 ), ldwork )
         jj = n + 1
         DO 30 j = 2, n
            CALL dcopy( n-j+1, ainv( jj ), 1, work( j, j-1 ), 1 )
            CALL dcopy( n-j, ainv( jj+1 ), 1, work( j, j ), ldwork )
            jj = jj + n - j + 1
   30    continue
*
*        Multiply by A
*
         DO 40 j = n, 2, -1
            CALL dspmv( 'Lower', n, -one, a, work( 1, j-1 ), 1, zero,
     $                  work( 1, j ), 1 )
   40    continue
         CALL dspmv( 'Lower', n, -one, a, ainv( 1 ), 1, zero,
     $               work( 1, 1 ), 1 )
*
      END IF
*
*     Add the identity matrix to WORK .
*
      DO 50 i = 1, n
         work( i, i ) = work( i, i ) + one
   50 continue
*
*     Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
*
      resid = dlange( '1', n, n, work, ldwork, rwork )
*
      resid = ( ( resid*rcond ) / eps ) / dble( n )
*
      return
*
*     End of DPPT03
*
      END