Created
July 18, 2014 09:23
-
-
Save wpoely86/d3c0a6e9760f381684ee to your computer and use it in GitHub Desktop.
Generates Clebsch-Gordan coefficients and outputs it to html
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| #!/usr/bin/env python3 | |
| """ | |
| Generates all Clebsh Gordan coefficients starting from a given j1 and j2 and | |
| outputs a html file. How to use: | |
| ./Clebsch-Gordan.py 0.5 0.5 > output.html | |
| Ward Poelmans <[email protected]> (2014) | |
| """ | |
| import sys | |
| import numpy as np | |
| import scipy.misc as sc | |
| import math | |
| import fractions | |
| def factorial(n): | |
| if n < 0: | |
| return -100000000000 | |
| else: | |
| return math.factorial(n) | |
| # return sc.factorial(n, exact=False) | |
| def clebsh(j1,j2,j,m): | |
| z = 0 | |
| a = 0.0 | |
| b = 0.0 | |
| c = 0.0 | |
| l = "" | |
| for m1 in np.arange(-j1-1,(j1+1)): | |
| for m2 in np.arange(-j2-1,(j2+1)): | |
| #These are just some conditions which need to give zero. | |
| if (m1 + m2) != m: | |
| d = 0 | |
| elif (j1 - j2 - m)%1 != 0.0: | |
| d = 0 | |
| elif (j1 - j2 + m)%1 != 0.0: | |
| d = 0 | |
| else: | |
| c = 0.0 | |
| z = 0 | |
| #This is the algorithm itself, Not very pretty, but that is what it is. | |
| at = ((factorial(j1+j2-j)*factorial(j1-j2+j)*factorial(-j1+j2+j))) | |
| an = (factorial(j1+j2+j+1.0)) #**.5 | |
| a = math.sqrt(at/an) | |
| b = (factorial(j1+m1)*factorial(j1-m1)*factorial(j2+m2)*factorial(j2-m2)*factorial(j-m)*factorial(j+m)) #**.5 | |
| while z<(j1-m1+3): | |
| ct = ((-1.0)**(z+j1-j2+m)) | |
| cn = (factorial(z)*factorial(j1+j2-j-z)*factorial(j1-m1-z)*factorial(j2+m2-z)*factorial(j-j2+m1+z)*factorial(j-j1-m2+z)) | |
| c += ct/cn; | |
| z += 1 | |
| pre = ((-1.0)**(j1-j2+m)) | |
| presqrt = (2.0*j+1.0) | |
| d = pre*math.sqrt(presqrt)*math.sqrt(at/an)*math.sqrt(b)*c | |
| if abs(d)> .0001: | |
| breuk = fractions.Fraction(int(at*b*presqrt*c*c),int(an)).limit_denominator(10000) | |
| pre_str = "-" if pre < 0 else "" | |
| l += "\n<tr><td><math><mn>%s</mn></math></td><td><math><mn>%s</mn></math></td><td><math><mn>%s</mn> <msqrt><mfrac><mn>%s</mn><mn>%s</mn></mfrac></msqrt></math></td></tr>" % (m1,m2,pre_str,breuk.numerator,breuk.denominator) | |
| return l | |
| if len(sys.argv) != 3: | |
| print("Usage: %s j1 j2" % sys.argv[0]) | |
| sys.exit(0) | |
| j1 = float(sys.argv[1]) | |
| j2 = float(sys.argv[2]) | |
| print("<html>\n<title>Clebsch Gordan</title>\n<body>\n<div>\n") | |
| for j in np.arange(abs(j1-j2),j1+j2+1): | |
| for m in np.arange(0,j+1): | |
| print("<math><msub><mi>j</mi><mn>1</mn></msub>=<mn>%s</mn></math> <math><msub><mi>j</mi><mn>2</mn></msub>=<mn>%s</mn></math> <math>j=<mn>%s</mn></math> <math>m=<mn>%s</mn></math><br/>\n" % (fractions.Fraction(j1), fractions.Fraction(j2), fractions.Fraction(j), fractions.Fraction(m))) | |
| print("<table border=1>") | |
| print("<thead><tr> <th><math><msub><mi>m</mi><mn>1</mn></msub></math></th> <th><math><msub><mi>m</mi><mn>2</mn></msub></math></th> </tr></thead>\n") | |
| print("%s" % clebsh(j1,j2,j,m)) | |
| print("</table><br/><br/>\n") | |
| print("</div>\n</body>\n</html>") |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment