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SUBROUTINE ZGET01( M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK,
$ RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER LDA, LDAFAC, M, N DOUBLE PRECISION RESID * .. * .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ) * .. * * Purpose * ======= * * ZGET01 reconstructs a matrix A from its L*U factorization and * computes the residual * norm(L*U - A) / ( N * norm(A) * EPS ), * where EPS is the machine epsilon. * * Arguments * ========== * * M (input) INTEGER * The number of rows of the matrix A. M >= 0. * * N (input) INTEGER * The number of columns of the matrix A. N >= 0. * * A (input) COMPLEX*16 array, dimension (LDA,N) * The original M x N matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,M). * * AFAC (input/output) COMPLEX*16 array, dimension (LDAFAC,N) * The factored form of the matrix A. AFAC contains the factors * L and U from the L*U factorization as computed by ZGETRF. * Overwritten with the reconstructed matrix, and then with the * difference L*U - A. * * LDAFAC (input) INTEGER * The leading dimension of the array AFAC. LDAFAC >= max(1,M). * * IPIV (input) INTEGER array, dimension (N) * The pivot indices from ZGETRF. * * RWORK (workspace) DOUBLE PRECISION array, dimension (M) * * RESID (output) DOUBLE PRECISION * norm(L*U - A) / ( N * norm(A) * EPS ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, J, K DOUBLE PRECISION ANORM, EPS COMPLEX*16 T * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, ZLANGE COMPLEX*16 ZDOTU EXTERNAL DLAMCH, ZLANGE, ZDOTU * .. * .. External Subroutines .. EXTERNAL ZGEMV, ZLASWP, ZSCAL, ZTRMV * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MIN * .. * .. Executable Statements .. * * Quick exit if M = 0 or N = 0. * IF( M.LE.0 .OR. N.LE.0 ) THEN RESID = ZERO RETURN END IF * * Determine EPS and the norm of A. * EPS = DLAMCH( 'Epsilon' ) ANORM = ZLANGE( '1', M, N, A, LDA, RWORK ) * * Compute the product L*U and overwrite AFAC with the result. * A column at a time of the product is obtained, starting with * column N. * DO 10 K = N, 1, -1 IF( K.GT.M ) THEN CALL ZTRMV( 'Lower', 'No transpose', 'Unit', M, AFAC, $ LDAFAC, AFAC( 1, K ), 1 ) ELSE * * Compute elements (K+1:M,K) * T = AFAC( K, K ) IF( K+1.LE.M ) THEN CALL ZSCAL( M-K, T, AFAC( K+1, K ), 1 ) CALL ZGEMV( 'No transpose', M-K, K-1, CONE, $ AFAC( K+1, 1 ), LDAFAC, AFAC( 1, K ), 1, $ CONE, AFAC( K+1, K ), 1 ) END IF * * Compute the (K,K) element * AFAC( K, K ) = T + ZDOTU( K-1, AFAC( K, 1 ), LDAFAC, $ AFAC( 1, K ), 1 ) * * Compute elements (1:K-1,K) * CALL ZTRMV( 'Lower', 'No transpose', 'Unit', K-1, AFAC, $ LDAFAC, AFAC( 1, K ), 1 ) END IF 10 CONTINUE CALL ZLASWP( N, AFAC, LDAFAC, 1, MIN( M, N ), IPIV, -1 ) * * Compute the difference L*U - A and store in AFAC. * DO 30 J = 1, N DO 20 I = 1, M AFAC( I, J ) = AFAC( I, J ) - A( I, J ) 20 CONTINUE 30 CONTINUE * * Compute norm( L*U - A ) / ( N * norm(A) * EPS ) * RESID = ZLANGE( '1', M, N, AFAC, LDAFAC, RWORK ) * IF( ANORM.LE.ZERO ) THEN IF( RESID.NE.ZERO ) $ RESID = ONE / EPS ELSE RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS END IF * RETURN * * End of ZGET01 * END |