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matheo.band_integration.band_integration

matheo.band_integration.band_integration#

Functions to band integrate spectra for given spectral response function.

matheo.band_integration.band_integration.band_int(d: ndarray, x: ndarray, r: ndarray, x_r: ndarray, d_axis_x: int = 0, x_r_centre: None | float = None, u_d: None | float | ndarray = None, u_x: None | float | ndarray = None, u_r: None | float | ndarray = None, u_x_r: None | float | ndarray = None, rint_norm: bool = True) → float | ndarray | Tuple[float | ndarray, float | ndarray][source]#

Returns integral of data array over a response band (i.e., d(x) * r(x_r))

N.B. In case where x == x_r and x is evenly sampled, an accelerated function is used.

Parameters:

  • d – data to be band integrated

  • x – data coordinates

  • r – band response function(s). For a single band, a 1D length-M array is required, where M is the length of x_r. Multiple bands may be defined in an N x M array, where N is number of response bands.

  • x_r – band response function coordinates

  • d_axis_x – (default 0) if d greater than 1D, specify axis to band integrate along

  • x_r_centre – (optional) centre of band response function in data coordinates, if there is an offset. Defined by location of band response function peak in data coordinates. Useful to define where sensor is looking along an extended input, e.g. spatially.

  • u_d – (optional) uncertainty in data

  • u_x – (optional) uncertainty in data coordinates

  • u_r – (optional) uncertainty in band response function

  • u_x_r – (optional) uncertainty in band response function coordinates

  • rint_norm – (default: True) option to normalise result by integral of r

Returns:

band integrated data

Returns:

uncertainty of band integrated data (skipped if no input uncertainties provided)

matheo.band_integration.band_integration.band_int2ax(d: ndarray, x: ndarray, y: ndarray, rx: ndarray, x_rx: ndarray, ry: ndarray, y_ry: ndarray, d_axis_x: int = 0, d_axis_y: int = 0, x_rx_centre: None | float = None, y_ry_centre: None | float = None, u_d: None | float | ndarray = None, u_x: None | float | ndarray = None, u_y: None | float | ndarray = None, u_rx: None | float | ndarray = None, u_x_rx: None | float | ndarray = None, u_ry: None | float | ndarray = None, u_y_ry: None | float | ndarray = None, rint_norm: bool = True) → float | ndarray | Tuple[float | ndarray, float | ndarray][source]#

Sequentially band integrates multi-dimensional data array along x axis and y axis

N.B. In case where x == x_rx and x is evenly sampled or y == y_ry and y is evenly spaced, an accelerated function is used.

Parameters:

  • d – data to be band integrated

  • x – data coordinates along first band integration axis

  • y – data coordinates along second band integration axis

  • rx – first axis band response function(s). For a single band, a 1D length-M array is required, where M is the length of x_rx. Multiple bands may be defined in an N x M array, where N is number of response bands.

  • x_rx – first band response function coordinates

  • ry – second axis band response function(s). For a single band, a 1D length-M array is required, where M is the length of y_ry. Multiple bands may be defined in an N x M array, where N is number of response bands.

  • y_ry – second band response function coordinates

  • d_axis_x – (default 0) x axis in data array

  • d_axis_y – (default 1) y axis in data array

  • x_rx_centre – (optional) centre of rx function in data coordinates, if there is an offset. Defined by location of band response function peak in data coordinates. Useful to define where sensor is looking along an extended input, e.g. spatially.

  • y_ry_centre – (optional) centre of ry function in data coordinates, if there is an offset (as for x_rx_centre)

  • u_d – (optional) uncertainty in data

  • u_x – (optional) uncertainty in data coordinates along first band integration axis

  • u_y – (optional) uncertainty in data coordinates along second band integration axis

  • u_rx – (optional) uncertainty in first band response function

  • u_x_rx – (optional) uncertainty in first band response function coordinates

  • u_ry – (optional) uncertainty in second band response function

  • u_y_ry – (optional) uncertainty in second band response function coordinates

  • rint_norm – (default: True) option to normalise result by integral of r

Returns:

band integrated data

Returns:

uncertainty of band integrated data (skipped if no input uncertainties provided)

matheo.band_integration.band_integration.band_int2d(d: ndarray, x: ndarray, y: ndarray, psf: ndarray, x_psf: ndarray, y_psf: ndarray, d_axis_x: int = 0, d_axis_y: int = 1, u_d: None | float | ndarray = None, u_x: None | float | ndarray = None, u_y: None | float | ndarray = None, u_psf: None | float | ndarray = None, u_x_psf: None | float | ndarray = None, u_y_psf: None | float | ndarray = None) → float | ndarray | Tuple[float | ndarray, float | ndarray][source]#

Returns integral of a 2D data array over a response band defined by a 2D point spread function (i.e., d(x, y) * psf(x_psf, y_psf))

Parameters:

  • d – two dimensional data to be band integrated

  • x – data x coordinates

  • y – data y coordinates

  • psf – two dimensional point spread function of band response

  • x_psf – psf x coordinates

  • y_psf – psf y coordinates

  • d_axis_x – (default 0) x axis in data array, if d more than 2D

  • d_axis_y – (default 1) y axis in data array, if d more than 2D

  • u_d – (optional) uncertainty in data

  • u_x – (optional) uncertainty in data x coordinates

  • u_y – (optional) uncertainty in data y coordinates

  • u_psf – (optional) uncertainty in point spread function of band response

  • u_x_psf – (optional) uncertainty in psf x coordinates

  • u_y_psf – (optional) uncertainty in psf x coordinates

Returns:

band integrated data

Returns:

uncertainty of band integrated data (skipped if no input uncertainties provided)

matheo.band_integration.band_integration.band_int3ax(d: ndarray, x: ndarray, y: ndarray, z: ndarray, rx: ndarray, x_rx: ndarray, ry: ndarray, y_ry: ndarray, rz: ndarray, z_rz: ndarray, d_axis_x: int = 0, d_axis_y: int = 1, d_axis_z: int = 2, x_rx_centre: None | float = None, y_ry_centre: None | float = None, z_rz_centre: None | float = None, u_d: None | float | ndarray = None, u_x: None | float | ndarray = None, u_y: None | float | ndarray = None, u_z: None | float | ndarray = None, u_rx: None | float | ndarray = None, u_x_rx: None | float | ndarray = None, u_ry: None | float | ndarray = None, u_y_ry: None | float | ndarray = None, u_rz: None | float | ndarray = None, u_z_rz: None | float | ndarray = None, rint_norm: bool = True) → float | ndarray | Tuple[float | ndarray, float | ndarray][source]#

Sequentially band integrates multi-dimensional data array along x, y and z axes

N.B. In case where x == x_rx and x is evenly sampled, y == y_ry and y is evenly spaced, or z == z_rz and z is evenly spaced, an accelerated function is used.

Parameters:

  • d – data to be band integrated

  • x – data coordinates along first band integration axis

  • y – data coordinates along second band integration axis

  • z – data coordinates along third band integration axis

  • rx – first axis band response function(s). For a single band, a 1D length-M array is required, where M is the length of x_rx. Multiple bands may be defined in an N x M array, where N is number of response bands.

  • x_rx – first band response function coordinates

  • ry – second axis band response function(s). For a single band, a 1D length-M array is required, where M is the length of y_ry. Multiple bands may be defined in an N x M array, where N is number of response bands.

  • y_ry – second band response function coordinates

  • rz – third axis band response function(s). For a single band, a 1D length-M array is required, where M is the length of z_rz. Multiple bands may be defined in an N x M array, where N is number of response bands.

  • z_rz – third band response function coordinates

  • d_axis_x – (default 0) x axis in data array

  • d_axis_y – (default 1) y axis in data array

  • d_axis_z – (default 2) z axis in data array

  • x_rx_centre – (optional) centre of rx function in data coordinates, if there is an offset. Defined by location of band response function peak in data coordinates. Useful to define where sensor is looking along an extended input, e.g. spatially.

  • y_ry_centre – (optional) centre of ry function in data coordinates, if there is an offset (as for x_rx_centre)

  • z_rz_centre – (optional) centre of rz function in data coordinates, if there is an offset (as for x_rx_centre)

  • u_d – (optional) uncertainty in data

  • u_x – (optional) uncertainty in data coordinates along first band integration axis

  • u_y – (optional) uncertainty in data coordinates along second band integration axis

  • u_z – (optional) uncertainty in data coordinates along third band integration axis

  • u_rx – (optional) uncertainty in first band response function

  • u_x_rx – (optional) uncertainty in first band response function coordinates

  • u_ry – (optional) uncertainty in second band response function

  • u_y_ry – (optional) uncertainty in second band response function coordinates

  • u_rz – (optional) uncertainty in second band response function

  • u_z_rz – (optional) uncertainty in third band response function coordinates

  • rint_norm – (default: True) option to normalise result by integral of r

Returns:

band integrated data

Returns:

uncertainty of band integrated data (skipped if no input uncertainties provided)

matheo.band_integration.band_integration.cutout_nonzero(y, x, buffer=0.2)[source]#

Returns continuous non-zero part of function y(x)

Parameters:

  • y (numpy.ndarray) – function data values

  • x (numpy.ndarray) – function coordinate data values

  • buffer (float) – fraction of non-zero section of y to include as buffer on either side (default: 0.2)

matheo.band_integration.band_integration.get_x_offset(y, x, x_centre)[source]#

Returns coordinate offset required to centre function on given position.

Parameters:

  • y – function values

  • x – function coordinates

  • x_centre – function centre defined my location of maximum value.

Returns:

coordinate offset to centre function on x_centre

matheo.band_integration.band_integration.iter_band_int(d: ndarray, x: ndarray, iter_r: Iterable, d_axis_x: int = 0, u_d: None | float | ndarray = None, u_x: None | float | ndarray = None, u_r: None | float | ndarray = None, u_x_r: None | float | ndarray = None, rint_norm: bool | None = True) → float | ndarray | Tuple[float | ndarray, float | ndarray][source]#

Returns integral of data array over a set of response bands defined by iterator

Parameters:

  • d – data to be band integrated

  • x – data coordinates

  • iter_r – iterable that returns band response function and band response function coordinates at each iteration

  • d_axis_x – (default 0) if d greater than 1D, specify axis to band integrate along

  • u_d – uncertainty in data

  • u_x – uncertainty in data coordinates

  • u_r – uncertainty in band response function

  • u_x_r – uncertainty in band response function coordinates

  • rint_norm – (default: True) option to normalise result by integral of r

Returns:

band integrated data

Returns:

uncertainty of band integrated data (skipped if no input uncertainties provided)

matheo.band_integration.band_integration.pixel_int(d: ndarray, x: ndarray, x_pixel: ndarray | None = None, width_pixel: ndarray | None = None, u_d: None | float | ndarray = None, u_x: None | float | ndarray = None, u_x_pixel: None | float | ndarray = None, u_width_pixel: None | float | ndarray = None, band_shape: Callable | str = 'triangle', r_sampling: None | float = None, d_axis_x: int = 0, x_pixel_centre: None | float = None, eval_iter: bool = False) → ndarray | Tuple[ndarray, ndarray][source]#

Returns integral of data array over a set of response bands (i.e., d(x) * r_i(x_r) for i pixels)

Parameters:

  • d – data to be band integrated

  • x – data coordinates

  • x_pixel – centre of band response per pixel

  • width_pixel – width of band response per pixel

  • u_d – uncertainty in data

  • u_x – uncertainty in data coordinates

  • u_x_pixel – uncertainty in centre of band response per pixel

  • u_width_pixel – uncertainty in width of band response per pixel

  • band_shape – (default: triangle) functional shape of response band - must be either a defined name, one of ‘triangle’, ‘tophat’, or ‘gaussian’, or a python function with the interface f(x, centre, width), where x is a numpy array of the x coordinates to define the function along, centre is the response band centre, and width is the response band width.

  • r_sampling – x sampling interval for derived pixel band response functions (if omitted pixel band response functions defined along x, this results in an accelerated computation)

  • d_axis_x – (default: 0) if d greater than 1D, specify axis pixels are along

  • x_pixel_centre – centre of pixels in data coordinates, if there is an offset. Defined as half way between max and min pixel values. Useful to define where sensor is looking along an extended input, e.g. spatially.

  • eval_iter – (default: False) option to evaluate each pixel iteratively, saving memory

Returns:

band integrated data

Returns:

uncertainty in band integrated data

matheo.band_integration.band_integration.pixel_int2d(d: ndarray, x: ndarray, y: ndarray, x_pixel: ndarray, y_pixel: ndarray, width_pixel: ndarray, psf_shape: str = 'triangle', d_axis_x: int = 0, d_axis_y: int = 0, u_d: None | float | ndarray = None, u_x: None | float | ndarray = None, u_y: None | float | ndarray = None, u_x_pixel: None | float | ndarray = None, u_y_pixel: None | float | ndarray = None, u_width_pixel: None | float | ndarray = None) → Tuple[ndarray, ndarray][source]#

Returns integral of data array over a response band (i.e., d(x) * r(x_r))

Parameters:

  • d – data to be band integrated

  • x – data x coordinates

  • y – data y coordinates

  • x_pixel – x positions of centre of psf per pixel

  • y_pixel – y positions of centre of psf per pixel

  • width_pixel – width of psf per pixel

  • psf_shape – (default X) psf shape - must be one of…

  • d_axis_x – (default 0) x axis in data array, if d more than 2D

  • d_axis_y – (default 1) y axis in data array, if d more than 2D

  • u_d – uncertainty in data

  • u_x – uncertainty in data x coordinates

  • u_y – uncertainty in data y coordinates

  • u_x_pixel – uncertainty in x positions of centre of psf per pixel

  • u_y_pixel – uncertainty in y positions of centre of psf per pixel

  • u_width_pixel – uncertainty in width of psf per pixel

Returns:

band integrated data

Returns:

uncertainty in band integrated data

matheo.band_integration.band_integration.return_r_pixel(x_pixel: ndarray, width_pixel: ndarray, x: ndarray, f: Callable, x_pixel_off: None | float = None) → ndarray[source]#

Returns per pixel response function, expressed as an n_x X n_pixel matrix, where n_x is the length of wavelength coordinates of the response function defintion and n_pixel matrix is the number of pixels.

Parameters:

  • x_pixel – centre of band response per pixel

  • width_pixel – width of band response per pixel

  • x – coordinates to define band response functions

  • f – functional shape of response band - a python function with the interface f(x, centre, width), where x is a numpy array of the x coordinates to define the function along, centre is the response band centre, and width is the response band width.

  • x_pixel_off – offset to pixel centre locations

Returns:

pixel response function matrix

matheo.band_integration.band_integration.spectral_band_int_sensor(d: ndarray, wl: ndarray, platform_name: str, sensor_name: str, detector_name: str | None = None, band_names: None | List[str] = None, d_axis_wl: int = 0, u_d: ndarray | None = None, u_wl: ndarray | None = None) → Tuple[ndarray, ndarray] | Tuple[ndarray, ndarray, ndarray][source]#

Returns spectral band integrated data array for named sensor spectral bands

Parameters:

  • d – data to be band integrated

  • wl – data wavelength coordinates

  • platform_name – satellite name (must be valid value for

  • sensor_name – name of instrument on satellite

  • detector_name – (optional) name of sensor detector. Can be used in sensor has SRF data for for different

detectors separately - if not specified in this case different :param band_names: (optional) sensor bands to evaluate band integral for, if omitted band integral evaluated for all bands within spectral range of data :param d_axis_wl: (default 0) spectral axis in data array :param u_d: (optional) uncertainty in data :param u_wl: (optional) uncertainty in data coordinates along first band integration axis

Returns:

band integrated data

Returns:

band integrated data centre wavelengths

Returns:

uncertainties in band integrated data (skipped if no input uncertainties provided)

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