Source Code for Module pod.util

  1  """ 
  2  Operations on matrices and various tools. 
  3   
  4  @author: Christophe Alexandre <ch.alexandre at bluewin dot ch> 
  5   
  6  @license: 
  7  Copyright(C) 2010 Christophe Alexandre 
  8   
  9  This program is free software: you can redistribute it and/or modify 
 10  it under the terms of the GNU Lesser General Public License as published by 
 11  the Free Software Foundation, either version 3 of the License, or 
 12  (at your option) any later version. 
 13   
 14  This program is distributed in the hope that it will be useful, 
 15  but WITHOUT ANY WARRANTY; without even the implied warranty of 
 16  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the 
 17  GNU General Public License for more details. 
 18   
 19  You should have received a copy of the GNU Lesser General Public License 
 20  along with this program.  If not, see <http://www.gnu.org/licenses/lgpl.txt>. 
 21  """ 
 22   
 23  import math 
 24  import logging 
 25   
 26 -class NullHandler(logging.Handler): 
 27    """ 
 28    Null logging in order to avoid warning messages in client applications. 
 29    """ 
 30 -  def emit(self, record): 
 31      pass 
 32     
 33  _h = NullHandler() 
 34  _logger = logging.getLogger('util') 
 35  _logger.addHandler(_h) 
 36   
 37 -def numbering(v): 
 38    """ Maps every element of to its position.""" 
 39    return zip(range(len(v)), v) 
 40   
 41 -def prod_scalar(v1, v2): 
 42    assert len(v1) == len(v2), 'input vectors must be of the same size' 
 43    prod = map(lambda x: x[0] * x[1], zip(v1, v2)) 
 44    return sum(prod) 
 45   
 46 -def norm(v): 
 47    return math.sqrt(prod_scalar(v, v)) 
 48   
 49 -def gauss_jordan(m, eps=1E-10): 
 50    """ 
 51    Puts given matrix (2D array) into the Reduced Row Echelon Form. 
 52     
 53    NOTE: make sure all the matrix items support fractions! Int matrix will NOT work! 
 54    Written by Jarno Elonen in April 2005, released into Public Domain 
 55        
 56    @return: True if successful, False if 'm' is singular. 
 57    """ 
 58    (h, w) = (len(m), len(m[0])) 
 59    for y in range(0,h): 
 60      maxrow = y 
 61      for y2 in range(y+1, h):    # Find max pivot 
 62        if abs(m[y2][y]) > abs(m[maxrow][y]): 
 63          maxrow = y2 
 64      (m[y], m[maxrow]) = (m[maxrow], m[y]) 
 65      if abs(m[y][y]) <= eps:     # Singular? 
 66        return False 
 67      for y2 in range(y+1, h):    # Eliminate column y 
 68        c = m[y2][y] / m[y][y] 
 69        for x in range(y, w): 
 70          m[y2][x] -= m[y][x] * c 
 71    for y in range(h-1, 0-1, -1): # Backsubstitute 
 72      c  = m[y][y] 
 73      for y2 in range(0,y): 
 74        for x in range(w-1, y-1, -1): 
 75          m[y2][x] -=  m[y][x] * m[y2][y] / c 
 76      m[y][y] /= c 
 77      for x in range(h, w):       # Normalize row y 
 78        m[y][x] /= c 
 79    return True 
 80   
 81  # Auxiliary functions contribution by Eric Atienza 
 82   
 83 -def system_solve(M, b): 
 84    """ 
 85    solves M*x = b 
 86    @param M: a matrix in the form of a list of list 
 87    @param b: a vector in the form of a simple list of scalars 
 88    @return: vector x so that M*x = b 
 89    """ 
 90    m2 = [row[:]+[right] for row,right in zip(M,b) ] 
 91    return [row[-1] for row in m2] if gauss_jordan(m2) else None 
 92   
 93 -def mat_inverse(M): 
 94    """ 
 95    @return: the inverse of the matrix M 
 96    """ 
 97    #clone the matrix and append the identity matrix 
 98    # [int(i==j) for j in range_M] is nothing but the i(th row of the identity matrix 
 99    m2 = [row[:]+[int(i==j) for j in range(len(M) )] for i,row in enumerate(M) ] 
100    # extract the appended matrix (kind of m2[m:,...] 
101    return [row[len(M[0]):] for row in m2] if gauss_jordan(m2) else None 
102   
103 -def zeros(size, zero=0): 
104    """ 
105    @param size: a tuple containing dimensions of the matrix 
106    @param zero: the value to use to fill the matrix (zero by default) 
107    @return: matrix of dimension size 
108    """ 
109    return [zeros(s[1:] ) for i in range(s[0] ) ] if not len(s) else zero 
110