 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dla_gbrpvgrw()

 double precision function dla_gbrpvgrw ( integer N, integer KL, integer KU, integer NCOLS, double precision, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( ldafb, * ) AFB, integer LDAFB )

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

Purpose:
``` DLA_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
 [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 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)``` [in] LDAB ``` LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1.``` [in] 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.``` [in] LDAFB ``` LDAFB is INTEGER The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.```

Definition at line 115 of file dla_gbrpvgrw.f.

117*
118* -- LAPACK computational routine --
119* -- LAPACK is a software package provided by Univ. of Tennessee, --
120* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
121*
122* .. Scalar Arguments ..
123 INTEGER N, KL, KU, NCOLS, LDAB, LDAFB
124* ..
125* .. Array Arguments ..
126 DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * )
127* ..
128*
129* =====================================================================
130*
131* .. Local Scalars ..
132 INTEGER I, J, KD
133 DOUBLE PRECISION AMAX, UMAX, RPVGRW
134* ..
135* .. Intrinsic Functions ..
136 INTRINSIC abs, max, min
137* ..
138* .. Executable Statements ..
139*
140 rpvgrw = 1.0d+0
141
142 kd = ku + 1
143 DO j = 1, ncols
144 amax = 0.0d+0
145 umax = 0.0d+0
146 DO i = max( j-ku, 1 ), min( j+kl, n )
147 amax = max( abs( ab( kd+i-j, j)), amax )
148 END DO
149 DO i = max( j-ku, 1 ), j
150 umax = max( abs( afb( kd+i-j, j ) ), umax )
151 END DO
152 IF ( umax /= 0.0d+0 ) THEN
153 rpvgrw = min( amax / umax, rpvgrw )
154 END IF
155 END DO
156 dla_gbrpvgrw = rpvgrw
157*
158* End of DLA_GBRPVGRW
159*
double precision function dla_gbrpvgrw(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)
DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.
Definition: dla_gbrpvgrw.f:117
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