Initial commit

1 files changed, 67 insertions, 0 deletions

diff --git a/math/interp/iif_spline.x b/math/interp/iif_spline.x
new file mode 100644
index 00000000..a8574e0b
--- /dev/null
+++ b/math/interp/iif_spline.x
@@ -0,0 +1,67 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+.help
+		procedure iif_spline
+
+     This fits uniformly spaced data with a cubic spline.  The spline is
+given as basis-spline coefficients that replace the data values.
+
+Storage at call time:
+
+b[1] = second derivative at x = 1
+b[2] = first data point y[1]
+b[3] = y[2]
+.
+.
+.
+b[n+1] = y[n]
+b[n+2] = second derivative at x = n
+
+Storage after call:
+
+b[1] ... b[n+2] = the n + 2 basis-spline coefficients for the basis splines
+    as defined in P. M. Prenter's book Splines and Variational Methods,
+    Wiley, 1975.
+
+.endhelp
+
+procedure iif_spline(b,d,n)
+
+real b[ARB]	# data in and also bspline coefficients out
+real d[ARB]     # needed for offdiagnol matrix elements
+int n           # number of data points
+
+int i
+
+begin
+    
+        d[1] = -2.
+        b[1] = b[1] / 6.
+
+        d[2] = 0.
+        b[2] = (b[2] - b[1]) / 6.
+
+        # Gaussian elimination - diagnol below main is made zero
+        # and main diagnol is made all 1's
+        do i = 3,n+1 {
+            d[i] = 1. / (4. - d[i-1])
+            b[i] = d[i] * (b[i] - b[i-1])
+        }
+
+        # Find last b spline coefficient first - overlay r.h.s.'s
+        b[n+2] = ( (d[n] + 2.) * b[n+1] - b[n] + b[n+2]/6.) / (1. +
+            d[n+1] * (d[n] + 2.))
+
+        # back substitute filling in coefficients for b splines
+        do i = n+1, 3, -1
+            b[i] = b[i]  - d[i] * b[i+1]
+
+        # note b[n+1] is evaluated correctly as can be checked 
+
+        # b[2] is already set since offdiagnol is 0.
+
+        # evaluate b[1]
+        b[1] = b[1] + 2. * b[2] - b[3]
+
+	return
+end