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# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
# SF_B1LEG -- Procedure to evaluate all the non-zero Legendrefunctions for
# a single point and given order.
procedure sf_b1leg (x, order, k1, k2, basis)
real x # array of data points
int order # order of polynomial, order = 1, constant
real k1, k2 # normalizing constants
real basis[ARB] # basis functions
int i
real ri, xnorm
begin
basis[1] = 1.
if (order == 1)
return
xnorm = (x + k1) * k2
basis[2] = xnorm
if (order == 2)
return
do i = 3, order {
ri = i
basis[i] = ((2. * ri - 3.) * xnorm * basis[i-1] -
(ri - 2.) * basis[i-2]) / (ri - 1.)
}
end
# SF_B1CHEB -- Procedure to evaluate all the non zero Chebyshev function
# for a given x and order.
procedure sf_b1cheb (x, order, k1, k2, basis)
real x # number of data points
int order # order of polynomial, 1 is a constant
real k1, k2 # normalizing constants
real basis[ARB] # array of basis functions
int i
real xnorm
begin
basis[1] = 1.
if (order == 1)
return
xnorm = (x + k1) * k2
basis[2] = xnorm
if (order == 2)
return
do i = 3, order
basis[i] = 2. * xnorm * basis[i-1] - basis[i-2]
end
# SF_B1SPLINE1 -- Evaluate all the non-zero spline1 functions for a
# single point.
procedure sf_b1spline1 (x, npieces, k1, k2, basis, left)
real x # set of data points
int npieces # number of polynomial pieces minus 1
real k1, k2 # normalizing constants
real basis[ARB] # basis functions
int left # index of the appropriate spline functions
real xnorm
begin
xnorm = (x + k1) * k2
left = min (int (xnorm), npieces)
basis[2] = xnorm - left
basis[1] = 1. - basis[2]
end
# SF_B1SPLINE3 -- Procedure to evaluate all the non-zero basis functions
# for a cubic spline.
procedure sf_b1spline3 (x, npieces, k1, k2, basis, left)
real x # array of data points
int npieces # number of polynomial pieces
real k1, k2 # normalizing constants
real basis[ARB] # array of basis functions
int left # array of indices for first non-zero spline
real sx, tx
begin
sx = (x + k1) * k2
left = min (int (sx), npieces)
sx = sx - left
tx = 1. - sx
basis[1] = tx * tx * tx
basis[2] = 1. + tx * (3. + tx * (3. - 3. * tx))
basis[3] = 1. + sx * (3. + sx * (3. - 3. * sx))
basis[4] = sx * sx * sx
end
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