Single Dish Radio Astronomy Software Tools

For an overview of SDRAST and the current status please visit https://sdrast.github.io/.

Todo

Change import * from math to import math.

Math Package

Local mathematical functions in addition to the Python ‘math’ module.

The smoothing functions are adapted from: http://www.swharden.com/blog/2008-11-17-linear-data-smoothing-in-python/

Functions

acos	Return the arc cosine (measured in radians) of x.
acosh	Return the inverse hyperbolic cosine of x.
allan_variance(data)	Computes Allan variance
asin	Return the arc sine (measured in radians) of x.
asinh	Return the inverse hyperbolic sine of x.
atan	Return the arc tangent (measured in radians) of x.
atan2	Return the arc tangent (measured in radians) of y/x.
atanh	Return the inverse hyperbolic tangent of x.
binary_to_decimal(string)	Converts a binary string, sign bit then msb on left, to an integer.
ceil	Return the ceiling of x as an Integral.
copysign	Return a float with the magnitude (absolute value) of x but the sign of y.
cos	Return the cosine of x (measured in radians).
cosh	Return the hyperbolic cosine of x.
decimal_to_binary(integer[, nbits, grouped])	Converts integer to binary string of length nbits, sign bit and then m.s.b.
degrees	Convert angle x from radians to degrees.
erf	Error function at x.
erfc	Complementary error function at x.
exp	Return e raised to the power of x.
expm1	Return exp(x)-1.
fabs	Return the absolute value of the float x.
factorial	Find x!.
floor	Return the floor of x as an Integral.
fmod	Return fmod(x, y), according to platform C.
frexp	Return the mantissa and exponent of x, as pair (m, e).
fsum	Return an accurate floating point sum of values in the iterable seq.
gamma	Gamma function at x.
gaussian(x, mean, stdev)	Un-normalized gaussian
gcd	greatest common divisor of x and y
group_variance(data, n_data, n_grps)	Computes the variance of n_data points of data[], averaged in groups of n_grps and returns the variance for these groups
hypot	Return the Euclidean distance, sqrt(x*x + y*y).
isclose	Determine whether two floating point numbers are close in value.
isfinite	Return True if x is neither an infinity nor a NaN, and False otherwise.
isinf	Return True if x is a positive or negative infinity, and False otherwise.
isnan	Return True if x is a NaN (not a number), and False otherwise.
ldexp	Return x * (2**i).
lgamma	Natural logarithm of absolute value of Gamma function at x.
log(x, [base=math.e])	Return the logarithm of x to the given base.
log10	Return the base 10 logarithm of x.
log1p	Return the natural logarithm of 1+x (base e).
log2	Return the base 2 logarithm of x.
modf	Return the fractional and integer parts of x.
normalized_gaussian(x, mean, stdev)	gaussian function whose area under the curve is unity.
pow	Return x**y (x to the power of y).
power_of_2_ge(number)	This finds the integer greater than ‘number’ which is a power of two.
radians	Convert angle x from degrees to radians.
remainder	Difference between x and the closest integer multiple of y.
scaled_gaussian(x, mean, fwhm)	returns a normalized gauusian’s value at x, given the mean and full width at half maximam
sin	Return the sine of x (measured in radians).
sinh	Return the hyperbolic sine of x.
smoothList(datalist[, degree])	Smooth a list of numbers by averaging ‘degree’ samples.
smoothListGaussian(datalist[, degree])	Gaussian data smoothing function.
smoothListTriangle(datalist[, degree])	Smooth a list of numbers by convolving with a triangle.
solid_angle(angle)	Solid angle for a circular pattern
sqrt	Return the square root of x.
tan	Return the tangent of x (measured in radians).
tanh	Return the hyperbolic tangent of x.
trunc	Truncates the Real x to the nearest Integral toward 0.

Math.Bin Module

Binary operations

Example::

In [1]: import Math.Bin as B

In [2]: B.setbit(0,12) Out[2]: 4096

In [3]: “%x” % B.setbit(0,12) Out[3]: ‘1000’

Functions

bitcnt(val)	Counts the number of set bits in the binary value.
clrbit(word, bit)	Clear bit in word (set to 0)
field_mask(bits[, leftshift])	Set a bit mask
get_field(word[, mask])	Extract a value from a range of bits (bit field)
getbit(word, bit)	get the value of bit in word
reverse(x, n)	Reverse the pattern
rol(val, r_bits, max_bits)
ror(val, r_bits, max_bits)
set_field(word, value[, mask])	Set a value into a bit field
setbit(word, bit)	set bit in word to 1

Math.geometry Module

Classes for properties of geometrical objects.

This isn’t exactly difficult math but it illustrates object-oriented programming pretty well.

For simple calculations it isn’t necessary to create instances of the objects. For example:

In [1]: from Math.geometry import *

In [2]: Sphere(6000).area
Out[2]: 452389342.11693019

In [3]: Sphere(6000).horizon(0.01)
Out[3]: 10.95443745708116

Sometimes, an instance is useful though:

In [4]: s = Sphere(6000)

In [5]: r = s.horizon(300)

In [6]: visible_fraction = Circle(r).area/s.area

In [7]: visible_fraction
Out[7]: 0.023242630385487552

Classes

Circle(radius)	Circle, a subclass of Circular()
Circular(radius)	Superclass for circular objects, like Circle() and Sphere()
Sphere(radius)	Sphere, a subclass of Circular()

Class Inheritance Diagram

Math.least_squares Module

leastsq_support - short-cuts for scipy.optimize.leastsq

Functions

factorial	Find x!.
fit_gaussian(error_function, initial_guess, x, y)	Invoke least squares fit to a Gaussian function
gaussian(x, p)	Gaussian function
gaussian_error_function(p, x, y)	Difference between model and actual data
leastsq(func, x0[, args, Dfun, full_output, …])	Minimize the sum of squares of a set of equations.
log(x, [base=math.e])	Return the logarithm of x to the given base.
savitzky_golay(y, window_size, order[, …])	Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
savitzky_golay_piecewise(xvals, data[, …])	In cyclic voltammetry, voltage (being the abcissa) changes like a triangle wave.
simple_gaussian(x, p)	un-normalized gaussian for fitting
sqrt	Return the square root of x.
st_dev(width_half_max)	Standard deviation from Gaussian full width at half maxiuam
width_half_max(st_dev)	Gaussian full width at half maximum from standard deviation

Math.multigauss Module

Functions

MMgauss(x, pos, std, *args)	A form of ‘multigauss’ that curfit can use.
gaussian(x, mean, stdev)	Un-normalized gaussian
multigaussian(x, pos, std, *args)	Returns the value of the sum of multiple Gaussians.

Math.statistics Module

Allan variance

not yet tested since bug fixes - tbhk 2007-10-12

Functions

allan_variance(data)	Computes Allan variance
group_variance(data, n_data, n_grps)	Computes the variance of n_data points of data[], averaged in groups of n_grps and returns the variance for these groups

Indices and tables

• Index

• Module Index

• Search Page