Questions tagged [linear-algebra]

Linear Algebra is a core body of mathematics studying vector spaces and linear mappings between these spaces. Key topics include: matrices, vectors, simultaneous systems of linear equations, diagonal form, eigenvalues, eigenvectors, projections, points, lines, planes, hyperplanes, rotations and reflections.

0
votes
0answers
16 views

How to solve nC2 variables having n equations?

I want to solve for values where there are nC2 variables and n equations on python using numpy.linalg.lstsq import numpy as np x = [[1,1,1,0,0,0],[1,0,0,1,1,0],[0,1,0,1,0,1],[0,0,1,0,1,1]] y = [1,1,1,...
1
vote
0answers
31 views

Avoiding memory allocations with linear algebra calculations in R

As a trivial case, let's say I'm interested in calculating: r = v*M^t Where r and v are vectors and M is an extremely large sparse matrix. I can solve it one of two ways: r = v*(M*M*M*M...) r = (((...
0
votes
1answer
37 views

python 3 how to use multithreading with numpy linalg norm

I am using python3 with np.linalg.norm to calculate the norms for rows in a matrix (norm(axis=1)), Is there a straightforward way, using only np to make it run using multithreading or multicoring?
-3
votes
1answer
27 views

in nueral network , WX+B is linear transformation?

in linear algebra, linear function is called linear transformation in neural network , linear transformation need two condition f(x+y) = f(x) + f(y) f(cx) = cf(x) but WX+B is not satisfied these ...
2
votes
1answer
67 views

Left and right eigenvectors in Julia

I have a general real matrix (i.e. not symmetric or Hermitian, etc.), and I would like to find its right eigenvectors and corresponding left eigenvectors in Julia. Julia's eigen function returns the ...
0
votes
0answers
39 views

how to check if vectors inside a matrix are independent?

Im trying to check if a matrix has vectors that are linearly independent or dependent (linear algebra) I make a first routine that successfully do the revision, but Im interested that in the linearly ...
-2
votes
0answers
13 views

For linear endomorphisms A, B given that tr(B) = 1 it is true that tr(AB) < biggest eigenvalue of A. Can you give me a proof for that?

In the density formalism of quantum mechanics B would denote the density matrix and A the projector of the corresponding eigenspace. From tr(AB) I can get the probability of obtaining the ...
0
votes
0answers
21 views

How to find euclidean distance from specific camera instead of perpendicular distance from base line in stereo triangulation?

I want to calculate the depth of image pixel in world unit using stereo triangulation principle. Using stereo triangulation principle one get perpendicular distance from base line connecting left and ...
-1
votes
1answer
47 views

Linear algebra with a sparse triagonol marix

I have a tridiagonal matrix A which I want to make a sparse matrix and then solve a linear system Ax =b using scipy, how is this done. i have tried the following code, which dosent work. from scipy....
1
vote
0answers
29 views

Triangular matrix matrix multiply `trmm` in TensorFlow

I need to get fastest possible matmul operation in TF for the case when one of the matrices is lower triangular. The cuBLAS and the BLAS have trmm functions, but looks like TensorFlow doesn't benefit ...
2
votes
0answers
43 views

How to plot a 2D plane of set area, using a point on a plane and a normal vector, in 3D space, using plotly and dash?

I would like to plot a 2d plane of a set area (e.g. 10x10 square or 5dia cicle) in 3D space using plotly so I can include it in my dash app. I would also like to be able to rotate and position the ...
0
votes
1answer
16 views

How to get a low dimensional rank of non-negative factorization matrix

I have a big matrix X = numpy.random.rand(1000, 1000) using sklearn.decomposition I factorized the matrix such as: from sklearn.decomposition import NMF model = NMF(n_components=1, init='random', ...
-1
votes
0answers
16 views

Looking for ways to transform time-series data recorded from object movement into equation describing the movement direction of the object

Looking for some time-series data transformation advice! I want to know what's the best way to transform data of 9-tuples time series data of IMU (Inertia Measurement Unit) sensor, recorded from a ...
0
votes
1answer
43 views

How can I plot this Octave\Matlab function output?

I everyone, I am pretty new in Octave\MatLab and I have the following doubt. I have this code calculating a sigmoid function for a parameter z: function g = sigmoid(z) %SIGMOID Compute sigmoid ...
0
votes
2answers
61 views

Is it possible to start indexing of matrices from 1 in Eigen?

I am using Eigen to do some linear algebra computations in my code. However, all of mathematical formulas are based on the fact that indexing starts from 1. So, each time that I want to implement them ...
0
votes
0answers
37 views

Scipy spsolve is order of magnitude slower than matlab mldivide

Ok, so I have a linear system. A is sparse 29791 by 29791 with 202771 stored elements. B is 29791 by 1 with 4561 stored elements. I have tried solving this system by storing A as csr_matrix and as ...
0
votes
1answer
42 views

Export function from mathematica to matlab

Im trying to export a function that draws a heart from mathematica... Export[NotebookDirectory[] <> "anim1.gif", Table[ Plot[Sqrt[Cos[x]]*Cos[200*x] + Sqrt[Abs[x]] - 0.7*(4 - x*x)^0.01, {...
0
votes
3answers
34 views

What is the best way to append a row to matrix?

I am trying to append a row to a pre-existing matrix. I wrote some code (shown below) that does the trick, but I can't help but feel there is a better way to do this (or perhaps there is already an ...
1
vote
2answers
84 views

Speeding Up Kronecker Products Numpy

So I am trying to compute the kronecker product of two matrices each of arbitrary dimension. (I use square matrices of the same dimension just for the examples) Initially I tried using kron : a = ...
3
votes
1answer
87 views

Confused about Eigen QR decomposition

I am confused about Eigen's QR decomposition. My understanding is that the matrix Q is stored implicitly as a sequence of Householder transformations, and that the matrix R is stored as an upper ...
1
vote
1answer
33 views

PyTorch and Chainer implementations of the Linear layer- are they equivalent?

I want to use a Linear, Fully-Connected Layer as one of the input layers in my network. The input has shape (batch_size, in_channels, num_samples). It is based on the Tacotron paper: https://arxiv.org/...
0
votes
1answer
72 views

Calculating euclidean distances with Python runs too slow

I read to datasets from file into numpy arrays like this: def read_data(filename): data = np.empty(shape=[0, 65], dtype=int) with open(filename) as f: for line in f: data = np....
0
votes
0answers
26 views

pyspark distributed linear algebra - possible to compute inverse matrix?

I have two questions: Is it possible in pyspark to compute the inverse of a real symmetric positive definite matrix via Cholesky Decomposition, similar to what is provided in the scala api (I had a ...
0
votes
1answer
44 views

how to plot a plane spanned by two vectors in matlab?

I have a matrix, lets say value = [ 1,0,0;0,1,0] and need to plot a plane in the space generated by these vectors, something like these: with the next code tt=-0.5:0.1:1.5; ss=-0.5:0.1:1.5; [s,...
-3
votes
1answer
2k views

matrix product of the two tensors [duplicate]

How would you calculate matrix product of the two tensors in PyTorch? x = torch.Tensor([[1, 2, 3], [1, 2, 3]]).view(-1, 2) y = torch.Tensor([[2, 1]]).view(2, -1) I am confused between these ...
1
vote
1answer
48 views

X X^T Matrix is not positive definite, although it should be

I have a matrix M where M.shape = (679, 512). I would like to find the eigenvectors and eigenvalues of M M^T, it's covatiance matrix, which should be positive definite in maths. I find them using: ...
0
votes
1answer
27 views

Sympy How To Set Value of every symbol in a list

i have been trying to solve a numerical problem. I used sympy to create symbolic equations such as : a = symbols('a0:8') b = symbols('b0:8') c = symbols('c0:8') d = symbols('d0:8') and then i ...
-1
votes
1answer
37 views

How to plot all the matrix elements in matlab whitout knowing the size?

Lets say there is the next matrix A = [ 1 2 2 ; 1 2 3 ; 2 3 4 ; 3 4 5 ; 4 4 6 ; 1 11 12] I try to use quiver3 to plot the row in the next way: quiver3(0,0,0,A(1:1),A(1:...
-2
votes
0answers
38 views

Octave Coding - Coding to determine a relationship between two matrix

Given an input 1 2 3 0 1 1 1 2 3 1 1 -1 0 1 1 The first 2 lines create a 2 x 3 matrix L while the last 3 lines create a 3 x 3 matrix P. The first row of L is a point A in L. The second row of L ...
-1
votes
2answers
52 views

Octave Coding - I need help coding coefficients of polynomial

This question fairly easy doing it manually however, I am struggling to have this written in code. There is a quartic polynomial: P(x)=ax^4+bx^3+cx^2+dx+e There is also a given matrix M: 5 0 -1 2 ...
0
votes
1answer
195 views

Linear Regression Using Linear Algebra in Python

Am I interpreting these formulas on wikipedia (https://en.wikipedia.org/wiki/Coefficient_of_determination) wrong in Python? Below is what I have tried. def ss_res(X, y, theta): y_diff=[] ...
0
votes
0answers
42 views

Calculation of triangle surface normal is off (not perpendicular)

I am trying to simply calculate the surface normal of a triangle made up of 3 points in 3-D space. I'm using the cross product for this, but the results are always off when I plot the vector. import ...
0
votes
1answer
39 views

Solve a Quadratic Equation in two variables using Python

I have got two equations, one linear say, , where m and c are constants and the other quadratic say, , where x1, y1 and r are constants. Is there a way I can solve for x and y using Python ? ...
-3
votes
0answers
15 views

Computing Chebyshev center in R

I am searching for a way to compute the Chebyshev center of a convex polytope, in R. I would like to have a function of the type: x0 = chebycenter(A,b); where x0 is the vector of coordinates of the ...
0
votes
1answer
76 views

How to find a new equidistant vector, given five existing vectors?

I have vectors v1, v2, v3, v4, v5, with 100 dim, I need to find a center vector, that will have equal distance with each. Uptdate: Looking at this answer from Mathmatics, is there a way to implement ...
0
votes
0answers
26 views

Calculating Least Squares solution from SVD

I want to calculate the least square solution of a dataset using SVD and I have gotten to the point of collecting the SVD functions U, s, VT =np.linalg.svd(data[:,:data.shape[1]-1],full_matrices=...
0
votes
1answer
39 views

How to add magnitude or value to a vector in Python?

I am using this function to calculate distance between 2 vectors a,b, of size 300, word2vec, I get the distance between 'hot' and 'cold' to be equal 1. How to add this value (1) to a vector, becz i ...
-1
votes
1answer
18 views

Given 2 coordinates, draw a line between them

I have given two coordinates (x1,y1) and (x2,y2) and would like to draw a line between them given a function drawdot(x,y). So to make it look like I draw a line I just want to draw 100 dots between ...
2
votes
0answers
52 views

Solving eigenvectors/eigenvalues of sparse matrix in different ranges successively

I'm looking for eigenvalues/eigenvectors of a huge sparse matrix A (250k*250k) that lie in different eigenvalue ranges without calculating all the eigenvalues in between since it would just take too ...
0
votes
0answers
27 views

Output from numpy.matrix_power differs from formulaic way of solving

I am supposed to use python to solve a Matrix A^1000. I have tried numpy's built in matrix_power function to compute the output, but when I try to compute the result step by step according to the ...
1
vote
1answer
59 views

Using python to solve basic equations [duplicate]

I am trying to solve linear equations using python. Is there any builtin functions or any modules that I can use to achieve my goal or Is there any code written from scratch? With Thanks, Roshan
0
votes
1answer
25 views

How to fix the plot of the symbolic eigenvalues of the 1st matrix (matlab)?

I'm calculating the eigenvalues of a 8x8-matrix including a symbolic variable "W". Plotting the 8 eigenvalues as functions of W returns a strange result in the plot which looks like someone rode his ...
1
vote
1answer
49 views

How to plot eigenvalues representing symbolic functions in Python?

I need to calculate the eigenvalues of an 8x8-matrix and plot each of the eigenvalues for a symbolic variable occuring in the matrix. For the matrix I'm using I get 8 different eigenvalues where each ...
1
vote
1answer
78 views

Getting Singular Values of NumPy Data Columns in Order

I would like to calculate the singular value decomposition of a matrix and the order of the singular values is important. By default, it seems numpy.linalg.svd (and scipy.linalg.svd) sort the singular ...
1
vote
1answer
108 views

How to performantly sum all products of unordered pairs in a set of binary strings

Given a set of binary strings S, where each binary string has length L, I want to find the sum of all products of unordered pairs of elements in these strings for each unique unordered pair. I then ...
6
votes
1answer
58 views

Quaternion division and hyperbolic tangent tanh

Quaternion multiplication is well-defined, and is known to me as "Hamilton product": // hamilton product vec4 qmul(in vec4 q1, in vec4 q2) { return vec4( q1.w * q2.xyz + q2.w * q1.xyz - ...
1
vote
0answers
27 views

Why is the RMSE on the training set decreasing while my matrix completion program is training, and the RMSE on the test set is rising?

I am writing a naive matrix completion program. Curiously, the RMSE on the training set is decreasing during training, but the RMSE on the test set is soaring at first and then slowly decreasing. I ...
2
votes
1answer
63 views

How to apply multiple axis rotations on a single rotate3d() call?

I'm trying to use a single rotate3d function to rotate multiple axes of a cube at the same time, but I get a weird rotation. If I use transform: rotateX(-30deg) rotateY(45deg) I get a nice looking ...
2
votes
1answer
60 views

Can camera.lookAt function be calculated from an angle and an axis of rotation, given a target point and the camera forward?

I am trying to understand three.js's camera.lookAt function, and to implement my own. I'm using eye = camera position, target = target look at point, and up is always (0, 1, 0). A friend proposed ...
1
vote
0answers
38 views

How to force python to perform an LU decomposition without a permutation

In MATLAB, it is possible to use a hack to force the builtin LU decomposition algorithm to not use a permutation matrix (i.e., force P=I), as shown here. Is there a similar hack in python? Namely, ...

http://mssss.yulina-kosm.ru