init

scratch/legendre.sage

@@ -0,0 +1,90 @@
+#!/usr/bin/sage
+
+# Schmidt Quasi-Normalized Legendre Functions for Spherical Harmonics
+
+x = var('x');
+
+def polypart(n,m):
+    pol = (x^2-1)^n
+    for I in range(1,n+1):
+        pol = diff(pol,x)
+    for I in range(1,m+1):
+        pol = diff(pol,x)
+    return pol
+
+def normpart(n,m):
+    if(m==0):
+        nrm = 1/2^n/factorial(n)
+    else:
+        nrm = (1/2^n/factorial(n)) * sqrt(2*factorial(n-m)/factorial(n+m))
+    return nrm
+
+NN = 20
+
+
+lns = []
+coefs = []
+nmaxcoefs = 0
+for I in range(0,NN+1):
+    for J in range(0,I+1):
+        pol = polypart(I,J)
+        nrm = normpart(I,J)
+        pol2 = expand(pol)
+        p2c = pol2.coefficients(sparse=False)
+
+        pol3 = nrm*pol2
+        p3c = pol3.coefficients(sparse=False)
+        for K in range(0,len(p3c)):
+            p3c[K] = p3c[K].n()
+
+        coefs.append(p3c)
+        if(nmaxcoefs<len(p3c)):
+            nmaxcoefs = len(p3c)
+        
+        #print("{:d}\t{:d}\t{}\t\t{}".format(I,J,nrm,p2c))
+        
+        s = ""
+        s = s + "{:d}\t{:d}\t".format(I,J)
+        for K in range(0,len(p3c)):
+            nn = p3c[K]
+            if(abs(nn)<1E-14):
+                nn = 0
+            s = s + "{:1.8g}\t".format(nn)
+        s = s + "\n"
+        print(s)
+        lns.append(s)
+
+##C style coefficient output
+
+fout = "c_legendrecoefs2.c"
+fp = open(fout,"w+")
+
+
+pref1 = "static const int amslegendre_ndegree = {:d};\n".format(NN)
+pref2 = "static const int amslegendre_maxporder = {:d};\n".format(nmaxcoefs-1)
+pref = pref1 + pref2 + "static const float amslegendrecoefs[] = { \n"
+
+for I in range(0,NN+1):
+    for J in range(0,I+1):
+        ind = I*(I+1)/2+J
+        for K in range(0,nmaxcoefs):
+            if(K<len(coefs[ind])):
+                nn = coefs[ind][K]
+                if(abs(nn)<1E-14):
+                    nn = 0
+            else:
+                nn = 0
+            
+            if(ind<len(coefs)-1):
+                if(K<nmaxcoefs-1):
+                    pref = pref + "{:1.8g},".format(nn)
+                else:
+                    pref = pref + "{:1.8g},\n".format(nn)
+            else:
+                if(K<nmaxcoefs-1):
+                    pref = pref + "{:1.8g},".format(nn)
+                else:
+                    pref = pref + "{:1.8g}".format(nn) + "\n};\n\n"
+
+fp.writelines(pref)
+fp.close()