a ž¬>> 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$t|ƒ}| |¡tƒ ||¡}|S©N)rZ _check_dimÚsuperÚ__new__)ÚclsÚnÚobj©Ú __class__©úr/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/matrices/expressions/fourier.pyr *s z DFT.__new__cCs |jdS)Nr)Úargs©ÚselfrrrÚ1óz DFT.cCs |j|jfSr )r rrrrr2rcKs.tdtjt|jƒ}|||t|jƒS©Néþÿÿÿ©rrÚPirr r©rÚiÚjÚkwargsÚwrrrÚ_entry4sz DFT._entrycCs t|jƒSr )ÚIDFTr rrrrÚ _eval_inverse8szDFT._eval_inverse) Ú__name__Ú __module__Ú __qualname__Ú__doc__r Úpropertyr Úshaper!r#Ú __classcell__rrrrr s    rc@s eZdZdZdd„Zdd„ZdS)r"a¢ Returns an inverse discrete Fourier transform matrix. The matrix is scaled with :math:`\frac{1}{\sqrt{n}}` so that it is unitary. Parameters ========== n : integer or Symbol Size of the transform Examples ======== >>> from sympy.matrices.expressions.fourier import DFT, IDFT >>> IDFT(3) IDFT(3) >>> IDFT(4)*DFT(4) I See Also ======== DFT cKs0tdtjt|jƒ}|| |t|jƒSrrrrrrr!Vsz IDFT._entrycCs t|jƒSr )rr rrrrr#ZszIDFT._eval_inverseN)r$r%r&r'r!r#rrrrr"<sr"N)Zsympy.core.sympifyrZsympy.matrices.expressionsrZsympy.core.numbersrZsympy.core.singletonrZ&sympy.functions.elementary.exponentialrZ(sympy.functions.elementary.miscellaneousrrr"rrrrÚs      3