如何在python中将矩阵乘以向量而不使用任何内置函数，其中向量和矩阵都是来自用户的输入

Question

My homework question is "Write a function which takes as input a vector and a matrix, and multiplies them. This means that it constructs a new vector, where the element at position i is the dot product of the input vector with column I from the matrix"

I have already tried to write out some code however it only works in some instances, in others it will say my j is out of range for the line 'b=v[j]'

rows = int(input("Enter how many rows you want in your matrix"))
matrix1 = []

for i in range(0, rows):
    x = input("enter some numbers for your matrix").split(' ')
    for j in range(len(x)):
        x[j]=int(x[j])
    matrix1.insert(i, x)

vector1 = []
y = input("enter some numbers for your vector").split(' ')

for i in range(0,len(y)):
    a = y[i]=int(y[i])
    vector1.insert(i,a)

def dotproduct(v,m):
    dot1 = []
    dotsum = 0
    for i in range(0,len(v)):
        for j in range (0, len(m)):
            a=m[j][i]
            b=v[j]
            mult=a*b
            if j==0:
                dotsum=0
            dotsum = dotsum+ mult
        dot1.append(dotsum)
    return(dot1)

print(dotproduct(vector1, matrix1))

Answer 1

You should try with b=v[i] but I don't think this will give you the correct dot product computation.

For validation, if I use the dot product from numpy , I get :

>>> import numpy as np
>>> a = [1, 2]
>>> b = [[4, 1], [2, 2]]
>>> np.dot(a, b)
array([8, 5])

A more general advice is to validate input dimensions.

Answer 2

Input validation

First, you should introduce some validation checks on the input.

• Check that the matrix is a matrix, I mean, all rows have the same number of elements. AN x M matrix has N row, each one with M elements.
• Matrix multiplication (or row column product) is possible if some constraints on matrix dimensions are satisfied. If matrix is N x M, the vector must have length M x 1 (multiplying matrix x vector) or 1 x N (multiplying vector x matrix). Consider the vector as a matrix with one row or one column.
  To keep things simple, you may consider only one of the two cases, say vector x matrix only, as it seems your professor asked.

Try to think on how to add these validation checks in your code. Ideally you want to check that the matrix is a matrix after the user has provided all the rows, and that the dimensions allow a row column product after the user has provided the vector.

An hypotethical validation for the matrix could be:

ncols = len(matrix1[0])
for row in matrix1[1:]:
    if len(row) != ncols:
        #stop the program and raise an error to the user.

I let to you the dimension validation (it is your homework, I don't want to do it all for you).

row column product

Second, your dotproduct() is not doing properly the row column product. I'll give you a tip:

for i in range(0,len(v)): i will be index of vector elements.
for j in range (0, len(m)): j will be index of matrix rows.
In a vector x matrix product, they are the same index: you are going to multiply the i-th element of the row with the i-th element of the vector. One of them should be instead the index of matrix columns.