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This modules implements the mathematics-related classes, functions and procedures. Classes: * QVectors: the class that actually performs the q vectors generation. Functions: * differentiate : performs a numerical differentiation of 1D Numeric array * correlation : performs the numerical correlation between two 1D Numeric arrays * convolution : performs the numerical convolution between two 1D Numeric arrays * FFT : performs the FFT of a 1D Numeric array * invFFT : performs the inverse FFT of a 1D Numeric array * gaussianWindow : performs a Gaussian smoothing of 1D Numeric array. * factorial : computes factorial (n) where n is an integer. * basisVectors : computes the basis vectors of the simulation cell from a set of values defining its geometry (3 distances and 3 angles). * randomPointInCircle: returns a vector within a circle of radius |r| and orthogonal to a given direction. * randomDirection2D : returns a normalized vector generated from a unit circle orthogonal to a given direction. * randomPlane2D : generates a normalized random q-vector on a plane defined by vect1, vect2. * qVectorGenerator : sets up and returns a set of q vectors generated from different user-defined parameters. * sphericalHarmonics : calculates the spherical functions Y from a set of j, m, n Wigner indexes * preparePP : sets up the calculation of spherical harmonics.
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NumPy array |
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NumPy array |
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NumPy array |
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NumPy array |
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NumPy array |
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NumPy array |
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integer |
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a list of three floats |
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Scientific Vector |
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list |
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Scientific.Geometry.Vector object |
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Scientific.Geometry.Vector object |
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Scientific.Geometry.Vector object |
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a2 = N.array([[-3., 4.,-1.], [-1., 0., 1.], [1.,-4., 3.]]) a3 = array used to perform order 3 numerical differentiation scheme. |
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a3 = N.array([[-11., 18.,-9., 2.], [-2.,-3., 6.,-1.], [1.,-6., a4 = array used to perform order 4 numerical differentiation scheme. |
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a4 = N.array([[-50., 96.,-72., 32.,-6.], [-6.,-20., 36.,-12., a5 = N.array used to perform order 5 numerical differentiation scheme. |
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a5 = N.array([[-274., 600.,-600., 400.,-150., 24.], [-24.,-130
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Returns the numerical derivative of order |order| of the signal |inputSeries| using the differentiation step |dx|.
See Also: M. Abramowitz, I.A. Stegun; 'Handbook of mathematical functions', Dover, New-York, 1972 p.914. |
Returns the numerical correlation between |inputSeries1| and |inputSeries2| multidimensional NumPy arrays.
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Returns the numerical convolution between |inputSeries1| and |inputSeries2| one-dimensional NumPy arrays.
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Returns the FFT of |inputSeries| multidimensional NumPy array.
Note: the FFT is computed using the fft function of Scientific.FFT package. |
Returns the inverse FFT of |inputSeries| multidimensional NumPy array.
Note: the inverse FFT is computed using the inverse_fft function of Scientific.FFT package. |
Returns a smoothed signal using |inputSeries| input signal and a gaussian kernel of width |alpha|.
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Returns n!
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This function returns the r, theta and phi spherical coordinates from the x, y z cartesian coordinates.
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This function return the coordinates
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Returns the basis vectors for the simulation cell from the six crystallographic parameters.
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Returns a vector drawn from an uniform distribution within a circle of radius |r| and orthogonal to vector |axis|.
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Returns a normalized vector drawn from an uniform distribution on the surface of a unit circle on a plane orthogonal to |axis|.
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Returns a normalized random vector on a plane or in space.
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a3a4 = array used to perform order 4 numerical differentiation scheme.
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a4a5 = N.array used to perform order 5 numerical differentiation scheme.
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a5
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