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SUBROUTINE ZGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK,
$ RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER KL, KU, LDA, LDAFAC, M, N DOUBLE PRECISION RESID * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), WORK( * ) * .. * * Purpose * ======= * * ZGBT01 reconstructs a band 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. * * The expression L*U - A is computed one column at a time, so A and * AFAC are not modified. * * 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. * * KL (input) INTEGER * The number of subdiagonals within the band of A. KL >= 0. * * KU (input) INTEGER * The number of superdiagonals within the band of A. KU >= 0. * * A (input/output) COMPLEX*16 array, dimension (LDA,N) * The original matrix A in band storage, stored in rows 1 to * KL+KU+1. * * LDA (input) INTEGER. * The leading dimension of the array A. LDA >= max(1,KL+KU+1). * * AFAC (input) COMPLEX*16 array, dimension (LDAFAC,N) * The factored form of the matrix A. AFAC contains the banded * factors L and U from the L*U factorization, as computed by * ZGBTRF. U is stored as an upper triangular band matrix with * KL+KU superdiagonals in rows 1 to KL+KU+1, and the * multipliers used during the factorization are stored in rows * KL+KU+2 to 2*KL+KU+1. See ZGBTRF for further details. * * LDAFAC (input) INTEGER * The leading dimension of the array AFAC. * LDAFAC >= max(1,2*KL*KU+1). * * IPIV (input) INTEGER array, dimension (min(M,N)) * The pivot indices from ZGBTRF. * * WORK (workspace) COMPLEX*16 array, dimension (2*KL+KU+1) * * 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 ) * .. * .. Local Scalars .. INTEGER I, I1, I2, IL, IP, IW, J, JL, JU, JUA, KD, LENJ DOUBLE PRECISION ANORM, EPS COMPLEX*16 T * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DZASUM EXTERNAL DLAMCH, DZASUM * .. * .. External Subroutines .. EXTERNAL ZAXPY, ZCOPY * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, MAX, MIN * .. * .. Executable Statements .. * * Quick exit if M = 0 or N = 0. * RESID = ZERO IF( M.LE.0 .OR. N.LE.0 ) $ RETURN * * Determine EPS and the norm of A. * EPS = DLAMCH( 'Epsilon' ) KD = KU + 1 ANORM = ZERO DO 10 J = 1, N I1 = MAX( KD+1-J, 1 ) I2 = MIN( KD+M-J, KL+KD ) IF( I2.GE.I1 ) $ ANORM = MAX( ANORM, DZASUM( I2-I1+1, A( I1, J ), 1 ) ) 10 CONTINUE * * Compute one column at a time of L*U - A. * KD = KL + KU + 1 DO 40 J = 1, N * * Copy the J-th column of U to WORK. * JU = MIN( KL+KU, J-1 ) JL = MIN( KL, M-J ) LENJ = MIN( M, J ) - J + JU + 1 IF( LENJ.GT.0 ) THEN CALL ZCOPY( LENJ, AFAC( KD-JU, J ), 1, WORK, 1 ) DO 20 I = LENJ + 1, JU + JL + 1 WORK( I ) = ZERO 20 CONTINUE * * Multiply by the unit lower triangular matrix L. Note that L * is stored as a product of transformations and permutations. * DO 30 I = MIN( M-1, J ), J - JU, -1 IL = MIN( KL, M-I ) IF( IL.GT.0 ) THEN IW = I - J + JU + 1 T = WORK( IW ) CALL ZAXPY( IL, T, AFAC( KD+1, I ), 1, WORK( IW+1 ), $ 1 ) IP = IPIV( I ) IF( I.NE.IP ) THEN IP = IP - J + JU + 1 WORK( IW ) = WORK( IP ) WORK( IP ) = T END IF END IF 30 CONTINUE * * Subtract the corresponding column of A. * JUA = MIN( JU, KU ) IF( JUA+JL+1.GT.0 ) $ CALL ZAXPY( JUA+JL+1, -DCMPLX( ONE ), A( KU+1-JUA, J ), $ 1, WORK( JU+1-JUA ), 1 ) * * Compute the 1-norm of the column. * RESID = MAX( RESID, DZASUM( JU+JL+1, WORK, 1 ) ) END IF 40 CONTINUE * * Compute norm( L*U - A ) / ( N * norm(A) * EPS ) * IF( ANORM.LE.ZERO ) THEN IF( RESID.NE.ZERO ) $ RESID = ONE / EPS ELSE RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS END IF * RETURN * * End of ZGBT01 * END |