Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - DLA_GBRCOND Estimate the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows CMODE = 1 op2(C) = C CMODE = 0 op2(C) = I CMODE = -1 op2(C) = inv(C) The Skeel condition number cond(A) = norminf( |inv(A)||A| ) is computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number

**SYNOPSIS**

DOUBLE PRECISION FUNCTION DLA_GBRCOND( TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, CMODE, C, INFO, WORK, IWORK ) IMPLICIT NONE CHARACTER TRANS INTEGER N, LDAB, LDAFB, INFO, KL, KU, CMODE INTEGER IWORK( * ), IPIV( * ) DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ), C( * )

**PURPOSE**

DLA_GBRCOND Estimates the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows CMODE = 1 op2(C) = C CMODE = 0 op2(C) = I CMODE = -1 op2(C) = inv(C) The Skeel condition number cond(A) = norminf( |inv(A)||A| ) is computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number.

**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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDAFB,N) Details of the LU factorization of the band matrix A, as computed by DGBTRF. 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 DGBTRF; row i of the matrix was interchanged with row IPIV(i). CMODE (input) INTEGER Determines op2(C) in the formula op(A) * op2(C) as follows: CMODE = 1 op2(C) = C CMODE = 0 op2(C) = I CMODE = -1 op2(C) = inv(C) C (input) DOUBLE PRECISION array, dimension (N) The vector C in the formula op(A) * op2(C). INFO (output) INTEGER = 0: Successful exit. i > 0: The ith argument is invalid. WORK (input) DOUBLE PRECISION array, dimension (5*N). Workspace. IWORK (input) INTEGER array, dimension (N). Workspace. LAPACK routine (version 3.2.2) April 2011 DLA_GBRCOND(3lapack)