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Implement order=0 in functions.interpolateArray; use scipy only for

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order>1.
This commit is contained in:
Luke Campagnola 2016-09-13 18:08:11 -07:00
parent 5195d9dd63
commit 7f0556b05f
1 changed files with 76 additions and 55 deletions
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127
pyqtgraph/functions.py
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@ -410,11 +410,44 @@ def eq(a, b):
raise Exception("== operator returned type %s" % str(type(e)))
def affineSliceCoords(shape, origin, vectors, axes):
"""Return the array of coordinates used to sample data arrays in affineSlice().
"""
# sanity check
if len(shape) != len(vectors):
raise Exception("shape and vectors must have same length.")
if len(origin) != len(axes):
raise Exception("origin and axes must have same length.")
for v in vectors:
if len(v) != len(axes):
raise Exception("each vector must be same length as axes.")
shape = list(map(np.ceil, shape))
## make sure vectors are arrays
if not isinstance(vectors, np.ndarray):
vectors = np.array(vectors)
if not isinstance(origin, np.ndarray):
origin = np.array(origin)
origin.shape = (len(axes),) + (1,)*len(shape)
## Build array of sample locations.
grid = np.mgrid[tuple([slice(0,x) for x in shape])] ## mesh grid of indexes
x = (grid[np.newaxis,...] * vectors.transpose()[(Ellipsis,) + (np.newaxis,)*len(shape)]).sum(axis=1) ## magic
x += origin
return x
def affineSlice(data, shape, origin, vectors, axes, order=1, returnCoords=False, **kargs):
"""
Take a slice of any orientation through an array. This is useful for extracting sections of multi-dimensional arrays such as MRI images for viewing as 1D or 2D data.
Take a slice of any orientation through an array. This is useful for extracting sections of multi-dimensional arrays
such as MRI images for viewing as 1D or 2D data.
The slicing axes are aribtrary; they do not need to be orthogonal to the original data or even to each other. It is possible to use this function to extract arbitrary linear, rectangular, or parallelepiped shapes from within larger datasets. The original data is interpolated onto a new array of coordinates using scipy.ndimage.map_coordinates if it is available (see the scipy documentation for more information about this). If scipy is not available, then a slower implementation of map_coordinates is used.
The slicing axes are aribtrary; they do not need to be orthogonal to the original data or even to each other. It is
possible to use this function to extract arbitrary linear, rectangular, or parallelepiped shapes from within larger
datasets. The original data is interpolated onto a new array of coordinates using either interpolateArray if order<2
or scipy.ndimage.map_coordinates otherwise.
For a graphical interface to this function, see :func:`ROI.getArrayRegion <pyqtgraph.ROI.getArrayRegion>`
@ -453,47 +486,24 @@ def affineSlice(data, shape, origin, vectors, axes, order=1, returnCoords=False,
affineSlice(data, shape=(20,20), origin=(40,0,0), vectors=((-1, 1, 0), (-1, 0, 1)), axes=(1,2,3))
"""
try:
import scipy.ndimage
have_scipy = True
except ImportError:
have_scipy = False
have_scipy = False
# sanity check
if len(shape) != len(vectors):
raise Exception("shape and vectors must have same length.")
if len(origin) != len(axes):
raise Exception("origin and axes must have same length.")
for v in vectors:
if len(v) != len(axes):
raise Exception("each vector must be same length as axes.")
shape = list(map(np.ceil, shape))
x = affineSliceCoords(shape, origin, vectors, axes)
## transpose data so slice axes come first
trAx = list(range(data.ndim))
for x in axes:
trAx.remove(x)
for ax in axes:
trAx.remove(ax)
tr1 = tuple(axes) + tuple(trAx)
data = data.transpose(tr1)
#print "tr1:", tr1
## dims are now [(slice axes), (other axes)]
## make sure vectors are arrays
if not isinstance(vectors, np.ndarray):
vectors = np.array(vectors)
if not isinstance(origin, np.ndarray):
origin = np.array(origin)
origin.shape = (len(axes),) + (1,)*len(shape)
if order > 1:
try:
import scipy.ndimage
except ImportError:
raise ImportError("Interpolating with order > 1 requires the scipy.ndimage module, but it could not be imported.")
## Build array of sample locations.
grid = np.mgrid[tuple([slice(0,x) for x in shape])] ## mesh grid of indexes
x = (grid[np.newaxis,...] * vectors.transpose()[(Ellipsis,) + (np.newaxis,)*len(shape)]).sum(axis=1) ## magic
x += origin
## iterate manually over unused axes since map_coordinates won't do it for us
if have_scipy:
# iterate manually over unused axes since map_coordinates won't do it for us
extraShape = data.shape[len(axes):]
output = np.empty(tuple(shape) + extraShape, dtype=data.dtype)
for inds in np.ndindex(*extraShape):
@ -502,8 +512,8 @@ def affineSlice(data, shape, origin, vectors, axes, order=1, returnCoords=False,
else:
# map_coordinates expects the indexes as the first axis, whereas
# interpolateArray expects indexes at the last axis.
tr = tuple(range(1,x.ndim)) + (0,)
output = interpolateArray(data, x.transpose(tr))
tr = tuple(range(1, x.ndim)) + (0,)
output = interpolateArray(data, x.transpose(tr), order=order)
tr = list(range(output.ndim))
trb = []
@ -520,16 +530,21 @@ def affineSlice(data, shape, origin, vectors, axes, order=1, returnCoords=False,
else:
return output
def interpolateArray(data, x, default=0.0):
def interpolateArray(data, x, default=0.0, order=1):
"""
N-dimensional interpolation similar to scipy.ndimage.map_coordinates.
This function returns linearly-interpolated values sampled from a regular
grid of data.
*data* is an array of any shape containing the values to be interpolated.
*x* is an array with (shape[-1] <= data.ndim) containing the locations
within *data* to interpolate.
============== ===========================================================================================
**Arguments:**
*data* Array of any shape containing the values to be interpolated.
*x* Array with (shape[-1] <= data.ndim) containing the locations within *data* to interpolate.
*default* Value to return for locations in *x* that are outside the bounds of *data*.
*order* Order of interpolation: 0=nearest, 1=linear.
============== ===========================================================================================
Returns array of shape (x.shape[:-1] + data.shape[x.shape[-1]:])
@ -574,6 +589,9 @@ def interpolateArray(data, x, default=0.0):
This is useful for interpolating from arrays of colors, vertexes, etc.
"""
if order not in (0, 1):
raise ValueError("interpolateArray requires order=0 or 1 (got %s)" % order)
prof = debug.Profiler()
nd = data.ndim
@ -583,7 +601,7 @@ def interpolateArray(data, x, default=0.0):
# First we generate arrays of indexes that are needed to
# extract the data surrounding each point
fields = np.mgrid[(slice(0,2),) * md]
fields = np.mgrid[(slice(0,order+1),) * md]
xmin = np.floor(x).astype(int)
xmax = xmin + 1
indexes = np.concatenate([xmin[np.newaxis, ...], xmax[np.newaxis, ...]])
@ -609,18 +627,21 @@ def interpolateArray(data, x, default=0.0):
prof()
## Interpolate
s = np.empty((md,) + fieldData.shape, dtype=float)
dx = x - xmin
# reshape fields for arithmetic against dx
for ax in range(md):
f1 = fields[ax].reshape(fields[ax].shape + (1,)*(dx.ndim-1))
sax = f1 * dx[...,ax] + (1-f1) * (1-dx[...,ax])
sax = sax.reshape(sax.shape + (1,) * (s.ndim-1-sax.ndim))
s[ax] = sax
s = np.product(s, axis=0)
result = fieldData * s
for i in range(md):
result = result.sum(axis=0)
if order == 0:
result = fieldData[0,0]
else:
s = np.empty((md,) + fieldData.shape, dtype=float)
dx = x - xmin
# reshape fields for arithmetic against dx
for ax in range(md):
f1 = fields[ax].reshape(fields[ax].shape + (1,)*(dx.ndim-1))
sax = f1 * dx[...,ax] + (1-f1) * (1-dx[...,ax])
sax = sax.reshape(sax.shape + (1,) * (s.ndim-1-sax.ndim))
s[ax] = sax
s = np.product(s, axis=0)
result = fieldData * s
for i in range(md):
result = result.sum(axis=0)
prof()