def mul_matrix(m1:list, m2:list)->list:
'''
Input of this function is two 2d list.
Output is a 2d list. If the result is a number,
then return [[num]].
Assume both matrixs are well structured (row & col)
'''
if len(m1[0]) != len(m2): # verify valid multiplication
print("Invalid multiplication attempted.")
return None
nrow = len(m1) # row number of product
ncol = len(m2[0]) # col number of product
product = []
temp = []
s = 0
m2 = transpose(m2) # transpose for simplicity
for rowm1 in m1:
for rowm2 in m2:
for i in range(len(m1[0])):
s += rowm1[i] * rowm2[i]
temp.append(s) # product's element
s = 0 # reset to zero in next loop
product.append(temp) # product's row
temp = [] # reset to empty list
return product
def inverse(M):
if (len(M) is not 4 or len(M[0]) is not 4):
raise ValueError('Matrix not 4X4')
MI = [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
# extract rotational matrix
R = [[0, 0, 0], [0, 0, 0], [0, 0, 0]]
for i in range(3):
for j in range(3):
R[i][j] = M[i][j]
# extract translation matrix
P = [[M[0][3]], [M[1][3]], [M[2][3]]]
#calc inverse of the rotation
RI = transpose(M)
#negative RI
P = negative(P)
#calc positional component
PI = multiply(RI, P)
# putting values of R-transpose in new matrix
for idx, i in enumerate(RI):
for jdx, j in enumerate(i):
MI[idx][jdx] = RI[idx][jdx]
# putting values of -(R-transpose * P) in new matrix
MI[0][3] = PI[0][0]
MI[1][3] = PI[1][0]
MI[2][3] = PI[2][0]
MI[3][3] = 1
return (MI)
def validsolution(l):
k = transpose(l)
for i in l:
if validrow(i) != True:
return False
for j in k:
if validrow(j) != True:
return False
for k in [0,3,6]:
if validrow(blocktorows(l[k:k+3])) != True:
return False
return True
def multiply(A, B):
if dimensionErr(A, B):
print("ERROR: Matrices dimensions do not allow multiplication.")
exit(0)
BT = transpose(B)
C = []
for rowA in A:
rowC = []
for rowBT in BT:
entry = 0
for i in range(len(A[0])):
entry += rowA[i] * rowBT[i]
rowC.append(entry)
C.append(rowC)
return C
print("Invalid multiplication attempted.")
return None
nrow = len(m1) # row number of product
ncol = len(m2[0]) # col number of product
product = []
temp = []
s = 0
m2 = transpose(m2) # transpose for simplicity
for rowm1 in m1:
for rowm2 in m2:
for i in range(len(m1[0])):
s += rowm1[i] * rowm2[i]
temp.append(s) # product's element
s = 0 # reset to zero in next loop
product.append(temp) # product's row
temp = [] # reset to empty list
return product
if __name__ == '__main__':
M1 = [[1,2,0,1],
[4,3,1,4],
[0,1,1,4],
[0,0,1,1],
[1,2,1,3]]
M2 = transpose(M1)
res = mul_matrix(M1, M2)
print(res)