cla_gbrcond_x (3)

Functions/Subroutines

real function cla_gbrcond_x (TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, X, INFO, WORK, RWORK)

CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.

real function cla_gbrcond_x (characterTRANS, integerN, integerKL, integerKU, complex, dimension( ldab, * )AB, integerLDAB, complex, dimension( ldafb, * )AFB, integerLDAFB, integer, dimension( * )IPIV, complex, dimension( * )X, integerINFO, complex, dimension( * )WORK, real, dimension( * )RWORK)

CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.

Purpose:

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

Parameters:

TRANS

          TRANS is 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

          N is INTEGER
     The number of linear equations, i.e., the order of the
     matrix A.  N >= 0.

KL

          KL is INTEGER
     The number of subdiagonals within the band of A.  KL >= 0.

KU

          KU is INTEGER
     The number of superdiagonals within the band of A.  KU >= 0.

AB

          AB is COMPLEX 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

          LDAB is INTEGER
     The leading dimension of the array AB.  LDAB >= KL+KU+1.

AFB

          AFB is COMPLEX array, dimension (LDAFB,N)
     Details of the LU factorization of the band matrix A, as
     computed by CGBTRF.  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

          LDAFB is INTEGER
     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.

IPIV

          IPIV is INTEGER array, dimension (N)
     The pivot indices from the factorization A = P*L*U
     as computed by CGBTRF; row i of the matrix was interchanged
     with row IPIV(i).

X

          X is COMPLEX array, dimension (N)
     The vector X in the formula op(A) * diag(X).

INFO

          INFO is INTEGER
       = 0:  Successful exit.
     i > 0:  The ith argument is invalid.

WORK

          WORK is COMPLEX array, dimension (2*N).
     Workspace.

RWORK

          RWORK is REAL array, dimension (N).
     Workspace.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 153 of file cla_gbrcond_x.f.

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