cddm.map

Data mapping and k-averaging functions.

Module Contents

cddm.map.sector_indexmap(kmap, anglemap, angle=0.0, sector=30.0, kstep=1.0)

Builds indexmap array of integers ranging from -1 (invalid data) and positive integers. Each non-negative integer is a valid k-index computed from sector parameters.

Parameters

  • kmap (ndarray) – Size of wavevector at each (i,j) indices in the rfft2 ouptut data.

  • anglemap (ndarray) – Angle of the wavevector at each (i,j) indices in the rfft2 ouptut data.

  • angle (float) – Mean angle of the sector in degrees (-90 to 90).

  • sector (float) – Width of the sector in degrees (between 0 and 180)

  • kstep (float, optional) – k resolution in units of minimum step size.

Returns

map – Ouput array of non-zero valued k-indices where data is valid, -1 elsewhere.

Return type

ndarray

cddm.map.fft2_sector_indexmap(kmap, anglemap, angle=0.0, sector=30.0, kstep=1.0)

Builds indexmap array of integers ranging from -1 (invalid data) and positive integers. Each non-negative integer is a valid k-index computed from sector parameters.

Parameters

  • kmap (ndarray) – Size of wavevector at each (i,j) indices in the rfft2 ouptut data.

  • anglemap (ndarray) – Angle of the wavevector at each (i,j) indices in the rfft2 ouptut data.

  • angle (float) – Mean angle of the sector in degrees (-180 to 180).

  • sector (float) – Width of the sector in degrees (between 0 and 180)

  • kstep (float, optional) – k resolution in units of minimum step size.

Returns

map – Ouput array of non-zero valued k-indices where data is valid, -1 elsewhere.

Return type

ndarray

cddm.map.rfft2_kangle(kisize=None, kjsize=None, shape=None)

Build k,angle arrays based on the size of the rfft2 data.

Parameters

  • kisize (int) – i-size of the cropped rfft2 data.

  • kjsize (int) – j-size of the cropped rfft2 data

  • shape ((int,int)) – Shape of the original data. This is used to calculate step size. If not given, rectangular data is assumed (equal steps).

Returns

k, angle – k, angle arrays

Return type

ndarray, ndarray

cddm.map.fft2_kangle(kisize=None, kjsize=None, shape=None)

Build k,angle arrays based on the size of the fft2 data.

Parameters

  • kisize (int) – i-size of the cropped fft2 data.

  • kjsize (int) – j-size of the cropped fft2 data

  • shape ((int,int)) – Shape of the original data. This is used to calculate step size. If not given, rectangular data is assumed (equal steps).

Returns

k, angle arrays

Return type

k, angle, ndarray, ndarray

cddm.map.rfft2_grid(kisize=None, kjsize=None, shape=None)

Build ki,kj coordinate arrays based on the size of the rfft2.

Parameters

  • kisize (int) – i-size of the cropped rfft2 data.

  • kjsize (int) – j-size of the cropped rfft2 data

  • shape ((int,int)) – Shape of the original data. This is used to calculate step size. If not given, rectangular data is assumed (equal steps).

Returns

ki,kj coordinate arrays

Return type

ki, kj, ndarray, ndarray

cddm.map.fft2_grid(kisize=None, kjsize=None, shape=None)

Build ki,kj coordinate arrays based on the size of the fft2.

Parameters

  • kisize (int) – i-size of the cropped fft2 data.

  • kjsize (int) – j-size of the cropped fft2 data

  • shape ((int,int)) – Shape of the original data. This is used to calculate step size. If not given, rectangular data is assumed (equal steps).

Returns

ki,kj coordinate arrays

Return type

ki, kj, ndarray, ndarray

cddm.map.k_indexmap(kisize, kjsize, angle=0, sector=5, kstep=1.0, shape=None)

Builds indexmap array of integers ranging from -1 (invalid data) and positive integers. Each non-negative integer is a valid k-index computed from sector parameters.

Parameters

  • kisize (int) – Height of the fft data

  • kjsize (int) – Width of the fft data

  • angle (float) – Mean angle of the sector in degrees (-90 to 90).

  • sector (float) – Width of the sector in degrees (between 0 and 180)

  • kstep (float, optional) – k resolution in units of minimum step size.

  • shape ((int,int), optional) – Shape of the original data. This is used to calculate step size. If not given, rectangular data is assumed (equal steps).

Returns

map – Ouput array of non-zero valued k-indices where data is valid, -1 elsewhere.

Return type

ndarray

cddm.map.as_rfft2_mask(a, axes=(- 2, - 1))

Converts fft2 (boolean) mask array into rfft2 (boolean) mask array.

cddm.map.as_rfft2_conj(a, axes=(- 2, - 1))

Converts data from fft2 space to rfft2 conjugate half space.

It stores the missing part in the rfft2 data from the full fft2 data. The shape of the ouptut is the same as that of the as_rfft2_data. Note that you should only access non-zero frequencies. First column does not hold any data.

Examples

>>> a = np.random.randn(32,32)
>>> f = np.fft.fft2(a)
>>> rf = np.fft.rfft2(a)
>>> cf = as_rfft2_conj(f)
>>> np.allclose(cf[2,5], f[-2,-5])
True
cddm.map.as_rfft2_data(a, axes=(- 2, - 1))

Converts data from fft2 space to rfft2 half space.

Examples

>>> a = np.random.randn(32,32)
>>> f = np.fft.fft2(a)
>>> rf = np.fft.rfft2(a)
>>> hf = as_rfft2_data(f)
>>> np.allclose(hf,rf)
True
cddm.map.from_rfft2_data(a, shape=None, axes=(- 2, - 1))

Converts halfspace rfft2 data to fullspace fft2 data.

Examples

>>> a = np.random.randn(32,32)
>>> f = np.fft.fft2(a)
>>> rf = np.fft.rfft2(a)
>>> hf = as_rfft2_data(f)
>>> np.allclose(hf,rf)
True
>>> np.allclose(from_rfft2_data(hf, shape = (32,32)), f)
True
cddm.map.fft2_k_indexmap(kisize, kjsize, angle=0, sector=5, kstep=1.0, shape=None, mode='rfft2')

Builds indexmap array of integers ranging from -1 (invalid data) and positive integers. Each non-negative integer is a valid k-index computed from the sector parameters.

Parameters

  • kisize (int) – Height of the fft2 or rfft2 data

  • kjsize (int) – Width of the fft2 or rfft2 data

  • angle (float) – Mean angle of the sector in degrees (-90 to 90).

  • sector (float) – Width of the sector in degrees (between 0 and 180)

  • kstep (float, optional) – k resolution in units of minimum step size.

  • shape ((int,int), optional) – Shape of the original data. This is used to calculate step size. If not given, rectangular data is assumed (equal steps).

  • mode (str, optional) – Describes inpud data mode. Either ‘rfft2’ or ‘fft2’.

Returns

map – A fullsize ouput array of non-zero valued k-indices where data is valid, -1 elsewhere.

Return type

ndarray

cddm.map.plot_indexmap(graph, mode='rfft2')

Plots indexmap array. If mode == “rfft2” it plots half-space data, If mode ==”fft2” it performs plotting of full-spaced data.

cddm.map.k_select(data, angle, sector=5, kstep=1, k=None, shape=None, mask=None, mode='rfft2')

k-selection and k-averaging of normalized (and merged) correlation data.

This function takes (…,i,j,n) correlation data and performs k-based selection and averaging of the data. If you analyzed masked video, you must provide the mask.

Parameters

  • deta (array_like) – Input correlation data of shape (…,i,j,n)

  • angle (float) – Angle between the j axis and the direction of k-vector

  • sector (float, optional) – Defines sector angle, k-data is avergaed between angle+sector and angle-sector angles

  • kstep (float, optional) – Defines an approximate k step in pixel units

  • k (float or list of floats, optional) – If provided, only return at a given k value (and not at all non-zero k values)

  • shape (tuple) – Shape of the original video frame. If shape is not rectangular, it must be provided.

  • mask (ndarray, optional) – A boolean array. This is the mask used in video.mask().

Returns

out – If k s not defined, this is an iterator that yields a tuple of (k_avg, data_avg) of actual (mean) k and averaged data. If k is a list of indices, it returns an iterator that yields a tuple of (k_avg, data_avg) for every non-zero data if k is an integer, it returns a tuple of (k_avg, data_avg) for a given k-index.

Return type

iterator, or tuple