sla_gbrcond.f man page

sla_gbrcond.f —

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

REAL function sla_gbrcond (characterTRANS, integerN, integerKL, integerKU, real, dimension( ldab, * )AB, integerLDAB, real, dimension( ldafb, * )AFB, integerLDAFB, integer, dimension( * )IPIV, integerCMODE, real, dimension( * )C, integerINFO, real, dimension( * )WORK, integer, dimension( * )IWORK)

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

Purpose:

SLA_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 REAL 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 REAL array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as
computed by SGBTRF.  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 SGBTRF; 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 REAL 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 REAL 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 168 of file sla_gbrcond.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

sla_gbrcond(3) is an alias of sla_gbrcond.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK