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---
:name: dlaqsb
:md5sum: c7dc33589acebc95caeb49a34f486200
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- kd:
:type: integer
:intent: input
- ab:
:type: doublereal
:intent: input/output
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- s:
:type: doublereal
:intent: input
:dims:
- n
- scond:
:type: doublereal
:intent: input
- amax:
:type: doublereal
:intent: input
- equed:
:type: char
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLAQSB equilibrates a symmetric band matrix A using the scaling\n\
* factors in the vector S.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* Specifies whether the upper or lower triangular part of the\n\
* symmetric matrix A is stored.\n\
* = 'U': Upper triangular\n\
* = 'L': Lower triangular\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* KD (input) INTEGER\n\
* The number of super-diagonals of the matrix A if UPLO = 'U',\n\
* or the number of sub-diagonals if UPLO = 'L'. KD >= 0.\n\
*\n\
* AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)\n\
* On entry, the upper or lower triangle of the symmetric band\n\
* matrix A, stored in the first KD+1 rows of the array. The\n\
* j-th column of A is stored in the j-th column of the array AB\n\
* as follows:\n\
* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;\n\
* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).\n\
*\n\
* On exit, if INFO = 0, the triangular factor U or L from the\n\
* Cholesky factorization A = U'*U or A = L*L' of the band\n\
* matrix A, in the same storage format as A.\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= KD+1.\n\
*\n\
* S (input) DOUBLE PRECISION array, dimension (N)\n\
* The scale factors for A.\n\
*\n\
* SCOND (input) DOUBLE PRECISION\n\
* Ratio of the smallest S(i) to the largest S(i).\n\
*\n\
* AMAX (input) DOUBLE PRECISION\n\
* Absolute value of largest matrix entry.\n\
*\n\
* EQUED (output) CHARACTER*1\n\
* Specifies whether or not equilibration was done.\n\
* = 'N': No equilibration.\n\
* = 'Y': Equilibration was done, i.e., A has been replaced by\n\
* diag(S) * A * diag(S).\n\
*\n\
* Internal Parameters\n\
* ===================\n\
*\n\
* THRESH is a threshold value used to decide if scaling should be done\n\
* based on the ratio of the scaling factors. If SCOND < THRESH,\n\
* scaling is done.\n\
*\n\
* LARGE and SMALL are threshold values used to decide if scaling should\n\
* be done based on the absolute size of the largest matrix element.\n\
* If AMAX > LARGE or AMAX < SMALL, scaling is done.\n\
*\n\n\
* =====================================================================\n\
*\n"
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