Python matrix instances

Python matrix instances

This example describes the matrix class implemented by Python. We will share this with you for your reference. The details are as follows:

Scientific Computing is inseparable from matrix calculation. Of course, python already has a very good ready-made Library: numpy (simple installation and use of numpy can refer to http://www.bkjia.com/article/66236.htm ).

I am writing this matrix class, instead of recreating a wheel, just as an exercise, recorded here.

Note: The functions of this class have not been fully implemented yet. Please gradually improve them.

All code:

Import copyclass Matrix: ''' Matrix class ''' def _ init _ (self, row, column, fill = 0.0): self. shape = (row, column) self. row = row self. column = column self. _ matrix = [[fill] * column for I in range (row)] # Return the value of the element m (I, j): m [I, j] def _ getitem _ (self, index): if isinstance (index, int): return self. _ matrix [index-1] elif isinstance (index, tuple): return self. _ matrix [index [0]-1] [index [1]-1] # set the value of element m (I, j) to s: m [I, J] = s def _ setitem _ (self, index, value): if isinstance (index, int): self. _ matrix [index-1] = copy. deepcopy (value) elif isinstance (index, tuple): self. _ matrix [index [0]-1] [index [1]-1] = value def _ eq _ (self, N ): '''equal ''' # A = B assert isinstance (N, Matrix), "Type mismatch, cannot compare" return N. shape = self. shape # Compare dimension, which can be changed to another def _ add _ (self, N): '''add''' # A + B assert N. shape = self. shape, "dimensions do not match, cannot be added" M = Matrix (self. row, self. column) for r in range (self. row): for c in range (self. column): M [r, c] = self [r, c] + N [r, c] return M def _ sub _ (self, N ): ''' subtraction ''' # A-B assert N. shape = self. shape, "dimensions do not match, cannot subtract" M = Matrix (self. row, self. column) for r in range (self. row): for c in range (self. column): M [r, c] = self [r, c]-N [r, c] return M def _ mul _ (self, N ): '''multiplication ''' # A * B (or: A * 2.0) if isinst Ance (N, int) or isinstance (N, float): M = Matrix (self. row, self. column) for r in range (self. row): for c in range (self. column): M [r, c] = self [r, c] * N else: assert N. row = self. column, "dimension does not match, cannot be multiplied" M = Matrix (self. row, N. column) for r in range (self. row): for c in range (N. column): sum = 0 for k in range (self. column): sum + = self [r, k] * N [k, r] M [r, c] = sum return M def _ div _ (self, N): ''' division '''# A/B pass def _ pow _ (self, k): ''' multiplication ''' # A ** k assert self. row = self. column, "not a square matrix, not a square" M = copy. deepcopy (self) for I in range (k): M = M * self return M def rank (self): ''' rank of the matrix ''' pass def trace (self): '''matrix trace ''' pass def adjoint (self): ''' adjoint matrix ''' pass def invert (self ): '''inverse matrix ''' assert self. row = self. column, "not a square Matrix" M = Matrix (self. row, self. column * 2) I = self. identity () # unit matrix I. show ()### ######################### Splice for r in range (1, M. row + 1): temp = self [r] temp. extend (I [r]) M [r] = copy. deepcopy (temp) M. show () ############################ transform primary rows for r in range (1, m. row + 1): # if the first element of the row (M [r, r]) is 0, the first element of the current column is switched downward. if M [r, r] = 0: for rr in range (r + 1, M. row + 1): if M [rr, r]! = 0: M [r], M [rr] = M [rr], M [r] # exchange two rows of break assert M [r, r]! = 0, 'matrix irreversible '# convert the first element (M [r, r]) of the row to 1 temp = M [r, r] # cache for c in range (r, M. column + 1): M [r, c]/= temp print ("M [{0}, {1}]/= {2 }". format (r, c, temp) M. show () # All elements in this column and below are converted to 0 for rr in range (1, M. row + 1): temp = M [rr, r] # cache for c in range (r, M. column + 1): if rr = r: continue M [rr, c]-= temp * M [r, c] print ("M [{0 }, {1}]-= {2} * M [{3}, {1}] ". format (rr, c, temp, r) M. show () # truncation inverse Matrix N = Matrix (self. row, self. column) for r in range (1, self. row + 1): N [r] = M [r] [self. row:] return N def jieti (self): ''' the row simplification step matrix ''' pass def transpose (self ): '''transpose ''' M = Matrix (self. column, self. row) for r in range (self. column): for c in range (self. row): M [r, c] = self [c, r] return M def cofactor (self, row, column): ''''algebraic remainder formula (used to expand the determinant) '''assert self. row = self. column, "not a square matrix, cannot calculate the algebra remainder" assert self. row> = 3, "at least three X three-level phalanx" assert row <= self. row and column <= self. column, "subscript out of range" M = Matrix (self. column-1, self. row-1) for r in range (self. row): if r = row: continue for c in range (self. column): if c = column: continue rr = R-1 if r> row else r cc = C-1 if c> column else c M [rr, cc] = self [r, c] return M def det (self): ''' determinant ''' assert self. row = self. column, "non-determinant, cannot calculate" if self. shape = (0.0): return self [] * self []-self [] * self [] else: sum = for c in range (self. column + 1): sum + = (-1) ** (c + 1) * self [1, c] * self. cofactor (1, c ). det () return sum def zeros (self): '''all zero Matrices ''' M = Matrix (self. column, self. row, fill = 0.0) return M def ones (self): '''all 1 matrices ''' M = Matrix (self. column, self. row, fill = 1.0) return M def identity (self): ''' unit matrix ''' assert self. row = self. column, "non-n * n Matrix, non-unit Matrix" M = Matrix (self. column, self. row) for r in range (self. row): for c in range (self. column): M [r, c] = 1.0 if r = c else 0.0 return M def show (self ): '''print matrix ''' for r in range (self. row): for c in range (self. column): print (self [r + 1, c + 1], end = '') print () if _ name _ = '_ main __': m = Matrix (3,3, fill = 2.0) n = Matrix (3,3, fill = 3.5) m [1] = [1 ., 1 ., 2.] m [2] = [1 ., 2 ., 1.] m [3] = [2 ., 1 ., 1.] p = m * n q = m * 2.1 r = m ** 3 # r. show () # q. show () # print (p [1, 1]) # r = m. invert () # s = r * m print () m. show () print () # r. show () print () # s. show () print (m. det ())