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Performance of matlab direct linear solver with respect to sparsity
For sparse matrices, the performance of backslash depends a lot on the specific structure of that sparse matrices (where the non...

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How can I return real-valued eigenvectors from diagonalization?
I don't think it's possible: Looking at the eigenvalues and eigenvectors of B, >> diag(D) ans = 0.0000 + 2.0000i 0.000...

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incorrect eigenvector using eig(A,B)
The residual MK*V-MM*V*w2 is expected to be numerically close to zero, however, you have to take into account the scaling of the...

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highlight Nodecolor for a graph using a color map (JET)
Since colors is a n-by-3 array, use colors(i, :) to access the complete row that represents the color for node i. You can also u...

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Path between 2 nodes in a graph
Compute a path between the nodes, then check if the result is empty (this is returned by shortestpath if no path exists): path ...

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Diagonalising a Skew-Symmetric Matrix
When EIG is called with an exactly symmetric/hermitian matrix, MATLAB falls back to a specialized algorithm that guarantees that...

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Properties of SVD of a hermitian matrix not holding at single precision
I'd suggest just calling EIG [V, S] = eig(A) instead of calling the SVD. If A is (exactly!) symmetric on input, this will retu...

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What is the difference between Gram-Smith QR decomposition procedure and qr.m function in Matlab?
MATLAB's QR decomposition is computed using Householder transformations, which is generally more numerically advantageous.

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Plotting a graph in layered fashion
Unfortunately, there is currently no way to do this with the 'layered' layout. I'll make a note of your need for this. For now,...

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Shortest path through nodes
As Bjorn mentioned, this is the traveling salesman problem. The optimization toolbox has an example of how to use their intlinpr...

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lsqminnorm- Tolerance to Reduce Impact of Noisy Data
The tolerance in lsqminnorm should be used if you expect your matrix A to be of low rank up to a tolerance. That is, for rank k,...

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How do I get Matlab to display a graph type data structure with decreasing weights
The Edges table attached to a digraph is always standardized so that its sorted by the EndNodes column. However, you can get a c...

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Ordering edge names in Digraph
The edges are reordered in the graph constructor, but it looks like the Power variable you're assigning is in the same order as ...

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SVD of each row of a matrix
The SVD of a row vector has the singular value equal to its norm, and the singular vectors 1 and the normalized vector. If this...

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qr decomposition run-time performance
When a "~" is used for a return value, this is only for code clarity. MATLAB still needs to compute that value, so the second ca...

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Sign difference between coeff=pca(X) and [~,~,v] = svd(X)
I'm not sure why this happens. As mentioned by others, it doesn't matter what sign these outputs have. You could try stepping th...

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How to use non-unique node names in a digraph?
Instead of setting these inputs as node names, add them as a separate variable in the nodes table. Then, pass them to the plotti...

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Is there any way to accelerate the solving of a series of large sparse positive definite linear equations "Ax=b" with same "A" and different "b"?
If you are able to solve for one vector using A \ b, you could pass in a matrix containing all your right-hand sides in instead:...

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Accelerate eigs with GPU
The eigs function is not supported on the GPU. There is support for sparse matrices on the GPU, since R2015a: Release notes para...

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Properties of adjacency matrix
In terms of the adjacency matrix, a disconnected graph means that you can permute the rows and columns of this matrix in a way w...

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Assigning values to an array of arbitrary dimensions in MATLAB.
Using the somewhat recent implicit expansion, this can also be done without indexing into every element of the array: function ...

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How to find all edges indexes if node indexes are given?
So you're looking for all edges where both end nodes are part of the set 4, 5, 6? This will compute them: >> [s, t] = findedge(...

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Create random graph with limited degree
You could start by just making an undirected graph, and then go through each node and compute its degree. If the degree is large...

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Maximum of ND-array
Find the maximum element of a N dimensional array. Example: A=[1 2 4 ; -20 4 10]; The maximum is 10.

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Result of A(:,:,1,1) coming as result of A(:,:,1,2)
The eigenvectors returned by EIG are returned in the same order as the eigenvalues, but the eigenvalues are not necessarily sort...

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How to find all related nodes in directed graph?
Another option is to use the weak connected components of the graph: bins = conncomp(G, 'Type', 'weak'); % bins(nid) gives th...

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rotation of graph node labels
The labels will be straight in most layouts (all but 'circle', 'layered'). You can first use 'circle' layout and then convert to...

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Error using matlab.graphics.chart.primitive.GraphPlot/highlight>checkSubgraph
Try using Gsol = graph(idxs(ledge,1),idxs(ledge,2), [], numnodes(G)); so that G and Gsol both have the same number of nodes. T...

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About "eigs" function
This was the case for old EIGS, it would use some random restart vectors that changed on every run. In the version of EIGS that ...

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Assign Numerical Node Labels
For the first call, use >> GG.Nodes.Name = num2str(Name)' - GG.Nodes.Name has to be a column vector. For the second call,...

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