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### LAPACK-3: ZLA_GBRCOND_X Compute the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX*16 vector

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## NAME

LAPACK-3 - ZLA_GBRCOND_X Compute the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX*16 vectorSYNOPSIS

DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, X, INFO, WORK, RWORK ) IMPLICIT NONE CHARACTER TRANS INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO INTEGER IPIV( * ) COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ), X( * ) DOUBLE PRECISION RWORK( * )## PURPOSE

ZLA_GBRCOND_X Computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX*16 vector.## ARGUMENTS

TRANS (input) CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate Transpose = Transpose) 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. 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. IPIV (input) INTEGER array, dimension (N) The pivot indices from the factorization A = P*L*U as computed by ZGBTRF; row i of the matrix was interchanged with row IPIV(i). X (input) COMPLEX*16 array, dimension (N) The vector X in the formula op(A) * diag(X). INFO (output) INTEGER = 0: Successful exit. i > 0: The ith argument is invalid. WORK (input) COMPLEX*16 array, dimension (2*N). Workspace. RWORK (input) DOUBLE PRECISION array, dimension (N). Workspace. LAPACK routine (version 3.2.1)March 2011 LAPACK-3(3)

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