This module provides a python interface (wrapper functions) for FNFT, a library for the numerical computation of nonlinear Fourier transforms.
For FNFTpy to work, a copy of FNFT has to be installed. For general information, source files and installation of FNFT, visit FNFT's github page: https://github.com/FastNFT
for changes and latest updates see Changelog
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Currently, the continuous spectrum can be calculated.
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Function kdvv:
- easy-to-use Python function, options can be passed as optional arguments
- minimal example:
import numpy as np from FNFTpy import kdvv print("\n\nkdvv example") # set values D = 256 tvec = np.linspace(-1, 1, D) q = np.zeros(D, dtype=np.complex128) q[:] = 2.0 + 0.0j Xi1 = -2 Xi2 = 2 M = 8 Xivec = np.linspace(Xi1, Xi2, M) # call function res = kdvv(q, tvec, M, Xi1=Xi1, Xi2=Xi2) # print results print("\n----- options used ----") print(res['options']) print("\n------ results --------") print("FNFT return value: %d (should be 0)" % res['return_value']) print("continuous spectrum: ") for i in range(len(res['cont'])): print("%d : Xi=%.4f %.6f %.6fj" % (i, Xivec[i], np.real(res['cont'][i]), np.imag(res['cont'][i]))) - for full description call
help(kdvv)
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function kdvv_wrapper:
- mimics the function fnft_kdvv from FNFT.
- for full description call
help(kdvv_wrapper)
- The main and auxiliary spectra can be calculated.
- Function nsep:
- easy-to-use Python function, options can be passed as optional arguments
- minimal example:
import numpy as np from FNFTpy import nsep print("\n\nnsep example") # set values D = 257 tvec = np.linspace(0, 2*np.pi, D) q = np.exp(2.0j * tvec) # call function res = nsep(q, 0, 2 * np.pi, bb=[-2, 2, -2, 2], filt=1, kappa=1) # print results print("\n----- options used ----") print(res['options']) print("\n------ results --------") print("FNFT return value: %d (should be 0)" % res['return_value']) print("number of samples: %d" % D) print('main spectrum') for i in range(res['K']): print("%d : %.6f %.6fj" % (i, np.real(res['main'][i]), np.imag(res['main'][i]))) print('auxiliary spectrum') for i in range(res['M']): print("%d : %.6f %.6fj" % (i, np.real(res['aux'][i]), np.imag(res['aux'][i])))
- for full description call
help(nsep) - Function nsep_wrapper:
- mimics the function fnft_nsep from FNFT.
- for full description call
help(nsep_wrapper)
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The discrete and continuous spectra can be calculated.
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Function nsev:
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easy-to-use Python function, options can be passed as optional arguments
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minimal example:
import numpy as np from FNFTpy import nsev # set values D = 256 tvec = np.linspace(-1, 1, D) q = np.zeros(len(tvec), dtype=np.complex128) q[:] = 2.0 + 0.0j M = 8 Xi1 = -2 Xi2 = 2 Xivec = np.linspace(Xi1, Xi2, M) # call function res = nsev(q, tvec, M=M, Xi1=Xi1, Xi2=Xi2) # print results print("\n----- options used ----") print(res['options']) print("\n------ results --------") print("FNFT return value: %d (should be 0)" % res['return_value']) print("continuous spectrum") for i in range(len(res['cont_ref'])): print("%d : Xi = %.4f %.6f %.6fj" % (i, Xivec[i], np.real(res['cont_ref'][i]), np.imag(res['cont_ref'][i]))) print("discrete spectrum") for i in range(len(res['bound_states'])): print("%d : %.6f %.6fj with norming const %.6f %.6fj" % (i, np.real(res['bound_states'][i]), np.imag(res['bound_states'][i]), np.real(res['disc_norm'][i]), np.imag(res['disc_norm'][i]))) -
for full description call
help(nsev)
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Function nsev_wrapper:
- mimics the function fnft_nsev from FNFT.
- for full description call
help(nsev_wrapper)
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Perform the Inverse Nonlinear Fourier transform: the temporal field is calculated from the nonlinear spectrum.
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the continuous part and (optional) the discrete part of the spectrum can be given.
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function nsev_inverse
- easy-to-use Python function, options can be passed as optional arguments
- minimal example:
from FNFTpy import nsev_inverse, nsev_inverse_xi_wrapper import numpy as np D = 1024 M = 2*D Tmax = 15 tvec = np.linspace(-Tmax, Tmax, D) # calculate suitable frequency bonds (xi) rv, xi = nsev_inverse_xi_wrapper(D, tvec[0], tvec[-1], M) xivec = xi[0] + np.arange(M) * (xi[1] - xi[0]) / (M - 1) # analytic field: chirp-free N=2.2 Satsuma-Yajima pulse q = 2.2 / np.cosh(tvec) # semi-analytic nonlinear spectrum bound_states = np.array([0.7j, 1.7j]) disc_norming_const_ana = [1.0, -1.0] cont_b_ana = 0.587783 / np.cosh(xivec * np.pi) * np.exp(1.0j * np.pi) # call the function res = nsev_inverse(xivec, tvec, cont_b_ana, bound_states, disc_norming_const_ana, cst=1, dst=0) # compare result to analytic function print("\n\nnsev-inverse example: Satsuma-Yajima N=2.2") print("Difference analytic - numeric: sum((q_ana-q_num)**2) = %.2e (should be approx 0) "%np.sum(np.abs(q-res['q'])**2))
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Function nsev_inverse_wrapper:
- mimics the function fnft_nsev_inverse from FNFT.
- for full description call
help(nsev_inverse_wrapper)
- Python 3
- additional Python module: NumPy (python-numpy)
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you may install FNFTpy locally using pip: From within the project root folder run
pip install . # Install system wide pip install -e . # Install in editable/development mode -
alternatively, you may add the FNFTpy folder to your Python path.
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Of course, you need a compiled version of the FNFT C-library. See the documentation for FNFT on how to build the library on your device.
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FNFTpy needs to know where the C-library is located. This configuration can be done by editing the function get_lib_path() in auxiliary.py.
Example:
def get_lib_path(): """Return the path of the FNFT file. Here you can set the location of the compiled library for FNFT. See example strings below. Returns: * libstring : string holding library path Example paths: * libstr = "C:/Libraries/local/libfnft.dll" # example for windows * libstr = "/usr/local/lib/libfnft.so" # example for linux """ libstr = "/usr/local/lib/libfnft.so" # example for linux return libstr
FNFTpy is provided under the terms of the GNU General Public License, version 2.
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for bug reports, please use the github issue tracker
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contributors:
- Christoph Mahnke (chmhnk_at_googlemail_dot_com)
- Shrinivas Chimmalgi
- Simone Gaiarin / simgunz [https://github.com/simgunz]