SUBROUTINE DTRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND, \$ WORK, RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER DIAG, UPLO INTEGER LDA, LDAINV, N DOUBLE PRECISION RCOND, RESID * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), AINV( LDAINV, * ), WORK( * ) * .. * * Purpose * ======= * * DTRT01 computes the residual for a triangular matrix A times its * inverse: * RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ), * where EPS is the machine epsilon. * * Arguments * ========== * * UPLO (input) CHARACTER*1 * Specifies whether the matrix A is upper or lower triangular. * = 'U': Upper triangular * = 'L': Lower triangular * * DIAG (input) CHARACTER*1 * Specifies whether or not the matrix A is unit triangular. * = 'N': Non-unit triangular * = 'U': Unit triangular * * N (input) INTEGER * The order of the matrix A. N >= 0. * * A (input) DOUBLE PRECISION array, dimension (LDA,N) * The triangular matrix A. If UPLO = 'U', the leading n by n * upper triangular part of the array A contains the upper * triangular matrix, and the strictly lower triangular part of * A is not referenced. If UPLO = 'L', the leading n by n lower * triangular part of the array A contains the lower triangular * matrix, and the strictly upper triangular part of A is not * referenced. If DIAG = 'U', the diagonal elements of A are * also not referenced and are assumed to be 1. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * AINV (input/output) DOUBLE PRECISION array, dimension (LDAINV,N) * On entry, the (triangular) inverse of the matrix A, in the * same storage format as A. * On exit, the contents of AINV are destroyed. * * LDAINV (input) INTEGER * The leading dimension of the array AINV. LDAINV >= max(1,N). * * RCOND (output) DOUBLE PRECISION * The reciprocal condition number of A, computed as * 1/(norm(A) * norm(AINV)). * * WORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESID (output) DOUBLE PRECISION * norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER J DOUBLE PRECISION AINVNM, ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, DLANTR EXTERNAL LSAME, DLAMCH, DLANTR * .. * .. External Subroutines .. EXTERNAL DTRMV * .. * .. Intrinsic Functions .. INTRINSIC DBLE * .. * .. Executable Statements .. * * Quick exit if N = 0 * IF( N.LE.0 ) THEN RCOND = ONE RESID = ZERO RETURN END IF * * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0. * EPS = DLAMCH( 'Epsilon' ) ANORM = DLANTR( '1', UPLO, DIAG, N, N, A, LDA, WORK ) AINVNM = DLANTR( '1', UPLO, DIAG, N, N, AINV, LDAINV, WORK ) IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCOND = ZERO RESID = ONE / EPS RETURN END IF RCOND = ( ONE / ANORM ) / AINVNM * * Set the diagonal of AINV to 1 if AINV has unit diagonal. * IF( LSAME( DIAG, 'U' ) ) THEN DO 10 J = 1, N AINV( J, J ) = ONE 10 CONTINUE END IF * * Compute A * AINV, overwriting AINV. * IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N CALL DTRMV( 'Upper', 'No transpose', DIAG, J, A, LDA, \$ AINV( 1, J ), 1 ) 20 CONTINUE ELSE DO 30 J = 1, N CALL DTRMV( 'Lower', 'No transpose', DIAG, N-J+1, A( J, J ), \$ LDA, AINV( J, J ), 1 ) 30 CONTINUE END IF * * Subtract 1 from each diagonal element to form A*AINV - I. * DO 40 J = 1, N AINV( J, J ) = AINV( J, J ) - ONE 40 CONTINUE * * Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS) * RESID = DLANTR( '1', UPLO, 'Non-unit', N, N, AINV, LDAINV, WORK ) * RESID = ( ( RESID*RCOND ) / DBLE( N ) ) / EPS * RETURN * * End of DTRT01 * END