DOUBLE PRECISION FUNCTION ZRZT02( M, N, AF, LDA, TAU, WORK, \$ LWORK ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER LDA, LWORK, M, N * .. * .. Array Arguments .. COMPLEX*16 AF( LDA, * ), TAU( * ), WORK( LWORK ) * .. * * Purpose * ======= * * ZRZT02 returns * || I - Q'*Q || / ( M * eps) * where the matrix Q is defined by the Householder transformations * generated by ZTZRZF. * * Arguments * ========= * * M (input) INTEGER * The number of rows of the matrix AF. * * N (input) INTEGER * The number of columns of the matrix AF. * * AF (input) COMPLEX*16 array, dimension (LDA,N) * The output of ZTZRZF. * * LDA (input) INTEGER * The leading dimension of the array AF. * * TAU (input) COMPLEX*16 array, dimension (M) * Details of the Householder transformations as returned by * ZTZRZF. * * WORK (workspace) COMPLEX*16 array, dimension (LWORK) * * LWORK (input) INTEGER * Length of WORK array. LWORK >= N*N+N. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. INTEGER I, INFO * .. * .. Local Arrays .. DOUBLE PRECISION RWORK( 1 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, ZLANGE EXTERNAL DLAMCH, ZLANGE * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLASET, ZUNMRZ * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, MAX * .. * .. Executable Statements .. * ZRZT02 = ZERO * IF( LWORK.LT.N*N+N ) THEN CALL XERBLA( 'ZRZT02', 7 ) RETURN END IF * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 ) \$ RETURN * * Q := I * CALL ZLASET( 'Full', N, N, DCMPLX( ZERO ), DCMPLX( ONE ), WORK, \$ N ) * * Q := P(1) * ... * P(m) * Q * CALL ZUNMRZ( 'Left', 'No transpose', N, N, M, N-M, AF, LDA, TAU, \$ WORK, N, WORK( N*N+1 ), LWORK-N*N, INFO ) * * Q := P(m)' * ... * P(1)' * Q * CALL ZUNMRZ( 'Left', 'Conjugate transpose', N, N, M, N-M, AF, LDA, \$ TAU, WORK, N, WORK( N*N+1 ), LWORK-N*N, INFO ) * * Q := Q - I * DO 10 I = 1, N WORK( ( I-1 )*N+I ) = WORK( ( I-1 )*N+I ) - ONE 10 CONTINUE * ZRZT02 = ZLANGE( 'One-norm', N, N, WORK, N, RWORK ) / \$ ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) ) RETURN * * End of ZRZT02 * END