SUBROUTINE CHET01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, \$ 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 LDA, LDAFAC, LDC, N REAL RESID * .. * .. Array Arguments .. INTEGER IPIV( * ) REAL RWORK( * ) COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ) * .. * * Purpose * ======= * * CHET01 reconstructs a Hermitian indefinite 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 (LDA,N) * The original Hermitian matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N) * * AFAC (input) COMPLEX array, dimension (LDAFAC,N) * The factored form of the matrix A. 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 CHETRF. * * LDAFAC (input) INTEGER * The leading dimension of the array AFAC. LDAFAC >= max(1,N). * * IPIV (input) INTEGER array, dimension (N) * The pivot indices from CHETRF. * * 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 REAL ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME REAL CLANHE, SLAMCH EXTERNAL LSAME, CLANHE, SLAMCH * .. * .. External Subroutines .. EXTERNAL CLAVHE, 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 = CLANHE( '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 10 J = 1, N IF( AIMAG( AFAC( J, J ) ).NE.ZERO ) THEN RESID = ONE / EPS RETURN END IF 10 CONTINUE * * Initialize C to the identity matrix. * CALL CLASET( 'Full', N, N, CZERO, CONE, C, LDC ) * * Call CLAVHE to form the product D * U' (or D * L' ). * CALL CLAVHE( UPLO, 'Conjugate', 'Non-unit', N, N, AFAC, LDAFAC, \$ IPIV, C, LDC, INFO ) * * Call CLAVHE again to multiply by U (or L ). * CALL CLAVHE( UPLO, 'No transpose', 'Unit', N, N, AFAC, LDAFAC, \$ IPIV, C, LDC, INFO ) * * Compute the difference C - A . * IF( LSAME( UPLO, 'U' ) ) THEN DO 30 J = 1, N DO 20 I = 1, J - 1 C( I, J ) = C( I, J ) - A( I, J ) 20 CONTINUE C( J, J ) = C( J, J ) - REAL( A( J, J ) ) 30 CONTINUE ELSE DO 50 J = 1, N C( J, J ) = C( J, J ) - REAL( A( J, J ) ) DO 40 I = J + 1, N C( I, J ) = C( I, J ) - A( I, J ) 40 CONTINUE 50 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 CHET01 * END