cla_gbrpvgrw-f(3)

cla_gbrpvgrw.f –

Synopsis

Functions/Subroutines

REAL function cla_gbrpvgrw (N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)
CLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

Function/Subroutine Documentation

REAL function cla_gbrpvgrw (integerN, integerKL, integerKU, integerNCOLS, complex, dimension( ldab, * )AB, integerLDAB, complex, dimension( ldafb, * )AFB, integerLDAFB)

CLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

Purpose:

 CLA_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.

Parameters:

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

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

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

NCOLS

 NCOLS is INTEGER
 The number of columns of the matrix A. NCOLS >= 0.

 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.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 117 of file cla_gbrpvgrw.f.

Author

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