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SUBROUTINE CHPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER LDC, N
REAL RESID
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
REAL RWORK( * )
COMPLEX A( * ), AFAC( * ), C( LDC, * )
* ..
*
* Purpose
* =======
*
* CHPT01 reconstructs a Hermitian indefinite packed matrix A from its
* block L*D*L' or U*D*U' factorization and computes the residual
* norm( C - A ) / ( N * norm(A) * EPS ),
* where C is the reconstructed matrix, 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) COMPLEX array, dimension (N*(N+1)/2)
* The factored form of the matrix A, stored as a packed
* triangular matrix. AFAC contains the block diagonal matrix D
* and the multipliers used to obtain the factor L or U from the
* block L*D*L' or U*D*U' factorization as computed by CHPTRF.
*
* IPIV (input) INTEGER array, dimension (N)
* The pivot indices from CHPTRF.
*
* C (workspace) COMPLEX array, dimension (LDC,N)
*
* LDC (integer) INTEGER
* The leading dimension of the array C. LDC >= max(1,N).
*
* RWORK (workspace) REAL array, dimension (N)
*
* RESID (output) REAL
* If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
* If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
COMPLEX CZERO, CONE
PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
$ CONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, INFO, J, JC
REAL ANORM, EPS
* ..
* .. External Functions ..
LOGICAL LSAME
REAL CLANHE, CLANHP, SLAMCH
EXTERNAL LSAME, CLANHE, CLANHP, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CLAVHP, CLASET
* ..
* .. Intrinsic Functions ..
INTRINSIC AIMAG, REAL
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0.
*
IF( N.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Determine EPS and the norm of A.
*
EPS = SLAMCH( 'Epsilon' )
ANORM = CLANHP( '1', UPLO, N, A, RWORK )
*
* Check the imaginary parts of the diagonal elements and return with
* an error code if any are nonzero.
*
JC = 1
IF( LSAME( UPLO, 'U' ) ) THEN
DO 10 J = 1, N
IF( AIMAG( AFAC( JC ) ).NE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
JC = JC + J + 1
10 CONTINUE
ELSE
DO 20 J = 1, N
IF( AIMAG( AFAC( JC ) ).NE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
JC = JC + N - J + 1
20 CONTINUE
END IF
*
* Initialize C to the identity matrix.
*
CALL CLASET( 'Full', N, N, CZERO, CONE, C, LDC )
*
* Call CLAVHP to form the product D * U' (or D * L' ).
*
CALL CLAVHP( UPLO, 'Conjugate', 'Non-unit', N, N, AFAC, IPIV, C,
$ LDC, INFO )
*
* Call CLAVHP again to multiply by U ( or L ).
*
CALL CLAVHP( UPLO, 'No transpose', 'Unit', N, N, AFAC, IPIV, C,
$ LDC, INFO )
*
* Compute the difference C - A .
*
IF( LSAME( UPLO, 'U' ) ) THEN
JC = 0
DO 40 J = 1, N
DO 30 I = 1, J - 1
C( I, J ) = C( I, J ) - A( JC+I )
30 CONTINUE
C( J, J ) = C( J, J ) - REAL( A( JC+J ) )
JC = JC + J
40 CONTINUE
ELSE
JC = 1
DO 60 J = 1, N
C( J, J ) = C( J, J ) - REAL( A( JC ) )
DO 50 I = J + 1, N
C( I, J ) = C( I, J ) - A( JC+I-J )
50 CONTINUE
JC = JC + N - J + 1
60 CONTINUE
END IF
*
* Compute norm( C - A ) / ( N * norm(A) * EPS )
*
RESID = CLANHE( '1', UPLO, N, C, LDC, RWORK )
*
IF( ANORM.LE.ZERO ) THEN
IF( RESID.NE.ZERO )
$ RESID = ONE / EPS
ELSE
RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS
END IF
*
RETURN
*
* End of CHPT01
*
END
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