o à8Va›ã@sTddlmZddlmZddlmZmZmZmZGdd„deƒZ Gdd„de ƒZ dS) é)Ú_sympify)Ú MatrixExpr)ÚSÚIÚsqrtÚexpcsHeZdZdZ‡fdd„Zedd„ƒZedd„ƒZdd„Zd d „Z ‡Z S) ÚDFTaß Returns a discrete Fourier transform matrix. The matrix is scaled with :math:`\frac{1}{\sqrt{n}}` so that it is unitary. Parameters ========== n : integer or Symbol Size of the transform. Examples ======== >>> from sympy.abc import n >>> from sympy.matrices.expressions.fourier import DFT >>> DFT(3) DFT(3) >>> DFT(3).as_explicit() Matrix([ [sqrt(3)/3, sqrt(3)/3, sqrt(3)/3], [sqrt(3)/3, sqrt(3)*exp(-2*I*pi/3)/3, sqrt(3)*exp(2*I*pi/3)/3], [sqrt(3)/3, sqrt(3)*exp(2*I*pi/3)/3, sqrt(3)*exp(-2*I*pi/3)/3]]) >>> DFT(n).shape (n, n) References ========== .. [1] https://en.wikipedia.org/wiki/DFT_matrix cs$t|ƒ}| |¡tƒ ||¡}|S©N)rZ _check_dimÚsuperÚ__new__)ÚclsÚnÚobj©Ú __class__©úD/usr/lib/python3/dist-packages/sympy/matrices/expressions/fourier.pyr 's z DFT.__new__cCs |jdS)Nr)Úargs©ÚselfrrrÚ.s z DFT.cCs |j|jfSr )r rrrrr/s cKs.tdtjt|jƒ}|||t|jƒS©Néþÿÿÿ©rrZPirr r©rÚiÚjÚkwargsÚwrrrÚ_entry1sz DFT._entrycCó t|jƒSr )ÚIDFTr rrrrÚ _eval_inverse5ó zDFT._eval_inverse) Ú__name__Ú __module__Ú __qualname__Ú__doc__r Úpropertyr Úshaperr"Ú __classcell__rrrrrs  rc@s eZdZdZdd„Zdd„ZdS)r!a¢ Returns an inverse discrete Fourier transform matrix. The matrix is scaled with :math:`\frac{1}{\sqrt{n}}` so that it is unitary. Parameters ========== n : integer or Symbol Size of the transform Examples ======== >>> from sympy.matrices.expressions.fourier import DFT, IDFT >>> IDFT(3) IDFT(3) >>> IDFT(4)*DFT(4) I See Also ======== DFT cKs0tdtjt|jƒ}|| |t|jƒSrrrrrrrSsz IDFT._entrycCr r )rr rrrrr"Wr#zIDFT._eval_inverseN)r$r%r&r'rr"rrrrr!9s r!N) Zsympy.core.sympifyrZsympy.matrices.expressionsrZsympyrrrrrr!rrrrÚs 3