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include <mach.h>
include <math/nlfit.h>
include "nlfitdefd.h"
# NL_CHFAC -- Routine to calculate the Cholesky factorization of a
# symmetric, positive semi-definite banded matrix. This routines was
# adapted from the bchfac.f routine described in "A Practical Guide
# to Splines", Carl de Boor (1978).
procedure nl_chfacd (matrix, nbands, nrows, matfac, ier)
double matrix[nbands, nrows] # data matrix
int nbands # number of bands
int nrows # number of rows
double matfac[nbands, nrows] # Cholesky factorization
int ier # error code
int i, n, j, imax, jmax
double ratio
begin
# Test for a single element matrix.
if (nrows == 1) {
if (matrix[1,1] > double (0.0))
matfac[1,1] = 1. / matrix[1,1]
return
}
# Copy the original matrix into matfac.
do n = 1, nrows {
do j = 1, nbands
matfac[j,n] = matrix[j,n]
}
# Compute the factorization of the matrix.
do n = 1, nrows {
# Test to see if matrix is singular.
if (((matfac[1,n] + matrix[1,n]) - matrix[1,n]) <= EPSILOND) {
#if (((matfac[1,n] + matrix[1,n]) - matrix[1,n]) <= PIXEL(0.0)) {
do j = 1, nbands
matfac[j,n] = double (0.0)
ier = SINGULAR
next
}
matfac[1,n] = double (1.0) / matfac[1,n]
imax = min (nbands - 1, nrows - n)
if (imax < 1)
next
jmax = imax
do i = 1, imax {
ratio = matfac[i+1,n] * matfac[1,n]
do j = 1, jmax
matfac[j,n+i] = matfac[j,n+i] - matfac[j+i,n] * ratio
jmax = jmax - 1
matfac[i+1,n] = ratio
}
}
end
# NL_CHSLV -- Solve the matrix whose Cholesky factorization was calculated in
# NL_CHFAC for the coefficients. This routine was adapted from bchslv.f
# described in "A Practical Guide to Splines", by Carl de Boor (1978).
procedure nl_chslvd (matfac, nbands, nrows, vector, coeff)
double matfac[nbands,nrows] # Cholesky factorization
int nbands # number of bands
int nrows # number of rows
double vector[nrows] # right side of matrix equation
double coeff[nrows] # coefficients
int i, n, j, jmax, nbndm1
begin
# Test for a single element matrix.
if (nrows == 1) {
coeff[1] = vector[1] * matfac[1,1]
return
}
# Copy input vector to coefficients vector.
do i = 1, nrows
coeff[i] = vector[i]
# Perform forward substitution.
nbndm1 = nbands - 1
do n = 1, nrows {
jmax = min (nbndm1, nrows - n)
if (jmax >= 1) {
do j = 1, jmax
coeff[j+n] = coeff[j+n] - matfac[j+1,n] * coeff[n]
}
}
# Perform backward substitution.
for (n = nrows; n >= 1; n = n - 1) {
coeff[n] = coeff[n] * matfac[1,n]
jmax = min (nbndm1, nrows - n)
if (jmax >= 1) {
do j = 1, jmax
coeff[n] = coeff[n] - matfac[j+1,n] * coeff[j+n]
}
}
end
# NL_DAMP -- Procedure to add damping to matrix
procedure nl_dampd (inmatrix, outmatrix, constant, nbands, nrows)
double inmatrix[nbands,ARB] # input matrix
double outmatrix[nbands,ARB] # output matrix
double constant # damping constant
int nbands, nrows # dimensions of matrix
int i
begin
do i = 1, nrows
outmatrix[1,i] = inmatrix[1,i] * constant
end
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