zhet01_3()

subroutine zhet01_3	(	character	uplo,
		integer	n,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		complex*16, dimension( ldafac, * )	afac,
		integer	ldafac,
		complex*16, dimension( * )	e,
		integer, dimension( * )	ipiv,
		complex*16, dimension( ldc, * )	c,
		integer	ldc,
		double precision, dimension( * )	rwork,
		double precision	resid
	)

ZHET01_3

Purpose:

 ZHET01_3 reconstructs a Hermitian indefinite matrix A from its
 block L*D*L' or U*D*U' factorization computed by ZHETRF_RK
 (or ZHETRF_BK) and computes the residual
    norm( C - A ) / ( N * norm(A) * EPS ),
 where C is the reconstructed matrix and EPS is the machine epsilon.

Parameters

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	A	A is COMPLEX*16 array, dimension (LDA,N) The original Hermitian matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)
[in]	AFAC	AFAC is COMPLEX*16 array, dimension (LDAFAC,N) Diagonal of the block diagonal matrix D and factors U or L as computed by ZHETRF_RK and ZHETRF_BK: a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A.
[in]	LDAFAC	LDAFAC is INTEGER The leading dimension of the array AFAC. LDAFAC >= max(1,N).
[in]	E	E is COMPLEX*16 array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
[in]	IPIV	IPIV is INTEGER array, dimension (N) The pivot indices from ZHETRF_RK (or ZHETRF_BK).
[out]	C	C is COMPLEX*16 array, dimension (LDC,N)
[in]	LDC	LDC is INTEGER The leading dimension of the array C. LDC >= max(1,N).
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 139 of file zhet01_3.f.

*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            LDA, LDAFAC, LDC, N
      DOUBLE PRECISION   RESID
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   RWORK( * )
      COMPLEX*16         A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
     $                   E( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
      COMPLEX*16         CZERO, CONE
      parameter( czero = ( 0.0d+0, 0.0d+0 ),
     $                   cone = ( 1.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            I, INFO, J
      DOUBLE PRECISION   ANORM, EPS
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   ZLANHE, DLAMCH
      EXTERNAL           lsame, zlanhe, dlamch
*     ..
*     .. External Subroutines ..
      EXTERNAL           zlaset, zlavhe_rook, zsyconvf_rook
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dimag, dble
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0.
*
      IF( n.LE.0 ) THEN
         resid = zero
         RETURN
      END IF
*
*     a) Revert to multipliers of L
*
      CALL zsyconvf_rook( uplo, 'R', n, afac, ldafac, e, ipiv, info )
*
*     1) Determine EPS and the norm of A.
*
      eps = dlamch( 'Epsilon' )
      anorm = zlanhe( '1', uplo, n, a, lda, rwork )
*
*     Check the imaginary parts of the diagonal elements and return with
*     an error code if any are nonzero.
*
      DO j = 1, n
         IF( dimag( afac( j, j ) ).NE.zero ) THEN
            resid = one / eps
            RETURN
         END IF
      END DO
*
*     2) Initialize C to the identity matrix.
*
      CALL zlaset( 'Full', n, n, czero, cone, c, ldc )
*
*     3) Call ZLAVHE_ROOK to form the product D * U' (or D * L' ).
*
      CALL zlavhe_rook( uplo, 'Conjugate', 'Non-unit', n, n, afac,
     $                  ldafac, ipiv, c, ldc, info )
*
*     4) Call ZLAVHE_RK again to multiply by U (or L ).
*
      CALL zlavhe_rook( uplo, 'No transpose', 'Unit', n, n, afac,
     $                  ldafac, ipiv, c, ldc, info )
*
*     5) Compute the difference  C - A .
*
      IF( lsame( uplo, 'U' ) ) THEN
         DO j = 1, n
            DO i = 1, j - 1
               c( i, j ) = c( i, j ) - a( i, j )
            END DO
            c( j, j ) = c( j, j ) - dble( a( j, j ) )
         END DO
      ELSE
         DO j = 1, n
            c( j, j ) = c( j, j ) - dble( a( j, j ) )
            DO i = j + 1, n
               c( i, j ) = c( i, j ) - a( i, j )
            END DO
         END DO
      END IF
*
*     6) Compute norm( C - A ) / ( N * norm(A) * EPS )
*
      resid = zlanhe( '1', uplo, n, c, ldc, rwork )
*
      IF( anorm.LE.zero ) THEN
         IF( resid.NE.zero )
     $      resid = one / eps
      ELSE
         resid = ( ( resid/dble( n ) )/anorm ) / eps
      END IF
*
*     b) Convert to factor of L (or U)
*
      CALL zsyconvf_rook( uplo, 'C', n, afac, ldafac, e, ipiv, info )
*
      RETURN
*
*     End of ZHET01_3
*

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