<gh_stars>1-10
#!/usr/bin/env python

# ===============================================================================
# Copyright 2015 Geoscience Australia
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ===============================================================================

from __future__ import absolute_import
from __future__ import print_function
import numpy
import numexpr


def bulk_stats(array, no_data=None, double=False, as_bip=False):
    """
    Calculates statistics over the temporal/spectral/z domain
    of a multiband image.

    Calculates statistics over the temporal/spectral/z domain of an array
    containing [z,y,x] data.
    Statistics produced in this order are:
    Sum
    Mean
    Valid Observations
    Variance
    Standard Deviation
    Skewness
    Kurtosis
    Max
    Min
    Median (non-interpolated value)
    Median Index (zero based index)
    1st Quantile (non-interpolated value)
    3rd Quantile (non-interpolated value)
    Geometric Mean

    Median, 1st and 3rd quantiles: For odd length arrays the middle value is
    taken. For even length arrays, the first of the two middle values is taken.
    Either way, no interpolation is used for calculation.
    The median index is the band that the median value came from.

    The numexpr module is used to handle most of the operations. Arrays are
    processed faster while using less memory.
    The moments are calculated using the unbiased method i.e. (n - 1).
    The moments are also calculated direct via the formula rather than built
    in functions. Why?? Because we can recycle previous computations rather
    than recompute, which will make the routine faster.

    :param array:
        A 3D numpy array containing [z,y,x] data.

    :param no_data:
        The data value to ignore for calculations. Default is None.
        If set and `array` is not of type float (32 or 64), then
        `array` will be cast to a `float32` array.

    :param double:
        If set to True then `array` will be converted to float64 and
        the output will be evaluted in double precision and returned
        as such. Default is False (float32).

    :param as_bip:
        **Experimental**
        If set to True, the array will be transposed to be
        [Lines,Samples,Bands], and processed as such. The default
        is to process the array as [Bands,Lines,Samples], ie False.
        Experimental to see if the computations are quicker after
        transposing the data to be computed along the fastest
        memory access order. No difference maybe apparent as the
        transposed data will just be a view.

    :Returns:
        A numpy float32 array, unless `double` is set to True,
        with NaN representing no data values.

    :Notes:
        The formulae for the skewness and kurtosis are taken from the
        IDL (Exelisvis) help menu. This may differ slightly from the
        scipy formulae, however both forms produce results in the
        expected range.
    """

    # assuming a 3D array, [bands,rows,cols]
    dims = array.shape
    if len(dims) != 3:
        msg = "Array must be 3D! Received: {}.".format(len(dims))
        raise TypeError(msg)

    bands = dims[0]
    cols = dims[2]
    rows = dims[1]

    # number of bands/stats to be output to be returned
    output_band_count = 14

    # Define our computation datatype
    nan = numpy.float32(numpy.NaN)
    dtype = 'float32'
    if double:
        array = numpy.float64(array)
        nan = numpy.NaN
        dtype = 'float64'

    if no_data:
        # Promote to float32 if we have ints
        if array.dtype.name not in ['float', 'float32', 'float64']:
            array = numpy.float32(array)
        wh = numexpr.evaluate("array == no_data")
        array[wh] = nan

    if as_bip:
        # a few transpositions will take place, but they are quick to create
        # and are mostly just views into the data, so no copies are made
        # !!!Hopefully!!!
        # The idea is that it will process the z-axis over the fastest
        # memory access order. But seeing as they're just views, it might not
        # have any effect.
        array_bip = numpy.transpose(array, (1, 2, 0))

        stats = numpy.zeros((output_band_count, rows, cols), dtype=dtype)

        # Sum
        stats[0] = numpy.nansum(array_bip, axis=2)

        # We need to keep an int for the valid observations
        vld_obsv = numpy.sum(numpy.isfinite(array_bip), axis=2)
        stats[2] = vld_obsv

        # Mean
        stats[1] = numexpr.evaluate("fsum / fvld_obsv",
                                    {'fsum': stats[0], 'fvld_obsv': stats[2]})

        residuals = numexpr.evaluate("array - mean", {'mean': stats[1],
                                                      'array': array})
        # Variance
        t_emp = numexpr.evaluate("residuals**2").transpose(1, 2, 0)
        nan_sum = numpy.nansum(t_emp, axis=2)
        stats[3] = numexpr.evaluate("nan_sum / (fvld_obsv - 1)",
                                    {'fvld_obsv': stats[2],
                                     'nan_sum': nan_sum})

        # Stddev
        stats[4] = numexpr.evaluate("sqrt(var)", {'var': stats[3]})

        # Skewness
        t_emp = numexpr.evaluate("(residuals / stddev)**3",
                                 {'stddev': stats[4],
                                  'residuals': residuals}).transpose(1, 2, 0)
        nan_sum = numpy.nansum(t_emp, axis=2)
        stats[5] = numexpr.evaluate("nan_sum / fvld_obsv",
                                    {'fvld_obsv': stats[2],
                                     'nan_sum': nan_sum})

        # Kurtosis
        t_emp = numexpr.evaluate("(residuals / stddev)**4",
                                 {'stddev': stats[4],
                                  'residuals': residuals}).transpose(1, 2, 0)
        nan_sum = numpy.nansum(t_emp, axis=2)
        stats[6] = numexpr.evaluate("(nan_sum / fvld_obsv) - 3",
                                    {'fvld_obsv': stats[2],
                                     'nan_sum': nan_sum})

        # Max and Min
        stats[7] = numpy.nanmax(array_bip, axis=2)
        stats[8] = numpy.nanmin(array_bip, axis=2)

        # 2nd quantile (aka median)
        # Don't want any interpolated values, so can't use the standard
        # numpy.median() function
        # For odd length arrays, the middle value is taken, for even length
        # arrays, the first of the two middle values is taken

        # Sort the array
        flat_sort = numpy.sort(array_bip, axis=2).ravel()

        # q2_offset, median locations
        q2_idx = numexpr.evaluate("((vld_obsv / 2) + ((vld_obsv % 2) - 1))")

        # array offsets
        a_off = numpy.arange(cols * rows).reshape((rows, cols))

        # turn the locations into a useable 1D index
        idx_1D = numexpr.evaluate("(q2_idx + a_off * bands)").astype('int')
        stats[9] = flat_sort[idx_1D]  # get median values

        # now to find the original index of the median value
        sort_orig_idx = numpy.argsort(array_bip, axis=2).ravel()
        stats[10] = sort_orig_idx[idx_1D]

        # 1st quantile
        length = numexpr.evaluate("q2_idx + 1")
        q1_idx = numexpr.evaluate("((length / 2) + ((length % 2) - 1))")
        idx_1D = numexpr.evaluate("(q1_idx + a_off * bands)").astype('int')
        stats[11] = flat_sort[idx_1D]  # get 1st quantile

        # 3rd quantile
        exp = "((q2_idx + q1_idx) + a_off * bands)"
        idx_1D = numexpr.evaluate(exp).astype('int')  # 1D index
        stats[12] = flat_sort[idx_1D]  # get 3rd quantile

        # Geometric Mean
        # need to handle nan's so can't use scipy.stats.gmean ## 28/02/2013
        # x**(1./n) gives nth root
        wh = ~(numpy.isfinite(array_bip))
        array_bip[wh] = 1
        stats[13] = numpy.prod(array_bip, axis=2)**(1. / vld_obsv)

        # Any nan's will evaluate to 1.0, convert back to NaN
        wh = numexpr.evaluate("vld_obsv == 0")
        stats[13][wh] = nan

        # Convert any potential inf values to a NaN for consistancy
        wh = ~(numpy.isfinite(stats))
        stats[wh] = nan

    else:
        stats = numpy.zeros((output_band_count, rows, cols), dtype=dtype)

        # Sum
        stats[0] = numpy.nansum(array, axis=0)

        # We need to keep an int for the valid observations
        vld_obsv = numpy.sum(numpy.isfinite(array), axis=0)
        stats[2] = vld_obsv

        # Mean
        stats[1] = numexpr.evaluate("fsum / fvld_obsv",
                                    {'fsum': stats[0], 'fvld_obsv': stats[2]})

        residuals = numexpr.evaluate("array - mean",
                                     {'mean': stats[1], 'array': array})

        # Variance
        t_emp = numexpr.evaluate("residuals**2")
        nan_sum = numpy.nansum(t_emp, axis=0)
        stats[3] = numexpr.evaluate("nan_sum / (fvld_obsv - 1)",
                                    {'fvld_obsv': stats[2],
                                     'nan_sum': nan_sum})

        # Stddev
        stats[4] = numexpr.evaluate("sqrt(var)", {'var': stats[3]})

        # skewness
        t_emp = numexpr.evaluate("(residuals / stddev)**3",
                                 {'stddev': stats[4], 'residuals': residuals})
        nan_sum = numpy.nansum(t_emp, axis=0)
        stats[5] = numexpr.evaluate("nan_sum / fvld_obsv",
                                    {'fvld_obsv': stats[2],
                                     'nan_sum': nan_sum})

        # Kurtosis
        t_emp = numexpr.evaluate("(residuals / stddev)**4",
                                 {'stddev': stats[4], 'residuals': residuals})
        nan_sum = numpy.nansum(t_emp, axis=0)
        stats[6] = numexpr.evaluate("(nan_sum / fvld_obsv) - 3",
                                    {'fvld_obsv': stats[2],
                                     'nan_sum': nan_sum})

        # MAx and Min
        stats[7] = numpy.nanmax(array, axis=0)
        stats[8] = numpy.nanmin(array, axis=0)

        # 2nd quantile (aka median)
        # Don't want any interpolated values, so can't use the standard
        # numpy.median() function
        # For odd length arrays, the middle value is taken, for even length
        # arrays, the first of the two middle values is taken

        flat_sort = numpy.sort(array, axis=0).ravel()

        # q2_offset, median locations
        q2_idx = numexpr.evaluate("((vld_obsv / 2) + ((vld_obsv % 2) - 1))")

        # array offsets
        a_off = numpy.arange(cols * rows).reshape((rows, cols))

        # turn the locations into a useable 1D index
        exp = "(q2_idx * cols * rows + a_off)"
        idx_1D = numexpr.evaluate(exp).astype('int')
        stats[9] = flat_sort[idx_1D]  # get median values

        # now to find the original index of the median value
        sort_orig_idx = numpy.argsort(array, axis=0).ravel()
        stats[10] = sort_orig_idx[idx_1D]

        # 1st quantile
        length = numexpr.evaluate("q2_idx + 1")
        q1_idx = numexpr.evaluate("((length / 2) + ((length % 2) - 1))")
        exp = "(q1_idx * cols * rows + a_off)"
        idx_1D = numexpr.evaluate(exp).astype('int')  # 1D index
        stats[11] = flat_sort[idx_1D]  # get 1st quantile

        # 3rd quantile
        exp = "((q2_idx + q1_idx) * cols * rows + a_off)"
        idx_1D = numexpr.evaluate(exp).astype('int')  # 1D index
        stats[12] = flat_sort[idx_1D]  # get 3rd quantile

        # Geometric Mean
        # need to handle nan's so can't use scipy.stats.gmean ## 28/02/2013
        # x**(1./n) gives nth root
        wh = ~(numpy.isfinite(array))
        array[wh] = 1
        stats[13] = numpy.prod(array, axis=0)**(1. / vld_obsv)

        # Any nan's will evaluate to 1.0, convert back to NaN
        wh = numexpr.evaluate("vld_obsv == 0")
        stats[13][wh] = nan

        # Convert any potential inf values to a NaN for consistancy
        wh = ~(numpy.isfinite(stats))
        stats[wh] = nan

    return stats

#!/usr/bin/env python

# ===============================================================================
# Copyright 2015 Geoscience Australia
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ===============================================================================

from __future__ import absolute_import
from __future__ import print_function
import numpy
import numexpr


def bulk_stats(array, no_data=None, double=False, as_bip=False):
    """
    Calculates statistics over the temporal/spectral/z domain
    of a multiband image.

    Calculates statistics over the temporal/spectral/z domain of an array
    containing [z,y,x] data.
    Statistics produced in this order are:
    Sum
    Mean
    Valid Observations
    Variance
    Standard Deviation
    Skewness
    Kurtosis
    Max
    Min
    Median (non-interpolated value)
    Median Index (zero based index)
    1st Quantile (non-interpolated value)
    3rd Quantile (non-interpolated value)
    Geometric Mean

    Median, 1st and 3rd quantiles: For odd length arrays the middle value is
    taken. For even length arrays, the first of the two middle values is taken.
    Either way, no interpolation is used for calculation.
    The median index is the band that the median value came from.

    The numexpr module is used to handle most of the operations. Arrays are
    processed faster while using less memory.
    The moments are calculated using the unbiased method i.e. (n - 1).
    The moments are also calculated direct via the formula rather than built
    in functions. Why?? Because we can recycle previous computations rather
    than recompute, which will make the routine faster.

    :param array:
        A 3D numpy array containing [z,y,x] data.

    :param no_data:
        The data value to ignore for calculations. Default is None.
        If set and `array` is not of type float (32 or 64), then
        `array` will be cast to a `float32` array.

    :param double:
        If set to True then `array` will be converted to float64 and
        the output will be evaluted in double precision and returned
        as such. Default is False (float32).

    :param as_bip:
        **Experimental**
        If set to True, the array will be transposed to be
        [Lines,Samples,Bands], and processed as such. The default
        is to process the array as [Bands,Lines,Samples], ie False.
        Experimental to see if the computations are quicker after
        transposing the data to be computed along the fastest
        memory access order. No difference maybe apparent as the
        transposed data will just be a view.

    :Returns:
        A numpy float32 array, unless `double` is set to True,
        with NaN representing no data values.

    :Notes:
        The formulae for the skewness and kurtosis are taken from the
        IDL (Exelisvis) help menu. This may differ slightly from the
        scipy formulae, however both forms produce results in the
        expected range.
    """

    # assuming a 3D array, [bands,rows,cols]
    dims = array.shape
    if len(dims) != 3:
        msg = "Array must be 3D! Received: {}.".format(len(dims))
        raise TypeError(msg)

    bands = dims[0]
    cols = dims[2]
    rows = dims[1]

    # number of bands/stats to be output to be returned
    output_band_count = 14

    # Define our computation datatype
    nan = numpy.float32(numpy.NaN)
    dtype = 'float32'
    if double:
        array = numpy.float64(array)
        nan = numpy.NaN
        dtype = 'float64'

    if no_data:
        # Promote to float32 if we have ints
        if array.dtype.name not in ['float', 'float32', 'float64']:
            array = numpy.float32(array)
        wh = numexpr.evaluate("array == no_data")
        array[wh] = nan

    if as_bip:
        # a few transpositions will take place, but they are quick to create
        # and are mostly just views into the data, so no copies are made
        # !!!Hopefully!!!
        # The idea is that it will process the z-axis over the fastest
        # memory access order. But seeing as they're just views, it might not
        # have any effect.
        array_bip = numpy.transpose(array, (1, 2, 0))

        stats = numpy.zeros((output_band_count, rows, cols), dtype=dtype)

        # Sum
        stats[0] = numpy.nansum(array_bip, axis=2)

        # We need to keep an int for the valid observations
        vld_obsv = numpy.sum(numpy.isfinite(array_bip), axis=2)
        stats[2] = vld_obsv

        # Mean
        stats[1] = numexpr.evaluate("fsum / fvld_obsv",
                                    {'fsum': stats[0], 'fvld_obsv': stats[2]})

        residuals = numexpr.evaluate("array - mean", {'mean': stats[1],
                                                      'array': array})
        # Variance
        t_emp = numexpr.evaluate("residuals**2").transpose(1, 2, 0)
        nan_sum = numpy.nansum(t_emp, axis=2)
        stats[3] = numexpr.evaluate("nan_sum / (fvld_obsv - 1)",
                                    {'fvld_obsv': stats[2],
                                     'nan_sum': nan_sum})

        # Stddev
        stats[4] = numexpr.evaluate("sqrt(var)", {'var': stats[3]})

        # Skewness
        t_emp = numexpr.evaluate("(residuals / stddev)**3",
                                 {'stddev': stats[4],
                                  'residuals': residuals}).transpose(1, 2, 0)
        nan_sum = numpy.nansum(t_emp, axis=2)
        stats[5] = numexpr.evaluate("nan_sum / fvld_obsv",
                                    {'fvld_obsv': stats[2],
                                     'nan_sum': nan_sum})

        # Kurtosis
        t_emp = numexpr.evaluate("(residuals / stddev)**4",
                                 {'stddev': stats[4],
                                  'residuals': residuals}).transpose(1, 2, 0)
        nan_sum = numpy.nansum(t_emp, axis=2)
        stats[6] = numexpr.evaluate("(nan_sum / fvld_obsv) - 3",
                                    {'fvld_obsv': stats[2],
                                     'nan_sum': nan_sum})

        # Max and Min
        stats[7] = numpy.nanmax(array_bip, axis=2)
        stats[8] = numpy.nanmin(array_bip, axis=2)

        # 2nd quantile (aka median)
        # Don't want any interpolated values, so can't use the standard
        # numpy.median() function
        # For odd length arrays, the middle value is taken, for even length
        # arrays, the first of the two middle values is taken

        # Sort the array
        flat_sort = numpy.sort(array_bip, axis=2).ravel()

        # q2_offset, median locations
        q2_idx = numexpr.evaluate("((vld_obsv / 2) + ((vld_obsv % 2) - 1))")

        # array offsets
        a_off = numpy.arange(cols * rows).reshape((rows, cols))

        # turn the locations into a useable 1D index
        idx_1D = numexpr.evaluate("(q2_idx + a_off * bands)").astype('int')
        stats[9] = flat_sort[idx_1D]  # get median values

        # now to find the original index of the median value
        sort_orig_idx = numpy.argsort(array_bip, axis=2).ravel()
        stats[10] = sort_orig_idx[idx_1D]

        # 1st quantile
        length = numexpr.evaluate("q2_idx + 1")
        q1_idx = numexpr.evaluate("((length / 2) + ((length % 2) - 1))")
        idx_1D = numexpr.evaluate("(q1_idx + a_off * bands)").astype('int')
        stats[11] = flat_sort[idx_1D]  # get 1st quantile

        # 3rd quantile
        exp = "((q2_idx + q1_idx) + a_off * bands)"
        idx_1D = numexpr.evaluate(exp).astype('int')  # 1D index
        stats[12] = flat_sort[idx_1D]  # get 3rd quantile

        # Geometric Mean
        # need to handle nan's so can't use scipy.stats.gmean ## 28/02/2013
        # x**(1./n) gives nth root
        wh = ~(numpy.isfinite(array_bip))
        array_bip[wh] = 1
        stats[13] = numpy.prod(array_bip, axis=2)**(1. / vld_obsv)

        # Any nan's will evaluate to 1.0, convert back to NaN
        wh = numexpr.evaluate("vld_obsv == 0")
        stats[13][wh] = nan

        # Convert any potential inf values to a NaN for consistancy
        wh = ~(numpy.isfinite(stats))
        stats[wh] = nan

    else:
        stats = numpy.zeros((output_band_count, rows, cols), dtype=dtype)

        # Sum
        stats[0] = numpy.nansum(array, axis=0)

        # We need to keep an int for the valid observations
        vld_obsv = numpy.sum(numpy.isfinite(array), axis=0)
        stats[2] = vld_obsv

        # Mean
        stats[1] = numexpr.evaluate("fsum / fvld_obsv",
                                    {'fsum': stats[0], 'fvld_obsv': stats[2]})

        residuals = numexpr.evaluate("array - mean",
                                     {'mean': stats[1], 'array': array})

        # Variance
        t_emp = numexpr.evaluate("residuals**2")
        nan_sum = numpy.nansum(t_emp, axis=0)
        stats[3] = numexpr.evaluate("nan_sum / (fvld_obsv - 1)",
                                    {'fvld_obsv': stats[2],
                                     'nan_sum': nan_sum})

        # Stddev
        stats[4] = numexpr.evaluate("sqrt(var)", {'var': stats[3]})

        # skewness
        t_emp = numexpr.evaluate("(residuals / stddev)**3",
                                 {'stddev': stats[4], 'residuals': residuals})
        nan_sum = numpy.nansum(t_emp, axis=0)
        stats[5] = numexpr.evaluate("nan_sum / fvld_obsv",
                                    {'fvld_obsv': stats[2],
                                     'nan_sum': nan_sum})

        # Kurtosis
        t_emp = numexpr.evaluate("(residuals / stddev)**4",
                                 {'stddev': stats[4], 'residuals': residuals})
        nan_sum = numpy.nansum(t_emp, axis=0)
        stats[6] = numexpr.evaluate("(nan_sum / fvld_obsv) - 3",
                                    {'fvld_obsv': stats[2],
                                     'nan_sum': nan_sum})

        # MAx and Min
        stats[7] = numpy.nanmax(array, axis=0)
        stats[8] = numpy.nanmin(array, axis=0)

        # 2nd quantile (aka median)
        # Don't want any interpolated values, so can't use the standard
        # numpy.median() function
        # For odd length arrays, the middle value is taken, for even length
        # arrays, the first of the two middle values is taken

        flat_sort = numpy.sort(array, axis=0).ravel()

        # q2_offset, median locations
        q2_idx = numexpr.evaluate("((vld_obsv / 2) + ((vld_obsv % 2) - 1))")

        # array offsets
        a_off = numpy.arange(cols * rows).reshape((rows, cols))

        # turn the locations into a useable 1D index
        exp = "(q2_idx * cols * rows + a_off)"
        idx_1D = numexpr.evaluate(exp).astype('int')
        stats[9] = flat_sort[idx_1D]  # get median values

        # now to find the original index of the median value
        sort_orig_idx = numpy.argsort(array, axis=0).ravel()
        stats[10] = sort_orig_idx[idx_1D]

        # 1st quantile
        length = numexpr.evaluate("q2_idx + 1")
        q1_idx = numexpr.evaluate("((length / 2) + ((length % 2) - 1))")
        exp = "(q1_idx * cols * rows + a_off)"
        idx_1D = numexpr.evaluate(exp).astype('int')  # 1D index
        stats[11] = flat_sort[idx_1D]  # get 1st quantile

        # 3rd quantile
        exp = "((q2_idx + q1_idx) * cols * rows + a_off)"
        idx_1D = numexpr.evaluate(exp).astype('int')  # 1D index
        stats[12] = flat_sort[idx_1D]  # get 3rd quantile

        # Geometric Mean
        # need to handle nan's so can't use scipy.stats.gmean ## 28/02/2013
        # x**(1./n) gives nth root
        wh = ~(numpy.isfinite(array))
        array[wh] = 1
        stats[13] = numpy.prod(array, axis=0)**(1. / vld_obsv)

        # Any nan's will evaluate to 1.0, convert back to NaN
        wh = numexpr.evaluate("vld_obsv == 0")
        stats[13][wh] = nan

        # Convert any potential inf values to a NaN for consistancy
        wh = ~(numpy.isfinite(stats))
        stats[wh] = nan

    return stats
#!/usr/bin/env python # =============================================================================== # Copyright 2015 Geoscience Australia # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # #     http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # =============================================================================== Calculates statistics over the temporal/spectral/z domain     of a multiband image.      Calculates statistics over the temporal/spectral/z domain of an array     containing [z,y,x] data.     Statistics produced in this order are:     Sum     Mean     Valid Observations     Variance     Standard Deviation     Skewness     Kurtosis     Max     Min     Median (non-interpolated value)     Median Index (zero based index)     1st Quantile (non-interpolated value)     3rd Quantile (non-interpolated value)     Geometric Mean      Median, 1st and 3rd quantiles: For odd length arrays the middle value is     taken. For even length arrays, the first of the two middle values is taken.     Either way, no interpolation is used for calculation.     The median index is the band that the median value came from.      The numexpr module is used to handle most of the operations. Arrays are     processed faster while using less memory.     The moments are calculated using the unbiased method i.e. (n - 1).     The moments are also calculated direct via the formula rather than built     in functions. Why?? Because we can recycle previous computations rather     than recompute, which will make the routine faster.      :param array:         A 3D numpy array containing [z,y,x] data.      :param no_data:         The data value to ignore for calculations. Default is None.         If set and `array` is not of type float (32 or 64), then         `array` will be cast to a `float32` array.      :param double:         If set to True then `array` will be converted to float64 and         the output will be evaluted in double precision and returned         as such. Default is False (float32).      :param as_bip:         **Experimental**         If set to True, the array will be transposed to be         [Lines,Samples,Bands], and processed as such. The default         is to process the array as [Bands,Lines,Samples], ie False.         Experimental to see if the computations are quicker after         transposing the data to be computed along the fastest         memory access order. No difference maybe apparent as the         transposed data will just be a view.      :Returns:         A numpy float32 array, unless `double` is set to True,         with NaN representing no data values.      :Notes:         The formulae for the skewness and kurtosis are taken from the         IDL (Exelisvis) help menu. This may differ slightly from the         scipy formulae, however both forms produce results in the         expected range. # assuming a 3D array, [bands,rows,cols] # number of bands/stats to be output to be returned # Define our computation datatype # Promote to float32 if we have ints # a few transpositions will take place, but they are quick to create # and are mostly just views into the data, so no copies are made # !!!Hopefully!!! # The idea is that it will process the z-axis over the fastest # memory access order. But seeing as they're just views, it might not # have any effect. # Sum # We need to keep an int for the valid observations # Mean # Variance # Stddev # Skewness # Kurtosis # Max and Min # 2nd quantile (aka median) # Don't want any interpolated values, so can't use the standard # numpy.median() function # For odd length arrays, the middle value is taken, for even length # arrays, the first of the two middle values is taken # Sort the array # q2_offset, median locations # array offsets # turn the locations into a useable 1D index # get median values # now to find the original index of the median value # 1st quantile # get 1st quantile # 3rd quantile # 1D index # get 3rd quantile # Geometric Mean # need to handle nan's so can't use scipy.stats.gmean ## 28/02/2013 # x**(1./n) gives nth root # Any nan's will evaluate to 1.0, convert back to NaN # Convert any potential inf values to a NaN for consistancy # Sum # We need to keep an int for the valid observations # Mean # Variance # Stddev # skewness # Kurtosis # MAx and Min # 2nd quantile (aka median) # Don't want any interpolated values, so can't use the standard # numpy.median() function # For odd length arrays, the middle value is taken, for even length # arrays, the first of the two middle values is taken # q2_offset, median locations # array offsets # turn the locations into a useable 1D index # get median values # now to find the original index of the median value # 1st quantile # 1D index # get 1st quantile # 3rd quantile # 1D index # get 3rd quantile # Geometric Mean # need to handle nan's so can't use scipy.stats.gmean ## 28/02/2013 # x**(1./n) gives nth root # Any nan's will evaluate to 1.0, convert back to NaN # Convert any potential inf values to a NaN for consistancy