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SciPy Cookbook
SciPy Cookbook

This is the SciPy Cookbook a collection of various user-contributed recipes, which once lived under wiki.scipy.org. Note that some are fairly old (20052009), and may not be as relevant today. If you want to contribute additions/corrections, see the the SciPy-CookBook repository.

Compiling Extensions
Graphics
Input Output
Matplotlib / 3D Plotting
Matplotlib / Embedding Plots in Apps
Matplotlib / Misc
Matplotlib / Pseudo Color Plots
Matplotlib / Simple Plotting
Matplotlib / Typesetting
Mayavi
Mayavi / TVTK
Numpy & Scipy / Advanced topics
Numpy & Scipy / Interpolation
Numpy & Scipy / Linear Algebra
Numpy & Scipy / Matplotlib
Numpy & Scipy / Optimization and fitting techniques
Numpy & Scipy / Ordinary differential equations
Numpy & Scipy / Other examples
Numpy & Scipy / Root finding
Numpy & Scipy / Tips and tricks
Other examples
Performance
Scientific GUIs
Scientific Scripts
Using NumPy With Other Languages (Advanced)
Outdated
Compiling Extensions
Compiling Extensions
Fortran I/O Formats
Fortran I/O Formats

NOTE: you may want to use scipy.io.FortranFile instead.

Files written by Fortran programs can be written using one of two formats: formatted or unformatted. Formatted files are written in human-readable formats and it should be possible to load them using numpy.fromfile. Unformatted files are written using a binary format that is unspecified by the Fortran standard. In practice, most compilers/runtimes use a record-based format with an integer header consisting of the length of the record in bytes, then the record itself followed by an integer footer with the length of the preceeding in bytes.

Given that the precision and endian-ness of the headers and the data are unspecified, there are a large number of possible combinations that may be seen in the wild. The class can deal with a great many of these.

The following is an example of how to read a particular unformatted output file. Note the presence of the i4 elements of the dtype representing the header and the footer.

Reading FORTRAN unformatted IO files

Lots of scientific code is written in FORTRAN. One of the most convenient file formats to create in FORTRAN is the so-called unformatted binary file. These files have all the disadvantages of raw binary IO - no metadata, data depends on host endianness, floating-point representation, and possibly word size - but are not simply raw binary. They are organized into records, which are padded with size information. Nevertheless, one does encounter such files from time to time. No prewritten code appears to be available to read them in numpy/scipy, but it can be done with relative ease using numpys record arrays:

>>> A = N.fromfile("/tmp/tmp_i7j_a/resid2.tmp",... N.dtype([('pad1','i4'),... ('TOA','f8'),... ('resid_p','f8'),... ('resid_s','f8'),... ('orb_p','f8'),... ('f','f8'),... ('wt','f8'),... ('sig','f8'),... ('preres_s','f8'),... ('pad3','i8'),... ('pad2','i4')]))

This example is designed to read [http://www.atnf.csiro.au/research/pulsar/tempo/ref_man_sections/output.txt a file] output by [http://www.atnf.csiro.au/research/pulsar/tempo/ TEMPO]. Most of the fields, TOA up to preres_s, are fields that are present and of interest in the file. The field pad3 is either an undocumented addition to the file format or some kind of padding (it is always zero in my test file). The FORTRAN unformatted I/O adds the fields pad1 and pad2. Each should contain the length, in bytes, of each record (so the presence of the extra pad3 field could be deduced). This code ignores t

Easy multithreading
Easy multithreading

Python includes a multithreading package, threading, but pythons multithreading is seriously limited by the Global Interpreter Lock, which allows only one thread to be interacting with the interpreter at a time. For purely interpreted code, this makes multithreading effectively cooperative and unable to take advantage of multiple cores.

However, numpy code often releases the GIL while it is calculating, so that simple parallelism can speed up the code. For sophisticated applications, one should look into MPI or using threading directly, but surprisingly often ones application is embarrassingly parallel, that is, one simply has to do the same operation to many objects, with no interaction between iterations. This kind of calculation can be easily parallelized:

dft = parallel_map(lambda f: sum(exp(2.j*pi*f*times)), frequencies)

The code implementing parallel_map is not too complicated, and is attached to this entry. Even simpler, if one doesnt want to return values:

def compute(n): ...do something...foreach(compute, range(100))

This replaces a for loop.

See attachments for code (written by AMArchibald). [[AttachList]]

See also ParallelProgramming for alternatives and more discussion.

Attachments
Eye Diagram
Eye Diagram

The code below generates the following plot:

The main script generates numtraces traces and on a grid of 600x600 it - photo 1

The main script generates num_traces traces, and on a grid of 600x600, it counts the number times a trace crosses a grid point. The grid is then plotted using matplotlibs imshow() function. The counting is performed using Bresenhams line algorithm, to ensure that the counting is correct, and steep parts of the curve dont result in missed counts.

Bresenhams algorithm is slow in pure Python, so a Cython version is included. If you do not build the Cython version of the Bresenham code, be sure to reduce num_traces before running the program!

Heres the main demo script, eye_demo.py.

#!pythonimport numpy as npuse_fast = Truetry: from brescount import bres_curve_countexcept ImportError: print "The cython version of the curve counter is not available." use_fast = Falsedef bres_segment_count_slow(x0, y0, x1, y1, grid): """Bresenham's algorithm. The value of grid[x,y] is incremented for each x,y in the line from (x0,y0) up to but not including (x1, y1). """ nrows, ncols = grid.shape dx = abs(x1 - x0) dy = abs(y1 - y0) sx = 0 if x0 < x1: sx = 1 else: sx = -1 sy = 0 if y0 < y1: sy = 1 else: sy = -1 err = dx - dy while True: # Note: this test is moved before setting # the value, so we don't set the last point. if x0 == x1 and y0 == y1: break if 0 <= x0 < nrows and 0 <= y0 < ncols: grid[x0, y0] += 1 e2 = 2 * err if e2 > -dy: err -= dy x0 += sx if e2 < dx: err += dx y0 += sydef bres_curve_count_slow(x, y, grid): for k in range(x.size - 1): x0 = x[k] y0 = y[k] x1 = x[k+1] y1 = y[k+1] bres_segment_count_slow(x0, y0, x1, y1, grid)def random_trace(t): s = 2*(np.random.randint(0, 5) % 2) - 1 r = 0.01 * np.random.randn() s += r a = 2.0 + 0.001 * np.random.randn() q = 2*(np.random.randint(0, 7) % 2) - 1 t2 = t + q*(6 + 0.01*np.random.randn()) t2 += 0.05*np.random.randn()*t y = a * (np.exp(s*t2) / (1 + np.exp(s*t2)) - 0.5) + 0.07*np.random.randn() return yif __name__ == "__main__": import matplotlib.pyplot as plt grid_size = 600 grid = np.zeros((grid_size, grid_size), dtype=np.int32) tmin = -10.0 tmax = 10.0 n = 81 t = np.linspace(tmin, tmax, n) dt = (tmax - tmin) / (n - 1) ymin = -1.5 ymax = 1.5 num_traces = 1000 for k in range(num_traces): # Add some noise to the times at which the signal # will be sampled. Without this, all the samples occur # at the same times, and this produces an aliasing # effect in the resulting bin counts. # If n == grid_size, this can be dropped, and t2 = t # can be used instead. (Or, implement an antialiased # version of bres_curve_count.) steps = dt + np.sqrt(0.01 * dt) * np.random.randn(n) steps[0] = 0 steps_sum = steps.cumsum() t2 = tmin + (tmax - tmin) * steps_sum / steps_sum[-1] td = (((t2 - tmin) / (tmax - tmin)) * grid_size).astype(np.int32) y = random_trace(t2) # Convert y to integers in the range [0,grid_size). yd = (((y - ymin) / (ymax - ymin)) * grid_size).astype(np.int32) if use_fast: bres_curve_count(td, yd, grid) else: bres_curve_count_slow(td, yd, grid) plt.figure() # Convert to float32 so we can use nan instead of 0. grid = grid.astype(np.float32) grid[grid==0] = np.nan plt.grid(color='w') plt.imshow(grid.T[::-1,:], extent=[0,1,0,1], cmap=plt.cm.coolwarm, interpolation='gaussian') ax = plt.gca() ax.set_axis_bgcolor('k') ax.set_xticks(np.linspace(0,1,11)) ax.set_yticks(np.linspace(0,1,11)) ax.set_xticklabels([]) ax.set_yticklabels([]) plt.colorbar() fig = plt.gcf() #plt.savefig("eye-diagram.jpg", bbox_inches='tight') plt.show()
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