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# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
# GS_DPOL -- Procedure to evaluate the polynomial derivative basis functions.
procedure rgs_dpol (x, npts, order, nder, k1, k2, basis)
real x[npts] # array of data points
int npts # number of points
int order # order of new polynomial, order = 1, constant
int nder # order of derivative, order = 0, no derivative
real k1, k2 # normalizing constants
real basis[ARB] # basis functions
int bptr, k, kk
real fac
begin
# Optimize for oth and first derivatives.
if (nder == 0) {
call rgs_bpol (x, npts, order, k1, k2, basis)
return
} else if (nder == 1) {
call rgs_bpol (x, npts, order, k1, k2, basis)
do k = 1, order {
call amulkr(basis[1+(k-1)*npts], real (k),
basis[1+(k-1)*npts], npts)
}
return
}
# Compute the polynomials.
bptr = 1
do k = 1, order {
if (k == 1)
call amovkr (real(1.0), basis, npts)
else if (k == 2)
call amovr (x, basis[bptr], npts)
else
call amulr (basis[bptr-npts], x, basis[bptr], npts)
bptr = bptr + npts
}
# Apply the derivative factor.
bptr = 1
do k = 1, order {
if (k == 1) {
fac = real(1.0)
do kk = 2, nder
fac = fac * real (kk)
} else {
fac = real(1.0)
do kk = k + nder - 1, k, -1
fac = fac * real(kk)
}
call amulkr (basis[bptr], fac, basis[bptr], npts)
bptr = bptr + npts
}
end
# GS_DCHEB -- Procedure to evaluate the chebyshev polynomial derivative
# basis functions using the usual recursion relation.
procedure rgs_dcheb (x, npts, order, nder, k1, k2, basis)
real x[npts] # array of data points
int npts # number of points
int order # order of polynomial, order = 1, constant
int nder # order of derivative, order = 0, no derivative
real k1, k2 # normalizing constants
real basis[ARB] # basis functions
int i, k
pointer fn, dfn, xnorm, bptr, fptr
real fac
begin
# Optimze the no derivatives case.
if (nder == 0) {
call rgs_bcheb (x, npts, order, k1, k2, basis)
return
}
# Allocate working space for the basis functions and derivatives.
call calloc (fn, npts * (order + nder), TY_REAL)
call calloc (dfn, npts * (order + nder), TY_REAL)
# Compute the normalized x values.
call malloc (xnorm, npts, TY_REAL)
call altar (x, Memr[xnorm], npts, k1, k2)
# Compute the current solution.
bptr = fn
do k = 1, order + nder {
if (k == 1)
call amovkr (real(1.0), Memr[bptr], npts)
else if (k == 2)
call amovr (Memr[xnorm], Memr[bptr], npts)
else {
call amulr (Memr[xnorm], Memr[bptr-npts], Memr[bptr], npts)
call amulkr (Memr[bptr], real(2.0), Memr[bptr], npts)
call asubr (Memr[bptr], Memr[bptr-2*npts], Memr[bptr], npts)
}
bptr = bptr + npts
}
# Compute the derivative basis functions.
do i = 1, nder {
# Compute the derivatives.
bptr = fn
fptr = dfn
do k = 1, order + nder {
if (k == 1)
call amovkr (real(0.0), Memr[fptr], npts)
else if (k == 2) {
if (i == 1)
call amovkr (real(1.0), Memr[fptr], npts)
else
call amovkr (real(0.0), Memr[fptr], npts)
} else {
call amulr (Memr[xnorm], Memr[fptr-npts], Memr[fptr],
npts)
call amulkr (Memr[fptr], real(2.0), Memr[fptr], npts)
call asubr (Memr[fptr], Memr[fptr-2*npts], Memr[fptr],
npts)
fac = real (2.0) * real (i)
call awsur (Memr[bptr-npts], Memr[fptr], Memr[fptr],
npts, fac, real(1.0))
}
bptr = bptr + npts
fptr = fptr + npts
}
# Make the derivatives the old solution
if (i < nder)
call amovr (Memr[dfn], Memr[fn], npts * (order + nder))
}
# Copy the solution into the basis functions.
call amovr (Memr[dfn+nder*npts], basis[1], order * npts)
call mfree (xnorm, TY_REAL)
call mfree (fn, TY_REAL)
call mfree (dfn, TY_REAL)
end
# GS_DLEG -- Procedure to evaluate the Legendre polynomial derivative basis
# functions using the usual recursion relation.
procedure rgs_dleg (x, npts, order, nder, k1, k2, basis)
real x[npts] # number of data points
int npts # number of points
int order # order of new polynomial, 1 is a constant
int nder # order of derivate, 0 is no derivative
real k1, k2 # normalizing constants
real basis[ARB] # array of basis functions
int i, k
pointer fn, dfn, xnorm, bptr, fptr
real ri, ri1, ri2, fac
begin
# Optimze the no derivatives case.
if (nder == 0) {
call rgs_bleg (x, npts, order, k1, k2, basis)
return
}
# Allocate working space for the basis functions and derivatives.
call calloc (fn, npts * (order + nder), TY_REAL)
call calloc (dfn, npts * (order + nder), TY_REAL)
# Compute the normalized x values.
call malloc (xnorm, npts, TY_REAL)
call altar (x, Memr[xnorm], npts, k1, k2)
# Compute the basis functions.
bptr = fn
do k = 1, order + nder {
if (k == 1)
call amovkr (real(1.0), Memr[bptr], npts)
else if (k == 2)
call amovr (Memr[xnorm], Memr[bptr], npts)
else {
ri = k
ri1 = (real(2.0) * ri - real(3.0)) / (ri - real(1.0))
ri2 = - (ri - real(2.0)) / (ri - real(1.0))
call amulr (Memr[xnorm], Memr[bptr-npts], Memr[bptr], npts)
call awsur (Memr[bptr], Memr[bptr-2*npts], Memr[bptr],
npts, ri1, ri2)
}
bptr = bptr + npts
}
# Compute the derivative basis functions.
do i = 1, nder {
# Compute the derivatives.
bptr = fn
fptr = dfn
do k = 1, order + nder {
if (k == 1)
call amovkr (real(0.0), Memr[fptr], npts)
else if (k == 2) {
if (i == 1)
call amovkr (real(1.0), Memr[fptr], npts)
else
call amovkr (real(0.0), Memr[fptr], npts)
} else {
ri = k
ri1 = (real(2.0) * ri - real(3.0)) / (ri - real(1.0))
ri2 = - (ri - real(2.0)) / (ri - real(1.0))
call amulr (Memr[xnorm], Memr[fptr-npts], Memr[fptr],
npts)
call awsur (Memr[fptr], Memr[fptr-2*npts], Memr[fptr],
npts, ri1, ri2)
fac = ri1 * real (i)
call awsur (Memr[bptr-npts], Memr[fptr], Memr[fptr],
npts, fac, real(1.0))
}
bptr = bptr + npts
fptr = fptr + npts
}
# Make the derivatives the old solution
if (i < nder)
call amovr (Memr[dfn], Memr[fn], npts * (order + nder))
}
# Copy the solution into the basis functions.
call amovr (Memr[dfn+nder*npts], basis[1], order * npts)
call mfree (xnorm, TY_REAL)
call mfree (fn, TY_REAL)
call mfree (dfn, TY_REAL)
end
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