matrix-multiplication

I was wondering how can matlab multiply two matrices so fast. When multiplying two NxN matrices, N^3 multiplications are performed. Even with the Strassen Algorithm it takes N^2.8 multiplications, which is still a large number. I was running the following test program: a = rand(2160); b = rand(2160); tic;a*b;toc 2160 was used because 2160^3=~10^10 ( a*b should be about 10^10 multiplications) I got: Elapsed time is 1.164289 seconds. (I'm running on 2.4Ghz notebook and no threading occurs) which mean my computer made ~10^10 operation in a little more than 1 second. How this could be?? It's a

I'm making my first real foray into Python and NumPy to do some image processing. I have an image loaded as a 3 dimensional NumPy Array, where axis 0 represents image bands, while axes 1 and 2 represent columns and rows of pixels. From this, I need to take the 3x1 matrix representing each pixel and perform a few operations which result in another 3x1 matrix, which will be used to build a results image. My first approach (simplified and with random data) looks like this: import numpy as np import random factor = np.random.rand(3,3) input = np.random.rand(3,100,100) results = np.zeros((3,100,100

An algorithm I'm working on requires computing, in a couple places, a type of matrix triple product. The operation takes three square matrices with identical dimensions, and produces a 3-index tensor. Labeling the operands A , B and C , the (i,j,k) -th element of the result is X[i,j,k] = \sum_a A[i,a] B[a,j] C[k,a] In numpy, you can compute this with einsum('ia,aj,ka->ijk', A, B, C) . Questions: Does this operation have a standard name? Can I compute this with a single BLAS call? Are there any other heavy-optimized numerical C/Fortran libraries that can compute expressions of this type?

So I was given a homework assignment that requires solving the coefficients of cubic splines. Now I clearly understand how to do the math on paper as well as with MatLab, I want to solve the problem with Python. Given an equation Ax = b where I know the values of A and b, I want to be able to solve for x with Python and I am having trouble finding a good resource to do such a thing. Ex. A = |1 0 0| |1 4 1| |0 0 1| x = Unknown 3x1 matrix b = |0 | |24| |0 | Solve for x ev-br In a general case, use solve : >>> import numpy as np >>> from scipy.linalg import solve >>> >>> A = np.random.random((3,

I have a 2D matrix M of shape [batch x dim] , I have a vector V of shape [batch] . How can I multiply each of the columns in the matrix by the corresponding element in the V? That is: I know an inefficient numpy implementation would look like this: import numpy as np M = np.random.uniform(size=(4, 10)) V = np.random.randint(4) def tst(M, V): rows = [] for i in range(len(M)): col = [] for j in range(len(M[i])): col.append(M[i][j] * V[i]) rows.append(col) return np.array(rows) In tensorflow, given two tensors, what is the most efficient way to achieve this? import tensorflow as tf sess = tf

CUDA runtime has a convenience function cudaGetErrorString(cudaError_t error) that translates an error enum into a readable string. cudaGetErrorString is used in the CUDA_SAFE_CALL(someCudaFunction()) macro that many people use for CUDA error handling. I'm familiarizing myself with cuBLAS now, and I'd like to create a macro similar to CUDA_SAFE_CALL for cuBLAS. To make my macro's printouts useful, I'd like to have something analogous to cudaGetErrorString in cuBLAS. Is there an equivalent of cudaGetErrorString() in cuBLAS? Or, have any cuBLAS users written a function like this? In CUDA 5.0,