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SUBROUTINE CPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, 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 LDA, LDAFAC, N
REAL RESID
* ..
* .. Array Arguments ..
REAL RWORK( * )
COMPLEX A( LDA, * ), AFAC( LDAFAC, * )
* ..
*
* Purpose
* =======
*
* CPOT01 reconstructs a Hermitian positive definite 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 (LDA,N)
* The original Hermitian matrix A.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N)
*
* AFAC (input/output) COMPLEX array, dimension (LDAFAC,N)
* On entry, the factor L or U from the L*L' or U'*U
* factorization of A.
* Overwritten with the reconstructed matrix, and then with the
* difference L*L' - A (or U'*U - A).
*
* LDAFAC (input) INTEGER
* The leading dimension of the array AFAC. LDAFAC >= max(1,N).
*
* 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, J, K
REAL ANORM, EPS, TR
COMPLEX TC
* ..
* .. External Functions ..
LOGICAL LSAME
REAL CLANHE, SLAMCH
COMPLEX CDOTC
EXTERNAL LSAME, CLANHE, SLAMCH, CDOTC
* ..
* .. External Subroutines ..
EXTERNAL CHER, CSCAL, CTRMV
* ..
* .. 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 = CLANHE( '1', UPLO, N, A, LDA, 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.
*
DO 10 J = 1, N
IF( AIMAG( AFAC( J, J ) ).NE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
10 CONTINUE
*
* Compute the product U'*U, overwriting U.
*
IF( LSAME( UPLO, 'U' ) ) THEN
DO 20 K = N, 1, -1
*
* Compute the (K,K) element of the result.
*
TR = CDOTC( K, AFAC( 1, K ), 1, AFAC( 1, K ), 1 )
AFAC( K, K ) = TR
*
* Compute the rest of column K.
*
CALL CTRMV( 'Upper', 'Conjugate', 'Non-unit', K-1, AFAC,
$ LDAFAC, AFAC( 1, K ), 1 )
*
20 CONTINUE
*
* Compute the product L*L', overwriting L.
*
ELSE
DO 30 K = N, 1, -1
*
* Add a multiple of column K of the factor L to each of
* columns K+1 through N.
*
IF( K+1.LE.N )
$ CALL CHER( 'Lower', N-K, ONE, AFAC( K+1, K ), 1,
$ AFAC( K+1, K+1 ), LDAFAC )
*
* Scale column K by the diagonal element.
*
TC = AFAC( K, K )
CALL CSCAL( N-K+1, TC, AFAC( K, K ), 1 )
*
30 CONTINUE
END IF
*
* Compute the difference L*L' - A (or U'*U - A).
*
IF( LSAME( UPLO, 'U' ) ) THEN
DO 50 J = 1, N
DO 40 I = 1, J - 1
AFAC( I, J ) = AFAC( I, J ) - A( I, J )
40 CONTINUE
AFAC( J, J ) = AFAC( J, J ) - REAL( A( J, J ) )
50 CONTINUE
ELSE
DO 70 J = 1, N
AFAC( J, J ) = AFAC( J, J ) - REAL( A( J, J ) )
DO 60 I = J + 1, N
AFAC( I, J ) = AFAC( I, J ) - A( I, J )
60 CONTINUE
70 CONTINUE
END IF
*
* Compute norm( L*U - A ) / ( N * norm(A) * EPS )
*
RESID = CLANHE( '1', UPLO, N, AFAC, LDAFAC, RWORK )
*
RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS
*
RETURN
*
* End of CPOT01
*
END
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