picos.glyphs¶

String templates used to print (algebraic) expressions.

PICOS internally uses this module to produce string representations for the algebraic expressions that you create. The function-like objects that are used to build such strings are called “glyphs” and are instanciated by this module following the singleton pattern. As a result, you can modify the glyph objects listed below to influence how PICOS will format future strings, for example to disable use of unicode symbols that your console does not suppport or to adapt PICOS’ output to the rest of your application.

Here’s an example of first swapping the entire character set to display expressions using only Latin-1 characters, and then modifying a single glyph to our liking:

>>> import picos
>>> X = picos.SymmetricVariable("X", (2,2))
>>> print(X >> 0)
X ≽ 0
>>> picos.glyphs.latin1()
>>> print(X >> 0)
X » 0
>>> picos.glyphs.psdge.template = "{} - {} is psd"
>>> print(X >> 0)
X - 0 is psd

Note that glyphs understand some algebraic rules such as operator precedence and associativity. This is possible because strings produced by glyphs remember how they were created.

>>> one_plus_two = picos.glyphs.add(1, 2)
>>> one_plus_two
'1 + 2'
>>> one_plus_two.glyph.template, one_plus_two.operands
('{} + {}', (1, 2))
>>> picos.glyphs.add(one_plus_two, 3)
'1 + 2 + 3'
>>> picos.glyphs.sub(0, one_plus_two)
'0 - (1 + 2)'

The positive semidefinite glyph above does not yet know how to properly handle arguments with respect to the - symbol involved, but we can modify it further:

>>> print(X + X >> X + X)
X + X - X + X is psd
>>> # Use the same operator binding strength as regular substraction.
>>> picos.glyphs.psdge.order = picos.glyphs.sub.order
>>> print(X + X >> X + X)
X + X - (X + X) is psd

You can reset all glyphs to their initial state as follows:

>>> picos.glyphs.default()

Classes

class picos.glyphs.Am(glyph)[source]¶

Bases: Op

A math atom glyph.

__init__(glyph)[source]¶

Construct an Am glyph.

Parameters: glyph (str) – The glyph’s format string template.

class picos.glyphs.Br(glyph)[source]¶

Bases: Op

A math operator glyph with enclosing brackets.

__init__(glyph)[source]¶

Construct a Br glyph.

Parameters: glyph (str) – The glyph’s format string template.

class picos.glyphs.Fn(glyph)[source]¶

Bases: Op

A math operator glyph in function form.

__init__(glyph)[source]¶

Construct a Fn glyph.

Parameters: glyph (str) – The glyph’s format string template.

class picos.glyphs.Gl(glyph)[source]¶

Bases: object

The basic “glyph”, an (algebraic) string formatting template.

Sublcasses are supposed to extend formatting routines, going beyond of what Python string formatting is capabale of. In particular, glyphs can be used to craft unambiguous algebraic expressions with the minimum amount of parenthesis.

__init__(glyph)[source]¶

Construct a glyph.

Parameters: glyph (str) – The glyph’s format string template.

rebuild()[source]¶

If the template was created using other glyphs, rebuild it.

Returns: True if the template has changed.

reset()[source]¶: Reset the glyph to its initial formatting template.

update(new)[source]¶: Change the glyph’s formatting template.

class picos.glyphs.GlStr(string, glyph, operands)[source]¶

Bases: str

A string created from a glyph.

It has an additional glyph field pointing to the glyph that created it, and a operands field containing the values used to create it.

__init__(string, glyph, operands)[source]¶: Augment the Python string with metadata on its origin.

static __new__(cls, string, glyph, operands)[source]¶: Create a regular Python string.

reglyphed(replace={})[source]¶

Returns a rebuilt version of the string using current glyphs.

Parameters: replace (dict) – Replace leaf-node (non GlStr) strings with new strings. This can be used, for instance, to change the names of varaibles.

glyph¶: The glyph used to create the string.

operands¶: The operands used to create the string.

class picos.glyphs.Op(glyph, order, assoc=False, closed=False)[source]¶

Bases: Gl

The basic math operator glyph.

__init__(glyph, order, assoc=False, closed=False)[source]¶

Construct a math operator glyph.

Parameters

glyph (str) – The glyph’s format string template.
order (int) – The operator’s position in the binding strength hierarchy. Operators with lower numbersbind more strongly.
assoc (bool) – If this is True, then the operator is associative, so that parenthesis are always omitted around operands with an equal outer operator. Otherwise, (1) parenthesis are used around the right hand side operand of a binary operation of same binding strength and (2) around all operands of non-binary operations of same binding strength.
closed (bool or list(bool)) – If True, the operator already encloses the operands in some sort of brackets, so that no additional parenthesis are needed. For glyphs where only some operands are enclosed, this can be specified per operand in the form of a list.

reset()[source]¶: Reset the glyph to its initial behavior.

update(new)[source]¶: Change the glyph’s behavior.

class picos.glyphs.OpStr(string, glyph, operands)[source]¶

Bases: GlStr

A string created from a math operator glyph.

class picos.glyphs.Rl(glyph)[source]¶

Bases: Op

A math relation glyph.

__init__(glyph)[source]¶

Construct a Rl glyph.

Parameters: glyph (str) – The glyph’s format string template.

class picos.glyphs.Tr(glyph)[source]¶

Bases: Op

A math glyph in superscript/trailer form.

__init__(glyph)[source]¶

Construct a Tr glyph.

Parameters: glyph (str) – The glyph’s format string template.

Functions

picos.glyphs.ascii()[source]¶: Let PICOS create future strings using only ASCII characters.

picos.glyphs.clever_add(left, right)[source]¶

Describe the addition of two values in a clever way.

A wrapper around add that resorts to sub if the second operand was created by neg or is a negative number (string). In both cases the second operand is adjusted accordingly.

Example

>>> from picos.glyphs import neg, add, clever_add, matrix
>>> add("x", neg("y"))
'x + -y'
>>> clever_add("x", neg("y"))
'x - y'
>>> add("X", matrix(neg("y")))
'X + [-y]'
>>> clever_add("X", matrix(neg("y")))
'X - [y]'
>>> clever_add("X", matrix(-1.5))
'X - [1.5]'

picos.glyphs.clever_div(left, right)[source]¶

Describe the division of one value by another in a clever way.

A wrapper around div that factors out identity factors.

picos.glyphs.clever_dotp(left, right, complexLHS, scalar=False)[source]¶

Describe an inner product in a clever way.

Parameters: complexRHS (bool) – Whether the right hand side is complex.

picos.glyphs.clever_mul(left, right)[source]¶

Describe the multiplocation of two values in a clever way.

A wrapper around mul that factors out identity factors.

picos.glyphs.clever_neg(value)[source]¶

Describe the negation of a value in a clever way.

A wrapper around neg that resorts to unnegating an already negated value.

Example

>>> from picos.glyphs import neg, clever_neg, matrix
>>> neg("x")
'-x'
>>> neg(neg("x"))
'-(-x)'
>>> clever_neg(neg("x"))
'x'
>>> neg(matrix(-1))
'-[-1]'
>>> clever_neg(matrix(-1))
'[1]'

picos.glyphs.clever_sub(left, right)[source]¶

Describe the substraction of a value from another in a clever way.

A wrapper around sub that resorts to add if the second operand was created by neg or is a negative number(string). In both cases the second operand is adjusted accordingly.

Example

>>> from picos.glyphs import neg, sub, clever_sub, matrix
>>> sub("x", neg("y"))
'x - -y'
>>> clever_sub("x", neg("y"))
'x + y'
>>> sub("X", matrix(neg("y")))
'X - [-y]'
>>> clever_sub("X", matrix(neg("y")))
'X + [y]'
>>> clever_sub("X", matrix(-1.5))
'X + [1.5]'

picos.glyphs.col_vectorize(*entries)[source]¶: Describe a column vector with the given symbolic entries.

picos.glyphs.default(rebuildDerivedGlyphs=True)¶: Let PICOS create future strings using only unicode characters.

picos.glyphs.free_var_name(string)[source]¶: Return a variable name not present in the given string.

picos.glyphs.from_glyph(string, theGlyph)[source]¶: Whether the given string was created by the given glyph.

picos.glyphs.is_negated(value)[source]¶: Check if a value can be unnegated by unnegate.

picos.glyphs.latin1(rebuildDerivedGlyphs=True)[source]¶: Let PICOS create future strings using only ISO 8859-1 characters.

picos.glyphs.make_function(*names)[source]¶

Create an ad-hoc composite function glyphs.

Example

>>> from picos.glyphs import make_function
>>> make_function("log", "sum", "exp")("x")
'log∘sum∘exp(x)'

picos.glyphs.matrix_cat(left, right, horizontal=True)[source]¶

Describe matrix concatenation in a clever way.

A wrapper around matrix, horicat and vertcat.

Example

>>> from picos.glyphs import matrix_cat
>>> Z = matrix_cat("X", "Y")
>>> Z
'[X, Y]'
>>> matrix_cat(Z, Z)
'[X, Y, X, Y]'
>>> matrix_cat(Z, Z, horizontal = False)
'[X, Y; X, Y]'

picos.glyphs.rebuild()[source]¶: Update glyphs that are based upon other glyphs.

picos.glyphs.row_vectorize(*entries)[source]¶: Describe a row vector with the given symbolic entries.

picos.glyphs.scalar(value)[source]¶

Format a scalar value.

This function mimics an operator glyph, but it returns a normal string (as opposed to an OpStr) for nonnegative numbers.

This is not realized as an atomic operator glyph to not increase the recursion depth of is_negated and unnegate unnecessarily.

Example

>>> from picos.glyphs import scalar
>>> str(1.0)
'1.0'
>>> scalar(1.0)
'1'

picos.glyphs.shape(theShape)[source]¶

Describe a matrix shape that can contain wildcards.

A wrapper around size that takes just one argument (the shape) that may contain wildcards which are printed as '?'.

picos.glyphs.show(*args)[source]¶

Show output from all glyphs.

Parameters: args (list(str)) – Strings to use as glyph operands.

picos.glyphs.unicode(rebuildDerivedGlyphs=True)[source]¶: Let PICOS create future strings using only unicode characters.

picos.glyphs.unnegate(value)[source]¶

Unnegate a value, usually a glyph-created string, in a sensible way.

Unnegates a operator glyph created string or other value in a sensible way, more precisely by recursing through a sequence of glyphs used to create the value and for which we can factor out negation, and negating the underlaying (numeric or string) value.

Raises: ValueError – When is_negated returns False.

Objects

picos.glyphs.CAN_FACTOR_OUT_NEGATION¶

Operator glyphs for which negation may be factored out.

Default value

(<picos.glyphs.Br object at 0x7dc21772d010>,
 <picos.glyphs.Fn object at 0x7dc217705bd0>,
 <picos.glyphs.Fn object at 0x7dc214b884b0>,
 <picos.glyphs.Fn object at 0x7dc21773a360>,
 <picos.glyphs.Fn object at 0x7dc214b88590>,
 <picos.glyphs.Fn object...

picos.glyphs.abs¶

Absolute value glyph.

Default value

<picos.glyphs.Br object at 0x7dc217706850>

picos.glyphs.add¶

Addition glyph.

Default value

<picos.glyphs.Op object at 0x7dc214b73250>

picos.glyphs.affpart¶

Affine part glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214b4ad50>

picos.glyphs.and_¶

Logical and glyph.

Default value

<picos.glyphs.Gl object at 0x7dc214d78dd0>

picos.glyphs.bcasted¶

Broadcasted glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214b2bd20>

picos.glyphs.blinpart¶

Bilinear part glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214b3f150>

picos.glyphs.closure¶

Set closure glyph.

Default value

<picos.glyphs.Fn object at 0x7dc21772dbe0>

picos.glyphs.comma¶

Seperated by comma glyph.

Default value

<picos.glyphs.Gl object at 0x7dc217731370>

picos.glyphs.compose¶

Function composition glyph.

Default value

<picos.glyphs.Gl object at 0x7dc21773a140>

picos.glyphs.compsep¶

Compact seperator glyph.

Default value

<picos.glyphs.Gl object at 0x7dc21774c180>

picos.glyphs.conj¶

Complex conugate glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214bf15a0>

picos.glyphs.cstpart¶

Constant part glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214b2b7e0>

picos.glyphs.cubed¶

Cubed value glyph.

Default value

<picos.glyphs.Tr object at 0x7dc217707750>

picos.glyphs.desvec¶

Symmetric de-vectorization glyph.

Default value

<picos.glyphs.Fn object at 0x7dc215532b70>

picos.glyphs.det¶

Determinant glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214d79010>

picos.glyphs.diag¶

Diagonal matrix glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214b88590>

picos.glyphs.div¶

Division glyph.

Default value

<picos.glyphs.Op object at 0x7dc214b94120>

picos.glyphs.dotp¶

Scalar product glyph.

Default value

<picos.glyphs.Br object at 0x7dc217706490>

picos.glyphs.element¶

Set element glyph.

Default value

<picos.glyphs.Rl object at 0x7dc21772e120>

picos.glyphs.eq¶

Equality glyph.

Default value

<picos.glyphs.Rl object at 0x7dc2177060d0>

picos.glyphs.exp¶

Exponentiation glyph.

Default value

<picos.glyphs.Fn object at 0x7dc217732210>

picos.glyphs.exparg¶

Expected value glyph.

Default value

<picos.glyphs.Op object at 0x7dc214b73150>

picos.glyphs.expected¶

Epected value glyph.

Default value

<picos.glyphs.Fn object at 0x7dc21452c1a0>

picos.glyphs.forall¶

Universal quantification glyph.

Default value

<picos.glyphs.Gl object at 0x7dc214b883d0>

picos.glyphs.fromto¶

Range glyph.

Default value

<picos.glyphs.Gl object at 0x7dc2155327b0>

picos.glyphs.frozen¶

Frozen mutables glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214b2b850>

picos.glyphs.ge¶

Greater or equal glyph.

Default value

<picos.glyphs.Rl object at 0x7dc214530050>

picos.glyphs.geomean¶

Matrix geometric mean glyph.

Default value

<picos.glyphs.Op object at 0x7dc214bf1650>

picos.glyphs.gt¶

Greater than glyph.

Default value

<picos.glyphs.Rl object at 0x7dc21774d0f0>

picos.glyphs.hadamard¶

Hadamard product glyph.

Default value

<picos.glyphs.Op object at 0x7dc215532d50>

picos.glyphs.horicat¶

Horizontal concatenation glyph.

Default value

<picos.glyphs.Op object at 0x7dc214b4adf0>

picos.glyphs.htransp¶

Matrix hermitian transposition glyph.

Default value

<picos.glyphs.Tr object at 0x7dc21773a690>

picos.glyphs.idmatrix¶

Identity matrix glyph.

Default value

<picos.glyphs.Am object at 0x7dc217707110>

picos.glyphs.imag¶

Imaginary part glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214bf14f0>

picos.glyphs.index¶

Index glyph.

Default value

<picos.glyphs.Tr object at 0x7dc21773a7a0>

picos.glyphs.infty¶

Infinity glyph.

Default value

<picos.glyphs.Am object at 0x7dc21772dd30>

picos.glyphs.interval¶

Interval glyph.

Default value

<picos.glyphs.Gl object at 0x7dc214b72e50>

picos.glyphs.intrange¶

Integer range glyph.

Default value

<picos.glyphs.Gl object at 0x7dc215532990>

picos.glyphs.inverse¶

Matrix inverse glyph.

Default value

<picos.glyphs.Tr object at 0x7dc21774ce90>

picos.glyphs.kron¶

Kronecker product glyph.

Default value

<picos.glyphs.Op object at 0x7dc214b88670>

picos.glyphs.lambda_¶

Lambda symbol glyph.

Default value

<picos.glyphs.Am object at 0x7dc2177065d0>

picos.glyphs.le¶

Lesser or equal glyph.

Default value

<picos.glyphs.Rl object at 0x7dc21774d220>

picos.glyphs.leadsto¶

Successorship glyph.

Default value

<picos.glyphs.Gl object at 0x7dc214ff3790>

picos.glyphs.linpart¶

Linear part glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214b259a0>

picos.glyphs.log¶

Logarithm glyph.

Default value

<picos.glyphs.Fn object at 0x7dc21773a250>

picos.glyphs.lt¶

Lesser than glyph.

Default value

<picos.glyphs.Rl object at 0x7dc2177329f0>

picos.glyphs.maindiag¶

Main diagonal glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214b94050>

picos.glyphs.matrix¶

Matrix glyph.

Default value

<picos.glyphs.Br object at 0x7dc21772d010>

picos.glyphs.max¶

Maximum glyph.

Default value

<picos.glyphs.Fn object at 0x7dc21774c510>

picos.glyphs.maxarg¶

The basic math operator glyph.

Default value

<picos.glyphs.Op object at 0x7dc214b25b50>

picos.glyphs.min¶

Minimum glyph.

Default value

<picos.glyphs.Fn object at 0x7dc21774c8a0>

picos.glyphs.minarg¶

The basic math operator glyph.

Default value

<picos.glyphs.Op object at 0x7dc214b3f250>

picos.glyphs.mul¶

Multiplication glyph.

Default value

<picos.glyphs.Op object at 0x7dc214b88750>

picos.glyphs.ncnorm¶

Nuclear Norm glyph.

Default value

<picos.glyphs.Op object at 0x7dc21774c9d0>

picos.glyphs.ncstpart¶

Nonconstant part glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214b3f1d0>

picos.glyphs.neg¶

Negation glyph.

Default value

<picos.glyphs.Op object at 0x7dc214d79190>

picos.glyphs.norm¶

Norm glyph.

Default value

<picos.glyphs.Br object at 0x7dc21774c770>

picos.glyphs.or_¶

Logical or glyph.

Default value

<picos.glyphs.Gl object at 0x7dc214d78710>

picos.glyphs.parenth¶

Parenthesis glyph.

Default value

<picos.glyphs.Gl object at 0x7dc217706710>

picos.glyphs.plsmns¶

Plus/Minus glyph.

Default value

<picos.glyphs.Op object at 0x7dc214d79250>

picos.glyphs.pnorm¶

p-Norm glyph.

Default value

<picos.glyphs.Op object at 0x7dc21772de80>

picos.glyphs.power¶

Power glyph.

Default value

<picos.glyphs.Tr object at 0x7dc21772dfd0>

picos.glyphs.pqnorm¶

pq-Norm glyph.

Default value

<picos.glyphs.Op object at 0x7dc217707890>

picos.glyphs.probdist¶

Probability distribution glyph.

Default value

<picos.glyphs.Fn object at 0x7dc21452c130>

picos.glyphs.prod¶

Product glyph.

Default value

<picos.glyphs.Fn object at 0x7dc217705e50>

picos.glyphs.psdge¶

Lesser or equal w.r.t. the p.s.d. cone glyph.

Default value

<picos.glyphs.Rl object at 0x7dc21773a8b0>

picos.glyphs.psdle¶

Greater or equal w.r.t. the p.s.d. cone glyph.

Default value

<picos.glyphs.Rl object at 0x7dc21773a9c0>

picos.glyphs.ptrace¶

Matrix p-Trace glyph.

Default value

<picos.glyphs.Op object at 0x7dc21774cd60>

picos.glyphs.ptrace_¶

Matrix partial trace glyph.

Default value

<picos.glyphs.Op object at 0x7dc21773a580>

picos.glyphs.ptransp¶

Matrix partial transposition glyph.

Default value

<picos.glyphs.Tr object at 0x7dc2177327b0>

picos.glyphs.ptransp_¶

Matrix partial transposition glyph.

Default value

<picos.glyphs.Op object at 0x7dc21773a470>

picos.glyphs.qe¶

Quantum entropy glyph.

Default value

<picos.glyphs.Fn object at 0x7dc21452c210>

picos.glyphs.qre¶

Quantum relative entropy glyph.

Default value

<picos.glyphs.Fn object at 0x7dc21452c280>

picos.glyphs.quadpart¶

Quadratic part glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214b4acb0>

picos.glyphs.real¶

Real part glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214d790d0>

picos.glyphs.renyi¶

Renyi entropy glyph.

Default value

<picos.glyphs.Fn object at 0x7dc21452c2f0>

picos.glyphs.repr1¶

Representation glyph.

Default value

<picos.glyphs.Gl object at 0x7dc21772da90>

picos.glyphs.repr2¶

Long representation glyph.

Default value

<picos.glyphs.Gl object at 0x7dc217705d10>

picos.glyphs.reshaped¶

Column-major (Fortran) reshaped glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214b2b9a0>

picos.glyphs.reshaprm¶

Row-major (C-order) reshaped glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214b2ba10>

picos.glyphs.sep¶

Seperator glyph.

Default value

<picos.glyphs.Gl object at 0x7dc21774c640>

picos.glyphs.set¶

Set glyph.

Default value

<picos.glyphs.Gl object at 0x7dc214b72d50>

picos.glyphs.shortint¶

Shortened interval glyph.

Default value

<picos.glyphs.Gl object at 0x7dc214b882f0>

picos.glyphs.shuffled¶

Matrix reshuffling glyph.

Default value

<picos.glyphs.Fn object at 0x7dc21452c0c0>

picos.glyphs.size¶

Matrix size/shape glyph.

Default value

<picos.glyphs.Gl object at 0x7dc21773a030>

picos.glyphs.slice¶

Expression slicing glyph.

Default value

<picos.glyphs.Op object at 0x7dc217732330>

picos.glyphs.spnorm¶

Spectral Norm glyph.

Default value

<picos.glyphs.Op object at 0x7dc217705f90>

picos.glyphs.sqrt¶

Square root glyph.

Default value

<picos.glyphs.Fn object at 0x7dc21452c050>

picos.glyphs.squared¶

Squared value glyph.

Default value

<picos.glyphs.Tr object at 0x7dc217707610>

picos.glyphs.sub¶

Substraction glyph.

Default value

<picos.glyphs.Op object at 0x7dc215532c60>

picos.glyphs.sum¶

Summation glyph.

Default value

<picos.glyphs.Fn object at 0x7dc217705bd0>

picos.glyphs.svec¶

Symmetric vectorization glyph.

Default value

<picos.glyphs.Fn object at 0x7dc215532a80>

picos.glyphs.trace¶

Matrix trace glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214b884b0>

picos.glyphs.transp¶

Matrix transposition glyph.

Default value

<picos.glyphs.Tr object at 0x7dc21774cfc0>

picos.glyphs.trilvec¶

Lower triangular vectorization glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214b72f50>

picos.glyphs.triuvec¶

Upper triangular vectorization glyph.

Default value

<picos.glyphs.Fn object at 0x7dc214b73050>

picos.glyphs.vec¶

Vectorization glyph.

Default value

<picos.glyphs.Fn object at 0x7dc21773a360>

picos.glyphs.vertcat¶

Vertical concatenation glyph.

Default value

<picos.glyphs.Op object at 0x7dc214b4ae90>

picos.glyphs.wgeomean¶

Weighted matrix geometric mean glyph.

Default value

<picos.glyphs.Op object at 0x7dc214bf1700>

Fork me on GitLab