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.Problem().add_variable("X", (2,2), "symmetric")
>>> 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, complexRHS, 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 0x7efe7b035690>,
 <picos.glyphs.Fn object at 0x7efe7b0363e0>,
 <picos.glyphs.Fn object at 0x7efe7b036890>,
 <picos.glyphs.Fn object at 0x7efe7b036680>,
 <picos.glyphs.Fn object at 0x7efe7b034d00>,
 <picos.glyphs.Fn object...

picos.glyphs.abs¶

Absolute value glyph.

Default value

<picos.glyphs.Br object at 0x7efe7b034550>

picos.glyphs.add¶

Addition glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b035b10>

picos.glyphs.affpart¶

Affine part glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b035c60>

picos.glyphs.and_¶

Logical and glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b036dd0>

picos.glyphs.bcasted¶

Broadcasted glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b034460>

picos.glyphs.blinpart¶

Bilinear part glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b035000>

picos.glyphs.closure¶

Set closure glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b036c50>

picos.glyphs.comma¶

Seperated by comma glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b0369b0>

picos.glyphs.compose¶

Function composition glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b036b30>

picos.glyphs.compsep¶

Compact seperator glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b036950>

picos.glyphs.conj¶

Complex conugate glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b035a80>

picos.glyphs.cstpart¶

Constant part glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b034fd0>

picos.glyphs.cubed¶

Cubed value glyph.

Default value

<picos.glyphs.Tr object at 0x7efe7b0348b0>

picos.glyphs.desvec¶

Symmetric de-vectorization glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b036590>

picos.glyphs.det¶

Determinant glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b035ff0>

picos.glyphs.diag¶

Diagonal matrix glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b034d00>

picos.glyphs.div¶

Division glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b034ac0>

picos.glyphs.dotp¶

Scalar product glyph.

Default value

<picos.glyphs.Br object at 0x7efe7b0343d0>

picos.glyphs.element¶

Set element glyph.

Default value

<picos.glyphs.Rl object at 0x7efe7b0349a0>

picos.glyphs.eq¶

Equality glyph.

Default value

<picos.glyphs.Rl object at 0x7efe7b037550>

picos.glyphs.exp¶

Exponentiation glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b0367d0>

picos.glyphs.exparg¶

Expected value glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b034f70>

picos.glyphs.expected¶

Epected value glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b035180>

picos.glyphs.forall¶

Universal quantification glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b036e90>

picos.glyphs.fromto¶

Range glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b036d10>

picos.glyphs.frozen¶

Frozen mutables glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b0351e0>

picos.glyphs.ge¶

Greater or equal glyph.

Default value

<picos.glyphs.Rl object at 0x7efe7afdb0a0>

picos.glyphs.gt¶

Greater than glyph.

Default value

<picos.glyphs.Rl object at 0x7efe7afdbca0>

picos.glyphs.hadamard¶

Hadamard product glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b034a30>

picos.glyphs.horicat¶

Horizontal concatenation glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b035600>

picos.glyphs.htransp¶

Matrix hermitian transposition glyph.

Default value

<picos.glyphs.Tr object at 0x7efe7b035b40>

picos.glyphs.idmatrix¶

Identity matrix glyph.

Default value

<picos.glyphs.Am object at 0x7efe7b036a40>

picos.glyphs.imag¶

Imaginary part glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b0344c0>

picos.glyphs.index¶

Index glyph.

Default value

<picos.glyphs.Tr object at 0x7efe7b0354e0>

picos.glyphs.infty¶

Infinity glyph.

Default value

<picos.glyphs.Am object at 0x7efe7b036fe0>

picos.glyphs.interval¶

Interval glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b036cb0>

picos.glyphs.intrange¶

Integer range glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b036f20>

picos.glyphs.inverse¶

Matrix inverse glyph.

Default value

<picos.glyphs.Tr object at 0x7efe7b0356f0>

picos.glyphs.kron¶

Kronecker product glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b034af0>

picos.glyphs.lambda_¶

Lambda symbol glyph.

Default value

<picos.glyphs.Am object at 0x7efe7b036aa0>

picos.glyphs.le¶

Lesser or equal glyph.

Default value

<picos.glyphs.Rl object at 0x7efe7afdad10>

picos.glyphs.leadsto¶

Successorship glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b036e60>

picos.glyphs.linpart¶

Linear part glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b034b80>

picos.glyphs.log¶

Logarithm glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b036710>

picos.glyphs.lt¶

Lesser than glyph.

Default value

<picos.glyphs.Rl object at 0x7efe7afdbc10>

picos.glyphs.maindiag¶

Main diagonal glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b035fc0>

picos.glyphs.matrix¶

Matrix glyph.

Default value

<picos.glyphs.Br object at 0x7efe7b035690>

picos.glyphs.max¶

Maximum glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b036530>

picos.glyphs.maxarg¶

The basic math operator glyph.

Default value

<picos.glyphs.Op object at 0x7efe7afdb2e0>

picos.glyphs.min¶

Minimum glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b036830>

picos.glyphs.minarg¶

The basic math operator glyph.

Default value

<picos.glyphs.Op object at 0x7efe7afdb880>

picos.glyphs.mul¶

Multiplication glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b034a00>

picos.glyphs.ncnorm¶

Nuclear Norm glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b0364d0>

picos.glyphs.ncstpart¶

Nonconstant part glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b0350f0>

picos.glyphs.neg¶

Negation glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b034ee0>

picos.glyphs.norm¶

Norm glyph.

Default value

<picos.glyphs.Br object at 0x7efe7b035de0>

picos.glyphs.or_¶

Logical or glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b036fb0>

picos.glyphs.parenth¶

Parenthesis glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b037220>

picos.glyphs.plsmns¶

Plus/Minus glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b035c90>

picos.glyphs.pnorm¶

p-Norm glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b034670>

picos.glyphs.power¶

Power glyph.

Default value

<picos.glyphs.Tr object at 0x7efe7b035e40>

picos.glyphs.pqnorm¶

pq-Norm glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b0362c0>

picos.glyphs.probdist¶

Probability distribution glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b0352a0>

picos.glyphs.prod¶

Product glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b036410>

picos.glyphs.psdge¶

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

Default value

<picos.glyphs.Rl object at 0x7efe7afdbf10>

picos.glyphs.psdle¶

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

Default value

<picos.glyphs.Rl object at 0x7efe7afdada0>

picos.glyphs.ptrace¶

Matrix p-Trace glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b0351b0>

picos.glyphs.ptrace_¶

Matrix partial trace glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b0347f0>

picos.glyphs.ptransp¶

Matrix partial transposition glyph.

Default value

<picos.glyphs.Tr object at 0x7efe7b035390>

picos.glyphs.ptransp_¶

Matrix partial transposition glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b034700>

picos.glyphs.quadpart¶

Quadratic part glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b034a60>

picos.glyphs.real¶

Real part glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b0345e0>

picos.glyphs.repr1¶

Representation glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b0373a0>

picos.glyphs.repr2¶

Long representation glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b0371c0>

picos.glyphs.reshaped¶

Column-major (Fortran) reshaped glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b034400>

picos.glyphs.reshaprm¶

Row-major (C-order) reshaped glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b034310>

picos.glyphs.sep¶

Seperator glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b034430>

picos.glyphs.set¶

Set glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b036bf0>

picos.glyphs.shortint¶

Shortened interval glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b037970>

picos.glyphs.shuffled¶

Matrix reshuffling glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b0340a0>

picos.glyphs.size¶

Matrix size/shape glyph.

Default value

<picos.glyphs.Gl object at 0x7efe7b036b90>

picos.glyphs.slice¶

Expression slicing glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b034130>

picos.glyphs.spnorm¶

Spectral Norm glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b036290>

picos.glyphs.sqrt¶

Square root glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b034340>

picos.glyphs.squared¶

Squared value glyph.

Default value

<picos.glyphs.Tr object at 0x7efe7b035e10>

picos.glyphs.sub¶

Substraction glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b035870>

picos.glyphs.sum¶

Summation glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b0363e0>

picos.glyphs.svec¶

Symmetric vectorization glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b036620>

picos.glyphs.trace¶

Matrix trace glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b036890>

picos.glyphs.transp¶

Matrix transposition glyph.

Default value

<picos.glyphs.Tr object at 0x7efe7b035420>

picos.glyphs.trilvec¶

Lower triangular vectorization glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b0365c0>

picos.glyphs.triuvec¶

Upper triangular vectorization glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b036650>

picos.glyphs.vec¶

Vectorization glyph.

Default value

<picos.glyphs.Fn object at 0x7efe7b036680>

picos.glyphs.vertcat¶

Vertical concatenation glyph.

Default value

<picos.glyphs.Op object at 0x7efe7b034910>

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