Questions on the manipulation of matrices in Mathematica.

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6
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294 views

Inverse of a large sparse Hermitian block matrix

I am looking for a method (if it exists) for the inverse of a large sparse Hermitian block matrix. The off diagonal sparse matrices, named δ are 4x4, and they have ...
5
votes
0answers
145 views

Is it possible to implement symbolic sub matrices?

The accepted answer in the following link: http://stackoverflow.com/questions/5708208/symbolic-matrices-in-mathematica-with-unknown-dimensions provides a functionality to create symbolic matrices ...
5
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0answers
70 views

Bug in PositiveDefiniteMatrixQ?

This seems like a bug in PositiveDefiniteMatrixQ to me: ...
5
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0answers
357 views

Export matrix to $\LaTeX$ with style

Is it possible to export a matrix to $\LaTeX$ with style? For example this code will create a matrix with equal spacing matrix and with background colors in some cell, is it possible to export that ...
4
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0answers
64 views

Eigensystem on HPC

I am submitting Mathematica jobs to an HPC. I have a large matrix that is a function of (x,y) and I am diagonalizing it for around 500 points in the plane. My initial idea was to request a node with ...
4
votes
0answers
168 views

Discriminant of Characteristic Polynomial

I'm doing a calculation which finds the characteristic polynomial of a matrix with rather complex entries and then determines the discriminant of that polynomial. For smaller matrices up to around 7x7 ...
4
votes
0answers
510 views

Analytically solve the eigenvalue problem with infinite dimensions by Mathematica?

If I am given a symbolic expression of all the matrix elements in an infinite-dimensional space, e.g., the Hamiltonian of a quantum mechanical system, is it possible to get the symbolic expression for ...
3
votes
0answers
48 views

Calculation the eigensystem of a matrix containing very small numbers

I'm dealing with a matrix containing very small numbers like 10^(-370). Whenever I'm trying to calculate the eigensystem of that matrix, it takes too much time, though the matrix size is not big that ...
3
votes
0answers
75 views

Fast principal component analysis

I'd like to speed up a principal value value analysis. The data contains a large set of vectors with a large dimension. Both are in the range of 1000. I want to obtain the loadings matrix for further ...
3
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0answers
125 views

How to accelerate updating some parts of sparse matrices?

I am trying to update some parts of an specific matrix as rapidly as possible. In what follows, I first set up the basics things that I want to use ...
3
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0answers
209 views

Mathematica Complains about Non Symmetric Covariance matrix, when it's not the case

I was doing some fitting with Mathematica7 using NonlinearModelFit. It's quite long the program to do the fit and that's why I am not displaying here ... It goes ok, and I can get the fit parameters ...
2
votes
0answers
27 views

Automatically discover the class of an arbitrary matrix

In Wolfram|Alpha it is possible to discover some specific classes to which a matrix belongs. For instance, typing this in Wolfram|Alpha ...
2
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0answers
56 views

CUDALink Error: A CUDALink kernel timed out?

I'm following the CUDALink tutorial [ http://reference.wolfram.com/language/CUDALink/tutorial/Introduction.html ] and everything is going fine until I get to the part that calls CUDADot on the ...
2
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0answers
98 views

A math function similar to “LatticeReduce” for finding linear independent basis

We would like to ask a math function similar to "LatticeReduce" for finding linear independent basis. The input is a list of vectors $M=\{v_1,v_2,v_3,\dots\}$, with the following property: There is a ...
2
votes
0answers
168 views

Fast calculation of commute distances on large graphs (i.e. fast computation of the pseudo-inverse of a large Laplacian / Kirchhoff matrix)

I have a large, locally connected and undirected graph $G$ with $\approx 10^4$ vertices and $\approx 10^5$ to $\approx 10^6$ edges. Moreover I can bound the maximum vertex degree as $Q_{max}$. I ...
1
vote
0answers
49 views

Lens profile in a grid

So I have a FDTD code which works and its all good the propagator of the code it self is: ...
1
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0answers
40 views

Understanding polyharmonic splines

Raul Narain and J.M. gives implementation of the thin plate polyharmonic splines in this post. Raul Narian's method is clear. J.M.'s is convenient to reuse. But J.M. used too many ...
1
vote
0answers
23 views

How to show Output of matrix in FortranForm with “&” character?

I have a matrix. and i have shown the output of matrix one by one element in FortranForm. the problem is i want to put "&" continuation charater in output because when i am copying the data into ...
1
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0answers
53 views

Programming for matrix manipulation

I want to write a programme which operates on nd x nd matrices. The programme looks the matrix as a n x n block matrix where ...
1
vote
0answers
101 views

Replace part in a matrix that matches specific pattern

I have the following problem. Given a matrix L which looks as follows, Matrix L is a link, route matrix. Further, I got the following vector (d), which indicates the demand per vertex combination. ...
1
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0answers
42 views

Creating a matrix from a list of simultaneous equations

I have a list of n simultaneous equations of the form, w A[n] = (K[n,n+1]+K[n-1,n])A[n] - K[n,n+1]A[n+1] - K[n-1,n]A[n-1] ...
1
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0answers
131 views

Symbolic matrix calculus: What's new in Version 9

I have seen some of the related posts, which ask about doing matrix calculation on tensors unknown dimensions. One of the posts mentioned that version 9 has some capability, but it was concerned about ...
1
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0answers
103 views

How to sequentially select, from a large set of tuples (of matrices), those with a certain property

I'm interested in finding a computationally efficient way for selecting all tuples of matrices which have a certain property. The property I'm interested in is that I want the column sum, of f[the ...
1
vote
0answers
58 views

How to find a scaling parameter in matrix inversion process by MMA?

I simply would like to find the inverse of a given matrix $A$ by the iterative method $X_{k+1}=X_k(2I-AX_k)$ using $X_0=\frac{1}{\sigma_{max}^2}A^*$. An example is as follows ...
1
vote
0answers
84 views

What is the fastest way to obtain the eigenvalues of a Wishart matrix?

I would like a fast method of creating a sample of random numbers which corresponds to the eigenvalues of a Wishart matrix: For M>N the eigenvalues \lambda_i are given by the jpd Where $K_N$ is ...
1
vote
0answers
80 views

Define inverse for the custom operator

I want to define simple matrix algebra (inspired by the following posts: Block Matrix Algebra with Mathematica ; How to define custom operators ). I assume the funtion ...
1
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0answers
198 views

How to extract connected bipartite graph from incidence matrix

I'm trying to extract a connected bipartite graph Bconn from the a given incidence matrix B- I have a matrix representing a bipartite graph - the incidence matrix B (weighted or not is unimportant). ...
1
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0answers
160 views

Efficient submatrix swaps for large sparse matrix

I am implementing the 'swap' algorithm for a binary matrix to generate matrix permutations that maintain row and column totals. My problem is that my matrices are large and sparse (e.g., 19774 x 942, ...
1
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0answers
158 views

matrix with IF/THEN condition

How to generate all posible matrices with some conditions on the elements? I need to make for given $n$ all $n\times n$ matrices $A=(a_{ij})$ with three conditions: I. $a_{ij}=+1$ or $0$ or $-1$. ...
1
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0answers
87 views

NMaximize with matrix input

I defined function f[x_, fixed_] := {...}. Here x is an $M\times N$ matrix. I want to maximize $f$ with respect to $x$. I have ...
1
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0answers
242 views

Can mathematica simplify an expression setting simplified answer equal to zero?

Basically I want to reduce something like: Subscript[P, 4] - Subscript[P, 5] == Subscript[R, 4, 5]* Subscript[i, 4, 5] when only one of them is known (...
0
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0answers
53 views

Solving for a Transfer Matrix

I am currently working on a program that will solve a transfer matrix and extract several elements. Particularly, the transfer matrix is characterized by four elements in a ...
0
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0answers
28 views

hOW TO PUT '&' OPERATOR in output of matrix elements that are in FortranForm?

i have matrix and i have shown the output in fortranForm. but due to large characters in elements of matrix, when i copied the data into fortran Code, it does not take copied data because of line ...
0
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0answers
108 views

Matrix multiplication

I want to multiply 1000by1000 matrices but MMA runs out of RAM. ...
0
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0answers
93 views

using elements from a matrix into a function

Hi this is what i have done so far i have a surface with the length "l" and width "w". and i have split this surface into m*n sub surfaces. as shown below. ...
0
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0answers
35 views

Numerical Error with Matrix operations

A is a 3x3 matrix, b is a 3x1 vector. I try to convert [A|b], a 3x4 matrix, to [I|0]. So the formula is right multiple ...
0
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0answers
99 views

Spectral Clustering

I am interested in the following question: How is it possible to check whether an algorithm is working properly? However, this question is too general for the post and I'd like to restrict attention ...
0
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0answers
58 views

how to solve an optimization problem in terms of matrices as the argument

How can I minimize an expression of the form a^T A a where a is a matrix. The following approach does not work if ...
0
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0answers
61 views

I see error messages when I use LogLinear Plot but not when I use Plot

I have written an application with Manipulate that plots the results of several calculations. What I find strange is that when I have my application use ...
0
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0answers
66 views

Geometric Transformation not working - degenerate points?

I've successfully used FindGeometricTransformation to project the simplex triangle onto the x-y plane: ...
0
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0answers
50 views

how to rewire the minimum number of edges in a disconnected bipartite graph, so to transform it in a connected one

Consider an incidence matrix A for a bipartite graph (Aij=1 if node i of group 1 and node j of group 2 are connected). A is not symmetric. Assume that A is disconnected or only weakly connected, i.e. ...
0
votes
0answers
51 views

Extracting Coefficient Matrices from partial differential equations

I have a system of differential equations which are in the form Dt[a01,t] + u*Dt[a01,x] + v*Dt[a01,y] + w*Dt[a01,z] I have ten of these equations and my ...
0
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0answers
47 views

TableDirection in TableForm

I got confused about what does "the outermost dimension" and "the first dimension" mean in the document I snipped. Does it mean row or column?
0
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0answers
51 views

Find the values of parameters so that the matrix is symmetric positive definite

Good evening , I have a matrix 20x20 in symbolic form. The matrix depends on 5 parameters (a,b,c,d,e). I would like to get the interval of each parameters that ensures that the matrix S is symmetric ...
0
votes
0answers
58 views

How to compute variances from a matrix/table

I have created a matrix/table with an imported dataset. I want to know what the variance is for 3 values at a time but across 68 columns. I would like to do this in an automated way rather than 1 set ...
0
votes
0answers
30 views

Mathematica program for PLUR decomposition of a symbolic matrix using full pivoting

I wanted to ask if there is a Mathematica program for PLUR decomposition of a symbolic matrix M, such that M = P*L*U*R, using FULL (row and column) pivoting, and where R = reduced row echelon form of ...
0
votes
0answers
67 views

Computing residues of matrix valued functions symbolically

I have a somewhat specific application in mind, but I've run into this kind of problem a few times and never found an elegant solution. Is there an efficient way to get Mathematica to recognize that ...
0
votes
0answers
137 views

Eigenvectors for a large symbolic matrix

I'm trying to compute the eigenvectors for a 42x42 symbolic matrix (with one variable) in Mathematica. I get the following error: Eigenvectors::eivec0: Unable to find all eigenvectors. >> and the ...
0
votes
0answers
738 views

Fastest way to create a NxNxNxN dimensional matrix

I have a function that outputs a complex number Func[x_,y_]:= blah blah; I have constructed a table of all possible values of this function. ...