pygsti.baseobjs.polynomial¶

Defines the Polynomial class

Module Contents¶

Classes¶

 FASTPolynomial A polynomial that behaves like a Python dict of coefficients.

Functions¶

 _vinds_to_int(vinds, vindices_per_int, max_num_vars) Convert tuple index of ints to single int given max_numvars bulk_load_compact_polynomials(vtape, ctape, keep_compact=False, max_num_vars=100) Create a list of Polynomial objects from a "tape" of their compact versions. compact_polynomial_list(list_of_polys) Create a single vtape,ctape pair from a list of normal Polynomals

Attributes¶

pygsti.baseobjs.polynomial.PLATFORM_BITS
pygsti.baseobjs.polynomial._vinds_to_int(vinds, vindices_per_int, max_num_vars)

Convert tuple index of ints to single int given max_numvars

class pygsti.baseobjs.polynomial.FASTPolynomial(coeffs=None, max_num_vars=100)

Bases: object

A polynomial that behaves like a Python dict of coefficients.

Variables are represented by integer indices, e.g. “2” means “x_2”. Keys are tuples of variable indices and values are numerical coefficients (floating point or complex numbers). To specify a variable to some power, its index is repeated in the key-tuple.

E.g. x_0^2 + 3*x_1 + 4 is stored as {(0,0): 1.0, (1,): 3.0, (): 4.0}

Parameters
• coeffs (dict) – A dictionary of coefficients. Keys are tuples of integers that specify the polynomial term the coefficient value multiplies (see above). If None, the zero polynomial (no terms) is created.

• max_num_vars (int) – The maximum number of independent variables this polynomial can hold. Placing a limit on the number of variables allows more compact storage and efficient evaluation of the polynomial.

coeffs

A dictionary whose keys are tuples of variable indices (e.g. x0^2*x1 would translate to (0,0,1)) and values are the coefficients.

Type

dict

max_num_vars

The maximum number of independent variables this polynomial can hold.

Type

int

vindices_per_int

The number of variable indices that can be compactly fit into a single int when there are at most max_num_vars variables.

Type

int

classmethod _vindices_per_int(cls, max_num_vars)

The number of variable indices that fit into a single int when there are at most max_num_vars variables.

This quantity is needed to directly construct Polynomial representations and is thus useful internally for forward simulators.

Parameters

max_num_vars (int) – The maximum number of independent variables.

Returns

int

classmethod from_rep(cls, rep)

Creates a Polynomial from a “representation” (essentially a lite-version) of a Polynomial.

Note: usually we only need to convert from full-featured Python objects to the lighter-weight “representation” objects. Polynomials are an exception, since as the results of probability computations they need to be converted back from “representation-form” to “full-form”.

Parameters

rep (PolynomialRep) – A polynomial representation.

Returns

Polynomial

classmethod product(cls, list_of_polys)

Take the product of multiple polynomials.

Parameters

list_of_polys (list) – List of polynomials to take the product of.

Returns

Polynomial

property coeffs(self)

A dictionary of this polynoial’s coefficients.

Keys are tuples of integers that specify the polynomial term the coefficient value multiplies (see above). If None, the zero polynomial (no terms) is created.

Returns

dict

property max_num_vars(self)

The maximum number of independent variables this polynomial can hold.

Powers of variables are not “independent”, e.g. the polynomial x0^2 + 2*x0 + 3 has a single indepdent variable.

Returns

int

property vindices_per_int(self)

The number of this polynoial’s variable indices that can be compactly fit into a single int.

Returns

int

deriv(self, wrt_param)

Take the derivative of this Polynomial with respect to a single variable.

The result is another Polynomial.

E.g. deriv(x_2^3 + 3*x_1, wrt_param=2) = 3x^2

Parameters

wrt_param (int) – The variable index to differentiate with respect to. E.g. “4” means “differentiate w.r.t. x_4”.

Returns

Polynomial

property degree(self)

The largest sum-of-exponents for any term (monomial) within this polynomial.

E.g. for x_2^3 + x_1^2*x_0^2 has degree 4.

Returns

int

evaluate(self, variable_values)

Evaluate this polynomial for a given set of variable values.

Parameters

variable_values (array-like) – An object that can be indexed so that variable_values[i] gives the numerical value for i-th variable (x_i).

Returns

float or complex – Depending on the types of the coefficients and variable_values.

compact(self, complex_coeff_tape=True)

Generate a compact form of this polynomial designed for fast evaluation.

The resulting “tapes” can be evaluated using :function:`opcalc.bulk_eval_compact_polynomials`.

Parameters

complex_coeff_tape (bool, optional) – Whether the ctape returned array is forced to be of complex type. If False, the real part of all coefficients is taken (even if they’re complex).

Returns

vtape, ctape (numpy.ndarray) – These two 1D arrays specify an efficient means for evaluating this polynomial.

copy(self)

Returns a copy of this polynomial.

Returns

Polynomial

map_indices(self, mapfn)

Performs a bulk find & replace on this polynomial’s variable indices.

This is useful when the variable indices have external significance (like being the indices of a gate’s parameters) and one want to convert to another set of indices (like a parent model’s parameters).

Parameters

mapfn (function) – A function that takes as input an “old” variable-index-tuple (a key of this Polynomial) and returns the updated “new” variable-index-tuple.

Returns

Polynomial

map_indices_inplace(self, mapfn)

Performs an in-place find & replace on this polynomial’s variable indices.

This is useful when the variable indices have external significance (like being the indices of a gate’s parameters) and one want to convert to another set of indices (like a parent model’s parameters).

Parameters

mapfn (function) – A function that takes as input an “old” variable-index-tuple (a key of this Polynomial) and returns the updated “new” variable-index-tuple.

Returns

None

mapvec_indices(self, mapvec)

Performs a bulk find & replace on this polynomial’s variable indices.

This function is similar to :method:`map_indices` but uses a vector to describe individual index updates instead of a function for increased performance.

Parameters

mapvec (numpy.ndarray) – An array whose i-th element gives the updated “new” index for the i-th variable. Note that this vector maps individual variable indices old->new, whereas mapfn in :method:`map_indices` maps between tuples of indices.

Returns

Polynomial

mapvec_indices_inplace(self, mapvec)

Performs an in-place bulk find & replace on this polynomial’s variable indices.

This function is similar to :method:`map_indices_inplace` but uses a vector to describe individual index updates instead of a function for increased performance.

Parameters

mapvec (numpy.ndarray) – An array whose i-th element gives the updated “new” index for the i-th variable. Note that this vector maps individual variable indices old->new, whereas mapfn in :method:`map_indices_inplace` maps between tuples of indices.

Returns

Polynomial

mult(self, x)

Multiplies this polynomial by another polynomial x.

Parameters

x (Polynomial) – The polynomial to multiply by.

Returns

Polynomial – The polynomial representing self * x.

scale(self, x)

Scale this polynomial by x (multiply all coefficients by x).

Parameters

x (float or complex) – The value to scale by.

Returns

None

scalar_mult(self, x)

Multiplies this polynomial by a scalar x.

Parameters

x (float or complex) – The value to multiply by.

Returns

Polynomial

__str__(self)

Return str(self).

__repr__(self)

Return repr(self).

Does self += x more efficiently

__mul__(self, x)
__rmul__(self, x)
__pow__(self, n)
__copy__(self)
to_rep(self)

Construct a representation of this polynomial.

“Representations” are lightweight versions of objects used to improve the efficiency of intensely computational tasks. Note that Polynomial representations must have the same max_order and max_num_vars in order to interact with each other (add, multiply, etc.).

Returns

PolynomialRep

pygsti.baseobjs.polynomial.Polynomial

Create a list of Polynomial objects from a “tape” of their compact versions.

Parameters
• vtape (numpy.ndarray) – A 1D array of variable indices that, together with ctape, specify an efficient means for evaluating a set of polynoials.

• ctape (numpy.ndarray) – A 1D array of coefficients that, together with vtape, specify an efficient means for evaluating a set of polynoials.

• keep_compact (bool, optional) – If True the returned list has elements which are (vtape,ctape) tuples for each individual polynomial. If False, then the elements are Polynomial objects.

• max_num_vars (int, optional) – The maximum number of variables the created polynomials are allowed to have.

Returns

list – A list of Polynomial objects.

pygsti.baseobjs.polynomial.compact_polynomial_list(list_of_polys)

Create a single vtape,ctape pair from a list of normal Polynomals

Parameters

list_of_polys (list) – A list of Polynomial objects.

Returns

• vtape (numpy.ndarray) – A “tape” of the variable indices.

• ctape (numpy.ndarray) – A “tape” of the polynomial coefficients.