LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ sla_gbrpvgrw()

real function sla_gbrpvgrw ( integer n,
integer kl,
integer ku,
integer ncols,
real, dimension( ldab, * ) ab,
integer ldab,
real, dimension( ldafb, * ) afb,
integer ldafb )

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

Download SLA_GBRPVGRW + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> SLA_GBRPVGRW computes the reciprocal pivot growth factor
!> norm(A)/norm(U). The  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
[in]N
!>          N is INTEGER
!>     The number of linear equations, i.e., the order of the
!>     matrix A.  N >= 0.
!> 
[in]KL
!>          KL is INTEGER
!>     The number of subdiagonals within the band of A.  KL >= 0.
!> 
[in]KU
!>          KU is INTEGER
!>     The number of superdiagonals within the band of A.  KU >= 0.
!> 
[in]NCOLS
!>          NCOLS is INTEGER
!>     The number of columns of the matrix A.  NCOLS >= 0.
!> 
[in]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)
!> 
[in]LDAB
!>          LDAB is INTEGER
!>     The leading dimension of the array AB.  LDAB >= KL+KU+1.
!> 
[in]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.
!> 
[in]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.

Definition at line 113 of file sla_gbrpvgrw.f.

115*
116* -- LAPACK computational routine --
117* -- LAPACK is a software package provided by Univ. of Tennessee, --
118* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119*
120* .. Scalar Arguments ..
121 INTEGER N, KL, KU, NCOLS, LDAB, LDAFB
122* ..
123* .. Array Arguments ..
124 REAL AB( LDAB, * ), AFB( LDAFB, * )
125* ..
126*
127* =====================================================================
128*
129* .. Local Scalars ..
130 INTEGER I, J, KD
131 REAL AMAX, UMAX, RPVGRW
132* ..
133* .. Intrinsic Functions ..
134 INTRINSIC abs, max, min
135* ..
136* .. Executable Statements ..
137*
138 rpvgrw = 1.0
139
140 kd = ku + 1
141 DO j = 1, ncols
142 amax = 0.0
143 umax = 0.0
144 DO i = max( j-ku, 1 ), min( j+kl, n )
145 amax = max( abs( ab( kd+i-j, j)), amax )
146 END DO
147 DO i = max( j-ku, 1 ), j
148 umax = max( abs( afb( kd+i-j, j ) ), umax )
149 END DO
150 IF ( umax /= 0.0 ) THEN
151 rpvgrw = min( amax / umax, rpvgrw )
152 END IF
153 END DO
154 sla_gbrpvgrw = rpvgrw
155*
156* End of SLA_GBRPVGRW
157*
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.
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