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SUBROUTINE ZGTT01( N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK,
$ LDWORK, RWORK, RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER LDWORK, N DOUBLE PRECISION RESID * .. * .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION RWORK( * ) COMPLEX*16 D( * ), DF( * ), DL( * ), DLF( * ), DU( * ), $ DU2( * ), DUF( * ), WORK( LDWORK, * ) * .. * * Purpose * ======= * * ZGTT01 reconstructs a tridiagonal matrix A from its LU factorization * and computes the residual * norm(L*U - A) / ( norm(A) * EPS ), * where EPS is the machine epsilon. * * Arguments * ========= * * N (input) INTEGTER * The order of the matrix A. N >= 0. * * DL (input) COMPLEX*16 array, dimension (N-1) * The (n-1) sub-diagonal elements of A. * * D (input) COMPLEX*16 array, dimension (N) * The diagonal elements of A. * * DU (input) COMPLEX*16 array, dimension (N-1) * The (n-1) super-diagonal elements of A. * * DLF (input) COMPLEX*16 array, dimension (N-1) * The (n-1) multipliers that define the matrix L from the * LU factorization of A. * * DF (input) COMPLEX*16 array, dimension (N) * The n diagonal elements of the upper triangular matrix U from * the LU factorization of A. * * DUF (input) COMPLEX*16 array, dimension (N-1) * The (n-1) elements of the first super-diagonal of U. * * DU2 (input) COMPLEX*16 array, dimension (N-2) * The (n-2) elements of the second super-diagonal of U. * * IPIV (input) INTEGER array, dimension (N) * The pivot indices; for 1 <= i <= n, row i of the matrix was * interchanged with row IPIV(i). IPIV(i) will always be either * i or i+1; IPIV(i) = i indicates a row interchange was not * required. * * WORK (workspace) COMPLEX*16 array, dimension (LDWORK,N) * * LDWORK (input) INTEGER * The leading dimension of the array WORK. LDWORK >= max(1,N). * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESID (output) DOUBLE PRECISION * The scaled residual: norm(L*U - A) / (norm(A) * EPS) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, IP, J, LASTJ DOUBLE PRECISION ANORM, EPS COMPLEX*16 LI * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, ZLANGT, ZLANHS EXTERNAL DLAMCH, ZLANGT, ZLANHS * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. External Subroutines .. EXTERNAL ZAXPY, ZSWAP * .. * .. Executable Statements .. * * Quick return if possible * IF( N.LE.0 ) THEN RESID = ZERO RETURN END IF * EPS = DLAMCH( 'Epsilon' ) * * Copy the matrix U to WORK. * DO 20 J = 1, N DO 10 I = 1, N WORK( I, J ) = ZERO 10 CONTINUE 20 CONTINUE DO 30 I = 1, N IF( I.EQ.1 ) THEN WORK( I, I ) = DF( I ) IF( N.GE.2 ) $ WORK( I, I+1 ) = DUF( I ) IF( N.GE.3 ) $ WORK( I, I+2 ) = DU2( I ) ELSE IF( I.EQ.N ) THEN WORK( I, I ) = DF( I ) ELSE WORK( I, I ) = DF( I ) WORK( I, I+1 ) = DUF( I ) IF( I.LT.N-1 ) $ WORK( I, I+2 ) = DU2( I ) END IF 30 CONTINUE * * Multiply on the left by L. * LASTJ = N DO 40 I = N - 1, 1, -1 LI = DLF( I ) CALL ZAXPY( LASTJ-I+1, LI, WORK( I, I ), LDWORK, $ WORK( I+1, I ), LDWORK ) IP = IPIV( I ) IF( IP.EQ.I ) THEN LASTJ = MIN( I+2, N ) ELSE CALL ZSWAP( LASTJ-I+1, WORK( I, I ), LDWORK, WORK( I+1, I ), $ LDWORK ) END IF 40 CONTINUE * * Subtract the matrix A. * WORK( 1, 1 ) = WORK( 1, 1 ) - D( 1 ) IF( N.GT.1 ) THEN WORK( 1, 2 ) = WORK( 1, 2 ) - DU( 1 ) WORK( N, N-1 ) = WORK( N, N-1 ) - DL( N-1 ) WORK( N, N ) = WORK( N, N ) - D( N ) DO 50 I = 2, N - 1 WORK( I, I-1 ) = WORK( I, I-1 ) - DL( I-1 ) WORK( I, I ) = WORK( I, I ) - D( I ) WORK( I, I+1 ) = WORK( I, I+1 ) - DU( I ) 50 CONTINUE END IF * * Compute the 1-norm of the tridiagonal matrix A. * ANORM = ZLANGT( '1', N, DL, D, DU ) * * Compute the 1-norm of WORK, which is only guaranteed to be * upper Hessenberg. * RESID = ZLANHS( '1', N, WORK, LDWORK, RWORK ) * * Compute norm(L*U - A) / (norm(A) * EPS) * IF( ANORM.LE.ZERO ) THEN IF( RESID.NE.ZERO ) $ RESID = ONE / EPS ELSE RESID = ( RESID / ANORM ) / EPS END IF * RETURN * * End of ZGTT01 * END |