l j[N6dZddlmZgdZddlZddlmZmZm Z ddl m Z m Z ddl ZddlmZddlmZdd lmZmZdd lmZmZd d lTd d lmZmZd'dZd(dZGddeeZGddeZ GddeZ!GddeZ" d)d*d&Z#dS)+axMobjects representing matrices. Examples -------- .. manim:: MatrixExamples :save_last_frame: class MatrixExamples(Scene): def construct(self): m0 = Matrix([["\\pi", 0], [-1, 1]]) m1 = IntegerMatrix([[1.5, 0.], [12, -1.3]], left_bracket="(", right_bracket=")") m2 = DecimalMatrix( [[3.456, 2.122], [33.2244, 12.33]], element_to_mobject_config={"num_decimal_places": 2}, left_bracket=r"\{", right_bracket=r"\}") m3 = MobjectMatrix( [[Circle().scale(0.3), Square().scale(0.3)], [MathTex("\\pi").scale(2), Star().scale(0.3)]], left_bracket="\\langle", right_bracket="\\rangle") g = Group(m0, m1, m2, m3).arrange_in_grid(buff=2) self.add(g) ) annotations)Matrix DecimalMatrix IntegerMatrix MobjectMatrixmatrix_to_tex_stringmatrix_to_mobject get_det_textN)CallableIterableSequence)AnySelf)Mobject)ConvertToOpenGL) DecimalNumberInteger)MathTexTex)*)VGroupVMobjectmatrix np.ndarrayreturnstrctj|d}|jdkr||jdf}|j\}}dd|zz}d}d|D}|d|z|zS)Nrz\left[ \begin{array}{%s}cz\end{array} \right]c8g|]}d|S)z & )join.0rows O/home/agentuser/manim-venv/lib/python3.11/site-packages/manim/mobject/matrix.py z(matrix_to_tex_string..Cs" . . .EJJsOO . . .z \\ )nparrayastypendimreshapesizeshaper")rn_rowsn_colsprefixsuffixrowss r&rr<s Xf   $ $U + +F {aa 011\NFF )S6\ :F $F . .v . . .D HMM$'' '& 00r(rc:tt|SN)rr)rs r&r r Gs '// 0 00r(c eZdZdZddeeddeiedddif d3fd Zd4d#Zd5d%Z d6d7d(Z d8d*Z d9d,Z d8d-Z d9d.Zd:d/Zd;d0Zd8d1Zd8d2ZxZS)r?rArBrDrFrHrIrJsuper__init___matrix_to_mob_matrix_organize_mob_matrixritchainelementsadd _add_bracketscenter mob_matrixadd_background_rectangle)selfrr:r<r=r>r?rArBrDrFrHrIrJrKrLrYmob __class__s r&rPzMatrix.__init__sc$  ,,4X1,H)"4)B&(@%(* 0""6"""//77  !!*---* 56  4,d.@SSNSSS $  4 /} / /,,....  , ,  ) ) + + + + + , ,r(rrlist[list[Mobject]]c fd|DS)Nc,g|]}fd|DS)c6g|]}j|fijSrNrBrD)r$itemr[s r&r'z;Matrix._matrix_to_mob_matrix...sA   ('OO0NOO   r(rN)r$r%r[s r&r'z0Matrix._matrix_to_mob_matrix..sL              r(rN)r[rs` r&rQzMatrix._matrix_to_mob_matrixs0         r(rct|D]f\}}t|D]Q\}}|||}|||jztz||jzt zz|jRg|Sr6) enumeratemove_tor:DOWNr<RIGHTrF)r[rir%j_r\s r&rRzMatrix._organize_mob_matrixs''  FAs!#  1Qil  Od*Q_u-DD1   r(leftrightc Pd}t|j|z dz}ddg|dgzd}dd|z|dg}dd |d |zg}t|fi|} t|fi|} t | | } |jr%| |jd |jzz| |t|j | |t|j | |_ | | | |S) alAdds the brackets to the Matrix mobject. See Latex document for various bracket types. Parameters ---------- left the left bracket, by default "[" right the right bracket, by default "]" Returns ------- :class:`Matrix` The current matrix object (self). g6[ ?rz\begin{array}{c}z\quad \\z \end{array}z\leftz\right.z\left.z\rightr)intheightr"rrrJstretch_to_fit_heightr>next_toLEFTr=rhbracketsrV) r[rlrmrLBRACKET_HEIGHTnempty_tex_arraytex_left tex_right l_bracket r_bracket bracket_pairs r&rWzMatrix._add_bracketsse$  . / /! 3''# k]"    774   GGE!   H//// I0000 i33   V  . .t{QAT=T/T U U U$d&9:::$t':;;;$  I&&& r(rc xtfdttjdDS)aReturn columns of the matrix as VGroups. Returns -------- :class:`~.VGroup` The VGroup contains a nested VGroup for each column of the matrix. Examples -------- .. manim:: GetColumnsExample :save_last_frame: class GetColumnsExample(Scene): def construct(self): m0 = Matrix([[r"\pi", 3], [1, 5]]) m0.add(SurroundingRectangle(m0.get_columns()[1])) self.add(m0) c3NK|]tfdjDVdS)c3(K|] }|V dSr6rN)r$r%ris r& z/Matrix.get_columns...0s';;CQ;;;;;;r(NrrY)r$rir[s @r&rz%Matrix.get_columns../sT;;;;4?;;;<r(r)rrangelenrYr[s`r& get_columnszMatrix.get_columnssO(s4?1#56677  r(colorsc|}t||dD]\}}|||S)aSet individual colors for each columns of the matrix. Parameters ---------- colors The list of colors; each color specified corresponds to a column. Returns ------- :class:`Matrix` The current matrix object (self). Examples -------- .. manim:: SetColumnColorsExample :save_last_frame: class SetColumnColorsExample(Scene): def construct(self): m0 = Matrix([["\\pi", 1], [-1, 3]], ).set_column_colors([RED,BLUE], GREEN) self.add(m0) Fstrict)rzip set_color)r[rcolumnscolorcolumns r&set_column_colorszMatrix.set_column_colors5sS2""$$ ??? $ $ME6   U # # # # r(c2td|jDS)aReturn rows of the matrix as VGroups. Returns -------- :class:`~.VGroup` The VGroup contains a nested VGroup for each row of the matrix. Examples -------- .. manim:: GetRowsExample :save_last_frame: class GetRowsExample(Scene): def construct(self): m0 = Matrix([["\\pi", 3], [1, 5]]) m0.add(SurroundingRectangle(m0.get_rows()[1])) self.add(m0) c3(K|] }t|VdSr6)rr#s r&rz"Matrix.get_rows..gs&@@ @@@@@@r(rrs r&get_rowszMatrix.get_rowsSs (@@@@@AAr(c|}t||dD]\}}|||S)apSet individual colors for each row of the matrix. Parameters ---------- colors The list of colors; each color specified corresponds to a row. Returns ------- :class:`Matrix` The current matrix object (self). Examples -------- .. manim:: SetRowColorsExample :save_last_frame: class SetRowColorsExample(Scene): def construct(self): m0 = Matrix([["\\pi", 1], [-1, 3]], ).set_row_colors([RED,BLUE], GREEN) self.add(m0) Fr)rrr)r[rr4rr%s r&set_row_colorszMatrix.set_row_colorsisM2}}fd5999 ! !JE3 MM%  r(c\|D]}||S)zAdd a black background rectangle to the matrix, see above for an example. Returns ------- :class:`Matrix` The current matrix object (self). ) get_entriesrZ)r[r\s r&add_background_to_entriesz Matrix.add_background_to_entriess9##%% + +C  ( ( * * * * r(c|jS)zReturn the underlying mob matrix mobjects. Returns -------- List[:class:`~.VGroup`] Each VGroup contains a row of the matrix. )rYrs r&get_mob_matrixzMatrix.get_mob_matrixs r(c|jS)azReturn the individual entries of the matrix. Returns -------- :class:`~.VGroup` VGroup containing entries of the matrix. Examples -------- .. manim:: GetEntriesExample :save_last_frame: class GetEntriesExample(Scene): def construct(self): m0 = Matrix([[2, 3], [1, 5]]) ent = m0.get_entries() colors = [BLUE, GREEN, YELLOW, RED] for k in range(len(colors)): ent[k].set_color(colors[k]) self.add(m0) )rUrs r&rzMatrix.get_entries .}r(c|jS)alReturn the bracket mobjects. Returns -------- :class:`~.VGroup` A VGroup containing the left and right bracket. Examples -------- .. manim:: GetBracketsExample :save_last_frame: class GetBracketsExample(Scene): def construct(self): m0 = Matrix([["\\pi", 3], [1, 5]]) bra = m0.get_brackets() colors = [BLUE, GREEN] for k in range(len(colors)): bra[k].set_color(colors[k]) self.add(m0) )rurs r& get_bracketszMatrix.get_bracketsrr()rr r:r;r<r;r=r;r>r;r?r@rAr@rBrCrDrErFrGrHrrIrrJr@rKrErLr)rrrr^)rr^rr)r8r9)rlrrmrrLrrr)rr)rrrr)rr)rr^)__name__ __module__ __qualname____doc__MED_SMALL_BUFFrDRrPrQrRrWrrrrrrrr __classcell__r]s@r&rrKs_WWx . .5:-2EL*,46 !%!*,*,*,*,*,*,*,X    44444l    6<BBBB,<    2r(r) metaclassc.eZdZdZeddifd fd ZxZS)raA mobject that displays a matrix with decimal entries on the screen. Examples -------- .. manim:: DecimalMatrixExample :save_last_frame: class DecimalMatrixExample(Scene): def construct(self): m0 = DecimalMatrix( [[3.456, 2.122], [33.2244, 12]], element_to_mobject_config={"num_decimal_places": 2}, left_bracket="\\{", right_bracket="\\}") self.add(m0) num_decimal_placesrrr rB type[Mobject]rDdict[str, Any]rLrc Btj|f||d|dS)a{ Will round/truncate the decimal places as per the provided config. Parameters ---------- matrix A numpy 2d array or list of lists element_to_mobject Mobject to use, by default DecimalNumber element_to_mobject_config Config for the desired mobject, by default {"num_decimal_places": 1} rbNrOrP)r[rrBrDrLr]s r&rPzDecimalMatrix.__init__sG&   1&?        r()rr rBrrDrrLr)rrrrrrPrrs@r&rrsY*-:5I14M            r(rc(eZdZdZefd fd ZxZS) raA mobject that displays a matrix with integer entries on the screen. Examples -------- .. manim:: IntegerMatrixExample :save_last_frame: class IntegerMatrixExample(Scene): def construct(self): m0 = IntegerMatrix( [[3.7, 2], [42.2, 12]], left_bracket="(", right_bracket=")") self.add(m0) rr rBrrLrc @tj|fd|i|dS)z Will round if there are decimal entries in the matrix. Parameters ---------- matrix A numpy 2d array or list of lists element_to_mobject Mobject to use, by default Integer rBNrr[rrBrLr]s r&rPzIntegerMatrix.__init__s0 QQ4FQ&QQQQQr()rr rBrrLr)rrrrrrPrrs@r&rrs\(-4RRRRRRRRRRRr(rc*eZdZdZdfd fd ZxZS) raA mobject that displays a matrix of mobject entries on the screen. Examples -------- .. manim:: MobjectMatrixExample :save_last_frame: class MobjectMatrixExample(Scene): def construct(self): a = Circle().scale(0.3) b = Square().scale(0.3) c = MathTex("\\pi").scale(2) d = Star().scale(0.3) m0 = MobjectMatrix([[a, b], [c, d]]) self.add(m0) c|Sr6rN)ms r&zMobjectMatrix.:sqr(rr rBrCrLrc @tj|fd|i|dS)NrBrrs r&rPzMobjectMatrix.__init__7s0 QQ4FQ&QQQQQr()rr rBrCrLr)rrrrrPrrs@r&rr$s`*FQ[RRRRRRRRRRRr(rF determinantint | str | Nonebackground_rectr@initial_scale_factorr;rctdd}||||j|\}}||t d||tdtd}||||t d|r| t|||}|{td} | |tdtt|} | | td| | | |S) aHelper function to create determinant. Parameters ---------- matrix The matrix whose determinant is to be created determinant The value of the determinant of the matrix background_rect The background rectangle initial_scale_factor The scale of the text `det` w.r.t the matrix Returns -------- :class:`~.VGroup` A VGroup containing the determinant Examples -------- .. manim:: DeterminantOfAMatrix :save_last_frame: class DeterminantOfAMatrix(Scene): def construct(self): matrix = Matrix([ [2, 0], [-1, 1] ]) # scaling down the `det` string det = get_det_text(matrix, determinant=3, initial_scale_factor=1) # must add the matrix self.add(matrix) self.add(det) ()g?)buffdetN=g?) rscalerrrqsplitrsrtrhrrZrrrV) rrrrparensl_parenr_parenrdet_texteqresults r&r r @sObS#  F LL%&&&   ///||~~GW OOFDsO+++ OOFEO,,, e**CII"###KKCK(((' $$&&&c7G,,H S\\ 7E ,,,[))**r5s+++ R   Or()rrrr)rrrr)NFr) rrrrrr@rr;rr)$r __future__r__all__ itertoolsrScollections.abcr r r typingrrnumpyr)manim.mobject.mobjectr)manim.mobject.opengl.opengl_compatibilityrmanim.mobject.text.numbersrrmanim.mobject.text.tex_mobjectrr constants mobject.types.vectorized_mobjectrrrr rrrrr rNr(r&rs$8#"""""   8888888888))))))EEEEEE========77777777???????? 11111111CCCCCXCCCCL + + + + + F+ + + \"R"R"R"R"RF"R"R"RJRRRRRFRRR<%)!"# CCCCCCCr(