a RG5d[@sdZddlmZmZddlmZmZmZm Z ddl m Z ddl m Z ddlmZmZddlmZgdZd d d d d dddZGddde ZdddZddZdS)a Julia code printer The `JuliaCodePrinter` converts SymPy expressions into Julia expressions. A complete code generator, which uses `julia_code` extensively, can be found in `sympy.utilities.codegen`. The `codegen` module can be used to generate complete source code files. )AnyDict)MulPowSRational) _keep_coeff) CodePrinter) precedence PRECEDENCEsearch)3sincostancotseccscasinacosatanacotasecacscsinhcoshtanhcothsechcschasinhacoshatanhacothasechacschsincatan2signfloorlogexpcbrtsqrterferfcerfi factorialgammadigammatrigamma polygammabetaairyai airyaiprimeairybi airybiprimebesseljbesselybesselibesselkerfinverfcinvabsceilconjZhankelh1Zhankelh2imagreal)Absceiling conjugatehankel1hankel2imrec seZdZdZdZdZddddZdd d id d d d d Ziffdd ZddZ ddZ ddZ ddZ ddZ ddZddZddZd d!Zd"d#Zd$d%Zfd&d'Zd(d)Zfd*d+Zfd,d-Zfd.d/Zfd0d1Zd2d3Zd4d5Zd6d7Zd8d9Zd:d;Zdd?Z!d@dAZ"dBdCZ#dDdEZ$dFdGZ%dHdIZ&dJdKZ'dLdMZ(dNdOZ)dPdQZ*dRdSZ+dTdUZ,dVdWZ-dXdYZ.dZd[Z/d\d]Z0d^d_Z1d`daZ2Z3S)bJuliaCodePrinterzD A printer to convert expressions to strings of Julia code. 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({}) :)rsr)r~rrrrkrlrsz5JuliaCodePrinter._print_Piecewise..z (%s) ()rzif (%s)relsez elseif (%s)r) rcond ValueErrorrrrr enumeraterr) rfrr{ecpairsZelastpwrrrcode0rkrrl_print_Piecewises*        z!JuliaCodePrinter._print_Piecewisecs|\}}d}|jr\|\}}|jr@|jr@t| |d}n|jr\|jr\t| |d}|dfddjDS)Nrrz * c3s|]}|tVqdSryr-r.r0rkrlrrz1JuliaCodePrinter._print_MatMul..) as_coeff_mmulr as_real_imagis_zerorrrr)rfrrmr(rLrKrkr0rl _print_MatMuls      zJuliaCodePrinter._print_MatMulc st|tr$||d}d|Sd}dddd|D}fdd|D}fd d|D}g}d }t|D]J\}} | d vr|| qr|||8}|d ||| f|||7}qr|S) z0Accepts a string of code or a list of code linesTrz )z ^function z^if ^elseif ^else$z^for )z^end$rJrKcSsg|]}|dqS)z )lstrip)r~linerkrkrlrrz0JuliaCodePrinter.indent_code..cs&g|]ttfddDqS)c3s|]}t|VqdSryr r~rLrMrkrlrr:JuliaCodePrinter.indent_code...intanyr~) inc_regexrOrlrscs&g|]ttfddDqS)c3s|]}t|VqdSryr rNrOrkrlrrrPrQrT) dec_regexrOrlrsr)rr:z%s%s)rrrz splitlinesrr@r) rfcode code_linestabincreasedecreaseprettylevelnrMrk)rVrUrlrzs.      zJuliaCodePrinter.indent_code)4__name__ __module__ __qualname____doc__ printmethodlanguage _operators_default_settingsr^rorqrurxr|rrrrrrrrrrrrrrrrrr _print_Tuplerrrrrrr(r*r+r,r1r2r3r8r9rDrIrz __classcell__rkrkrirlrM.sv J      $rMNcKst|||S)a)Converts `expr` to a string of Julia code. Parameters ========== expr : Expr A SymPy expression to be converted. assign_to : optional When given, the argument is used as the name of the variable to which the expression is assigned. Can be a string, ``Symbol``, ``MatrixSymbol``, or ``Indexed`` type. This can be helpful for expressions that generate multi-line statements. precision : integer, optional The precision for numbers such as pi [default=16]. user_functions : dict, optional A dictionary where keys are ``FunctionClass`` instances and values are their string representations. Alternatively, the dictionary value can be a list of tuples i.e. [(argument_test, cfunction_string)]. See below for examples. human : bool, optional If True, the result is a single string that may contain some constant declarations for the number symbols. If False, the same information is returned in a tuple of (symbols_to_declare, not_supported_functions, code_text). [default=True]. contract: bool, optional If True, ``Indexed`` instances are assumed to obey tensor contraction rules and the corresponding nested loops over indices are generated. Setting contract=False will not generate loops, instead the user is responsible to provide values for the indices in the code. [default=True]. inline: bool, optional If True, we try to create single-statement code instead of multiple statements. [default=True]. Examples ======== >>> from sympy import julia_code, symbols, sin, pi >>> x = symbols('x') >>> julia_code(sin(x).series(x).removeO()) 'x .^ 5 / 120 - x .^ 3 / 6 + x' >>> from sympy import Rational, ceiling >>> x, y, tau = symbols("x, y, tau") >>> julia_code((2*tau)**Rational(7, 2)) '8 * sqrt(2) * tau .^ (7 // 2)' Note that element-wise (Hadamard) operations are used by default between symbols. This is because its possible in Julia to write "vectorized" code. It is harmless if the values are scalars. >>> julia_code(sin(pi*x*y), assign_to="s") 's = sin(pi * x .* y)' If you need a matrix product "*" or matrix power "^", you can specify the symbol as a ``MatrixSymbol``. >>> from sympy import Symbol, MatrixSymbol >>> n = Symbol('n', integer=True, positive=True) >>> A = MatrixSymbol('A', n, n) >>> julia_code(3*pi*A**3) '(3 * pi) * A ^ 3' This class uses several rules to decide which symbol to use a product. Pure numbers use "*", Symbols use ".*" and MatrixSymbols use "*". A HadamardProduct can be used to specify componentwise multiplication ".*" of two MatrixSymbols. There is currently there is no easy way to specify scalar symbols, so sometimes the code might have some minor cosmetic issues. For example, suppose x and y are scalars and A is a Matrix, then while a human programmer might write "(x^2*y)*A^3", we generate: >>> julia_code(x**2*y*A**3) '(x .^ 2 .* y) * A ^ 3' Matrices are supported using Julia inline notation. When using ``assign_to`` with matrices, the name can be specified either as a string or as a ``MatrixSymbol``. The dimensions must align in the latter case. >>> from sympy import Matrix, MatrixSymbol >>> mat = Matrix([[x**2, sin(x), ceiling(x)]]) >>> julia_code(mat, assign_to='A') 'A = [x .^ 2 sin(x) ceil(x)]' ``Piecewise`` expressions are implemented with logical masking by default. Alternatively, you can pass "inline=False" to use if-else conditionals. Note that if the ``Piecewise`` lacks a default term, represented by ``(expr, True)`` then an error will be thrown. This is to prevent generating an expression that may not evaluate to anything. >>> from sympy import Piecewise >>> pw = Piecewise((x + 1, x > 0), (x, True)) >>> julia_code(pw, assign_to=tau) 'tau = ((x > 0) ? (x + 1) : (x))' Note that any expression that can be generated normally can also exist inside a Matrix: >>> mat = Matrix([[x**2, pw, sin(x)]]) >>> julia_code(mat, assign_to='A') 'A = [x .^ 2 ((x > 0) ? (x + 1) : (x)) sin(x)]' Custom printing can be defined for certain types by passing a dictionary of "type" : "function" to the ``user_functions`` kwarg. Alternatively, the dictionary value can be a list of tuples i.e., [(argument_test, cfunction_string)]. This can be used to call a custom Julia function. >>> from sympy import Function >>> f = Function('f') >>> g = Function('g') >>> custom_functions = { ... "f": "existing_julia_fcn", ... "g": [(lambda x: x.is_Matrix, "my_mat_fcn"), ... (lambda x: not x.is_Matrix, "my_fcn")] ... } >>> mat = Matrix([[1, x]]) >>> julia_code(f(x) + g(x) + g(mat), user_functions=custom_functions) 'existing_julia_fcn(x) + my_fcn(x) + my_mat_fcn([1 x])' Support for loops is provided through ``Indexed`` types. With ``contract=True`` these expressions will be turned into loops, whereas ``contract=False`` will just print the assignment expression that should be looped over: >>> from sympy import Eq, IndexedBase, Idx >>> len_y = 5 >>> y = IndexedBase('y', shape=(len_y,)) >>> t = IndexedBase('t', shape=(len_y,)) >>> Dy = IndexedBase('Dy', shape=(len_y-1,)) >>> i = Idx('i', len_y-1) >>> e = Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i])) >>> julia_code(e.rhs, assign_to=e.lhs, contract=False) 'Dy[i] = (y[i + 1] - y[i]) ./ (t[i + 1] - t[i])' )rMdoprint)r assign_torgrkrkrl julia_codesrlcKstt|fi|dS)z~Prints the Julia representation of the given expression. See `julia_code` for the meaning of the optional arguments. N)printrl)rrgrkrkrlprint_julia_codesrn)N)rctypingrrtDict sympy.corerrrrZsympy.core.mulrZsympy.printing.codeprinterr sympy.printing.precedencer r rLr rardrMrlrnrkrkrkrls,     W