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11 votes

What algorithm(s) do numpy and scipy use to calculate matrix inverses?

Documentation to numpy.linalg.inv and scipy.linalg.inv does not mention the algorithm used. Judging from the source, ...
Vladimir Lysikov's user avatar
10 votes
Accepted

Computing numeric derivative via FFT - SciPy

FFT returns a complex array that has the same dimensions as the input array. The output array is ordered as follows: Element 0 contains the zero frequency component, F0. The array element F1 ...
Maxim Umansky's user avatar
10 votes

How are scientific computing workflows faring on Apple's M1 hardware

The way I have been measuring whether the eco-system is ready is how things are going with the transition for the homebrew package manager. They have been carefully documenting the progress of ...
Kyle Mandli's user avatar
9 votes

Methods for solving $x'=Ax+b$ for small, sparse, singular $A$

Any general-purpose ODE solver should be able to handle this linear coupled system of ODE very easily, for example: scipy.integrate.ode CVODE from the Sundials solver suite; it appears to have Python ...
Kirill's user avatar
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9 votes

Computing numeric derivative via FFT - SciPy

Maxim Umansky’s answer describes the storage convention of the FFT frequency components in detail, but doesn’t necessarily explain why the original code didn’t work. There are three main problems in ...
Socob's user avatar
  • 191
9 votes

Is LAPACK behind the cutting edge of dense linear algebra?

When one says an algorithm is of order $O(n)$, that may mean that the complexity is given by: $c + b*n$. With every new element you add you increase in runtime (effectively). What mathematically ...
MPIchael's user avatar
  • 2,935
9 votes
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Number of function calls and jacobian calls in scipy.root

At the point where you print out the Jacobian, adding traceback.print_stack() reveals that the first evaluation comes from ...
jdgleeson's user avatar
  • 376
8 votes
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Why does LSODA fail to integrate the logistic function?

When you use $r=5$, the initial condition is $$ x(-10) \approx e^{-50} \approx 1.9\times 10^{-22}. $$ This is much smaller than the machine epsilon, $2\times 10^{-16}$, and it is very likely that ...
Kirill's user avatar
  • 11.4k
8 votes

Is LAPACK behind the cutting edge of dense linear algebra?

LAPACK has been on the cutting edge for just about three decades, and probably still is for its niche. However, given given recent developments in libraries for the simpler BLAS-type matrix operations ...
cbk's user avatar
  • 181
8 votes
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Python scipy eigh(Arpack) giving wrong eigenvalues for generalized eigenvalue problem

The matrix B (M in the documentation) needs to positive definite according to the documentation: "If sigma is None, M is positive definite", this is in addition to the first requirement &...
user3209427's user avatar
8 votes

How are scientific computing workflows faring on Apple's M1 hardware

From this, it looks like there is no functional native Fortran compiler yet. If that is really the case, things look bleak. Almost anything that uses linear algebra includes some Fortran code (Lapack),...
Federico Poloni's user avatar
7 votes
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Matrix Balancing Algorithm

Took me quite a while to figure this out and as usual it becomes obvious after you find the culprit. After checking the problematic cases reported in David S. Watkins. A case where balancing is ...
percusse's user avatar
  • 393
7 votes
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Applying the result of Cuthill-McKee in SciPy

The reverse Cuthill-McKee algorithm produces a reordering that applies to both the rows and columns. This is because it works by considering matrices as graphs of (undirected) connected nodes. ...
Nick C.'s user avatar
  • 188
7 votes
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Integration of the Fermi distribution using Python

One of your problems is the system of units that you are using. Just changing the units improves the results ...
nicoguaro's user avatar
  • 8,510
7 votes

Is there an efficient way to form this block matrix with numpy or scipy?

The code proposed by the OP can indeed made be more efficient, mainly by noting the fact that to form the sequence $A^i B$, with $i=0\,\dots,N$ you do not have to compute $A^i$ at each step, but you ...
Stefano M's user avatar
  • 3,839
7 votes
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Algorithm to factorize matrix whose many rows are already of upper triangular form?

I believe you can accomplish what you want efficiently using the recursive LU algorithm. In brief, recursive LU on a $M \times N$ matrix $A$ proceeds by partitioning the matrix into 4 blocks: \begin{...
vibe's user avatar
  • 1,058
7 votes
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Functions from Scipy, Blas, or Lapack that compute only upper triangular matrix

I think you are overestimating the overhead of computing L. There are zero extra operations needed; the only additional cost is writing to RAM some numbers that you ...
Federico Poloni's user avatar
7 votes
Accepted

Why is my curve_fit not producing the covariance matrix and the correct values for the unknown variables?

The problem seems to be one of scaling. When I added the jacobian of the function an overflow warning appeared. Thus, I divided the data by their maximum values and it worked. Following is the code. <...
nicoguaro's user avatar
  • 8,510
6 votes

What does Python offer for distributed/parallel/GPU computing?

Here's a few options that are relatively easy to work with: One node - multiprocessing is the most straightforward thing to do. multiprocessing.map works well for ...
Danielle's user avatar
6 votes
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Fast c++ library to solve very big sparse systems

I second the idea of using Eigen, which is pretty efficient, but also very simple to include. If you need a lot more performance, you could try to use PETSc or Trilinos. They are very powerful ...
BlaB's user avatar
  • 1,157
6 votes
Accepted

Correct use of scipy's sparse.linalg.spilu

If $\mathbf L$ and $\mathbf U$ give an approximate factorization of $\mathbf A$, you wouldn't want to use $\mathbf P = \mathbf L\cdot \mathbf U$ as a preconditioner (that's approximately $\mathbf A$), ...
rchilton1980's user avatar
  • 4,862
6 votes
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Solving for a set of coupled ODEs to get correct variable values

The function $q(e)$ satisfies a first order linear ODE $$ \frac{\mathrm{d}q}{\mathrm{d}e} = \frac{111 e^4+876 e^2+288}{(e^2-1) (121 e^2+304)} q(e), $$ which can be solved very easily by using an ...
Kirill's user avatar
  • 11.4k
6 votes
Accepted

Ways to solve $Ax=b$ for a sparse (banded) $A$ with updates

If the only non-zero entries of $A_{ij}$ have $j$ in $\{i - 1, i, i + 1\}$, then $A$ is a banded matrix with bandwidth 1. More generally, you can talk about matrices of bandwidth $k$ where $k$ is any ...
Daniel Shapero's user avatar
6 votes

Numerical integration in Python with unknown constant

What you want seems inherently impossible, and that’s not due to restrictions of Python. The only way we can arrive at a situation where we only need to apply a single quadrature is to get ...
Wrzlprmft's user avatar
  • 2,032
6 votes
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Forward and backward integration -- cause of errors

Do you have more suggestions to improve the precision and accuracy of the method ? What are the cause of such errors from the mathematical point of view ? For instance if we have different time scale ...
Chris Rackauckas's user avatar
6 votes

Get the roots of a Hermite interpolating polynomial

The interpolated polynomial does not have roots. Considering that the behavior outside the interpolation region holds is termed extrapolation. You can explicitly use the polynomial, given by (as I ...
nicoguaro's user avatar
  • 8,510
6 votes

Numerical derivative in python

The Savitzky-Golay filter uses a constant delta (the spacing of the samples,) and the default value of the delta in the filter implementation is 1, according to https://docs.scipy.org/doc/scipy-0.16.1/...
KJ Nam's user avatar
  • 81
6 votes

solve_ivp from scipy does not integrate the whole range of tspan

You can examine the sol object to see why the integration failed. It provides the message 'Required step size is less than spacing between numbers.' This usually ...
Steven Roberts's user avatar
6 votes
Accepted

Calculate determinant of unitary matrices based on SVD implementation

If you are prepared to go digging around in the fortran code: The SVD algorithm consists of a few parts: Bidiagonalization (usually using Householder reflectors) Use QR shifts to reduce the ...
Thijs Steel's user avatar
  • 1,693

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