DOUBLE PRECISION FUNCTION ZLA_GBRPVGRW( N, KL, KU, NCOLS, AB, \$ LDAB, AFB, LDAFB ) * * -- LAPACK routine (version 3.2.2) -- * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- * -- Jason Riedy of Univ. of California Berkeley. -- * -- June 2010 -- * * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley and NAG Ltd. -- * IMPLICIT NONE * .. * .. Scalar Arguments .. INTEGER N, KL, KU, NCOLS, LDAB, LDAFB * .. * .. Array Arguments .. COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ) * .. * * Purpose * ======= * * ZLA_GBRPVGRW computes the reciprocal pivot growth factor * norm(A)/norm(U). The "max absolute element" norm is used. If this is * much less than 1, the stability of the LU factorization of the * (equilibrated) matrix A could be poor. This also means that the * solution X, estimated condition numbers, and error bounds could be * unreliable. * * Arguments * ========= * * N (input) INTEGER * The number of linear equations, i.e., the order 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. * * NCOLS (input) INTEGER * The number of columns of the matrix A. NCOLS >= 0. * * AB (input) COMPLEX*16 array, dimension (LDAB,N) * On entry, the matrix A in band storage, in rows 1 to KL+KU+1. * The j-th column of A is stored in the j-th column of the * array AB as follows: * AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) * * LDAB (input) INTEGER * The leading dimension of the array AB. LDAB >= KL+KU+1. * * AFB (input) COMPLEX*16 array, dimension (LDAFB,N) * Details of the LU factorization of the band matrix A, 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. * * LDAFB (input) INTEGER * The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. * * ===================================================================== * * .. Local Scalars .. INTEGER I, J, KD DOUBLE PRECISION AMAX, UMAX, RPVGRW COMPLEX*16 ZDUM * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, REAL, DIMAG * .. * .. Statement Functions .. DOUBLE PRECISION CABS1 * .. * .. Statement Function Definitions .. CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) * .. * .. Executable Statements .. * RPVGRW = 1.0D+0 KD = KU + 1 DO J = 1, NCOLS AMAX = 0.0D+0 UMAX = 0.0D+0 DO I = MAX( J-KU, 1 ), MIN( J+KL, N ) AMAX = MAX( CABS1( AB( KD+I-J, J ) ), AMAX ) END DO DO I = MAX( J-KU, 1 ), J UMAX = MAX( CABS1( AFB( KD+I-J, J ) ), UMAX ) END DO IF ( UMAX /= 0.0D+0 ) THEN RPVGRW = MIN( AMAX / UMAX, RPVGRW ) END IF END DO ZLA_GBRPVGRW = RPVGRW END