 LAPACK  3.9.1 LAPACK: Linear Algebra PACKage

## ◆ cla_gbrpvgrw()

 real function cla_gbrpvgrw ( integer N, integer KL, integer KU, integer NCOLS, complex, dimension( ldab, * ) AB, integer LDAB, complex, dimension( ldafb, * ) AFB, integer LDAFB )

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

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Purpose:
``` CLA_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 COMPLEX 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 COMPLEX array, dimension (LDAFB,N) Details of the LU factorization of the band matrix A, as computed by CGBTRF. 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 cla_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  COMPLEX AB( LDAB, * ), AFB( LDAFB, * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. Local Scalars ..
132  INTEGER I, J, KD
133  REAL AMAX, UMAX, RPVGRW
134  COMPLEX ZDUM
135 * ..
136 * .. Intrinsic Functions ..
137  INTRINSIC abs, max, min, real, aimag
138 * ..
139 * .. Statement Functions ..
140  REAL CABS1
141 * ..
142 * .. Statement Function Definitions ..
143  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
144 * ..
145 * .. Executable Statements ..
146 *
147  rpvgrw = 1.0
148
149  kd = ku + 1
150  DO j = 1, ncols
151  amax = 0.0
152  umax = 0.0
153  DO i = max( j-ku, 1 ), min( j+kl, n )
154  amax = max( cabs1( ab( kd+i-j, j ) ), amax )
155  END DO
156  DO i = max( j-ku, 1 ), j
157  umax = max( cabs1( afb( kd+i-j, j ) ), umax )
158  END DO
159  IF ( umax /= 0.0 ) THEN
160  rpvgrw = min( amax / umax, rpvgrw )
161  END IF
162  END DO
163  cla_gbrpvgrw = rpvgrw
real function cla_gbrpvgrw(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)
CLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.
Definition: cla_gbrpvgrw.f:117
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