sla_gercond.f (3)

Functions/Subroutines

real function sla_gercond (TRANS, N, A, LDA, AF, LDAF, IPIV, CMODE, C, INFO, WORK, IWORK)

SLA_GERCOND estimates the Skeel condition number for a general matrix.

real function sla_gercond (characterTRANS, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( ldaf, * )AF, integerLDAF, integer, dimension( * )IPIV, integerCMODE, real, dimension( * )C, integerINFO, real, dimension( * )WORK, integer, dimension( * )IWORK)

SLA_GERCOND estimates the Skeel condition number for a general matrix.

Purpose:

    SLA_GERCOND 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.

A

          A is REAL array, dimension (LDA,N)
     On entry, the N-by-N matrix A.

LDA

          LDA is INTEGER
     The leading dimension of the array A.  LDA >= max(1,N).

AF

          AF is REAL array, dimension (LDAF,N)
     The factors L and U from the factorization
     A = P*L*U as computed by SGETRF.

LDAF

          LDAF is INTEGER
     The leading dimension of the array AF.  LDAF >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
     The pivot indices from the factorization A = P*L*U
     as computed by SGETRF; 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 (3*N).
     Workspace.

IWORK

          IWORK is INTEGER array, dimension (N).
     Workspace.2

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 150 of file sla_gercond.f.

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