Mathematical utilities

pymodaq_utils.math_utils.find_index(x, threshold)

find_index finds the index ix such that x(ix) is the closest from threshold

Parameters:

• x (vector)

• threshold (Union[Number, List[Number]])

Returns:

out – out=[(ix0,xval0),(ix1,xval1),…]

Return type:

List[tuple]

pymodaq_utils.math_utils.ft(x, dim=-1)

Process the 1D fast fourier transform and swaps the axis to get coorect results using ftAxis :type x: (ndarray) the array on which the FFT should be done :param x: :type x: (ndarray) the array on which the FFT should be done :type dim: the axis over which is done the FFT (default is the last of the array) :param dim: :type dim: the axis over which is done the FFT (default is the last of the array)

See also

ftAxis, ftAxis_time, ift, ft2, ift2

pymodaq_utils.math_utils.ft2(x, dim=(-2, -1))

Process the 2D fast fourier transform and swaps the axis to get correct results using ftAxis :type x: (ndarray) the array on which the FFT should be done :param x: :type x: (ndarray) the array on which the FFT should be done :type dim: the axis over which is done the FFT (default is the last of the array) :param dim: :type dim: the axis over which is done the FFT (default is the last of the array)

See also

ftAxis, ftAxis_time, ift, ft2, ift2

pymodaq_utils.math_utils.ftAxis(Npts, omega_max)

Given two numbers Npts,omega_max, return two vectors spanning the temporal and spectral range. They are related by Fourier Transform

Parameters:

• Npts ((int)) – A number of points defining the length of both grids

• omega_max ((float)) – The maximum circular frequency in the spectral domain. its unit defines the temporal units. ex: omega_max in rad/fs implies time_grid in fs

Returns:

• omega_grid ((ndarray)) – The spectral axis of the FFT

• time_grid ((ndarray))) – The temporal axis of the FFT

See also

ftAxis, ftAxis_time, ift, ft2, ift2

pymodaq_utils.math_utils.ftAxis_time(Npts, time_max)

Given two numbers Npts,omega_max, return two vectors spanning the temporal and spectral range. They are related by Fourier Transform

Parameters:

• Npts (number) – A number of points defining the length of both grids

• time_max (number) – The maximum tmporal window

Returns:

• omega_grid (vector) – The spectral axis of the FFT

• time_grid (vector) – The temporal axis of the FFT

See also

ftAxis, ftAxis_time, ift, ft2, ift2

pymodaq_utils.math_utils.gauss1D(x, x0, dx, n=1)

compute the gaussian function along a vector x, centered in x0 and with a FWHM i intensity of dx. n=1 is for the standart gaussian while n>1 defines a hypergaussian

Parameters:

• x ((ndarray) first axis of the 2D gaussian)

• x0 ((float) the central position of the gaussian)

• dx ((float) :the FWHM of the gaussian)

• n=1 (an integer to define hypergaussian, n=1 by default for regular gaussian)

Returns:

out – the value taken by the gaussian along x axis

Return type:

vector

pymodaq_utils.math_utils.gauss2D(x, x0, dx, y, y0, dy, n=1, angle=0)

compute the 2D gaussian function along a vector x, centered in x0 and with a FWHM in intensity of dx and smae along y axis. n=1 is for the standard gaussian while n>1 defines a hypergaussian. optionally rotate it by an angle in degree

Parameters:

• x ((ndarray) first axis of the 2D gaussian)

• x0 ((float) the central position of the gaussian)

• dx ((float) :the FWHM of the gaussian)

• y ((ndarray) second axis of the 2D gaussian)

• y0 ((float) the central position of the gaussian)

• dy ((float) :the FWHM of the gaussian)

• n=1 (an integer to define hypergaussian, n=1 by default for regular gaussian)

• angle ((float) a float to rotate main axes, in degree)

Returns:

out

Return type:

ndarray 2 dimensions

pymodaq_utils.math_utils.ift(x, dim=0)

Process the inverse 1D fast fourier transform and swaps the axis to get correct results using ftAxis :type x: (ndarray) the array on which the FFT should be done :param x: :type x: (ndarray) the array on which the FFT should be done :type dim: the axis over which is done the FFT (default is the last of the array) :param dim: :type dim: the axis over which is done the FFT (default is the last of the array)

See also

ftAxis, ftAxis_time, ift, ft2, ift2

pymodaq_utils.math_utils.ift2(x, dim=(-2, -1))

Process the inverse 2D fast fourier transform and swaps the axis to get correct results using ftAxis :type x: (ndarray) the array on which the FFT should be done :param x: :type x: (ndarray) the array on which the FFT should be done :type dim: the axis (or a tuple of axes) over which is done the FFT (default is the last of the array) :param dim: :type dim: the axis (or a tuple of axes) over which is done the FFT (default is the last of the array)

See also

ftAxis, ftAxis_time, ift, ft2, ift2

pymodaq_utils.math_utils.linspace_step(start, stop, step)

Compute a regular linspace_step distribution from start to stop values.

Parameters	Type	Description
start	scalar	the starting value of distribution
stop	scalar	the stopping value of distribution
step	scalar	the length of a distribution step

Returns:

• scalar array – The computed distribution axis as an array.

pymodaq_utils.math_utils.my_moment(x, y)

Returns the moments of a distribution y over an axe x

Parameters:

• x (list or ndarray) – vector of floats

• y (list or ndarray) – vector of floats corresponding to the x axis

Returns:

m – Contains moment of order 0 (mean) and of order 1 (std) of the distribution y

Return type:

list

pymodaq_utils.math_utils.odd_even(x)

odd_even tells if a number (or an array) is odd (return True) or even (return False)

Parameters:

x (Union[int, ndarray])

Returns:

bool

Return type:

boolean or array of boolean