How do you multiply a sparse matrix?
To Multiply the matrices, we first calculate transpose of the second matrix to simplify our comparisons and maintain the sorted order. So, the resultant matrix is obtained by traversing through the entire length of both matrices and summing the appropriate multiplied values.
What is the time complexity of following code?
| Code | Time complexity |
|---|---|
| sum = 0 | O(1) |
| for (i=1; I <= n; i*=2) | O(logn) because I is incremented exponentially and loop will run for less number of times than n. |
| for(j=1; j<=n; j++) | O(n) because j is incremented linearly and loop will run for n number of times. |
| sum++ | O(1) |
How do you multiply sparse matrices Scipy?
We use the multiply() method provided in both csc_matrix and csr_matrix classes to multiply two sparse matrices. We can multiply two matrices of same format( both matrices are csc or csr format) and also of different formats ( one matrix is csc and other is csr format).
What is the time complexity of the matrix multiplication and Strassen’s algorithm?
The general algorithm’s time complexity is O(n^3), while the Strassen’s algorithm is O(n^2.80).
What is the time complexity of matrix multiplied recursively?
Explanation: The time complexity of recursive multiplication of two square matrices by Strassen’s Method is found to be O(nlog7) since there are total 7 recursive calls.
Why is Strassen matrix multiplication better than conventional method of multiplication?
In linear algebra, the Strassen algorithm, named after Volker Strassen, is an algorithm for matrix multiplication. It is faster than the standard matrix multiplication algorithm for large matrices, with a better asymptotic complexity, although the naive algorithm is often better for smaller matrices.
What are the disadvantages of a sparse matrix?
– when solving what really is a FEATURE SELECTION problem – questions like this are common in business ‘what are Top X factors that drive my sales/ profits/ customer loyalty’ – linear models yield both ‘direction of influence’ & ‘global interpretability’. – i would consider Lasso GLM (with polynomial features) for this – robustn
How to convert a matrix into a sparse matrix?
– Row: Index of row, where non-zero element is located – Column: Index of column, where non-zero element is located – Value: Value of the non zero element located at index – (row,column)
How do you multiply a matrix by a vector?
It is “square” (has same number of rows as columns)
What are sparse matrices used for?
– data: the values of the non-zero values — these are the non-zero values that are stored within the sparse matrix – indices: an array of column indices — starting from the first row (from left to right), we identify non-zero positions and return their indices in that row. – indptr: stands for index pointer and returns an array of row starts.