# -*- coding: utf-8 -*-
# mathtoolspy
# -----------
# A fast, efficient Python library for mathematically operations, like
# integration, solver, distributions and other useful functions.
#
# Author: sonntagsgesicht, based on a fork of Deutsche Postbank [pbrisk]
# Version: 0.3, copyright Wednesday, 18 September 2019
# Website: https://github.com/sonntagsgesicht/mathtoolspy
# License: Apache License 2.0 (see LICENSE file)
import bisect
from ..interpolation import interpolation_bilinear, interpolation_linear
[docs]class Surface(object):
""" A matrix with interpolation and extrapolation. """
def __init__(self, xaxis, yaxis, values):
'''
The values has to be a float matrix implementing the method get_item(i, j).
@params xaxis: list of float values.
@params yaxis: list of float values.
@params values: some object implementing a get_item(i, j) method or nested list.
'''
self.xaxis = xaxis
self.yaxis = yaxis
if hasattr(values, 'get_item'):
self.values = values.get_item
else:
self.values = (lambda x, y: values[x][y])
self.nx = len(self.xaxis)
self.ny = len(self.yaxis)
self.x0 = xaxis[0]
self.y0 = yaxis[0]
[docs] def get_value(self, x, y):
ix = bisect.bisect_left(self.xaxis, x) # x <= self.xaxis[ix]
iy = bisect.bisect_left(self.yaxis, y)
if ix > 0 and ix < self.nx and iy > 0 and iy < self.ny:
# x between, y between
x1 = self.xaxis[ix - 1]
x2 = self.xaxis[ix]
y1 = self.yaxis[iy - 1]
y2 = self.yaxis[iy]
z11 = self.values(ix - 1, iy - 1)
z21 = self.values(ix, iy - 1)
z22 = self.values(ix, iy)
z12 = self.values(ix - 1, iy)
return interpolation_bilinear(x, y, x1, x2, y1, y2, z11, z21, z22, z12)
elif ix == 0 and iy > 0 and iy < self.ny:
# x left, y between
y1 = self.yaxis[iy - 1]
y2 = self.yaxis[iy]
z1 = self.values(0, iy - 1)
z2 = self.values(0, iy)
return interpolation_linear(y, y1, y2, z1, z2)
elif ix == self.nx and iy > 0 and iy < self.ny:
# x right, y between
y1 = self.yaxis[iy - 1]
y2 = self.yaxis[iy]
z1 = self.values(self.nx - 1, iy - 1)
z2 = self.values(self.nx - 1, iy)
return interpolation_linear(y, y1, y2, z1, z2)
elif ix > 0 and ix < self.nx and iy == 0:
# x between, y left
x1 = self.xaxis[ix - 1]
x2 = self.xaxis[ix]
z1 = self.values(ix - 1, 0)
z2 = self.values(ix, 0)
return interpolation_linear(x, x1, x2, z1, z2)
elif ix > 0 and ix < self.nx and iy == -1:
# x between, y right
x1 = self.xaxis[ix - 1]
x2 = self.xaxis[ix]
z1 = self.values(ix - 1, self.ny - 1)
z2 = self.values(ix, self.ny - 1)
return interpolation_linear(x, x1, x2, z1, z2)
elif ix == 0 and iy == 0:
# left lower edge
return self.values(0, 0)
elif ix == self.nx and iy == 0:
# right lower edge
return self.values(self.nx - 1, 0)
elif ix == 0 and iy == self.ny:
# left upper edge
return self.values(0, self.ny - 1)
else:
# right upper edge
return self.values(self.nx - 1, self.ny - 1)
def __call__(self, x, y):
return self.get_value(x, y)