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+include <mach.h>
+include <math/nlfit.h>
+include "nlfitdefr.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_chfacr (matrix, nbands, nrows, matfac, ier)
+
+real   matrix[nbands, nrows]	# data matrix
+int	nbands			# number of bands
+int	nrows			# number of rows
+real   matfac[nbands, nrows]	# Cholesky factorization
+int	ier			# error code
+
+int	i, n, j, imax, jmax
+real   ratio
+
+begin
+	# Test for a single element matrix.
+	if (nrows == 1) {
+	    if (matrix[1,1] > real (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]) <= EPSILONR) {
+	    #if (((matfac[1,n] + matrix[1,n]) - matrix[1,n]) <= PIXEL(0.0)) {
+		do j = 1, nbands
+		    matfac[j,n] = real (0.0)
+		ier = SINGULAR
+		next
+	    }
+
+	    matfac[1,n] = real (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_chslvr (matfac, nbands, nrows, vector, coeff)
+
+real	matfac[nbands,nrows] 		# Cholesky factorization
+int	nbands				# number of bands
+int	nrows				# number of rows
+real	vector[nrows]			# right side of matrix equation
+real	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_dampr (inmatrix, outmatrix, constant, nbands, nrows)
+
+real	inmatrix[nbands,ARB]		# input matrix
+real	outmatrix[nbands,ARB]		# output matrix
+real	constant			# damping constant
+int	nbands, nrows			# dimensions of matrix
+
+int	i
+
+begin
+	do i = 1, nrows
+	    outmatrix[1,i] = inmatrix[1,i] * constant
+end