sla_gbrpvgrw.f (3)

Functions/Subroutines

real function sla_gbrpvgrw (N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)

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

real function sla_gbrpvgrw (integerN, integerKL, integerKU, integerNCOLS, real, dimension( ldab, * )AB, integerLDAB, real, dimension( ldafb, * )AFB, integerLDAFB)

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

Purpose:

 SLA_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

          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.

NCOLS

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

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 117 of file sla_gbrpvgrw.f.

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