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---
:name: zla_gbrpvgrw
:md5sum: 93b4b0e0e44371aacf2dcc4f944acec7
:category: :function
:type: doublereal
:arguments:
- n:
:type: integer
:intent: input
- kl:
:type: integer
:intent: input
- ku:
:type: integer
:intent: input
- ncols:
:type: integer
:intent: input
- ab:
:type: doublecomplex
:intent: input
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- afb:
:type: doublecomplex
:intent: input
:dims:
- ldafb
- n
- ldafb:
:type: integer
:intent: input
:substitutions: {}
:fortran_help: " DOUBLE PRECISION FUNCTION ZLA_GBRPVGRW( N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZLA_GBRPVGRW computes the reciprocal pivot growth factor\n\
* norm(A)/norm(U). The \"max absolute element\" norm is used. If this is\n\
* much less than 1, the stability of the LU factorization of the\n\
* (equilibrated) matrix A could be poor. This also means that the\n\
* solution X, estimated condition numbers, and error bounds could be\n\
* unreliable.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The number of linear equations, i.e., the order of the\n\
* matrix A. N >= 0.\n\
*\n\
* KL (input) INTEGER\n\
* The number of subdiagonals within the band of A. KL >= 0.\n\
*\n\
* KU (input) INTEGER\n\
* The number of superdiagonals within the band of A. KU >= 0.\n\
*\n\
* NCOLS (input) INTEGER\n\
* The number of columns of the matrix A. NCOLS >= 0.\n\
*\n\
* AB (input) COMPLEX*16 array, dimension (LDAB,N)\n\
* On entry, the matrix A in band storage, in rows 1 to KL+KU+1.\n\
* The j-th column of A is stored in the j-th column of the\n\
* array AB as follows:\n\
* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= KL+KU+1.\n\
*\n\
* AFB (input) COMPLEX*16 array, dimension (LDAFB,N)\n\
* Details of the LU factorization of the band matrix A, as\n\
* computed by ZGBTRF. U is stored as an upper triangular\n\
* band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,\n\
* and the multipliers used during the factorization are stored\n\
* in rows KL+KU+2 to 2*KL+KU+1.\n\
*\n\
* LDAFB (input) INTEGER\n\
* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.\n\
*\n\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n INTEGER I, J, KD\n DOUBLE PRECISION AMAX, UMAX, RPVGRW\n COMPLEX*16 ZDUM\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC ABS, MAX, MIN, REAL, DIMAG\n\
* ..\n\
* .. Statement Functions ..\n DOUBLE PRECISION CABS1\n\
* ..\n\
* .. Statement Function Definitions ..\n CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )\n\
* ..\n"
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