sympyextensions.py 22.3 KB
Newer Older
1
import itertools
Martin Bauer's avatar
Martin Bauer committed
2
import operator
Martin Bauer's avatar
Martin Bauer committed
3
4
5
6
7
import warnings
from collections import Counter, defaultdict
from functools import partial, reduce
from typing import Callable, Dict, Iterable, List, Optional, Sequence, Tuple, TypeVar, Union

Martin Bauer's avatar
Martin Bauer committed
8
import sympy as sp
Martin Bauer's avatar
Martin Bauer committed
9
from sympy.functions import Abs
10
from sympy.core.numbers import Zero
Martin Bauer's avatar
Martin Bauer committed
11

12
from pystencils.assignment import Assignment
Martin Bauer's avatar
Martin Bauer committed
13
from pystencils.data_types import cast_func, get_base_type, get_type_of_expression
14

Martin Bauer's avatar
Martin Bauer committed
15
16
T = TypeVar('T')

17

Martin Bauer's avatar
Martin Bauer committed
18
def prod(seq: Iterable[T]) -> T:
19
20
21
22
    """Takes a sequence and returns the product of all elements"""
    return reduce(operator.mul, seq, 1)


23
24
25
26
27
28
29
30
31
32
33
34
35
36
def remove_small_floats(expr, threshold):
    """Removes all sp.Float objects whose absolute value is smaller than threshold

    >>> expr = sp.sympify("x + 1e-15 * y")
    >>> remove_small_floats(expr, 1e-14)
    x
    """
    if isinstance(expr, sp.Float) and sp.Abs(expr) < threshold:
        return 0
    else:
        new_args = [remove_small_floats(c, threshold) for c in expr.args]
        return expr.func(*new_args) if new_args else expr


Martin Bauer's avatar
Martin Bauer committed
37
38
def is_integer_sequence(sequence: Iterable) -> bool:
    """Checks if all elements of the passed sequence can be cast to integers"""
39
    try:
Martin Bauer's avatar
Martin Bauer committed
40
41
        for i in sequence:
            int(i)
42
43
44
45
46
        return True
    except TypeError:
        return False


Martin Bauer's avatar
Martin Bauer committed
47
48
def scalar_product(a: Iterable[T], b: Iterable[T]) -> T:
    """Scalar product between two sequences."""
49
50
51
    return sum(a_i * b_i for a_i, b_i in zip(a, b))


Martin Bauer's avatar
Martin Bauer committed
52
53
def kronecker_delta(*args):
    """Kronecker delta for variable number of arguments, 1 if all args are equal, otherwise 0"""
Martin Bauer's avatar
Martin Bauer committed
54
55
56
57
58
59
    for a in args:
        if a != args[0]:
            return 0
    return 1


60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
def tanh_step_function_approximation(x, step_location, kind='right', steepness=0.0001):
    """Approximation of step function by a tanh function

    >>> tanh_step_function_approximation(1.2, step_location=1.0, kind='right')
    1.00000000000000
    >>> tanh_step_function_approximation(0.9, step_location=1.0, kind='right')
    0
    >>> tanh_step_function_approximation(1.1, step_location=1.0, kind='left')
    0
    >>> tanh_step_function_approximation(0.9, step_location=1.0, kind='left')
    1.00000000000000
    >>> tanh_step_function_approximation(0.5, step_location=(0, 1), kind='middle')
    1
    """
    if kind == 'left':
        return (1 - sp.tanh((x - step_location) / steepness)) / 2
    elif kind == 'right':
        return (1 + sp.tanh((x - step_location) / steepness)) / 2
    elif kind == 'middle':
        x1, x2 = step_location
Martin Bauer's avatar
Martin Bauer committed
80
81
        return 1 - (tanh_step_function_approximation(x, x1, 'left', steepness)
                    + tanh_step_function_approximation(x, x2, 'right', steepness))
82
83


Martin Bauer's avatar
Martin Bauer committed
84
85
def multidimensional_sum(i, dim):
    """Multidimensional summation
Martin Bauer's avatar
Martin Bauer committed
86

Martin Bauer's avatar
Martin Bauer committed
87
88
89
    Example:
        >>> list(multidimensional_sum(2, dim=3))
        [(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)]
90
    """
Martin Bauer's avatar
Martin Bauer committed
91
92
93
94
95
96
97
98
99
100
101
102
103
    prod_args = [range(dim)] * i
    return itertools.product(*prod_args)


def normalize_product(product: sp.Expr) -> List[sp.Expr]:
    """Expects a sympy expression that can be interpreted as a product and returns a list of all factors.

    Removes sp.Pow nodes that have integer exponent by representing them as single factors in list.

    Returns:
        * for a Mul node list of factors ('args')
        * for a Pow node with positive integer exponent a list of factors
        * for other node types [product] is returned
104
    """
Martin Bauer's avatar
Martin Bauer committed
105
    def handle_pow(power):
106
107
108
109
110
        if power.exp.is_integer and power.exp.is_number and power.exp > 0:
            return [power.base] * power.exp
        else:
            return [power]

Martin Bauer's avatar
Martin Bauer committed
111
112
113
    if isinstance(product, sp.Pow):
        return handle_pow(product)
    elif isinstance(product, sp.Mul):
114
115
116
        result = []
        for a in product.args:
            if a.func == sp.Pow:
Martin Bauer's avatar
Martin Bauer committed
117
                result += handle_pow(a)
118
119
120
121
122
123
124
            else:
                result.append(a)
        return result
    else:
        return [product]


Martin Bauer's avatar
Martin Bauer committed
125
126
127
128
129
130
131
132
133
def symmetric_product(*args, with_diagonal: bool = True) -> Iterable:
    """Similar to itertools.product but yields only values where the index is ascending i.e. values below/up to diagonal

    Examples:
        >>> list(symmetric_product([1, 2, 3], ['a', 'b', 'c']))
        [(1, 'a'), (1, 'b'), (1, 'c'), (2, 'b'), (2, 'c'), (3, 'c')]
        >>> list(symmetric_product([1, 2, 3], ['a', 'b', 'c'], with_diagonal=False))
        [(1, 'b'), (1, 'c'), (2, 'c')]
    """
134
135
    ranges = [range(len(a)) for a in args]
    for idx in itertools.product(*ranges):
Martin Bauer's avatar
Martin Bauer committed
136
        valid_index = True
137
        for t in range(1, len(idx)):
Martin Bauer's avatar
Martin Bauer committed
138
139
            if (with_diagonal and idx[t - 1] > idx[t]) or (not with_diagonal and idx[t - 1] >= idx[t]):
                valid_index = False
140
                break
Martin Bauer's avatar
Martin Bauer committed
141
        if valid_index:
142
143
144
            yield tuple(a[i] for a, i in zip(args, idx))


Martin Bauer's avatar
Martin Bauer committed
145
def fast_subs(expression: T, substitutions: Dict,
Martin Bauer's avatar
Martin Bauer committed
146
              skip: Optional[Callable[[sp.Expr], bool]] = None) -> T:
147
    """Similar to sympy subs function.
Martin Bauer's avatar
Martin Bauer committed
148
149
150
151
152
153
154
155
156
157
158
159

    Args:
        expression: expression where parts should be substituted
        substitutions: dict defining substitutions by mapping from old to new terms
        skip: function that marks expressions to be skipped (if True is returned) - that means that in these skipped
              expressions no substitutions are done

    This version is much faster for big substitution dictionaries than sympy version
    """
    if type(expression) is sp.Matrix:
        return expression.copy().applyfunc(partial(fast_subs, substitutions=substitutions))

160
    def visit(expr):
161
162
        if skip and skip(expr):
            return expr
Martin Bauer's avatar
Martin Bauer committed
163
        if hasattr(expr, "fast_subs"):
164
            return expr.fast_subs(substitutions, skip)
Martin Bauer's avatar
Martin Bauer committed
165
166
        if expr in substitutions:
            return substitutions[expr]
167
168
        if not hasattr(expr, 'args'):
            return expr
Martin Bauer's avatar
Martin Bauer committed
169
170
        param_list = [visit(a) for a in expr.args]
        return expr if not param_list else expr.func(*param_list)
171

Martin Bauer's avatar
Martin Bauer committed
172
173
    if len(substitutions) == 0:
        return expression
174
    else:
Martin Bauer's avatar
Martin Bauer committed
175
176
        return visit(expression)

177

178
179
180
181
182
183
184
def is_constant(expr):
    """Simple version of checking if a sympy expression is constant.
    Works also for piecewise defined functions - sympy's is_constant() has a problem there, see:
    https://github.com/sympy/sympy/issues/16662
    """
    return len(expr.free_symbols) == 0

185

Martin Bauer's avatar
Martin Bauer committed
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
def subs_additive(expr: sp.Expr, replacement: sp.Expr, subexpression: sp.Expr,
                  required_match_replacement: Optional[Union[int, float]] = 0.5,
                  required_match_original: Optional[Union[int, float]] = None) -> sp.Expr:
    """Transformation for replacing a given subexpression inside a sum.

    Examples:
        The next example demonstrates the advantage of replace_additive compared to sympy.subs:
        >>> x, y, z, k = sp.symbols("x y z k")
        >>> subs_additive(3*x + 3*y, replacement=k, subexpression=x + y)
        3*k

        Terms that don't match completely can be substituted at the cost of additional terms.
        This trade-off is managed using the required_match parameters.
        >>> subs_additive(3*x + 3*y + z, replacement=k, subexpression=x+y+z, required_match_original=1.0)
        3*x + 3*y + z
        >>> subs_additive(3*x + 3*y + z, replacement=k, subexpression=x+y+z, required_match_original=0.5)
        3*k - 2*z
203
204
        >>> subs_additive(3*x + 3*y + z, replacement=k, subexpression=x+y+z, required_match_original=2)
        3*k - 2*z
Martin Bauer's avatar
Martin Bauer committed
205
206
207

    Args:
        expr: input expression
Martin Bauer's avatar
Martin Bauer committed
208
        replacement: expression that is inserted for subexpression (if found)
Martin Bauer's avatar
Martin Bauer committed
209
210
        subexpression: expression to replace
        required_match_replacement:
Martin Bauer's avatar
Martin Bauer committed
211
             * if float: the percentage of terms of the subexpression that has to be matched in order to replace
Martin Bauer's avatar
Martin Bauer committed
212
213
214
215
216
217
218
219
220
221
             * if integer: the total number of terms that has to be matched in order to replace
             * None: is equal to integer 1
             * if both match parameters are given, both restrictions have to be fulfilled (i.e. logical AND)
        required_match_original:
             * if float: the percentage of terms of the original addition expression that has to be matched
             * if integer: the total number of terms that has to be matched in order to replace
             * None: is equal to integer 1

    Returns:
        new expression with replacement
222
    """
Martin Bauer's avatar
Martin Bauer committed
223
224
    def normalize_match_parameter(match_parameter, expression_length):
        if match_parameter is None:
225
            return 1
Martin Bauer's avatar
Martin Bauer committed
226
227
228
        elif isinstance(match_parameter, float):
            assert 0 <= match_parameter <= 1
            res = int(match_parameter * expression_length)
229
            return max(res, 1)
Martin Bauer's avatar
Martin Bauer committed
230
231
232
        elif isinstance(match_parameter, int):
            assert match_parameter > 0
            return match_parameter
233
234
        raise ValueError("Invalid parameter")

Martin Bauer's avatar
Martin Bauer committed
235
    normalized_replacement_match = normalize_match_parameter(required_match_replacement, len(subexpression.args))
236

Martin Bauer's avatar
Martin Bauer committed
237
238
239
240
241
242
243
244
    def visit(current_expr):
        if current_expr.is_Add:
            expr_max_length = max(len(current_expr.args), len(subexpression.args))
            normalized_current_expr_match = normalize_match_parameter(required_match_original, expr_max_length)
            expr_coefficients = current_expr.as_coefficients_dict()
            subexpression_coefficient_dict = subexpression.as_coefficients_dict()
            intersection = set(subexpression_coefficient_dict.keys()).intersection(set(expr_coefficients))
            if len(intersection) >= max(normalized_replacement_match, normalized_current_expr_match):
245
                # find common factor
246
                factors = defaultdict(int)
247
                skips = 0
Martin Bauer's avatar
Martin Bauer committed
248
249
                for common_symbol in subexpression_coefficient_dict.keys():
                    if common_symbol not in expr_coefficients:
250
251
                        skips += 1
                        continue
Martin Bauer's avatar
Martin Bauer committed
252
                    factor = expr_coefficients[common_symbol] / subexpression_coefficient_dict[common_symbol]
253
254
                    factors[sp.simplify(factor)] += 1

Martin Bauer's avatar
Martin Bauer committed
255
256
257
                common_factor = max(factors.items(), key=operator.itemgetter(1))[0]
                if factors[common_factor] >= max(normalized_current_expr_match, normalized_replacement_match):
                    return current_expr - common_factor * subexpression + common_factor * replacement
258
259

        # if no subexpression was found
Martin Bauer's avatar
Martin Bauer committed
260
261
262
        param_list = [visit(a) for a in current_expr.args]
        if not param_list:
            return current_expr
263
        else:
264
265
            if current_expr.func == sp.Mul and Zero() in param_list:
                return Zero()
266
267
            else:
                return current_expr.func(*param_list, evaluate=False)
268
269
270
271

    return visit(expr)


Martin Bauer's avatar
Martin Bauer committed
272
273
274
def replace_second_order_products(expr: sp.Expr, search_symbols: Iterable[sp.Symbol],
                                  positive: Optional[bool] = None,
                                  replace_mixed: Optional[List[Assignment]] = None) -> sp.Expr:
275
    """Replaces second order mixed terms like 4*x*y by 2*( (x+y)**2 - x**2 - y**2 ).
Martin Bauer's avatar
Martin Bauer committed
276

277
278
    This makes the term longer - simplify usually is undoing these - however this
    transformation can be done to find more common sub-expressions
Martin Bauer's avatar
Martin Bauer committed
279
280
281
282
283
284
285
286
287
288
289

    Args:
        expr: input expression
        search_symbols: symbols that are searched for
                         for example, given [x,y,z] terms like x*y, x*z, z*y are replaced
        positive: there are two ways to do this substitution, either with term
                 (x+y)**2 or (x-y)**2 . if positive=True the first version is done,
                 if positive=False the second version is done, if positive=None the
                 sign is determined by the sign of the mixed term that is replaced
        replace_mixed: if a list is passed here, the expr x+y or x-y is replaced by a special new symbol
                       and the replacement equation is added to the list
290
    """
Martin Bauer's avatar
Martin Bauer committed
291
    mixed_symbols_replaced = set([e.lhs for e in replace_mixed]) if replace_mixed is not None else set()
292
293

    if expr.is_Mul:
Martin Bauer's avatar
Martin Bauer committed
294
295
        distinct_search_symbols = set()
        nr_of_search_terms = 0
296
        other_factors = sp.Integer(1)
297
        for t in expr.args:
Martin Bauer's avatar
Martin Bauer committed
298
299
300
            if t in search_symbols:
                nr_of_search_terms += 1
                distinct_search_symbols.add(t)
301
            else:
Martin Bauer's avatar
Martin Bauer committed
302
303
304
                other_factors *= t
        if len(distinct_search_symbols) == 2 and nr_of_search_terms == 2:
            u, v = sorted(list(distinct_search_symbols), key=lambda symbol: symbol.name)
305
            if positive is None:
Martin Bauer's avatar
Martin Bauer committed
306
307
308
309
                other_factors_without_symbols = other_factors
                for s in other_factors.atoms(sp.Symbol):
                    other_factors_without_symbols = other_factors_without_symbols.subs(s, 1)
                positive = other_factors_without_symbols.is_positive
310
311
                assert positive is not None
            sign = 1 if positive else -1
Martin Bauer's avatar
Martin Bauer committed
312
313
314
315
316
317
318
            if replace_mixed is not None:
                new_symbol_str = 'P' if positive else 'M'
                mixed_symbol_name = u.name + new_symbol_str + v.name
                mixed_symbol = sp.Symbol(mixed_symbol_name.replace("_", ""))
                if mixed_symbol not in mixed_symbols_replaced:
                    mixed_symbols_replaced.add(mixed_symbol)
                    replace_mixed.append(Assignment(mixed_symbol, u + sign * v))
319
            else:
Martin Bauer's avatar
Martin Bauer committed
320
321
                mixed_symbol = u + sign * v
            return sp.Rational(1, 2) * sign * other_factors * (mixed_symbol ** 2 - u ** 2 - v ** 2)
322

Martin Bauer's avatar
Martin Bauer committed
323
324
    param_list = [replace_second_order_products(a, search_symbols, positive, replace_mixed) for a in expr.args]
    result = expr.func(*param_list, evaluate=False) if param_list else expr
325
326
327
    return result


Martin Bauer's avatar
Martin Bauer committed
328
329
def remove_higher_order_terms(expr: sp.Expr, symbols: Sequence[sp.Symbol], order: int = 3) -> sp.Expr:
    """Removes all terms that contain more than 'order' factors of given 'symbols'
Martin Bauer's avatar
Martin Bauer committed
330
331
332
333

    Example:
        >>> x, y = sp.symbols("x y")
        >>> term = x**2 * y + y**2 * x + y**3 + x + y ** 2
Martin Bauer's avatar
Martin Bauer committed
334
        >>> remove_higher_order_terms(term, order=2, symbols=[x, y])
Martin Bauer's avatar
Martin Bauer committed
335
        x + y**2
336
337
338
339
340
    """
    from sympy.core.power import Pow
    from sympy.core.add import Add, Mul

    result = 0
Martin Bauer's avatar
Martin Bauer committed
341
    expr = expr.expand()
342

Martin Bauer's avatar
Martin Bauer committed
343
344
    def velocity_factors_in_product(product):
        factor_count = 0
Martin Bauer's avatar
Martin Bauer committed
345
346
347
348
        if type(product) is Mul:
            for factor in product.args:
                if type(factor) == Pow:
                    if factor.args[0] in symbols:
Martin Bauer's avatar
Martin Bauer committed
349
                        factor_count += factor.args[1]
Martin Bauer's avatar
Martin Bauer committed
350
                if factor in symbols:
Martin Bauer's avatar
Martin Bauer committed
351
                    factor_count += 1
Martin Bauer's avatar
Martin Bauer committed
352
353
        elif type(product) is Pow:
            if product.args[0] in symbols:
Martin Bauer's avatar
Martin Bauer committed
354
355
                factor_count += product.args[1]
        return factor_count
356

Martin Bauer's avatar
Martin Bauer committed
357
358
359
    if type(expr) == Mul or type(expr) == Pow:
        if velocity_factors_in_product(expr) <= order:
            return expr
360
361
362
        else:
            return sp.Rational(0, 1)

Martin Bauer's avatar
Martin Bauer committed
363
364
    if type(expr) != Add:
        return expr
365

Martin Bauer's avatar
Martin Bauer committed
366
367
368
    for sum_term in expr.args:
        if velocity_factors_in_product(sum_term) <= order:
            result += sum_term
369
370
371
    return result


Martin Bauer's avatar
Martin Bauer committed
372
373
374
def complete_the_square(expr: sp.Expr, symbol_to_complete: sp.Symbol,
                        new_variable: sp.Symbol) -> Tuple[sp.Expr, Optional[Tuple[sp.Symbol, sp.Expr]]]:
    """Transforms second order polynomial into only squared part.
375

Martin Bauer's avatar
Martin Bauer committed
376
377
378
379
380
381
382
383
    Examples:
        >>> a, b, c, s, n = sp.symbols("a b c s n")
        >>> expr = a * s**2 + b * s + c
        >>> completed_expr, substitution = complete_the_square(expr, symbol_to_complete=s, new_variable=n)
        >>> completed_expr
        a*n**2 + c - b**2/(4*a)
        >>> substitution
        (n, s + b/(2*a))
384

Martin Bauer's avatar
Martin Bauer committed
385
    Returns:
Martin Bauer's avatar
Martin Bauer committed
386
        (replaced_expr, tuple to pass to subs, such that old expr comes out again)
387
    """
Martin Bauer's avatar
Martin Bauer committed
388
389
390
    p = sp.Poly(expr, symbol_to_complete)
    coefficients = p.all_coeffs()
    if len(coefficients) != 3:
391
        return expr, None
Martin Bauer's avatar
Martin Bauer committed
392
393
394
    a, b, _ = coefficients
    expr = expr.subs(symbol_to_complete, new_variable - b / (2 * a))
    return sp.simplify(expr), (new_variable, symbol_to_complete + b / (2 * a))
395
396


Martin Bauer's avatar
Martin Bauer committed
397
398
399
400
401
402
def complete_the_squares_in_exp(expr: sp.Expr, symbols_to_complete: Sequence[sp.Symbol]):
    """Completes squares in arguments of exponential which makes them simpler to integrate.

    Very useful for integrating Maxwell-Boltzmann equilibria and its moment generating function
    """
    dummies = [sp.Dummy() for _ in symbols_to_complete]
403
404
405

    def visit(term):
        if term.func == sp.exp:
Martin Bauer's avatar
Martin Bauer committed
406
407
408
409
            exp_arg = term.args[0]
            for symbol_to_complete, dummy in zip(symbols_to_complete, dummies):
                exp_arg, substitution = complete_the_square(exp_arg, symbol_to_complete, dummy)
            return sp.exp(sp.expand(exp_arg))
410
        else:
Martin Bauer's avatar
Martin Bauer committed
411
412
            param_list = [visit(a) for a in term.args]
            if not param_list:
413
414
                return term
            else:
Martin Bauer's avatar
Martin Bauer committed
415
                return term.func(*param_list)
416
417

    result = visit(expr)
Martin Bauer's avatar
Martin Bauer committed
418
419
    for s, d in zip(symbols_to_complete, dummies):
        result = result.subs(d, s)
420
421
422
    return result


Martin Bauer's avatar
Martin Bauer committed
423
def extract_most_common_factor(term):
424
    """Processes a sum of fractions: determines the most common factor and splits term in common factor and rest"""
Martin Bauer's avatar
Martin Bauer committed
425
426
427
    coefficient_dict = term.as_coefficients_dict()
    counter = Counter([Abs(v) for v in coefficient_dict.values()])
    common_factor, occurrences = max(counter.items(), key=operator.itemgetter(1))
Martin Bauer's avatar
Martin Bauer committed
428
    if occurrences == 1 and (1 in counter):
Martin Bauer's avatar
Martin Bauer committed
429
430
        common_factor = 1
    return common_factor, term / common_factor
431
432


Martin Bauer's avatar
Martin Bauer committed
433
434
435
def count_operations(term: Union[sp.Expr, List[sp.Expr]],
                     only_type: Optional[str] = 'real') -> Dict[str, int]:
    """Counts the number of additions, multiplications and division.
Martin Bauer's avatar
Martin Bauer committed
436

Martin Bauer's avatar
Martin Bauer committed
437
438
439
    Args:
        term: a sympy expression (term, assignment) or sequence of sympy objects
        only_type: 'real' or 'int' to count only operations on these types, or None for all
Martin Bauer's avatar
Martin Bauer committed
440

Martin Bauer's avatar
Martin Bauer committed
441
442
    Returns:
        dict with 'adds', 'muls' and 'divs' keys
443
    """
444
445
446
447
    from pystencils.fast_approximation import fast_sqrt, fast_inv_sqrt, fast_division

    result = {'adds': 0, 'muls': 0, 'divs': 0, 'sqrts': 0,
              'fast_sqrts': 0, 'fast_inv_sqrts': 0, 'fast_div': 0}
448
449
450

    if isinstance(term, Sequence):
        for element in term:
Martin Bauer's avatar
Martin Bauer committed
451
            r = count_operations(element, only_type)
Martin Bauer's avatar
Martin Bauer committed
452
453
            for operation_name in result.keys():
                result[operation_name] += r[operation_name]
454
        return result
455
    elif isinstance(term, Assignment):
456
457
        term = term.rhs

458
459
    if hasattr(term, 'evalf'):
        term = term.evalf()
460

Martin Bauer's avatar
Martin Bauer committed
461
462
    def check_type(e):
        if only_type is None:
463
464
            return True
        try:
Martin Bauer's avatar
Martin Bauer committed
465
            base_type = get_base_type(get_type_of_expression(e))
466
467
        except ValueError:
            return False
Martin Bauer's avatar
Martin Bauer committed
468
        if only_type == 'int' and (base_type.is_int() or base_type.is_uint()):
469
            return True
Martin Bauer's avatar
Martin Bauer committed
470
        if only_type == 'real' and (base_type.is_float()):
471
472
            return True
        else:
Martin Bauer's avatar
Martin Bauer committed
473
            return base_type == only_type
474

475
    def visit(t):
Martin Bauer's avatar
Martin Bauer committed
476
        visit_children = True
477
        if t.func is sp.Add:
Martin Bauer's avatar
Martin Bauer committed
478
            if check_type(t):
479
                result['adds'] += len(t.args) - 1
Julian Hammer's avatar
Julian Hammer committed
480
481
        elif t.func in [sp.Or, sp.And]:
            pass
482
        elif t.func is sp.Mul:
Martin Bauer's avatar
Martin Bauer committed
483
            if check_type(t):
Markus Holzer's avatar
Markus Holzer committed
484
                result['muls'] += len(t.args) - 1
485
486
487
                for a in t.args:
                    if a == 1 or a == -1:
                        result['muls'] -= 1
Martin Bauer's avatar
Martin Bauer committed
488
        elif isinstance(t, sp.Float) or isinstance(t, sp.Rational):
489
490
            pass
        elif isinstance(t, sp.Symbol):
Martin Bauer's avatar
Martin Bauer committed
491
            visit_children = False
492
        elif isinstance(t, sp.Indexed):
Martin Bauer's avatar
Martin Bauer committed
493
            visit_children = False
494
495
        elif t.is_integer:
            pass
496
        elif isinstance(t, cast_func):
Martin Bauer's avatar
Martin Bauer committed
497
498
            visit_children = False
            visit(t.args[0])
499
500
501
502
503
504
        elif t.func is fast_sqrt:
            result['fast_sqrts'] += 1
        elif t.func is fast_inv_sqrt:
            result['fast_inv_sqrts'] += 1
        elif t.func is fast_division:
            result['fast_div'] += 1
505
        elif t.func is sp.Pow:
Martin Bauer's avatar
Martin Bauer committed
506
            if check_type(t.args[0]):
507
                visit_children = True
508
509
510
511
                if t.exp.is_integer and t.exp.is_number:
                    if t.exp >= 0:
                        result['muls'] += int(t.exp) - 1
                    else:
Markus Holzer's avatar
Markus Holzer committed
512
513
                        if result['muls'] > 0:
                            result['muls'] -= 1
514
515
                        result['divs'] += 1
                        result['muls'] += (-int(t.exp)) - 1
516
517
518
                elif sp.nsimplify(t.exp) == sp.Rational(1, 2):
                    result['sqrts'] += 1
                else:
519
                    warnings.warn(f"Cannot handle exponent {t.exp} of sp.Pow node")
520
521
522
            else:
                warnings.warn("Counting operations: only integer exponents are supported in Pow, "
                              "counting will be inaccurate")
523
524
525
526
        elif t.func is sp.Piecewise:
            for child_term, condition in t.args:
                visit(child_term)
            visit_children = False
527
528
        elif isinstance(t, sp.Rel):
            pass
529
        else:
530
            warnings.warn(f"Unknown sympy node of type {str(t.func)} counting will be inaccurate")
531

Martin Bauer's avatar
Martin Bauer committed
532
        if visit_children:
533
534
535
536
537
            for a in t.args:
                visit(a)

    visit(term)
    return result
538
539


Martin Bauer's avatar
Martin Bauer committed
540
541
def count_operations_in_ast(ast) -> Dict[str, int]:
    """Counts number of operations in an abstract syntax tree, see also :func:`count_operations`"""
542
    from pystencils.astnodes import SympyAssignment
543
    result = defaultdict(int)
544
545
546

    def visit(node):
        if isinstance(node, SympyAssignment):
Martin Bauer's avatar
Martin Bauer committed
547
            r = count_operations(node.rhs)
548
549
            for k, v in r.items():
                result[k] += v
550
551
552
553
554
555
556
        else:
            for arg in node.args:
                visit(arg)
    visit(ast)
    return result


Martin Bauer's avatar
Martin Bauer committed
557
558
def common_denominator(expr: sp.Expr) -> sp.Expr:
    """Finds least common multiple of all denominators occurring in an expression"""
559
560
    denominators = [r.q for r in expr.atoms(sp.Rational)]
    return sp.lcm(denominators)
561

Martin Bauer's avatar
Martin Bauer committed
562

Martin Bauer's avatar
Martin Bauer committed
563
def get_symmetric_part(expr: sp.Expr, symbols: Iterable[sp.Symbol]) -> sp.Expr:
Martin Bauer's avatar
Martin Bauer committed
564
565
566
    """
    Returns the symmetric part of a sympy expressions.

Martin Bauer's avatar
Martin Bauer committed
567
568
569
570
571
572
    Args:
        expr: sympy expression, labeled here as :math:`f`
        symbols: sequence of symbols which are considered as degrees of freedom, labeled here as :math:`x_0, x_1,...`

    Returns:
        :math:`\frac{1}{2} [ f(x_0, x_1, ..) + f(-x_0, -x_1) ]`
Martin Bauer's avatar
Martin Bauer committed
573
    """
Martin Bauer's avatar
Martin Bauer committed
574
575
    substitution_dict = {e: -e for e in symbols}
    return sp.Rational(1, 2) * (expr + expr.subs(substitution_dict))
576
577


Martin Bauer's avatar
Martin Bauer committed
578
579
580
class SymbolCreator:
    def __getattribute__(self, name):
        return sp.Symbol(name)