source: sasview/src/sas/sascalc/calculator/resolution_calculator.py @ a4a1ac9

"""
This object is a small tool to allow user to quickly
determine the variance in q  from the
instrumental parameters.
"""
import sys
from math import pi, sqrt
import math
import logging

import numpy as np

from .instrument import Sample
from .instrument import Detector
from .instrument import TOF as Neutron
from .instrument import Aperture

logger = logging.getLogger(__name__)

#Plank's constant in cgs unit
_PLANK_H = 6.62606896E-27
#Gravitational acc. in cgs unit
_GRAVITY = 981.0


class ResolutionCalculator(object):
    """
    compute resolution in 2D
    """
    def __init__(self):

        # wavelength
        self.wave = Neutron()
        # sample
        self.sample = Sample()
        # aperture
        self.aperture = Aperture()
        # detector
        self.detector = Detector()
        # 2d image of the resolution
        self.image = []
        self.image_lam = []
        # resolutions
        # lamda in r-direction
        self.sigma_lamd = 0
        # x-dir (no lamda)
        self.sigma_1 = 0
        #y-dir (no lamda)
        self.sigma_2 = 0
        # 1D total
        self.sigma_1d = 0
        self.gravity_phi = None
        # q min and max
        self.qx_min = -0.3
        self.qx_max = 0.3
        self.qy_min = -0.3
        self.qy_max = 0.3
        # q min and max of the detector
        self.detector_qx_min = -0.3
        self.detector_qx_max = 0.3
        self.detector_qy_min = -0.3
        self.detector_qy_max = 0.3
        # possible max qrange
        self.qxmin_limit = 0
        self.qxmax_limit = 0
        self.qymin_limit = 0
        self.qymax_limit = 0

        # plots
        self.plot = None
        # instrumental params defaults
        self.mass = 0
        self.intensity = 0
        self.wavelength = 0
        self.wavelength_spread = 0
        self.source_aperture_size = []
        self.source2sample_distance = []
        self.sample2sample_distance = []
        self.sample_aperture_size = []
        self.sample2detector_distance = []
        self.detector_pix_size = []
        self.detector_size = []
        self.get_all_instrument_params()
        # max q range for all lambdas
        self.qxrange = []
        self.qyrange = []

    def compute_and_plot(self, qx_value, qy_value, qx_min, qx_max,
                         qy_min, qy_max, coord='cartesian'):
        """
        Compute the resolution
        : qx_value: x component of q
        : qy_value: y component of q
        """
        # make sure to update all the variables need.
        # except lambda, dlambda, and intensity
        self.get_all_instrument_params()
        # wavelength etc.
        lamda_list, dlamb_list = self.get_wave_list()
        intens_list = []
        sig1_list = []
        sig2_list = []
        sigr_list = []
        sigma1d_list = []
        num_lamda = len(lamda_list)
        for num in range(num_lamda):
            lam = lamda_list[num]
            # wavelength spread
            dlam = dlamb_list[num]
            intens = self.setup_tof(lam, dlam)
            intens_list.append(intens)
            # cehck if tof
            if num_lamda > 1:
                tof = True
            else:
                tof = False
            # compute 2d resolution
            _, _, sigma_1, sigma_2, sigma_r, sigma1d = \
                        self.compute(lam, dlam, qx_value, qy_value, coord, tof)
            # make image
            image = self.get_image(qx_value, qy_value, sigma_1, sigma_2,
                                   sigma_r, qx_min, qx_max, qy_min, qy_max,
                                   coord, False)
            if qx_min > self.qx_min:
                qx_min = self.qx_min
            if qx_max < self.qx_max:
                qx_max = self.qx_max
            if qy_min > self.qy_min:
                qy_min = self.qy_min
            if qy_max < self.qy_max:
                qy_max = self.qy_max

            # set max qranges
            self.qxrange = [qx_min, qx_max]
            self.qyrange = [qy_min, qy_max]
            sig1_list.append(sigma_1)
            sig2_list.append(sigma_2)
            sigr_list.append(sigma_r)
            sigma1d_list.append(sigma1d)
        # redraw image in global 2d q-space.
        self.image_lam = []
        total_intensity = 0
        sigma_1 = 0
        sigma_r = 0
        sigma_2 = 0
        sigma1d = 0
        for ind in range(num_lamda):
            lam = lamda_list[ind]
            dlam = dlamb_list[ind]
            intens = self.setup_tof(lam, dlam)
            out = self.get_image(qx_value, qy_value, sig1_list[ind],
                                 sig2_list[ind], sigr_list[ind],
                                 qx_min, qx_max, qy_min, qy_max, coord)
            # this is the case of q being outside the detector
            #if numpy.all(out==0.0):
            #    continue
            image = out
            # set variance as sigmas
            sigma_1 += sig1_list[ind] * sig1_list[ind] * self.intensity
            sigma_r += sigr_list[ind] * sigr_list[ind] * self.intensity
            sigma_2 += sig2_list[ind] * sig2_list[ind] * self.intensity
            sigma1d += sigma1d_list[ind] * sigma1d_list[ind] * self.intensity
            total_intensity += self.intensity

        if total_intensity != 0:
            # average variance
            image_out = image / total_intensity
            sigma_1 = sigma_1 / total_intensity
            sigma_r = sigma_r / total_intensity
            sigma_2 = sigma_2 / total_intensity
            sigma1d = sigma1d / total_intensity
            # set sigmas
            self.sigma_1 = sqrt(sigma_1)
            self.sigma_lamd = sqrt(sigma_r)
            self.sigma_2 = sqrt(sigma_2)
            self.sigma_1d = sqrt(sigma1d)
            # rescale
            max_im_val = 1
            if max_im_val > 0:
                image_out /= max_im_val
        else:
            image_out = image * 0.0
            # Don't calculate sigmas nor set self.sigmas!
            sigma_1 = 0
            sigma_r = 0
            sigma_2 = 0
            sigma1d = 0
        if len(self.image) > 0:
            self.image += image_out
        else:
            self.image = image_out

        # plot image
        return self.plot_image(self.image)

    def setup_tof(self, wavelength, wavelength_spread):
        """
        Setup all parameters in instrument

        : param ind: index of lambda, etc
        """

        # set wave.wavelength
        self.set_wavelength(wavelength)
        self.set_wavelength_spread(wavelength_spread)
        self.intensity = self.wave.get_intensity()

        if wavelength == 0:
            msg = "Can't compute the resolution: the wavelength is zero..."
            raise RuntimeError(msg)
        return self.intensity

    def compute(self, wavelength, wavelength_spread, qx_value, qy_value,
                coord='cartesian', tof=False):
        """
        Compute the Q resoltuion in || and + direction of 2D
        : qx_value: x component of q
        : qy_value: y component of q
        """
        coord = 'cartesian'
        lamb = wavelength
        lamb_spread = wavelength_spread
        # the shape of wavelength distribution

        if tof:
            # rectangular
            tof_factor = 2
        else:
            # triangular
            tof_factor = 1
        # Find polar values
        qr_value, phi = self._get_polar_value(qx_value, qy_value)
        # vacuum wave transfer
        knot = 2*pi/lamb
        # scattering angle theta; always true for plane detector
        # aligned vertically to the ko direction
        if qr_value > knot:
            theta = pi/2
        else:
            theta = math.asin(qr_value/knot)
        # source aperture size
        rone = self.source_aperture_size
        # sample aperture size
        rtwo = self.sample_aperture_size
        # detector pixel size
        rthree = self.detector_pix_size
        # source to sample(aperture) distance
        l_ssa = self.source2sample_distance[0]
        # sample(aperture) to detector distance
        l_sad = self.sample2detector_distance[0]
        # sample (aperture) to sample distance
        l_sas = self.sample2sample_distance[0]
        # source to sample distance
        l_one = l_ssa + l_sas
        # sample to detector distance
        l_two = l_sad - l_sas

        # Sample offset correction for l_one and Lp on variance calculation
        l1_cor = (l_ssa * l_two) / (l_sas + l_two)
        lp_cor = (l_ssa * l_two) / (l_one + l_two)
        # the radial distance to the pixel from the center of the detector
        radius = math.tan(theta) * l_two
        #Lp = l_one*l_two/(l_one+l_two)
        # default polar coordinate
        comp1 = 'radial'
        comp2 = 'phi'
        # in the case of the cartesian coordinate
        if coord == 'cartesian':
            comp1 = 'x'
            comp2 = 'y'

        # sigma in the radial/x direction
        # for source aperture
        sigma_1 = self.get_variance(rone, l1_cor, phi, comp1)
        # for sample apperture
        sigma_1 += self.get_variance(rtwo, lp_cor, phi, comp1)
        # for detector pix
        sigma_1 += self.get_variance(rthree, l_two, phi, comp1)
        # for gravity term for 1d
        sigma_1grav1d = self.get_variance_gravity(l_ssa, l_sad, lamb,
                                                  lamb_spread, phi, comp1, 'on') / tof_factor
        # for wavelength spread
        # reserve for 1d calculation
        A_value = self._cal_A_value(lamb, l_ssa, l_sad)
        sigma_wave_1, sigma_wave_1_1d = self.get_variance_wave(A_value,
                                                               radius, l_two, lamb_spread,
                                                               phi, 'radial', 'on')
        sigma_wave_1 /= tof_factor
        sigma_wave_1_1d /= tof_factor
        # for 1d
        variance_1d_1 = (sigma_1 + sigma_1grav1d) / 2 + sigma_wave_1_1d
        # normalize
        variance_1d_1 = knot * knot * variance_1d_1 / 12

        # for 2d
        #sigma_1 += sigma_wave_1
        # normalize
        sigma_1 = knot * sqrt(sigma_1 / 12)
        sigma_r = knot * sqrt(sigma_wave_1 / (tof_factor *12))
        # sigma in the phi/y direction
        # for source apperture
        sigma_2 = self.get_variance(rone, l1_cor, phi, comp2)

        # for sample apperture
        sigma_2 += self.get_variance(rtwo, lp_cor, phi, comp2)

        # for detector pix
        sigma_2 += self.get_variance(rthree, l_two, phi, comp2)

        # for gravity term for 1d
        sigma_2grav1d = self.get_variance_gravity(l_ssa, l_sad, lamb,
                                                  lamb_spread, phi, comp2, 'on') / tof_factor

        # for wavelength spread
        # reserve for 1d calculation
        sigma_wave_2, sigma_wave_2_1d = self.get_variance_wave(A_value,
                                                               radius, l_two, lamb_spread,
                                                               phi, 'phi', 'on')
        sigma_wave_2 /= tof_factor
        sigma_wave_2_1d /= tof_factor
        # for 1d
        variance_1d_2 = (sigma_2 + sigma_2grav1d) / 2 + sigma_wave_2_1d
        # normalize
        variance_1d_2 = knot * knot * variance_1d_2 / 12

        # for 2d
        #sigma_2 =  knot*sqrt(sigma_2/12)
        #sigma_2 += sigma_wave_2
        # normalize
        sigma_2 = knot * sqrt(sigma_2 / 12)
        sigma1d = sqrt(variance_1d_1 + variance_1d_2)
        # set sigmas
        self.sigma_1 = sigma_1
        self.sigma_lamd = sigma_r
        self.sigma_2 = sigma_2
        self.sigma_1d = sigma1d
        return qr_value, phi, sigma_1, sigma_2, sigma_r, sigma1d

    def _within_detector_range(self, qx_value, qy_value):
        """
        check if qvalues are within detector range
        """
        # detector range
        detector_qx_min = self.detector_qx_min
        detector_qx_max = self.detector_qx_max
        detector_qy_min = self.detector_qy_min
        detector_qy_max = self.detector_qy_max
        if self.qxmin_limit > detector_qx_min:
            self.qxmin_limit = detector_qx_min
        if self.qxmax_limit < detector_qx_max:
            self.qxmax_limit = detector_qx_max
        if self.qymin_limit > detector_qy_min:
            self.qymin_limit = detector_qy_min
        if self.qymax_limit < detector_qy_max:
            self.qymax_limit = detector_qy_max
        if qx_value < detector_qx_min or qx_value > detector_qx_max:
            return False
        if qy_value < detector_qy_min or qy_value > detector_qy_max:
            return False
        return True

    def get_image(self, qx_value, qy_value, sigma_1, sigma_2, sigma_r,
                  qx_min, qx_max, qy_min, qy_max,
                  coord='cartesian', full_cal=True):
        """
        Get the resolution in polar coordinate ready to plot
        : qx_value: qx_value value
        : qy_value: qy_value value
        : sigma_1: variance in r direction
        : sigma_2: variance in phi direction
        : coord: coordinate system of image, 'polar' or 'cartesian'
        """
        # Get  qx_max and qy_max...
        self._get_detector_qxqy_pixels()

        qr_value, phi = self._get_polar_value(qx_value, qy_value)

        # Check whether the q value is within the detector range
        if qx_min < self.qx_min:
            self.qx_min = qx_min
            #raise ValueError(msg)
        if qx_max > self.qx_max:
            self.qx_max = qx_max
            #raise ValueError(msg)
        if qy_min < self.qy_min:
            self.qy_min = qy_min
            #raise ValueError(msg)
        if qy_max > self.qy_max:
            self.qy_max = qy_max
            #raise ValueError(msg)
        if not full_cal:
            return None

        # Make an empty graph in the detector scale
        dx_size = (self.qx_max - self.qx_min) / (1000 - 1)
        dy_size = (self.qy_max - self.qy_min) / (1000 - 1)
        x_val = np.arange(self.qx_min, self.qx_max, dx_size)
        y_val = np.arange(self.qy_max, self.qy_min, -dy_size)
        q_1, q_2 = np.meshgrid(x_val, y_val)
        #q_phi = numpy.arctan(q_1,q_2)
        # check whether polar or cartesian
        if coord == 'polar':
            # Find polar values
            qr_value, phi = self._get_polar_value(qx_value, qy_value)
            q_1, q_2 = self._rotate_z(q_1, q_2, phi)
            qc_1 = qr_value
            qc_2 = 0.0
            # Calculate the 2D Gaussian distribution image
            image = self._gaussian2d_polar(q_1, q_2, qc_1, qc_2,
                                           sigma_1, sigma_2, sigma_r)
        else:
            # catesian coordinate
            # qx_center
            qc_1 = qx_value
            # qy_center
            qc_2 = qy_value

            # Calculate the 2D Gaussian distribution image
            image = self._gaussian2d(q_1, q_2, qc_1, qc_2,
                                     sigma_1, sigma_2, sigma_r)
        # out side of detector
        if not self._within_detector_range(qx_value, qy_value):
            image *= 0.0
            self.intensity = 0.0
            #return self.image

        # Add it if there are more than one inputs.
        if len(self.image_lam) > 0:
            self.image_lam += image * self.intensity
        else:
            self.image_lam = image * self.intensity

        return self.image_lam

    def plot_image(self, image):
        """
        Plot image using pyplot
        : image: 2d resolution image

        : return plt: pylab object
        """
        import matplotlib.pyplot as plt

        self.plot = plt
        plt.xlabel('$\\rm{Q}_{x} [A^{-1}]$')
        plt.ylabel('$\\rm{Q}_{y} [A^{-1}]$')
        # Max value of the image
        # max = numpy.max(image)
        qx_min, qx_max, qy_min, qy_max = self.get_detector_qrange()

        # Image
        im = plt.imshow(image,
                        extent=[qx_min, qx_max, qy_min, qy_max])

        # bilinear interpolation to make it smoother
        im.set_interpolation('bilinear')

        return plt

    def reset_image(self):
        """
        Reset image to default (=[])
        """
        self.image = []

    def get_variance(self, size=[], distance=0, phi=0, comp='radial'):
        """
        Get the variance when the slit/pinhole size is given
        : size: list that can be one(diameter for circular) or two components(lengths for rectangular)
        : distance: [z, x] where z along the incident beam, x // qx_value
        : comp: direction of the sigma; can be 'phi', 'y', 'x', and 'radial'

        : return variance: sigma^2
        """
        # check the length of size (list)
        len_size = len(size)

        # define sigma component direction
        if comp == 'radial':
            phi_x = math.cos(phi)
            phi_y = math.sin(phi)
        elif comp == 'phi':
            phi_x = math.sin(phi)
            phi_y = math.cos(phi)
        elif comp == 'x':
            phi_x = 1
            phi_y = 0
        elif comp == 'y':
            phi_x = 0
            phi_y = 1
        else:
            phi_x = 0
            phi_y = 0
        # calculate each component
        # for pinhole w/ radius = size[0]/2
        if len_size == 1:
            x_comp = (0.5 * size[0]) * sqrt(3)
            y_comp = 0
        # for rectangular slit
        elif len_size == 2:
            x_comp = size[0] * phi_x
            y_comp = size[1] * phi_y
        # otherwise
        else:
            raise ValueError(" Improper input...")
        # get them squared
        sigma = x_comp * x_comp
        sigma += y_comp * y_comp
        # normalize by distance
        sigma /= (distance * distance)

        return sigma

    def get_variance_wave(self, A_value, radius, distance, spread, phi,
                          comp='radial', switch='on'):
        """
        Get the variance when the wavelength spread is given

        : radius: the radial distance from the beam center to the pix of q
        : distance: sample to detector distance
        : spread: wavelength spread (ratio)
        : comp: direction of the sigma; can be 'phi', 'y', 'x', and 'radial'

        : return variance: sigma^2 for 2d, sigma^2 for 1d [tuple]
        """
        if switch.lower() == 'off':
            return 0, 0
        # check the singular point
        if distance == 0 or comp == 'phi':
            return 0, 0
        else:
            # calculate sigma^2 for 1d
            sigma1d = 2 * math.pow(radius/distance*spread, 2)
            if comp == 'x':
                sigma1d *= (math.cos(phi)*math.cos(phi))
            elif comp == 'y':
                sigma1d *= (math.sin(phi)*math.sin(phi))
            else:
                sigma1d *= 1
            # sigma^2 for 2d
            # shift the coordinate due to the gravitational shift
            rad_x = radius * math.cos(phi)
            rad_y = A_value - radius * math.sin(phi)
            radius = math.sqrt(rad_x * rad_x + rad_y * rad_y)
            # new phi
            phi = math.atan2(-rad_y, rad_x)
            self.gravity_phi = phi
            # calculate sigma^2
            sigma = 2 * math.pow(radius/distance*spread, 2)
            if comp == 'x':
                sigma *= (math.cos(phi)*math.cos(phi))
            elif comp == 'y':
                sigma *= (math.sin(phi)*math.sin(phi))
            else:
                sigma *= 1

            return sigma, sigma1d

    def get_variance_gravity(self, s_distance, d_distance, wavelength, spread,
                             phi, comp='radial', switch='on'):
        """
        Get the variance from gravity when the wavelength spread is given

        : s_distance: source to sample distance
        : d_distance: sample to detector distance
        : wavelength: wavelength
        : spread: wavelength spread (ratio)
        : comp: direction of the sigma; can be 'phi', 'y', 'x', and 'radial'

        : return variance: sigma^2
        """
        if switch.lower() == 'off':
            return 0
        if self.mass == 0.0:
            return 0
        # check the singular point
        if d_distance == 0 or comp == 'x':
            return 0
        else:
            a_value = self._cal_A_value(None, s_distance, d_distance)
            # calculate sigma^2
            sigma = math.pow(a_value / d_distance, 2)
            sigma *= math.pow(wavelength, 4)
            sigma *= math.pow(spread, 2)
            sigma *= 8
            return sigma

    def _cal_A_value(self, lamda, s_distance, d_distance):
        """
        Calculate A value for gravity

        : s_distance: source to sample distance
        : d_distance: sample to detector distance
        """
        # neutron mass in cgs unit
        self.mass = self.get_neutron_mass()
        # plank constant in cgs unit
        h_constant = _PLANK_H
        # gravity in cgs unit
        gravy = _GRAVITY
        # m/h
        m_over_h = self.mass / h_constant
        # A value
        a_value = d_distance * (s_distance + d_distance)
        a_value *= math.pow(m_over_h / 2, 2)
        a_value *= gravy
        # unit correction (1/cm to 1/A) for A and d_distance below
        a_value *= 1.0E-16
        # if lamda is give (broad meanning of A)  return 2* lamda^2 * A
        if lamda is not None:
            a_value *= (4 * lamda * lamda)
        return a_value

    def get_intensity(self):
        """
        Get intensity
        """
        return self.wave.intensity

    def get_wavelength(self):
        """
        Get wavelength
        """
        return self.wave.wavelength

    def get_default_spectrum(self):
        """
        Get default_spectrum
        """
        return self.wave.get_default_spectrum()

    def get_spectrum(self):
        """
        Get _spectrum
        """
        return self.wave.get_spectrum()

    def get_wavelength_spread(self):
        """
        Get wavelength spread
        """
        return self.wave.wavelength_spread

    def get_neutron_mass(self):
        """
        Get Neutron mass
        """
        return self.wave.mass

    def get_source_aperture_size(self):
        """
        Get source aperture size
        """
        return self.aperture.source_size

    def get_sample_aperture_size(self):
        """
        Get sample aperture size
        """
        return self.aperture.sample_size

    def get_detector_pix_size(self):
        """
        Get detector pixel size
        """
        return self.detector.pix_size

    def get_detector_size(self):
        """
        Get detector size
        """
        return self.detector.size

    def get_source2sample_distance(self):
        """
        Get detector source2sample_distance
        """
        return self.aperture.sample_distance

    def get_sample2sample_distance(self):
        """
        Get detector sampleslitsample_distance
        """
        return self.sample.distance

    def get_sample2detector_distance(self):
        """
        Get detector sample2detector_distance
        """
        return self.detector.distance

    def set_intensity(self, intensity):
        """
        Set intensity
        """
        self.wave.set_intensity(intensity)

    def set_wave(self, wavelength):
        """
        Set wavelength list or wavelength
        """
        if wavelength.__class__.__name__ == 'list':
            self.wave.set_wave_list(wavelength)
        elif wavelength.__class__.__name__ == 'float':
            self.wave.set_wave_list([wavelength])
            #self.set_wavelength(wavelength)
        else:
            raise TypeError("invalid wavlength---should be list or float")

    def set_wave_spread(self, wavelength_spread):
        """
        Set wavelength spread  or wavelength spread
        """
        if wavelength_spread.__class__.__name__ == 'list':
            self.wave.set_wave_spread_list(wavelength_spread)
        elif wavelength_spread.__class__.__name__ == 'float':
            self.wave.set_wave_spread_list([wavelength_spread])
        else:
            raise TypeError("invalid wavelength spread---should be list or float")

    def set_wavelength(self, wavelength):
        """
        Set wavelength
        """
        self.wavelength = wavelength
        self.wave.set_wavelength(wavelength)

    def set_spectrum(self, spectrum):
        """
        Set spectrum
        """
        self.spectrum = spectrum
        self.wave.set_spectrum(spectrum)

    def set_wavelength_spread(self, wavelength_spread):
        """
        Set wavelength spread
        """
        self.wavelength_spread = wavelength_spread
        self.wave.set_wavelength_spread(wavelength_spread)

    def set_wave_list(self, wavelength_list, wavelengthspread_list):
        """
        Set wavelength and its spread list
        """
        self.wave.set_wave_list(wavelength_list)
        self.wave.set_wave_spread_list(wavelengthspread_list)

    def get_wave_list(self):
        """
        Set wavelength spread
        """
        return self.wave.get_wave_list()

    def get_intensity_list(self):
        """
        Set wavelength spread
        """
        return self.wave.get_intensity_list()

    def set_source_aperture_size(self, size):
        """
        Set source aperture size

        : param size: [dia_value] or [x_value, y_value]
        """
        if len(size) < 1 or len(size) > 2:
            raise RuntimeError("The length of the size must be one or two.")
        self.aperture.set_source_size(size)

    def set_neutron_mass(self, mass):
        """
        Set Neutron mass
        """
        self.wave.set_mass(mass)
        self.mass = mass

    def set_sample_aperture_size(self, size):
        """
        Set sample aperture size

        : param size: [dia_value] or [xheight_value, yheight_value]
        """
        if len(size) < 1 or len(size) > 2:
            raise RuntimeError("The length of the size must be one or two.")
        self.aperture.set_sample_size(size)

    def set_detector_pix_size(self, size):
        """
        Set detector pixel size
        """
        self.detector.set_pix_size(size)

    def set_detector_size(self, size):
        """
        Set detector size in number of pixels
        : param size: [pixel_nums] or [x_pix_num, yx_pix_num]
        """
        self.detector.set_size(size)

    def set_source2sample_distance(self, distance):
        """
        Set detector source2sample_distance

        : param distance: [distance, x_offset]
        """
        if len(distance) < 1 or len(distance) > 2:
            raise RuntimeError("The length of the size must be one or two.")
        self.aperture.set_sample_distance(distance)

    def set_sample2sample_distance(self, distance):
        """
        Set detector sample_slit2sample_distance

        : param distance: [distance, x_offset]
        """
        if len(distance) < 1 or len(distance) > 2:
            raise RuntimeError("The length of the size must be one or two.")
        self.sample.set_distance(distance)

    def set_sample2detector_distance(self, distance):
        """
        Set detector sample2detector_distance

        : param distance: [distance, x_offset]
        """
        if len(distance) < 1 or len(distance) > 2:
            raise RuntimeError("The length of the size must be one or two.")
        self.detector.set_distance(distance)

    def get_all_instrument_params(self):
        """
        Get all instrumental parameters
        """
        self.mass = self.get_neutron_mass()
        self.spectrum = self.get_spectrum()
        self.source_aperture_size = self.get_source_aperture_size()
        self.sample_aperture_size = self.get_sample_aperture_size()
        self.detector_pix_size = self.get_detector_pix_size()
        self.detector_size = self.get_detector_size()
        self.source2sample_distance = self.get_source2sample_distance()
        self.sample2sample_distance = self.get_sample2sample_distance()
        self.sample2detector_distance = self.get_sample2detector_distance()

    def get_detector_qrange(self):
        """
        get max detector q ranges

        : return: qx_min, qx_max, qy_min, qy_max tuple
        """
        if len(self.qxrange) != 2 or len(self.qyrange) != 2:
            return None
        qx_min = self.qxrange[0]
        qx_max = self.qxrange[1]
        qy_min = self.qyrange[0]
        qy_max = self.qyrange[1]

        return qx_min, qx_max, qy_min, qy_max

    def _rotate_z(self, x_value, y_value, theta=0.0):
        """
        Rotate x-y cordinate around z-axis by theta
        : x_value: numpy array of x values
        : y_value: numpy array of y values
        : theta: angle to rotate by in rad

        :return: x_prime, y-prime
        """
        # rotate by theta
        x_prime = x_value * math.cos(theta) + y_value * math.sin(theta)
        y_prime = -x_value * math.sin(theta) + y_value * math.cos(theta)

        return x_prime, y_prime

    def _gaussian2d(self, x_val, y_val, x0_val, y0_val,
                    sigma_x, sigma_y, sigma_r):
        """
        Calculate 2D Gaussian distribution
        : x_val: x value
        : y_val: y value
        : x0_val: mean value in x-axis
        : y0_val: mean value in y-axis
        : sigma_x: variance in x-direction
        : sigma_y: variance in y-direction

        : return: gaussian (value)
        """
        # phi values at each points (not at the center)
        x_value = x_val - x0_val
        y_value = y_val - y0_val
        phi_i = np.arctan2(y_val, x_val)

        # phi correction due to the gravity shift (in phi)
        phi_0 = math.atan2(y0_val, x0_val)
        phi_i = phi_i - phi_0 + self.gravity_phi

        sin_phi = np.sin(self.gravity_phi)
        cos_phi = np.cos(self.gravity_phi)

        x_p = x_value * cos_phi + y_value * sin_phi
        y_p = -x_value * sin_phi + y_value * cos_phi

        new_sig_x = sqrt(sigma_r * sigma_r / (sigma_x * sigma_x) + 1)
        new_sig_y = sqrt(sigma_r * sigma_r / (sigma_y * sigma_y) + 1)
        new_x = x_p * cos_phi / new_sig_x - y_p * sin_phi
        new_x /= sigma_x
        new_y = x_p * sin_phi / new_sig_y + y_p * cos_phi
        new_y /= sigma_y

        nu_value = -0.5 * (new_x * new_x + new_y * new_y)

        gaussian = np.exp(nu_value)
        # normalizing factor correction
        gaussian /= gaussian.sum()

        return gaussian

    def _gaussian2d_polar(self, x_val, y_val, x0_val, y0_val,
                          sigma_x, sigma_y, sigma_r):
        """
        Calculate 2D Gaussian distribution for polar coodinate
        : x_val: x value
        : y_val: y value
        : x0_val: mean value in x-axis
        : y0_val: mean value in y-axis
        : sigma_x: variance in r-direction
        : sigma_y: variance in phi-direction
        : sigma_r: wavelength variance in r-direction

        : return: gaussian (value)
        """
        sigma_x = sqrt(sigma_x * sigma_x + sigma_r * sigma_r)
        # call gaussian1d
        gaussian = self._gaussian1d(x_val, x0_val, sigma_x)
        gaussian *= self._gaussian1d(y_val, y0_val, sigma_y)

        # normalizing factor correction
        if sigma_x != 0 and sigma_y != 0:
            gaussian *= sqrt(2 * pi)
        return gaussian

    def _gaussian1d(self, value, mean, sigma):
        """
        Calculate 1D Gaussian distribution
        : value: value
        : mean: mean value
        : sigma: variance

        : return: gaussian (value)
        """
        # default
        gaussian = 1.0
        if sigma != 0:
            # get exponent
            nu_value = (value - mean) / sigma
            nu_value *= nu_value
            nu_value *= -0.5
            gaussian *= np.exp(nu_value)
            gaussian /= sigma
            # normalize
            gaussian /= sqrt(2 * pi)

        return gaussian

    def _atan_phi(self, qy_value, qx_value):
        """
        Find the angle phi of q on the detector plane for qx_value, qy_value given
        : qx_value: x component of q
        : qy_value: y component of q

        : return phi: the azimuthal angle of q on x-y plane
        """
        phi = math.atan2(qy_value, qx_value)
        return phi

    def _get_detector_qxqy_pixels(self):
        """
        Get the pixel positions of the detector in the qx_value-qy_value space
        """

        # update all param values
        self.get_all_instrument_params()

        # wavelength
        wavelength = self.wave.wavelength
        # Gavity correction
        delta_y = self._get_beamcenter_drop()  # in cm

        # detector_pix size
        detector_pix_size = self.detector_pix_size
        # Square or circular pixel
        if len(detector_pix_size) == 1:
            pix_x_size = detector_pix_size[0]
            pix_y_size = detector_pix_size[0]
        # rectangular pixel pixel
        elif len(detector_pix_size) == 2:
            pix_x_size = detector_pix_size[0]
            pix_y_size = detector_pix_size[1]
        else:
            raise ValueError(" Input value format error...")
        # Sample to detector distance = sample slit to detector
        # minus sample offset
        sample2detector_distance = self.sample2detector_distance[0] - \
                                    self.sample2sample_distance[0]
        # detector offset in x-direction
        detector_offset = 0
        try:
            detector_offset = self.sample2detector_distance[1]
        except:
            logger.error(sys.exc_value)

        # detector size in [no of pix_x,no of pix_y]
        detector_pix_nums_x = self.detector_size[0]

        # get pix_y if it exists, otherwse take it from [0]
        try:
            detector_pix_nums_y = self.detector_size[1]
        except:
            detector_pix_nums_y = self.detector_size[0]

        # detector offset in pix number
        offset_x = detector_offset / pix_x_size
        offset_y = delta_y / pix_y_size

        # beam center position in pix number (start from 0)
        center_x, center_y = self._get_beamcenter_position(detector_pix_nums_x,
                                                           detector_pix_nums_y,
                                                           offset_x, offset_y)
        # distance [cm] from the beam center on detector plane
        detector_ind_x = np.arange(detector_pix_nums_x)
        detector_ind_y = np.arange(detector_pix_nums_y)

        # shif 0.5 pixel so that pix position is at the center of the pixel
        detector_ind_x = detector_ind_x + 0.5
        detector_ind_y = detector_ind_y + 0.5

        # the relative postion from the beam center
        detector_ind_x = detector_ind_x - center_x
        detector_ind_y = detector_ind_y - center_y

        # unit correction in cm
        detector_ind_x = detector_ind_x * pix_x_size
        detector_ind_y = detector_ind_y * pix_y_size

        qx_value = np.zeros(len(detector_ind_x))
        qy_value = np.zeros(len(detector_ind_y))
        i = 0

        for indx in detector_ind_x:
            qx_value[i] = self._get_qx(indx, sample2detector_distance, wavelength)
            i += 1
        i = 0
        for indy in detector_ind_y:
            qy_value[i] = self._get_qx(indy, sample2detector_distance, wavelength)
            i += 1

        # qx_value and qy_value values in array
        qx_value = qx_value.repeat(detector_pix_nums_y)
        qx_value = qx_value.reshape(detector_pix_nums_x, detector_pix_nums_y)
        qy_value = qy_value.repeat(detector_pix_nums_x)
        qy_value = qy_value.reshape(detector_pix_nums_y, detector_pix_nums_x)
        qy_value = qy_value.transpose()

        # p min and max values among the center of pixels
        self.qx_min = np.min(qx_value)
        self.qx_max = np.max(qx_value)
        self.qy_min = np.min(qy_value)
        self.qy_max = np.max(qy_value)

        # Appr. min and max values of the detector display limits
        # i.e., edges of the last pixels.
        self.qy_min += self._get_qx(-0.5 * pix_y_size,
                                    sample2detector_distance, wavelength)
        self.qy_max += self._get_qx(0.5 * pix_y_size,
                                    sample2detector_distance, wavelength)
        #if self.qx_min == self.qx_max:
        self.qx_min += self._get_qx(-0.5 * pix_x_size,
                                    sample2detector_distance, wavelength)
        self.qx_max += self._get_qx(0.5 * pix_x_size,
                                    sample2detector_distance, wavelength)

        # min and max values of detecter
        self.detector_qx_min = self.qx_min
        self.detector_qx_max = self.qx_max
        self.detector_qy_min = self.qy_min
        self.detector_qy_max = self.qy_max

        # try to set it as a Data2D otherwise pass (not required for now)
        try:
            from sas.sascalc.dataloader.data_info import Data2D
            output = Data2D()
            inten = np.zeros_like(qx_value)
            output.data = inten
            output.qx_data = qx_value
            output.qy_data = qy_value
        except:
            logger.error(sys.exc_value)

        return output

    def _get_qx(self, dx_size, det_dist, wavelength):
        """
        :param dx_size: x-distance from beam center [cm]
        :param det_dist: sample to detector distance [cm]

        :return: q-value at the given position
        """
        # Distance from beam center in the plane of detector
        plane_dist = dx_size
        # full scattering angle on the x-axis
        theta = np.arctan(plane_dist / det_dist)
        qx_value = (2.0 * pi / wavelength) * np.sin(theta)
        return qx_value

    def _get_polar_value(self, qx_value, qy_value):
        """
        Find qr_value and phi from qx_value and qy_value values

        : return qr_value, phi
        """
        # find |q| on detector plane
        qr_value = sqrt(qx_value*qx_value + qy_value*qy_value)
        # find angle phi
        phi = self._atan_phi(qy_value, qx_value)

        return qr_value, phi

    def _get_beamcenter_position(self, num_x, num_y, offset_x, offset_y):
        """
        :param num_x: number of pixel in x-direction
        :param num_y: number of pixel in y-direction
        :param offset: detector offset in x-direction in pix number

        :return: pix number; pos_x, pos_y in pix index
        """
        # beam center position
        pos_x = num_x / 2
        pos_y = num_y / 2

        # correction for offset
        pos_x += offset_x
        # correction for gravity that is always negative
        pos_y -= offset_y

        return pos_x, pos_y

    def _get_beamcenter_drop(self):
        """
        Get the beam center drop (delta y) in y diection due to gravity

        :return delta y: the beam center drop in cm
        """
        # Check if mass == 0 (X-ray).
        if self.mass == 0:
            return 0
        # Covert unit from A to cm
        unit_cm = 1e-08
        # Velocity of neutron in horizontal direction (~ actual velocity)
        velocity = _PLANK_H / (self.mass * self.wave.wavelength * unit_cm)
        # Compute delta y
        delta_y = 0.5
        delta_y *= _GRAVITY
        sampletodetector = self.sample2detector_distance[0] - \
                                    self.sample2sample_distance[0]
        delta_y *= sampletodetector
        delta_y *= (self.source2sample_distance[0] + self.sample2detector_distance[0])
        delta_y /= (velocity * velocity)

        return delta_y