dla_gbrcond-f(3)

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 (characterTRANS, integerN, integerKL, integerKU, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( ldafb, * )AFB, integerLDAFB, integer, dimension( * )IPIV, integerCMODE, double precision, dimension( * )C, integerINFO, 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 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.

 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 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:

September 2012

Definition at line 169 of file dla_gbrcond.f.

Author

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