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# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
# CV_EVCHEB -- Procedure to evaluate a Chebyshev polynomial assuming that
# the coefficients have been calculated.
procedure rcv_evcheb (coeff, x, yfit, npts, order, k1, k2)
real coeff[ARB] # 1D array of coefficients
real x[npts] # x values of points to be evaluated
real yfit[npts] # the fitted points
int npts # number of points to be evaluated
int order # order of the polynomial, 1 = constant
real k1, k2 # normalizing constants
int i
pointer sx, pn, pnm1, pnm2
pointer sp
real c1, c2
begin
# fit a constant
if (order == 1) {
call amovkr (coeff[1], yfit, npts)
return
}
# fit a linear function
c1 = k2 * coeff[2]
c2 = c1 * k1 + coeff[1]
call altmr (x, yfit, npts, c1, c2)
if (order == 2)
return
# allocate temporary space
call smark (sp)
call salloc (sx, npts, TY_REAL)
call salloc (pn, npts, TY_REAL)
call salloc (pnm1, npts, TY_REAL)
call salloc (pnm2, npts, TY_REAL)
# a higher order polynomial
call amovkr (real(1.0), Memr[pnm2], npts)
call altar (x, Memr[sx], npts, k1, k2)
call amovr (Memr[sx], Memr[pnm1], npts)
call amulkr (Memr[sx], real(2.0), Memr[sx], npts)
do i = 3, order {
call amulr (Memr[sx], Memr[pnm1], Memr[pn], npts)
call asubr (Memr[pn], Memr[pnm2], Memr[pn], npts)
if (i < order) {
call amovr (Memr[pnm1], Memr[pnm2], npts)
call amovr (Memr[pn], Memr[pnm1], npts)
}
call amulkr (Memr[pn], coeff[i], Memr[pn], npts)
call aaddr (yfit, Memr[pn], yfit, npts)
}
# free temporary space
call sfree (sp)
end
# CV_EVLEG -- Procedure to evaluate a Legendre polynomial assuming that
# the coefficients have been calculated.
procedure rcv_evleg (coeff, x, yfit, npts, order, k1, k2)
real coeff[ARB] # 1D array of coefficients
real x[npts] # x values of points to be evaluated
real yfit[npts] # the fitted points
int npts # number of data points
int order # order of the polynomial, 1 = constant
real k1, k2 # normalizing constants
int i
pointer sx, pn, pnm1, pnm2
pointer sp
real ri, ri1, ri2
begin
# fit a constant
if (order == 1) {
call amovkr (coeff[1], yfit, npts)
return
}
# fit a linear function
ri1 = k2 * coeff[2]
ri2 = ri1 * k1 + coeff[1]
call altmr (x, yfit, npts, ri1, ri2)
if (order == 2)
return
# allocate temporary space
call smark (sp)
call salloc (sx, npts, TY_REAL)
call salloc (pn, npts, TY_REAL)
call salloc (pnm1, npts, TY_REAL)
call salloc (pnm2, npts, TY_REAL)
# a higher order polynomial
call amovkr (real(1.0), Memr[pnm2], npts)
call altar (x, Memr[sx], npts, k1, k2)
call amovr (Memr[sx], Memr[pnm1], npts)
do i = 3, order {
ri = i
ri1 = (real(2.0) * ri - real(3.0)) / (ri - real(1.0))
ri2 = - (ri - real(2.0)) / (ri - real(1.0))
call amulr (Memr[sx], Memr[pnm1], Memr[pn], npts)
call awsur (Memr[pn], Memr[pnm2], Memr[pn], npts, ri1, ri2)
if (i < order) {
call amovr (Memr[pnm1], Memr[pnm2], npts)
call amovr (Memr[pn], Memr[pnm1], npts)
}
call amulkr (Memr[pn], coeff[i], Memr[pn], npts)
call aaddr (yfit, Memr[pn], yfit, npts)
}
# free temporary space
call sfree (sp)
end
# CV_EVSPLINE1 -- Procedure to evaluate a piecewise linear spline function
# assuming that the coefficients have been calculated.
procedure rcv_evspline1 (coeff, x, yfit, npts, npieces, k1, k2)
real coeff[ARB] # array of coefficients
real x[npts] # array of x values
real yfit[npts] # array of fitted values
int npts # number of data points
int npieces # number of fitted points minus 1
real k1, k2 # normalizing constants
int j
pointer sx, tx, azindex, aindex, index
pointer sp
begin
# allocate the required space
call smark (sp)
call salloc (sx, npts, TY_REAL)
call salloc (tx, npts, TY_REAL)
call salloc (index, npts, TY_INT)
# calculate the index of the first non-zero coefficient
# for each point
call altar (x, Memr[sx], npts, k1, k2)
call achtri (Memr[sx], Memi[index], npts)
call aminki (Memi[index], npieces, Memi[index], npts)
# transform sx to range 0 to 1
azindex = sx - 1
do j = 1, npts {
aindex = azindex + j
Memr[aindex] = max (real(0.0), min (real(1.0), Memr[aindex] -
Memi[index+j-1]))
Memr[tx+j-1] = max (real(0.0), min (real(1.0), real(1.0) -
Memr[aindex]))
}
# calculate yfit using the two non-zero basis function
do j = 1, npts
yfit[j] = Memr[tx+j-1] * coeff[1+Memi[index+j-1]] +
Memr[sx+j-1] * coeff[2+Memi[index+j-1]]
# free space
call sfree (sp)
end
# CV_EVSPLINE3 -- Procedure to evaluate the cubic spline assuming that
# the coefficients of the fit are known.
procedure rcv_evspline3 (coeff, x, yfit, npts, npieces, k1, k2)
real coeff[ARB] # array of coeffcients
real x[npts] # array of x values
real yfit[npts] # array of fitted values
int npts # number of data points
int npieces # number of polynomial pieces
real k1, k2 # normalizing constants
int i, j
pointer sx, tx, temp, index, sp
begin
# allocate the required space
call smark (sp)
call salloc (sx, npts, TY_REAL)
call salloc (tx, npts, TY_REAL)
call salloc (temp, npts, TY_REAL)
call salloc (index, npts, TY_INT)
# calculate to which coefficients the x values contribute to
call altar (x, Memr[sx], npts, k1, k2)
call achtri (Memr[sx], Memi[index], npts)
call aminki (Memi[index], npieces, Memi[index], npts)
# transform sx to range 0 to 1
do j = 1, npts {
Memr[sx+j-1] = max (real(0.0), min (real(1.0), Memr[sx+j-1] -
Memi[index+j-1]))
Memr[tx+j-1] = max (real(0.0), min (real(1.0), real(1.0) -
Memr[sx+j-1]))
}
# calculate yfit using the four non-zero basis function
call aclrr (yfit, npts)
do i = 1, 4 {
switch (i) {
case 1:
call apowkr (Memr[tx], 3, Memr[temp], npts)
case 2:
do j = 1, npts {
Memr[temp+j-1] = real(1.0) + Memr[tx+j-1] *
(real(3.0) + Memr[tx+j-1] * (real(3.0) -
real(3.0) * Memr[tx+j-1]))
}
case 3:
do j = 1, npts {
Memr[temp+j-1] = real(1.0) + Memr[sx+j-1] *
(real(3.0) + Memr[sx+j-1] * (real(3.0) -
real(3.0) * Memr[sx+j-1]))
}
case 4:
call apowkr (Memr[sx], 3, Memr[temp], npts)
}
do j = 1, npts
Memr[temp+j-1] = Memr[temp+j-1] * coeff[i+Memi[index+j-1]]
call aaddr (yfit, Memr[temp], yfit, npts)
}
# free space
call sfree (sp)
end
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