matrix-code.py (original) (raw)

""" a numerically-inclined student asked for examples related to matrix processing (in the core language, not using NumPy which has better built-in support for vector and matrix processing); the following is a quick tour through some simple matrix code, showing equivalents coded in for loops and list comprehensions; requires Python 2.7 for some tests, one line works in 3.X only; """

######################################################################################

Vectors: 1D lists (added mar-12-11)

######################################################################################

L = [1, 2, 3, 4, 5, 6] M = [7, 8, 9, 10, 11, 12]

#-------------------------------------------------------------

[L ** 2]: print squares of all in one vector: 1 4 9 16 25 36

#-------------------------------------------------------------

for i in range(len(L)): print(L[i] ** 2)

for x in L: # simpler, probably faster print(x ** 2)

---3.X only---

list( map(print, (x ** 2 for x in L)) ) # 3.X print(), map() generator

#------------------------------------------------------------

[N = L ** 2]: make new result vector: [1, 4, 9, 16, 25, 36]

#------------------------------------------------------------

N = [x ** 2 for x in L] print(N)

N = [] for x in L: N.append(x ** 2) print(N)

N = list(map((lambda x: x ** 2), L)) # list() required in 3.X only print(N)

other: generators produce results on demand

G = (x ** 2 for x in L) print(list(G)) # list() requests results

def gensquares(L): for x in L: yield x ** 2 print(list(gensquares(L))) # list() requests results

other: set and dict comprehensions (3.X, 2.7)

print({x ** 2 for x in L}) # set: {1, 36, 9, 16, 25, 4} in 3.X, set(...) in 2.X

print({x: x ** 2 for x in L}) # dict: {1: 1, 2: 4, 3: 9, 4: 16, 5: 25, 6: 36}

#--------------------------------------------------------------

[L + M]: print pairwise sums of two vectors: 8 10 12 14 16 18

#--------------------------------------------------------------

for i in range(len(L)): print(L[i] + M[i])

for (x, y) in zip(L, M): print(x + y)

#----------------------------------------------------------------------

[N = L + M]: create new pairwise sums vector: [8, 10, 12, 14, 16, 18]

#----------------------------------------------------------------------

N = [L[i] + M[i] for i in range(len(L))] print(N)

N = [x + y for (x, y) in zip(L, M)] print(N)

N = [] for i in range(len(L)): N.append(L[i] + M[i]) print(N)

N = [] for (x, y) in zip(L, M): N.append(x + y) print(N)

other ops

print([x * y for (x, y) in zip(L, M)]) # [7, 16, 27, 40, 55, 72]

print([y / x for (x, y) in zip(L, M)]) # [7.0, 4.0, 3.0, 2.5, 2.2, 2.0] (3.X)

print([y // x for (x, y) in zip(L, M)]) # [7, 4, 3, 2, 2, 2]

print(list( map((lambda x, y: x * y), L, M) )) # [7, 16, 27, 40, 55, 72]

######################################################################################

Matrixes: 2D lists (original code)

######################################################################################

def init(): global M, N # reset state for new tests

M = [[1, 2, 3],
     [4, 5, 6],
     [7, 8, 9]]

N = [[10, 20, 30],
     [40, 50, 60],
     [70, 80, 90]]

#---------------------------------------------------------------

[M ** 2]: print squares of one matrix: 1 4 9 16 25 36 49 64 81

#---------------------------------------------------------------

init() for row in M: for col in row: print(col ** 2)

for i in range(3): for j in range(3): print(M[i][j] ** 2)

#-----------------------------------------------------------------------------

[M **= 2]: matrix squares, in-place: [[1, 4, 9], [16, 25, 36], [49, 64, 81]]

#-----------------------------------------------------------------------------

init() for i in range(3): for j in range(3): M[i][j] **= 2 print(M)

init() for i in range(len(M)): for j in range(len(M[i])): M[i][j] **= 2 print(M)

similar, but make new 1D vector: [1, 4, 9, 16, 25, 36, 49, 64, 81]

init() print( [col ** 2 for row in M for col in row] )

print( [M[i][j] ** 2 for i in range(len(M)) for j in range(len(M[i]))] )

#--------------------------------------------------------------------------------

[X = M ** 2]: new 2D matrix of squares: [[1, 4, 9], [16, 25, 36], [49, 64, 81]]

#--------------------------------------------------------------------------------

X = [] for i in range(len(M)): row = [] for j in range(len(M[i])): row.append(M[i][j] ** 2) X.append(row) print(X)

X = [] for row in M: tmp = [] for col in row: tmp.append(col ** 2) X.append(tmp) print(X)

nest comprehensions for 2D data

print( [[M[i][j] ** 2 for j in range(len(M[i]))] for i in range(len(M))] )

print( [[col ** 2 for col in row] for row in M] )

#-------------------------------------------------------------------------------------

[X = M + N]: new matrix of pairwise sums: [[11, 22, 33], [44, 55, 66], [77, 88, 99]]

#-------------------------------------------------------------------------------------

X = [] for i in range(len(M)): row = [] for j in range(len(M[i])): row.append(M[i][j] + N[i][j]) X.append(row) print(X)

X = [] for (row1, row2) in zip(M, N): tmp = [] for (col1, col2) in zip(row1, row2): tmp.append(col1 + col2) X.append(tmp) print(X)

print( [[M[i][j] + N[i][j] for j in range(3)] for i in range(3)] )

print( [[col1 + col2 for (col1, col2) in zip(row1, row2)] for (row1, row2) in zip(M, N)] )