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authorJoseph Hunkeler <jhunkeler@gmail.com>2015-07-08 20:46:52 -0400
committerJoseph Hunkeler <jhunkeler@gmail.com>2015-07-08 20:46:52 -0400
commitfa080de7afc95aa1c19a6e6fc0e0708ced2eadc4 (patch)
treebdda434976bc09c864f2e4fa6f16ba1952b1e555 /math/curfit/cv_beval.gx
downloadiraf-linux-fa080de7afc95aa1c19a6e6fc0e0708ced2eadc4.tar.gz
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+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# CV_BCHEB -- Procedure to evaluate all the non-zero Chebyshev functions for
+# a set of points and given order.
+
+procedure $tcv_bcheb (x, npts, order, k1, k2, basis)
+
+PIXEL x[npts] # array of data points
+int npts # number of points
+int order # order of polynomial, order = 1, constant
+PIXEL k1, k2 # normalizing constants
+PIXEL basis[ARB] # basis functions
+
+int k, bptr
+
+begin
+ bptr = 1
+ do k = 1, order {
+ if (k == 1)
+ call amovk$t (PIXEL(1.0), basis, npts)
+ else if (k == 2)
+ call alta$t (x, basis[bptr], npts, k1, k2)
+ else {
+ call amul$t (basis[1+npts], basis[bptr-npts], basis[bptr],
+ npts)
+ call amulk$t (basis[bptr], PIXEL(2.0), basis[bptr], npts)
+ call asub$t (basis[bptr], basis[bptr-2*npts], basis[bptr], npts)
+ }
+ bptr = bptr + npts
+ }
+end
+
+
+# CV_BLEG -- Procedure to evaluate all the non zero Legendre function
+# for a given order and set of points.
+
+procedure $tcv_bleg (x, npts, order, k1, k2, basis)
+
+PIXEL x[npts] # number of data points
+int npts # number of points
+int order # order of polynomial, 1 is a constant
+PIXEL k1, k2 # normalizing constants
+PIXEL basis[ARB] # array of basis functions
+
+int k, bptr
+PIXEL ri, ri1, ri2
+
+begin
+ bptr = 1
+ do k = 1, order {
+ if (k == 1)
+ call amovk$t (PIXEL(1.0), basis, npts)
+ else if (k == 2)
+ call alta$t (x, basis[bptr], npts, k1, k2)
+ else {
+ ri = k
+ ri1 = (PIXEL(2.0) * ri - PIXEL(3.0)) / (ri - PIXEL(1.0))
+ ri2 = - (ri - PIXEL(2.0)) / (ri - PIXEL(1.0))
+ call amul$t (basis[1+npts], basis[bptr-npts], basis[bptr],
+ npts)
+ call awsu$t (basis[bptr], basis[bptr-2*npts],
+ basis[bptr], npts, ri1, ri2)
+ }
+ bptr = bptr + npts
+ }
+end
+
+
+# CV_BSPLINE1 -- Evaluate all the non-zero spline1 functions for a set
+# of points.
+
+procedure $tcv_bspline1 (x, npts, npieces, k1, k2, basis, left)
+
+PIXEL x[npts] # set of data points
+int npts # number of points
+int npieces # number of polynomial pieces minus 1
+PIXEL k1, k2 # normalizing constants
+PIXEL basis[ARB] # basis functions
+int left[ARB] # indices of the appropriate spline functions
+
+int k
+
+begin
+ call alta$t (x, basis[1+npts], npts, k1, k2)
+ call acht$ti (basis[1+npts], left, npts)
+ call aminki (left, npieces, left, npts)
+
+ do k = 1, npts {
+ basis[npts+k] = max (PIXEL(0.0), min (PIXEL(1.0),
+ basis[npts+k] - left[k]))
+ basis[k] = max (PIXEL(0.0), min (PIXEL(1.0), PIXEL(1.0) -
+ basis[npts+k]))
+ }
+end
+
+
+# CV_BSPLINE3 -- Procedure to evaluate all the non-zero basis functions
+# for a cubic spline.
+
+procedure $tcv_bspline3 (x, npts, npieces, k1, k2, basis, left)
+
+PIXEL x[npts] # array of data points
+int npts # number of data points
+int npieces # number of polynomial pieces minus 1
+PIXEL k1, k2 # normalizing constants
+PIXEL basis[ARB] # array of basis functions
+int left[ARB] # array of indices for first non-zero spline
+
+int i
+pointer sp, sx, tx
+PIXEL dsx, dtx
+
+begin
+ # allocate space
+ call smark (sp)
+ call salloc (sx, npts, TY_PIXEL)
+ call salloc (tx, npts, TY_PIXEL)
+
+ # calculate the index of the first non-zero coeff
+ call alta$t (x, Mem$t[sx], npts, k1, k2)
+ call acht$ti (Mem$t[sx], left, npts)
+ call aminki (left, npieces, left, npts)
+
+ do i = 1, npts {
+ Mem$t[sx+i-1] = max (PIXEL(0.0), min (PIXEL(1.0),
+ Mem$t[sx+i-1] - left[i]))
+ Mem$t[tx+i-1] = max (PIXEL(0.0), min (PIXEL(1.0), PIXEL(1.0) -
+ Mem$t[sx+i-1]))
+ }
+
+ # calculate the basis function
+ #call apowk$t (Mem$t[tx], 3, basis, npts)
+ do i = 1, npts {
+ dsx = Mem$t[sx+i-1]
+ dtx = Mem$t[tx+i-1]
+ basis[i] = dtx * dtx * dtx
+ basis[npts+i] = PIXEL(1.0) + dtx * (PIXEL(3.0) + dtx *
+ (PIXEL(3.0) - PIXEL(3.0) * dtx))
+ basis[2*npts+i] = PIXEL(1.0) + dsx * (PIXEL(3.0) + dsx *
+ (PIXEL(3.0) - PIXEL(3.0) * dsx))
+ basis[3*npts+i] = dsx * dsx * dsx
+ }
+ #call apowk$t (Mem$t[sx], 3, basis[1+3*npts], npts)
+
+ # release space
+ call sfree (sp)
+end