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dla_gbrcond.f(3) LAPACK dla_gbrcond.f(3)

NAME

dla_gbrcond.f

SYNOPSIS

Functions/Subroutines


double precision function dla_gbrcond (TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, CMODE, C, INFO, WORK, IWORK)
DLA_GBRCOND estimates the Skeel condition number for a general banded matrix.

Function/Subroutine Documentation

double precision function dla_gbrcond (character TRANS, integer N, integer KL, integer KU, double precision, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( ldafb, * ) AFB, integer LDAFB, integer, dimension( * ) IPIV, integer CMODE, double precision, dimension( * ) C, integer INFO, double precision, dimension( * ) WORK, integer, dimension( * ) IWORK)

DLA_GBRCOND estimates the Skeel condition number for a general banded matrix.

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.

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 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


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

AFB


AFB is 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


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 DGBTRF; row i of the matrix was interchanged
with row IPIV(i).

CMODE


CMODE is 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


C is DOUBLE PRECISION array, dimension (N)
The vector C in the formula op(A) * op2(C).

INFO


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

WORK


WORK is DOUBLE PRECISION array, dimension (5*N).
Workspace.

IWORK


IWORK is INTEGER array, dimension (N).
Workspace.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Definition at line 172 of file dla_gbrcond.f.

Author

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Tue Nov 14 2017 Version 3.8.0