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()

Outline¶

Classes¶

`Am`	A math atom glyph.
`Br`	A math operator glyph with enclosing brackets.
`Fn`	A math operator glyph in function form.
`Gl`	The basic “glyph”, an (algebraic) string formatting template.
`GlStr`	A string created from a `glyph`.
`Op`	The basic math operator glyph.
`OpStr`	A string created from a math operator glyph.
`Rl`	A math relation glyph.
`Tr`	A math glyph in superscript/trailer form.

Functions¶

`ascii`	Let PICOS create future strings using only ASCII characters.
`clever_add`	Describe the addition of two values in a clever way.
`clever_div`	Describe the division of one value by another in a clever way.
`clever_dotp`	Describe an inner product in a clever way.
`clever_mul`	Describe the multiplocation of two values in a clever way.
`clever_neg`	Describe the negation of a value in a clever way.
`clever_sub`	Describe the substraction of a value from another in a clever way.
`col_vectorize`	Describe a column vector with the given symbolic entries.
`default`	Let PICOS create future strings using only unicode characters.
`free_var_name`	Return a variable name not present in the given string.
`from_glyph`	Whether the given string was created by the given glyph.
`is_negated`	Check if a value can be unnegated by `unnegate`.
`latin1`	Let PICOS create future strings using only ISO 8859-1 characters.
`make_function`	Create an ad-hoc composite function glyphs.
`matrix_cat`	Describe matrix concatenation in a clever way.
`rebuild`	Update glyphs that are based upon other glyphs.
`row_vectorize`	Describe a row vector with the given symbolic entries.
`scalar`	Format a scalar value.
`shape`	Describe a matrix shape that can contain wildcards.
`show`	Show output from all glyphs.
`unicode`	Let PICOS create future strings using only unicode characters.
`unnegate`	Unnegate a value, usually a glyph-created string, in a sensible way.

Data¶

CAN_FACTOR_OUT_NEGATION
abs
add
affpart
and_
bcasted
blinpart
closure
comma
compose
compsep
conj
cstpart
cubed
desvec
det
diag
div
dotp
element
eq
exp
exparg
expected

forall
fromto
frozen
ge
gt
hadamard
horicat
htransp
idmatrix
imag
index
infty
interval
intrange
inverse
kron
lambda_
le
leadsto
linpart
log
lt
maindiag
matrix

max
maxarg
min
minarg
mul
ncnorm
ncstpart
neg
norm
or_
parenth
plsmns
pnorm
power
pqnorm
probdist
prod
psdge
psdle
ptrace
ptrace_
ptransp
ptransp_

quadpart
real
repr1
repr2
reshaped
sep
set
shortint
shuffled
size
slice
spnorm
sqrt
squared
sub
sum
svec
trace
transp
trilvec
triuvec
vec
vertcat

Classes¶

Am¶

class picos.glyphs.Am(glyph)[source]¶

Bases: picos.glyphs.Op

A math atom glyph.

__init__(glyph)[source]¶

Construct an Am glyph.

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

Br¶

class picos.glyphs.Br(glyph)[source]¶

Bases: picos.glyphs.Op

A math operator glyph with enclosing brackets.

__init__(glyph)[source]¶

Construct a Br glyph.

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

Fn¶

class picos.glyphs.Fn(glyph)[source]¶

Bases: picos.glyphs.Op

A math operator glyph in function form.

__init__(glyph)[source]¶

Construct a Fn glyph.

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

Gl¶

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.

GlStr¶

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.

Op¶

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

Bases: picos.glyphs.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.

OpStr¶

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

Bases: picos.glyphs.GlStr

A string created from a math operator glyph.

Rl¶

class picos.glyphs.Rl(glyph)[source]¶

Bases: picos.glyphs.Op

A math relation glyph.

__init__(glyph)[source]¶

Construct a Rl glyph.

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

Tr¶

class picos.glyphs.Tr(glyph)[source]¶

Bases: picos.glyphs.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¶

ascii¶

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

clever_add¶

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]'

clever_div¶

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.

clever_dotp¶

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.

clever_mul¶

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.

clever_neg¶

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]'

clever_sub¶

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]'

col_vectorize¶

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

default¶

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

free_var_name¶

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

from_glyph¶

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

is_negated¶

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

latin1¶

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

make_function¶

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)'

matrix_cat¶

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]'

rebuild¶

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

row_vectorize¶

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

scalar¶

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'

shape¶

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 '?'.

show¶

picos.glyphs.show(*args)[source]¶

Show output from all glyphs.

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

unicode¶

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

unnegate¶

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.

Data¶

picos.glyphs.CAN_FACTOR_OUT_NEGATION¶: Operator glyphs for which negation may be factored out.

picos.glyphs.abs¶: Absolute value glyph.

picos.glyphs.add¶: Addition glyph.

picos.glyphs.affpart¶: Affine part glyph.

picos.glyphs.and_¶: Logical and glyph.

picos.glyphs.bcasted¶: Broadcasted glyph.

picos.glyphs.blinpart¶: Bilinear part glyph.

picos.glyphs.closure¶: Set closure glyph.

picos.glyphs.comma¶: Seperated by comma glyph.

picos.glyphs.compose¶: Function composition glyph.

picos.glyphs.compsep¶: Compact seperator glyph.

picos.glyphs.conj¶: Complex conugate glyph.

picos.glyphs.cstpart¶: Constant part glyph.

picos.glyphs.cubed¶: Cubed value glyph.

picos.glyphs.desvec¶: Symmetric de-vectorization glyph.

picos.glyphs.det¶: Determinant glyph.

picos.glyphs.diag¶: Diagonal matrix glyph.

picos.glyphs.div¶: Division glyph.

picos.glyphs.dotp¶: Scalar product glyph.

picos.glyphs.element¶: Set element glyph.

picos.glyphs.eq¶: Equality glyph.

picos.glyphs.exp¶: Exponentiation glyph.

picos.glyphs.exparg¶: Expected value glyph.

picos.glyphs.expected¶: Epected value glyph.

picos.glyphs.forall¶: Universal quantification glyph.

picos.glyphs.fromto¶: Range glyph.

picos.glyphs.frozen¶: Frozen mutables glyph.

picos.glyphs.ge¶: Greater or equal glyph.

picos.glyphs.gt¶: Greater than glyph.

picos.glyphs.hadamard¶: Hadamard product glyph.

picos.glyphs.horicat¶: Horizontal concatenation glyph.

picos.glyphs.htransp¶: Matrix hermitian transposition glyph.

picos.glyphs.idmatrix¶: Identity matrix glyph.

picos.glyphs.imag¶: Imaginary part glyph.

picos.glyphs.index¶: Index glyph.

picos.glyphs.infty¶: Infinity glyph.

picos.glyphs.interval¶: Interval glyph.

picos.glyphs.intrange¶: Integer range glyph.

picos.glyphs.inverse¶: Matrix inverse glyph.

picos.glyphs.kron¶: Kronecker product glyph.

picos.glyphs.lambda_¶: Lambda symbol glyph.

picos.glyphs.le¶: Lesser or equal glyph.

picos.glyphs.leadsto¶: Successorship glyph.

picos.glyphs.linpart¶: Linear part glyph.

picos.glyphs.log¶: Logarithm glyph.

picos.glyphs.lt¶: Lesser than glyph.

picos.glyphs.maindiag¶: Main diagonal glyph.

picos.glyphs.matrix¶: Matrix glyph.

picos.glyphs.max¶: Maximum glyph.

picos.glyphs.maxarg¶: The basic math operator glyph.

picos.glyphs.min¶: Minimum glyph.

picos.glyphs.minarg¶: The basic math operator glyph.

picos.glyphs.mul¶: Multiplication glyph.

picos.glyphs.ncnorm¶: Nuclear Norm glyph.

picos.glyphs.ncstpart¶: Nonconstant part glyph.

picos.glyphs.neg¶: Negation glyph.

picos.glyphs.norm¶: Norm glyph.

picos.glyphs.or_¶: Logical or glyph.

picos.glyphs.parenth¶: Parenthesis glyph.

picos.glyphs.plsmns¶: Plus/Minus glyph.

picos.glyphs.pnorm¶: p-Norm glyph.

picos.glyphs.power¶: Power glyph.

picos.glyphs.pqnorm¶: pq-Norm glyph.

picos.glyphs.probdist¶: Probability distribution glyph.

picos.glyphs.prod¶: Product glyph.

picos.glyphs.psdge¶: Lesser or equal w.r.t. the p.s.d. cone glyph.

picos.glyphs.psdle¶: Greater or equal w.r.t. the p.s.d. cone glyph.

picos.glyphs.ptrace¶: Matrix p-Trace glyph.

picos.glyphs.ptrace_¶: Matrix partial trace glyph.

picos.glyphs.ptransp¶: Matrix partial transposition glyph.

picos.glyphs.ptransp_¶: Matrix partial transposition glyph.

picos.glyphs.quadpart¶: Quadratic part glyph.

picos.glyphs.real¶: Real part glyph.

picos.glyphs.repr1¶: Representation glyph.

picos.glyphs.repr2¶: Long representation glyph.

picos.glyphs.reshaped¶: Reshaped glyph.

picos.glyphs.sep¶: Seperator glyph.

picos.glyphs.set¶: Set glyph.

picos.glyphs.shortint¶: Shortened interval glyph.

picos.glyphs.shuffled¶: Matrix reshuffling glyph.

picos.glyphs.size¶: Matrix size/shape glyph.

picos.glyphs.slice¶: Expression slicing glyph.

picos.glyphs.spnorm¶: Spectral Norm glyph.

picos.glyphs.sqrt¶: Square root glyph.

picos.glyphs.squared¶: Squared value glyph.

picos.glyphs.sub¶: Substraction glyph.

picos.glyphs.sum¶: Summation glyph.

picos.glyphs.svec¶: Symmetric vectorization glyph.

picos.glyphs.trace¶: Matrix trace glyph.

picos.glyphs.transp¶: Matrix transposition glyph.

picos.glyphs.trilvec¶: Lower triangular vectorization glyph.

picos.glyphs.triuvec¶: Upper triangular vectorization glyph.

picos.glyphs.vec¶: Vectorization glyph.

picos.glyphs.vertcat¶: Vertical concatenation glyph.