SUBROUTINE ZPBT01( UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK, \$ RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER KD, LDA, LDAFAC, N DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ) * .. * * Purpose * ======= * * ZPBT01 reconstructs a Hermitian positive definite band matrix A from * its L*L' or U'*U factorization and computes the residual * norm( L*L' - A ) / ( N * norm(A) * EPS ) or * norm( U'*U - A ) / ( N * norm(A) * EPS ), * where EPS is the machine epsilon, L' is the conjugate transpose of * L, and U' is the conjugate transpose of U. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * Hermitian matrix A is stored: * = 'U': Upper triangular * = 'L': Lower triangular * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * KD (input) INTEGER * The number of super-diagonals of the matrix A if UPLO = 'U', * or the number of sub-diagonals if UPLO = 'L'. KD >= 0. * * A (input) COMPLEX*16 array, dimension (LDA,N) * The original Hermitian band matrix A. If UPLO = 'U', the * upper triangular part of A is stored as a band matrix; if * UPLO = 'L', the lower triangular part of A is stored. The * columns of the appropriate triangle are stored in the columns * of A and the diagonals of the triangle are stored in the rows * of A. See ZPBTRF for further details. * * LDA (input) INTEGER. * The leading dimension of the array A. LDA >= max(1,KD+1). * * AFAC (input) COMPLEX*16 array, dimension (LDAFAC,N) * The factored form of the matrix A. AFAC contains the factor * L or U from the L*L' or U'*U factorization in band storage * format, as computed by ZPBTRF. * * LDAFAC (input) INTEGER * The leading dimension of the array AFAC. * LDAFAC >= max(1,KD+1). * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESID (output) DOUBLE PRECISION * If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ) * If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS ) * * ===================================================================== * * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J, K, KC, KLEN, ML, MU DOUBLE PRECISION AKK, ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, ZLANHB COMPLEX*16 ZDOTC EXTERNAL LSAME, DLAMCH, ZLANHB, ZDOTC * .. * .. External Subroutines .. EXTERNAL ZDSCAL, ZHER, ZTRMV * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DIMAG, MAX, MIN * .. * .. Executable Statements .. * * Quick exit if N = 0. * IF( N.LE.0 ) THEN RESID = ZERO RETURN END IF * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = DLAMCH( 'Epsilon' ) ANORM = ZLANHB( '1', UPLO, N, KD, A, LDA, RWORK ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Check the imaginary parts of the diagonal elements and return with * an error code if any are nonzero. * IF( LSAME( UPLO, 'U' ) ) THEN DO 10 J = 1, N IF( DIMAG( AFAC( KD+1, J ) ).NE.ZERO ) THEN RESID = ONE / EPS RETURN END IF 10 CONTINUE ELSE DO 20 J = 1, N IF( DIMAG( AFAC( 1, J ) ).NE.ZERO ) THEN RESID = ONE / EPS RETURN END IF 20 CONTINUE END IF * * Compute the product U'*U, overwriting U. * IF( LSAME( UPLO, 'U' ) ) THEN DO 30 K = N, 1, -1 KC = MAX( 1, KD+2-K ) KLEN = KD + 1 - KC * * Compute the (K,K) element of the result. * AKK = ZDOTC( KLEN+1, AFAC( KC, K ), 1, AFAC( KC, K ), 1 ) AFAC( KD+1, K ) = AKK * * Compute the rest of column K. * IF( KLEN.GT.0 ) \$ CALL ZTRMV( 'Upper', 'Conjugate', 'Non-unit', KLEN, \$ AFAC( KD+1, K-KLEN ), LDAFAC-1, \$ AFAC( KC, K ), 1 ) * 30 CONTINUE * * UPLO = 'L': Compute the product L*L', overwriting L. * ELSE DO 40 K = N, 1, -1 KLEN = MIN( KD, N-K ) * * Add a multiple of column K of the factor L to each of * columns K+1 through N. * IF( KLEN.GT.0 ) \$ CALL ZHER( 'Lower', KLEN, ONE, AFAC( 2, K ), 1, \$ AFAC( 1, K+1 ), LDAFAC-1 ) * * Scale column K by the diagonal element. * AKK = AFAC( 1, K ) CALL ZDSCAL( KLEN+1, AKK, AFAC( 1, K ), 1 ) * 40 CONTINUE END IF * * Compute the difference L*L' - A or U'*U - A. * IF( LSAME( UPLO, 'U' ) ) THEN DO 60 J = 1, N MU = MAX( 1, KD+2-J ) DO 50 I = MU, KD + 1 AFAC( I, J ) = AFAC( I, J ) - A( I, J ) 50 CONTINUE 60 CONTINUE ELSE DO 80 J = 1, N ML = MIN( KD+1, N-J+1 ) DO 70 I = 1, ML AFAC( I, J ) = AFAC( I, J ) - A( I, J ) 70 CONTINUE 80 CONTINUE END IF * * Compute norm( L*L' - A ) / ( N * norm(A) * EPS ) * RESID = ZLANHB( '1', UPLO, N, KD, AFAC, LDAFAC, RWORK ) * RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS * RETURN * * End of ZPBT01 * END