## numerical

### How to Test Numerical Analysis Routines?

Are there any good online resources for how to create, maintain and think about writing test routines for numerical analysis code? One of the limitations I can see for something like testing matrix multiplication is that the obvious tests (like having one matrix being the identity) may not fully test the functionality of the code. Also...

### Open source alternative to MATLAB's fmincon function?

Is there an open-source alternative to MATLAB's fmincon function for constrained linear optimization? I'm rewriting a MATLAB program to use Python / NumPy / SciPy and this is the only function I haven't found an equivalent to. A NumPy-based solution would be ideal, but any language will do. ...

### Computationally efficient three dimensional arrays in C

I am trying to solve numerically a set of partial differential equations in three dimensions. In each of the equations the next value of the unknown in a point depends on the current value of each unknown in the closest points. To write an efficient code I need to keep the points close in the three dimensions close in the (one-dimension...

### .NET NumericTextBox

Does anyone know why Microsoft does not ship a numeric text box with its .NET framework e.g. a text box which would ensure that the characters entered are always a valid number? It's something which is commonly used across applications of different flavours and indeed something which most GUI libraries (well, those that I know) deliver i...

### What is the best Java numerical method package?

I am looking for a Java-based numerical method package that provides functionality including: Solving systems of equations using different numerical analysis algorithms. Matrix methods (e.g., inversion). Spline approximations. Probability distributions and statistical methods. In this case, "best" is defined as a package with a matur...

### Test if a floating point number is an integer

This code works (C# 3) double d; if(d == (double)(int)d) ...; Is there a better way to do this? For extraneous reasons I want to avoid the double cast so; what nice ways exist other than this? (even if they aren't as good) Note: Several people pointed out the (important) point that == is often problematic regrading floating point. ...

### Is one's complement a real-world issue, or just a historical one?

Another question asked about determining odd/evenness in C, and the idiomatic (x & 1) approach was correctly flagged as broken for one's complement-based systems, which the C standard allows for. Do systems really exist in the 'real world' outside of computer museums? I've been coding since the 1970's and I'm pretty sure I've never met ...

### When to use Fixed Point these days

For intense number-crunching i'm considering using fixed point instead of floating point. Of course it'll matter how many bytes the fixed point type is in size, on what CPU it'll be running on, if i can use (for Intel) the MMX or SSE or whatever new things come up... I'm wondering if these days when floating point runs faster than ever...

### A C library for finding local maxima?

I'm trying to write an audio analysis application, and I need to identify local maxima in a 2D array which represents a spectrogram. I've already got an open source library that can generate the spectrogram using Fast Fourier Transforms, but I was wondering if anybody knew of any good libraries to help me with actually finding the maxima...

### Using GNU Scientific "multimin" to find all local minima

The GNU Scientific library has a multi-dimensional function minimization framework. However, its caveats explicitly says that when used on a function with several different local minima it just returns one arbitrary solution. Does anybody know how you might go about adapting it so that it would return a list of all local minima (subject ...

### Least Squares C# library

I am looking to perform a polynomial least squares regression and am looking for a C# library to do the calculations for me. I pass in the data points and the degree of polynomal (2nd order, 3rd order, etc) and it returns either the C0, C1, C2 etc. constant values or the calculated values "predictions". Note: I am using Least Squares...

### Anyone know where a good windows constant list lives

I'm trying to set an invalid value to -1.. But I don't like magic numbers.. Anyone know where to find a set of common constants. I'm working in VS6 (ish). I'm trying to read a file from across a network, and I need a bad value for the total file size,so I know if I got valid info on it.. 0 is a valid size so I can't use that. Harper ...

### MATLAB: Using ODE solvers?

This is a really basic question but this is the first time I've used MATLAB and I'm stuck. I need to simulate a simple series RC network using 3 different numerical integration techniques. I think I understand how to use the ode solvers, but I have no idea how to enter the differential equation of the system. Do I need to do it via an m-...

### Derivatives in C/C++?

I have some expressions such as x^2+y^2 that I'd like to use for some math calculations. On of the things I'd like to do is to take partial derivatives of the expressions. So if f(x,y) = x^2 + y^2 then the partial of f with respect to x would be 2x, the partial with respect to y would be 2y. I wrote a dinky function using a finite differ...

### What is the best book on numerical methods?

I need to use some heavy-duty numerical methods - quadrature, interpolation, ODE solution with expensive derivative terms, etc. What's the best book on the subject? I will be using packages where I can, but I can already tell there will be times when I need to write my own routines... ...

### Efficient evaluation of hypergeometric functions

Does anyone have experience with algorithms for evaluating hypergeometric functions? I would be interested in general references, but I'll describe my particular problem in case someone has dealt with it. My specific problem is evaluating a function of the form 3F2(a, b, 1; c, d; 1) where a, b, c, and d are all positive reals and c+d >...

### SQL ORDER chars numerically

I have a column of numbers stored as chars. When I do a ORDER BY for this column I get the following: 100 131 200 21 30 31000 etc. How can I order these chars numerically? Do I need to convert something or is there already an SQL command or function for this? Thank You. ...

### Looking for ODE integrator/solver with a relaxed attitude to derivative precision

I have a system of (first order) ODEs with fairly expensive to compute derivatives. However, the derivatives can be computed considerably cheaper to within given error bounds, either because the derivatives are computed from a convergent series and bounds can be placed on the maximum contribution from dropped terms, or through use of pr...

### Solving nonlinear equations numerically

Hello, I need to solve nonlinear minimization (least residual squares of N unknowns) problems in my Java program. The usual way to solve these is the Levenberg-Marquardt algorithm. I have a couple of questions Does anybody have experience on the different LM implementations available? There exist slightly different flavors of LM, and ...

### How to do numerical integration with quantum harmonic oscillator wavefunction?

How to do numerical integration (what numerical method, and what tricks to use) for one-dimensional integration over infinite range, where one or more functions in the integrand are 1d quantum harmonic oscillator wave functions. Among others I want to calculate matrix elements of some function in the harmonic oscillator basis: phin(x...