matrix.py

   1 import cgi
   2 from scipy import compress, transpose
   3 from scipy.linalg import svd, det
   4 import json
   5
   6 def calculate_nullspace(A, eps=1e-15):
   7     u, s, vh = svd(A)
   8     null_mask = (s <= eps)
   9     null_space = compress(null_mask, vh, axis=0)
  10     return transpose(null_space)
  11
  12 def calculate_eigenvalues(A, eps=1e-15):
  13     u, s, vh = svd(A)
  14     return s
  15
  16 def fail(start_response, message):
  17     start_response('400 Bad Request', [])
  18     return 'error: ' + message
  19
  20 def application(environ, start_response):
  21     parameters = cgi.parse_qs(environ.get('QUERY_STRING'))
  22
  23     if not 'matrix' in parameters or parameters['matrix'] == '':
  24         return fail(start_response, 'missing matrix')
  25     query_string = str(parameters['matrix'][0])
  26     matrix = query_string.splitlines()
  27     for index, row in enumerate(matrix):
  28         matrix[index] = row.split()
  29         if len(matrix[index]) != len(matrix[0]):
  30             return fail(start_response, 'ragged matrix')
  31         for index, n in enumerate(matrix[index]):
  32             try: float(n)
  33             except ValueError:
  34                 return fail(start_response, 'invalid matrix element')
  35
  36     while len(matrix) < len(matrix[0]):
  37         matrix.append([0]*len(matrix[0]))
  38
  39     nullspace = calculate_nullspace(matrix)
  40     if nullspace.max() != 0:
  41         nullspace = nullspace / nullspace.max()
  42
  43     eigenvalues = calculate_eigenvalues(matrix)
  44     determinant = det(matrix)
  45
  46     output = json.dumps({
  47         'nullspace' : str(nullspace),
  48         'eigenvalues' : str(eigenvalues),
  49         'determinant' : str(determinant)
  50         })
  51
  52     output_len = sum(len(line) for line in output)
  53     start_response('200 OK', [('Content-type', 'application/json'),
  54                               ('Content-Length', str(output_len))])
  55     return output