cppt01.f

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      SUBROUTINE cppt01( UPLO, N, A, AFAC, RWORK, RESID )
*
*  -- LAPACK test routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          uplo
      INTEGER            n
      REAL               resid
*     ..
*     .. Array Arguments ..
      REAL               rwork( * )
      COMPLEX            a( * ), afac( * )
*     ..
*
*  Purpose
*  =======
*
*  CPPT01 reconstructs a Hermitian positive definite packed matrix A
*  from its L*L' or U'*U factorization and computes the residual
*     norm( L*L' - A ) / ( N * norm(A) * EPS ) or
*     norm( U'*U - A ) / ( N * norm(A) * EPS ),
*  where EPS is the machine epsilon, L' is the conjugate transpose of
*  L, and U' is the conjugate transpose of U.
*
*  Arguments
*  ==========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the upper or lower triangular part of the
*          Hermitian 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) COMPLEX array, dimension (N*(N+1)/2)
*          The original Hermitian matrix A, stored as a packed
*          triangular matrix.
*
*  AFAC    (input/output) COMPLEX array, dimension (N*(N+1)/2)
*          On entry, the factor L or U from the L*L' or U'*U
*          factorization of A, stored as a packed triangular matrix.
*          Overwritten with the reconstructed matrix, and then with the
*          difference L*L' - A (or U'*U - A).
*
*  RWORK   (workspace) REAL array, dimension (N)
*
*  RESID   (output) REAL
*          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               zero, one
      parameter( zero = 0.0e+0, one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            i, k, kc
      REAL               anorm, eps, tr
      COMPLEX            tc
*     ..
*     .. External Functions ..
      LOGICAL            lsame
      REAL               clanhp, slamch
      COMPLEX            cdotc
      EXTERNAL           lsame, clanhp, slamch, cdotc
*     ..
*     .. External Subroutines ..
      EXTERNAL           chpr, cscal, ctpmv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          aimag, real
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0
*
      IF( n.LE.0 ) THEN
         resid = zero
         return
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0.
*
      eps = slamch( 'Epsilon' )
      anorm = clanhp( '1', uplo, n, a, rwork )
      IF( anorm.LE.zero ) THEN
         resid = one / eps
         return
      END IF
*
*     Check the imaginary parts of the diagonal elements and return with
*     an error code if any are nonzero.
*
      kc = 1
      IF( lsame( uplo, 'U' ) ) THEN
         DO 10 k = 1, n
            IF( aimag( afac( kc ) ).NE.zero ) THEN
               resid = one / eps
               return
            END IF
            kc = kc + k + 1
   10    continue
      ELSE
         DO 20 k = 1, n
            IF( aimag( afac( kc ) ).NE.zero ) THEN
               resid = one / eps
               return
            END IF
            kc = kc + n - k + 1
   20    continue
      END IF
*
*     Compute the product U'*U, overwriting U.
*
      IF( lsame( uplo, 'U' ) ) THEN
         kc = ( n*( n-1 ) ) / 2 + 1
         DO 30 k = n, 1, -1
*
*           Compute the (K,K) element of the result.
*
            tr = cdotc( k, afac( kc ), 1, afac( kc ), 1 )
            afac( kc+k-1 ) = tr
*
*           Compute the rest of column K.
*
            IF( k.GT.1 ) THEN
               CALL ctpmv( 'Upper', 'Conjugate', 'Non-unit', k-1, afac,
     $                     afac( kc ), 1 )
               kc = kc - ( k-1 )
            END IF
   30    continue
*
*        Compute the difference  L*L' - A
*
         kc = 1
         DO 50 k = 1, n
            DO 40 i = 1, k - 1
               afac( kc+i-1 ) = afac( kc+i-1 ) - a( kc+i-1 )
   40       continue
            afac( kc+k-1 ) = afac( kc+k-1 ) - REAL( A( KC+K-1 ) )
            kc = kc + k
   50    continue
*
*     Compute the product L*L', overwriting L.
*
      ELSE
         kc = ( n*( n+1 ) ) / 2
         DO 60 k = n, 1, -1
*
*           Add a multiple of column K of the factor L to each of
*           columns K+1 through N.
*
            IF( k.LT.n )
     $         CALL chpr( 'Lower', n-k, one, afac( kc+1 ), 1,
     $                    afac( kc+n-k+1 ) )
*
*           Scale column K by the diagonal element.
*
            tc = afac( kc )
            CALL cscal( n-k+1, tc, afac( kc ), 1 )
*
            kc = kc - ( n-k+2 )
   60    continue
*
*        Compute the difference  U'*U - A
*
         kc = 1
         DO 80 k = 1, n
            afac( kc ) = afac( kc ) - REAL( A( KC ) )
            DO 70 i = k + 1, n
               afac( kc+i-k ) = afac( kc+i-k ) - a( kc+i-k )
   70       continue
            kc = kc + n - k + 1
   80    continue
      END IF
*
*     Compute norm( L*U - A ) / ( N * norm(A) * EPS )
*
      resid = clanhp( '1', uplo, n, afac, rwork )
*
      resid = ( ( resid / REAL( N ) ) / anorm ) / eps
*
      return
*
*     End of CPPT01
*
      END