4×4 matrix multiplication is 64 multiplications and 48 additions. Using SSE this can be reduced to 16 multiplications and 12 additions (and 16 broadcasts). The following code will do this for you. It only requires SSE (#include <xmmintrin.h>). The arrays A, B, and C need to be 16 byte aligned. Using horizontal instructions such as … Read more
Yes, it is possible and you should also use a doubly block circulant matrix (which is a special case of Toeplitz matrix). I will give you an example with a small size of kernel and the input, but it is possible to construct Toeplitz matrix for any kernel. So you have a 2d input x … Read more
Speaking of speed-up, your function will be more cache-friendly if you swap the order of the k and j loop iterations: matrix mult_std(matrix a, matrix b) { matrix c(a.dim(), false, false); for (int i = 0; i < a.dim(); i++) for (int k = 0; k < a.dim(); k++) for (int j = 0; j … Read more
In general you want to size your blocks/grid to match your data and simultaneously maximize occupancy, that is, how many threads are active at one time. The major factors influencing occupancy are shared memory usage, register usage, and thread block size. A CUDA enabled GPU has its processing capability split up into SMs (streaming multiprocessors), … Read more
Use np.einsum – np.einsum(‘ijk,ik->ij’,matrices,vectors) Steps : 1) Keep the first axes aligned. 2) Sum-reduce the last axes from the input arrays against each other. 3) Let the remainining axes(second axis from matrices) be element-wise multiplied.
Definition General array slicing can be implemented (whether or not built into the language) by referencing every array through a dope vector or descriptor — a record that contains the address of the first array element, and then the range of each index and the corresponding coefficient in the indexing formula. This technique also allows … Read more
The state-of-the-art implementation of matrix multiplication on CPUs uses GotoBLAS algorithm. Basically the loops are organized in the following order: Loop5 for jc = 0 to N-1 in steps of NC Loop4 for kc = 0 to K-1 in steps of KC //Pack KCxNC block of B Loop3 for ic = 0 to M-1 in … Read more
You could factor the matrix into eigenvalues and eigenvectors. Then you get M = V * D * V^-1 Where V is the eigenvector matrix and D is a diagonal matrix. To raise this to the Nth power, you get something like: M^n = (V * D * V^-1) * (V * D * V^-1) … Read more
You can try this code: public class MyMatrix { Double[][] A = { { 4.00, 3.00 }, { 2.00, 1.00 } }; Double[][] B = { { -0.500, 1.500 }, { 1.000, -2.0000 } }; public static Double[][] multiplicar(Double[][] A, Double[][] B) { int aRows = A.length; int aColumns = A[0].length; int bRows = B.length; … Read more