pydrake.symbolic¶
Symbolic variable, variables, monomial, expression, polynomial, and formula
-
pydrake.symbolic.
abs
(arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
acos
(arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
asin
(arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
atan
(arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
atan2
(arg0: pydrake.symbolic.Expression, arg1: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
ceil
(arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
cos
(arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
cosh
(arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
Evaluate
(*args, **kwargs)¶ Overloaded function.
- Evaluate(m: numpy.ndarray[object[m, n]], env: Dict[pydrake.symbolic.Variable, float] = {}, generator: pydrake.common._module_py.RandomGenerator = None) -> numpy.ndarray[numpy.float64[m, n]]
Evaluates a symbolic matrix
m
usingenv
andrandom_generator
.If there is a random variable in
m
which is unassigned inenv
, this function usesrandom_generator
to sample a value and use the value to substitute all occurrences of the random variable inm
.Returns: a matrix of double whose size is the size of
m
.Raises: RuntimeError if NaN is detected during evaluation.
Raises: - RuntimeError if
m
includes unassigned random variables but random_generator
isnullptr
.
- Evaluate(m: numpy.ndarray[object[m, n]], env: Dict[pydrake.symbolic.Variable, float]) -> numpy.ndarray[numpy.float64[m, n]]
Evaluates a matrix
m
of symbolic polynomials usingenv
.Returns: a matrix of double whose size is the size of m
.Raises: RuntimeError if NaN is detected during evaluation.
-
pydrake.symbolic.
EvenDegreeMonomialBasis
(vars: pydrake.symbolic.Variables, degree: int) → numpy.ndarray[object[m, 1]]¶ Returns all even degree monomials up to a given degree under the graded reverse lexicographic order. A monomial has an even degree if its total degree is even. So xy is an even degree monomial (degree 2) while x²y is not (degree 3). Note that graded reverse lexicographic order uses the total order among Variable which is based on a variable’s unique ID. For example, for a given variable ordering x > y > z,
EvenDegreeMonomialBasis({x, y, z}, 2)
returns a column vector[x², xy, y², xz, yz, z², 1]
.- Precondition:
vars
is a non-empty set.- Precondition:
degree
is a non-negative integer.
-
pydrake.symbolic.
exp
(arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
class
pydrake.symbolic.
Expression
¶ Represents a symbolic form of an expression.
Its syntax tree is as follows:
E := Var | Constant | E + ... + E | E * ... * E | E / E | log(E) | abs(E) | exp(E) | sqrt(E) | pow(E, E) | sin(E) | cos(E) | tan(E) | asin(E) | acos(E) | atan(E) | atan2(E, E) | sinh(E) | cosh(E) | tanh(E) | min(E, E) | max(E, E) | ceil(E) | floor(E) | if_then_else(F, E, E) | NaN | uninterpreted_function(name, {v_1, ..., v_n})
In the implementation, Expression is a simple wrapper including a shared pointer to ExpressionCell class which is a super-class of different kinds of symbolic expressions (i.e. ExpressionAdd, ExpressionMul, ExpressionLog, ExpressionSin). Note that it includes a shared pointer, not a unique pointer, to allow sharing sub-expressions.
Note
The sharing of sub-expressions is not yet implemented.
Note
-E is represented as -1 * E internally.
Note
A subtraction E1 - E2 is represented as E1 + (-1 * E2) internally.
The following simple simplifications are implemented:
E + 0 -> E 0 + E -> E E - 0 -> E E - E -> 0 E * 1 -> E 1 * E -> E E * 0 -> 0 0 * E -> 0 E / 1 -> E E / E -> 1 pow(E, 0) -> 1 pow(E, 1) -> E E * E -> E^2 (= pow(E, 2)) sqrt(E * E) -> |E| (= abs(E)) sqrt(E) * sqrt(E) -> E
Constant folding is implemented:
E(c1) + E(c2) -> E(c1 + c2) // c1, c2 are constants E(c1) - E(c2) -> E(c1 - c2) E(c1) * E(c2) -> E(c1 * c2) E(c1) / E(c2) -> E(c1 / c2) f(E(c)) -> E(f(c)) // c is a constant, f is a math function
For the math functions which are only defined over a restricted domain (namely, log, sqrt, pow, asin, acos), we check the domain of argument(s), and throw ValueError exception if a function is not well-defined for a given argument(s).
Relational operators over expressions (==, !=, <, >, <=, >=) return symbolic::Formula instead of bool. Those operations are declared in symbolic_formula.h file. To check structural equality between two expressions a separate function, Expression::EqualTo, is provided.
Regarding NaN, we have the following rules: 1. NaN values are extremely rare during typical computations. Because they are difficult to handle symbolically, we will round that up to “must never occur”. We allow the user to form ExpressionNaN cells in a symbolic tree. For example, the user can initialize an Expression to NaN and then overwrite it later. However, evaluating a tree that has NaN in its evaluated sub-trees is an error (see rule (3) below). 2. It’s still valid for code to check
isnan
in order to fail-fast. So we provide isnan(const Expression&) for the common case of non-NaN value returning False. This way, code can fail-fast with double yet still compile with Expression. 3. If there are expressions that embed separate cases (if_then_else
), some of the sub-expressions may be not used in evaluation when they are in the not-taken case (for NaN reasons or any other reason). Bad values within those not-taken branches does not cause exceptions. 4. The isnan check is different than if_then_else. In the latter, the ExpressionNaN is within a dead sub-expression branch. In the former, it appears in an evaluated trunk. That goes against rule (1) where a NaN anywhere in a computation (other than dead code) is an error.symbolic::Expression can be used as a scalar type of Eigen types.
-
__init__
(*args, **kwargs)¶ Overloaded function.
- __init__(self: pydrake.symbolic.Expression) -> None
Default constructor. It constructs Zero().
- __init__(self: pydrake.symbolic.Expression, arg0: float) -> None
Constructs a constant.
- __init__(self: pydrake.symbolic.Expression, arg0: pydrake.symbolic.Variable) -> None
Constructs an expression from
var
.- Precondition:
var
is neither a dummy nor a BOOLEAN variable.
-
arccos
(self: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
arcsin
(self: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
arctan2
(self: pydrake.symbolic.Expression, arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
ceil
(self: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
cos
(self: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
cosh
(self: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
Differentiate
(self: pydrake.symbolic.Expression, arg0: pydrake.symbolic.Variable) → pydrake.symbolic.Expression¶ Differentiates this symbolic expression with respect to the variable
var
.Raises: RuntimeError if it is not differentiable.
-
EqualTo
(self: pydrake.symbolic.Expression, arg0: pydrake.symbolic.Expression) → bool¶ Checks structural equality.
Two expressions e1 and e2 are structurally equal when they have the same internal AST(abstract-syntax tree) representation. Please note that we can have two computationally (or extensionally) equivalent expressions which are not structurally equal. For example, consider:
e1 = 2 * (x + y) e2 = 2x + 2y
Obviously, we know that e1 and e2 are evaluated to the same value for all assignments to x and y. However, e1 and e2 are not structurally equal by the definition. Note that e1 is a multiplication expression (is_multiplication(e1) is true) while e2 is an addition expression (is_addition(e2) is true).
One main reason we use structural equality in EqualTo is due to Richardson’s Theorem. It states that checking ∀x. E(x) = F(x) is undecidable when we allow sin, asin, log, exp in E and F. Read https://en.wikipedia.org/wiki/Richardson%27s_theorem for details.
Note that for polynomial cases, you can use Expand method and check if two polynomial expressions p1 and p2 are computationally equal. To do so, you check the following:
(p1.Expand() - p2.Expand()).EqualTo(0).
-
Evaluate
(*args, **kwargs)¶ Overloaded function.
- Evaluate(self: pydrake.symbolic.Expression, env: Dict[pydrake.symbolic.Variable, float] = {}, generator: pydrake.common._module_py.RandomGenerator = None) -> float
Evaluates using a given environment (by default, an empty environment) and a random number generator. If there is a random variable in this expression which is unassigned in
env
, this method usesrandom_generator
to sample a value and use the value to substitute all occurrences of the variable in this expression.Raises: - RuntimeError if there exists a non-random variable in this
- expression whose assignment is not provided by
env
.
Raises: - RuntimeError if an unassigned random variable is detected while
random_generator
isnullptr
.
Raises: RuntimeError if NaN is detected during evaluation.
- Evaluate(self: pydrake.symbolic.Expression, generator: pydrake.common._module_py.RandomGenerator) -> float
Evaluates using an empty environment and a random number generator. It uses
random_generator
to sample values for the random variables in this expression.See the above overload for the exceptions that it might throw.
-
EvaluatePartial
(self: pydrake.symbolic.Expression, arg0: Dict[pydrake.symbolic.Variable, float]) → pydrake.symbolic.Expression¶ Partially evaluates this expression using an environment
env
. Internally, this method promotesenv
into a substitution (Variable → Expression) and call Evaluate::Substitute with it.Raises: RuntimeError if NaN is detected during evaluation.
-
exp
(self: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
Expand
(self: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶ Expands out products and positive integer powers in expression. For example,
(x + 1) * (x - 1)
is expanded tox^2 - 1
and(x + y)^2
is expanded tox^2 + 2xy + y^2
. Note that Expand applies recursively to sub-expressions. For instance,sin(2 * (x + y))
is expanded tosin(2x + 2y)
. It also simplifies “division by constant” cases. See “drake/common/test/symbolic_expansion_test.cc” to find the examples.Raises: RuntimeError if NaN is detected during expansion.
-
floor
(self: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
GetVariables
(self: pydrake.symbolic.Expression) → pydrake.symbolic.Variables¶ Collects variables in expression.
-
is_polynomial
(self: pydrake.symbolic.Expression) → bool¶ Checks if this symbolic expression is convertible to Polynomial.
-
Jacobian
(self: pydrake.symbolic.Expression, arg0: numpy.ndarray[object[m, 1]]) → numpy.ndarray[object[1, n]]¶ Let
f
be this Expression, computes a row vector of derivatives,[∂f/∂vars(0), ... , ∂f/∂vars(n-1)]
with respect to the variablesvars
.
-
log
(self: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
max
(self: pydrake.symbolic.Expression, arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
min
(self: pydrake.symbolic.Expression, arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
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sin
(self: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
sinh
(self: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
sqrt
(self: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
Substitute
(*args, **kwargs)¶ Overloaded function.
- Substitute(self: pydrake.symbolic.Expression, arg0: pydrake.symbolic.Variable, arg1: pydrake.symbolic.Expression) -> pydrake.symbolic.Expression
Returns a copy of this expression replacing all occurrences of
var
withe
.Raises: RuntimeError if NaN is detected during substitution. - Substitute(self: pydrake.symbolic.Expression, arg0: Dict[pydrake.symbolic.Variable, pydrake.symbolic.Expression]) -> pydrake.symbolic.Expression
Returns a copy of this expression replacing all occurrences of the variables in
s
with corresponding expressions ins
. Note that the substitutions occur simultaneously. For example, (x / y).Substitute({{x, y}, {y, x}}) gets (y / x).Raises: RuntimeError if NaN is detected during substitution.
-
tan
(self: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
tanh
(self: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
to_string
(self: pydrake.symbolic.Expression) → str¶ Returns string representation of Expression.
-
-
pydrake.symbolic.
floor
(arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
class
pydrake.symbolic.
Formula
¶ Represents a symbolic form of a first-order logic formula.
It has the following grammar:
F := ⊥ | ⊤ | Var | E = E | E ≠ E | E > E | E ≥ E | E < E | E ≤ E | E ∧ ... ∧ E | E ∨ ... ∨ E | ¬F | ∀ x₁, ..., xn. F
In the implementation, Formula is a simple wrapper including a shared pointer to FormulaCell class which is a super-class of different kinds of symbolic formulas (i.e. FormulaAnd, FormulaOr, FormulaEq). Note that it includes a shared pointer, not a unique pointer, to allow sharing sub-expressions.
Note
The sharing of sub-expressions is not yet implemented.
The following simple simplifications are implemented:
E1 = E2 -> True (if E1 and E2 are structurally equal) E1 ≠ E2 -> False (if E1 and E2 are structurally equal) E1 > E2 -> False (if E1 and E2 are structurally equal) E1 ≥ E2 -> True (if E1 and E2 are structurally equal) E1 < E2 -> False (if E1 and E2 are structurally equal) E1 ≤ E2 -> True (if E1 and E2 are structurally equal) F1 ∧ F2 -> False (if either F1 or F2 is False) F1 ∨ F2 -> True (if either F1 or F2 is True) ¬(¬(F)) -> F
We flatten nested conjunctions (or disjunctions) at the construction. A conjunction (resp. disjunction) takes a set of conjuncts (resp. disjuncts). Note that any duplicated conjunct/disjunct is removed. For example, both of
f1 && (f2 && f1)
and(f1 && f2) && f1
are flattened tof1 && f2 && f1
and simplified intof1 && f2
. As a result, the two are identified as the same formula.Note
Formula class has an explicit conversion operator to bool. It evaluates a symbolic formula under an empty environment. If a symbolic formula includes variables, the conversion operator throws an exception. This operator is only intended for third-party code doing things like
(imag(SymbolicExpression(0)) == SymbolicExpression(0)) { ... };
that we found in Eigen3 codebase. In general, a user of this class should explicitly callEvaluate
from within Drake for readability.-
__init__
¶ Initialize self. See help(type(self)) for accurate signature.
-
EqualTo
(self: pydrake.symbolic.Formula, arg0: pydrake.symbolic.Formula) → bool¶ Checks structural equality.
-
Evaluate
(self: pydrake.symbolic.Formula, arg0: Dict[pydrake.symbolic.Variable, float]) → bool¶ Evaluates using a given environment (by default, an empty environment) and a random number generator. If there is a random variable in this formula which is unassigned in
env
, it usesrandom_generator
to sample a value and use it to substitute all occurrences of the random variable in this formula.Raises: - RuntimeError if a variable
v
is needed for an evaluation but - not provided by
env
.
Raises: - RuntimeError if an unassigned random variable is detected while
random_generator
isnullptr
.
- RuntimeError if a variable
-
static
False
() → pydrake.symbolic.Formula¶ Symbolic formula representing false.
-
static
False_
() → pydrake.symbolic.Formula¶ Symbolic formula representing false.
-
GetFreeVariables
(self: pydrake.symbolic.Formula) → pydrake.symbolic.Variables¶ Gets free variables (unquantified variables).
-
Substitute
(*args, **kwargs)¶ Overloaded function.
- Substitute(self: pydrake.symbolic.Formula, arg0: pydrake.symbolic.Variable, arg1: pydrake.symbolic.Expression) -> pydrake.symbolic.Formula
Returns a copy of this formula replacing all occurrences of
var
withe
.Raises: RuntimeError if NaN is detected during substitution. - Substitute(self: pydrake.symbolic.Formula, arg0: pydrake.symbolic.Variable, arg1: pydrake.symbolic.Variable) -> pydrake.symbolic.Formula
Returns a copy of this formula replacing all occurrences of
var
withe
.Raises: RuntimeError if NaN is detected during substitution. - Substitute(self: pydrake.symbolic.Formula, arg0: pydrake.symbolic.Variable, arg1: float) -> pydrake.symbolic.Formula
Returns a copy of this formula replacing all occurrences of
var
withe
.Raises: RuntimeError if NaN is detected during substitution. - Substitute(self: pydrake.symbolic.Formula, arg0: Dict[pydrake.symbolic.Variable, pydrake.symbolic.Expression]) -> pydrake.symbolic.Formula
Returns a copy of this formula replacing all occurrences of the variables in
s
with corresponding expressions ins
. Note that the substitutions occur simultaneously. For example, (x / y > 0).Substitute({{x, y}, {y, x}}) gets (y / x > 0).Raises: RuntimeError if NaN is detected during substitution.
-
to_string
(self: pydrake.symbolic.Formula) → str¶ Returns string representation of Formula.
-
static
True
() → pydrake.symbolic.Formula¶ Symbolic formula representing true.
-
static
True_
() → pydrake.symbolic.Formula¶ Symbolic formula representing true.
-
-
pydrake.symbolic.
if_then_else
(arg0: drake::symbolic::Formula, arg1: pydrake.symbolic.Expression, arg2: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
intersect
(arg0: pydrake.symbolic.Variables, arg1: pydrake.symbolic.Variables) → pydrake.symbolic.Variables¶
-
pydrake.symbolic.
inv
(arg0: numpy.ndarray[object[m, n]]) → numpy.ndarray[object[m, n]]¶
-
pydrake.symbolic.
IsAffine
(*args, **kwargs)¶ Overloaded function.
- IsAffine(arg0: numpy.ndarray[object[m, n], flags.f_contiguous], arg1: pydrake.symbolic.Variables) -> bool
Checks if every element in
m
is affine invars
.Note
If
m
is an empty matrix, it returns true.- IsAffine(arg0: numpy.ndarray[object[m, n], flags.f_contiguous]) -> bool
Checks if every element in
m
is affine.Note
If
m
is an empty matrix, it returns true.
-
pydrake.symbolic.
Jacobian
(*args, **kwargs)¶ Overloaded function.
- Jacobian(arg0: numpy.ndarray[object[m, 1]], arg1: numpy.ndarray[object[m, 1]]) -> numpy.ndarray[object[m, n]]
Computes the Jacobian matrix J of the vector function
f
with respect tovars
. J(i,j) contains ∂f(i)/∂vars(j).For example, Jacobian([x * cos(y), x * sin(y), x^2], {x, y}) returns the following 3x2 matrix:
= |cos(y) -x * sin(y)| |sin(y) x * cos(y)| | 2 * x 0|
- Precondition:
- {
vars
is non-empty}.
- Jacobian(arg0: numpy.ndarray[object[m, 1]], arg1: numpy.ndarray[object[m, 1]]) -> numpy.ndarray[object[m, n]]
Computes the Jacobian matrix J of the vector function
f
with respect tovars
. J(i,j) contains ∂f(i)/∂vars(j).- Precondition:
- {
vars
is non-empty}.
-
pydrake.symbolic.
log
(arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
logical_and
(*formulas)¶
-
pydrake.symbolic.
logical_not
(arg0: pydrake.symbolic.Formula) → pydrake.symbolic.Formula¶
-
pydrake.symbolic.
logical_or
(*formulas)¶
-
pydrake.symbolic.
max
(arg0: pydrake.symbolic.Expression, arg1: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
min
(arg0: pydrake.symbolic.Expression, arg1: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
class
pydrake.symbolic.
Monomial
¶ Represents a monomial, a product of powers of variables with non-negative integer exponents. Note that it does not include the coefficient part of a monomial.
-
__init__
(*args, **kwargs)¶ Overloaded function.
- __init__(self: pydrake.symbolic.Monomial, arg0: pydrake.symbolic.Variable) -> None
Constructs a Monomial from
var
.- __init__(self: pydrake.symbolic.Monomial, arg0: pydrake.symbolic.Variable, arg1: int) -> None
Constructs a Monomial from
var
andexponent
.- __init__(self: pydrake.symbolic.Monomial, arg0: Dict[pydrake.symbolic.Variable, int]) -> None
Constructs a Monomial from
powers
.Raises: RuntimeError if powers
includes a negative exponent.
-
degree
(self: pydrake.symbolic.Monomial, arg0: pydrake.symbolic.Variable) → int¶ Returns the degree of this Monomial in a variable
v
.
-
EqualTo
(self: pydrake.symbolic.Monomial, arg0: pydrake.symbolic.Monomial) → bool¶
-
Evaluate
(self: pydrake.symbolic.Monomial, arg0: Dict[pydrake.symbolic.Variable, float]) → float¶ Evaluates under a given environment
env
.Raises: - ValueError exception if there is a variable in this monomial whose
- assignment is not provided by
env
.
-
get_powers
(self: pydrake.symbolic.Monomial) → Dict[pydrake.symbolic.Variable, int]¶ Returns the internal representation of Monomial, the map from a base (Variable) to its exponent (int).
-
GetVariables
(self: pydrake.symbolic.Monomial) → pydrake.symbolic.Variables¶ Returns the set of variables in this monomial.
-
pow_in_place
(self: pydrake.symbolic.Monomial, arg0: int) → pydrake.symbolic.Monomial¶ Returns this monomial raised to
p
.Raises: RuntimeError if p
is negative.
-
ToExpression
(self: pydrake.symbolic.Monomial) → pydrake.symbolic.Expression¶ Returns a symbolic expression representing this monomial.
-
total_degree
(self: pydrake.symbolic.Monomial) → int¶ Returns the total degree of this Monomial.
-
-
pydrake.symbolic.
MonomialBasis
(*args, **kwargs)¶ Overloaded function.
- MonomialBasis(arg0: numpy.ndarray[object[m, 1]], arg1: int) -> numpy.ndarray[object[m, 1]]
Returns all monomials up to a given degree under the graded reverse lexicographic order. Note that graded reverse lexicographic order uses the total order among Variable which is based on a variable’s unique ID. For example, for a given variable ordering x > y > z,
MonomialBasis({x, y, z}, 2)
returns a column vector[x^2, xy, y^2, xz, yz, z^2, x, y, z, 1]
.- Precondition:
vars
is a non-empty set.- Precondition:
degree
is a non-negative integer.
- MonomialBasis(arg0: pydrake.symbolic.Variables, arg1: int) -> numpy.ndarray[object[m, 1]]
Returns all monomials up to a given degree under the graded reverse lexicographic order. Note that graded reverse lexicographic order uses the total order among Variable which is based on a variable’s unique ID. For example, for a given variable ordering x > y > z,
MonomialBasis({x, y, z}, 2)
returns a column vector[x^2, xy, y^2, xz, yz, z^2, x, y, z, 1]
.- Precondition:
vars
is a non-empty set.- Precondition:
degree
is a non-negative integer.
-
pydrake.symbolic.
OddDegreeMonomialBasis
(vars: pydrake.symbolic.Variables, degree: int) → numpy.ndarray[object[m, 1]]¶ Returns all odd degree monomials up to a given degree under the graded reverse lexicographic order. A monomial has an odd degree if its total degree is odd. So x²y is an odd degree monomial (degree 3) while xy is not (degree 2). Note that graded reverse lexicographic order uses the total order among Variable which is based on a variable’s unique ID. For example, for a given variable ordering x > y > z,
OddDegreeMonomialBasis({x, y, z}, 3)
returns a column vector[x³, x²y, xy², y³, x²z, xyz, y²z, xz², yz², z³, x, y, z]
- Precondition:
vars
is a non-empty set.- Precondition:
degree
is a non-negative integer.
-
class
pydrake.symbolic.
Polynomial
¶ Represents symbolic polynomials. A symbolic polynomial keeps a mapping from a monomial of indeterminates to its coefficient in a symbolic expression.
A polynomial
p
has to satisfy an invariant such thatp.decision_variables() ∩ p.indeterminates() = ∅
. We have CheckInvariant() method to check the invariant.Note that arithmetic operations (+,-,*) between a Polynomial and a Variable are not provided. The problem is that Variable class has no intrinsic information if a variable is a decision variable or an indeterminate while we need this information to perform arithmetic operations over Polynomials.
-
__init__
(*args, **kwargs)¶ Overloaded function.
- __init__(self: pydrake.symbolic.Polynomial) -> None
Constructs a zero polynomial.
- __init__(self: pydrake.symbolic.Polynomial, arg0: Dict[pydrake.symbolic.Monomial, pydrake.symbolic.Expression]) -> None
Constructs a polynomial from a map, Monomial → Expression.
- __init__(self: pydrake.symbolic.Polynomial, arg0: pydrake.symbolic.Monomial) -> None
Constructs a polynomial from a monomial
m
. Note that all variables inm
are considered as indeterminates.- __init__(self: pydrake.symbolic.Polynomial, arg0: pydrake.symbolic.Expression) -> None
Constructs a polynomial from an expression
e
. Note that all variables ine
are considered as indeterminates.Raises: RuntimeError if e
is not a polynomial.- __init__(self: pydrake.symbolic.Polynomial, arg0: pydrake.symbolic.Expression, arg1: pydrake.symbolic.Variables) -> None
Constructs a polynomial from an expression
e
by decomposing it with respect toindeterminates
.Note
It collects the intersection of the variables appeared in
e
and the providedindeterminates
.Raises: RuntimeError if e
is not a polynomial inindeterminates
.- __init__(self: pydrake.symbolic.Polynomial, arg0: pydrake.symbolic.Expression, arg1: numpy.ndarray[object[m, 1]]) -> None
Constructs a polynomial from an expression
e
by decomposing it with respect toindeterminates
.Note
It collects the intersection of the variables appeared in
e
and the providedindeterminates
.Raises: RuntimeError if e
is not a polynomial inindeterminates
.
-
AddProduct
(self: pydrake.symbolic.Polynomial, arg0: pydrake.symbolic.Expression, arg1: pydrake.symbolic.Monomial) → pydrake.symbolic.Polynomial¶ Adds
coeff
*m
to this polynomial.
-
CoefficientsAlmostEqual
(self: pydrake.symbolic.Polynomial, p: pydrake.symbolic.Polynomial, tolerance: float) → bool¶ Returns true if this polynomial and
are
almost equal (the difference in the corresponding coefficients are all less thantol)
, after expanding the coefficients.
-
decision_variables
(self: pydrake.symbolic.Polynomial) → pydrake.symbolic.Variables¶ Returns the decision variables of this polynomial.
-
Degree
(self: pydrake.symbolic.Polynomial, arg0: pydrake.symbolic.Variable) → int¶ Returns the highest degree of this polynomial in a variable
v
.
-
Differentiate
(self: pydrake.symbolic.Polynomial, arg0: pydrake.symbolic.Variable) → pydrake.symbolic.Polynomial¶ Differentiates this polynomial with respect to the variable
x
. Note that a variablex
can be either a decision variable or an indeterminate.
-
EqualTo
(self: pydrake.symbolic.Polynomial, arg0: pydrake.symbolic.Polynomial) → bool¶ Returns true if this polynomial and
p
are structurally equal.
-
Evaluate
(self: pydrake.symbolic.Polynomial, arg0: Dict[pydrake.symbolic.Variable, float]) → float¶ Evaluates this polynomial under a given environment
env
.Raises: - ValueError if there is a variable in this polynomial whose
- assignment is not provided by
env
.
-
EvaluatePartial
(*args, **kwargs)¶ Overloaded function.
- EvaluatePartial(self: pydrake.symbolic.Polynomial, env: Dict[pydrake.symbolic.Variable, float]) -> pydrake.symbolic.Polynomial
Partially evaluates this polynomial using an environment
env
.Raises: RuntimeError if NaN is detected during evaluation. - EvaluatePartial(self: pydrake.symbolic.Polynomial, var: pydrake.symbolic.Variable, c: float) -> pydrake.symbolic.Polynomial
Partially evaluates this polynomial by substituting
var
withc
.Raises: RuntimeError if NaN is detected at any point during evaluation.
-
indeterminates
(self: pydrake.symbolic.Polynomial) → pydrake.symbolic.Variables¶ Returns the indeterminates of this polynomial.
-
Jacobian
(self: pydrake.symbolic.Polynomial, arg0: numpy.ndarray[object[m, 1]]) → numpy.ndarray[object[1, n]]¶ Computes the Jacobian matrix J of the polynomial with respect to
vars
. J(0,i) contains ∂f/∂vars(i).
-
monomial_to_coefficient_map
(self: pydrake.symbolic.Polynomial) → Dict[pydrake.symbolic.Monomial, pydrake.symbolic.Expression]¶ Returns the mapping from a Monomial to its corresponding coefficient of this polynomial.
-
RemoveTermsWithSmallCoefficients
(self: pydrake.symbolic.Polynomial, coefficient_tol: float) → pydrake.symbolic.Polynomial¶ Removes the terms whose absolute value of the coefficients are smaller than or equal to
coefficient_tol
For example, if the polynomial is 2x² + 3xy + 10⁻⁴x - 10⁻⁵, then after calling RemoveTermsWithSmallCoefficients(1e-3), the returned polynomial becomes 2x² + 3xy.- Parameter
coefficient_tol
: - A positive scalar.
- Returns
polynomial_cleaned
: - A polynomial whose terms with small coefficients are removed.
- Parameter
-
SetIndeterminates
(self: pydrake.symbolic.Polynomial, arg0: pydrake.symbolic.Variables) → None¶ Sets the indeterminates to
new_indeterminates
.Changing the indeterminates would change
monomial_to_coefficient_map()
, and also potentially the degree of the polynomial. Here is an example.// p is a quadratic polynomial with x being the indeterminates. symbolic::Polynomial p(a * x * x + b * x + c, {x}); // p.monomial_to_coefficient_map() contains {1: c, x: b, x*x:a}. std::cout << p.TotalDegree(); // prints 2. // Now set (a, b, c) to the indeterminates. p becomes a linear // polynomial of a, b, c. p.SetIndeterminates({a, b, c}); // p.monomial_to_coefficient_map() now is {a: x * x, b: x, c: 1}. std::cout << p.TotalDegree(); // prints 1.
-
ToExpression
(self: pydrake.symbolic.Polynomial) → pydrake.symbolic.Expression¶ Returns an equivalent symbolic expression of this polynomial.
-
TotalDegree
(self: pydrake.symbolic.Polynomial) → int¶ Returns the total degree of this polynomial.
-
-
pydrake.symbolic.
pow
(arg0: pydrake.symbolic.Expression, arg1: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
sin
(arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
sinh
(arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
sqrt
(arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
Substitute
(*args, **kwargs)¶ Overloaded function.
- Substitute(m: numpy.ndarray[object[m, n]], subst: Dict[pydrake.symbolic.Variable, pydrake.symbolic.Expression]) -> numpy.ndarray[object[m, n]]
Substitutes a symbolic matrix
m
using a given substitutionsubst
.Returns: a matrix of symbolic expressions whose size is the size of m
.Raises: RuntimeError if NaN is detected during substitution. - Substitute(m: numpy.ndarray[object[m, n]], var: pydrake.symbolic.Variable, e: pydrake.symbolic.Expression) -> numpy.ndarray[object[m, n]]
Substitutes
var
withe
in a symbolic matrixm
.Returns: a matrix of symbolic expressions whose size is the size of m
.Raises: RuntimeError if NaN is detected during substitution.
-
pydrake.symbolic.
tan
(arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
pydrake.symbolic.
tanh
(arg0: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶
-
class
pydrake.symbolic.
Variable
¶ Represents a symbolic variable.
Note
Expression::Evaluate and Formula::Evaluate methods take a symbolic environment (Variable → double) and a random number generator. When an expression or a formula includes random variables,
Evaluate
methods use the random number generator to draw a number for a random variable from the given distribution. Then this numeric value is used to substitute all the occurrences of the corresponding random variable in an expression or a formula.-
__init__
(self: pydrake.symbolic.Variable, name: str, type: pydrake.symbolic.Variable.Type = Type.CONTINUOUS) → None¶ Constructs a variable with a string. If not specified, it has CONTINUOUS type by default.
-
EqualTo
(self: pydrake.symbolic.Variable, arg0: pydrake.symbolic.Variable) → bool¶ Checks the equality of two variables based on their ID values.
-
get_id
(self: pydrake.symbolic.Variable) → int¶
-
get_type
(self: pydrake.symbolic.Variable) → pydrake.symbolic.Variable.Type¶
-
class
Type
¶ Members:
CONTINUOUS : A CONTINUOUS variable takes a
double
value.INTEGER : An INTEGER variable takes an
int
value.BINARY : A BINARY variable takes an integer value from {0, 1}.
BOOLEAN : A BOOLEAN variable takes a
bool
value.RANDOM_UNIFORM : A random variable whose value will be drawn from uniform real
distributed ∈ [0,1).
RANDOM_GAUSSIAN : A random variable whose value will be drawn from mean-zero,unit-variance normal.
RANDOM_EXPONENTIAL : A random variable whose value will be drawn from exponentialdistribution with λ=1.
-
__init__
(self: pydrake.symbolic.Variable.Type, arg0: int) → None¶
-
BINARY
= Type.BINARY¶
-
BOOLEAN
= Type.BOOLEAN¶
-
CONTINUOUS
= Type.CONTINUOUS¶
-
INTEGER
= Type.INTEGER¶
-
name
¶
-
RANDOM_EXPONENTIAL
= Type.RANDOM_EXPONENTIAL¶
-
RANDOM_GAUSSIAN
= Type.RANDOM_GAUSSIAN¶
-
RANDOM_UNIFORM
= Type.RANDOM_UNIFORM¶
-
-
-
class
pydrake.symbolic.
Variables
¶ Represents a set of variables.
This class is based on std::set<Variable>. The intent is to add things that we need including set-union (Variables::insert, operator+, operator+=), set-minus (Variables::erase, operator-, operator-=), and subset/superset checking functions (Variables::IsSubsetOf, Variables::IsSupersetOf, Variables::IsStrictSubsetOf, Variables::IsStrictSupersetOf).
-
__init__
(*args, **kwargs)¶ Overloaded function.
- __init__(self: pydrake.symbolic.Variables) -> None
Default constructor.
- __init__(self: pydrake.symbolic.Variables, arg0: numpy.ndarray[object[m, 1]]) -> None
Constructs from an Eigen vector of variables.
-
empty
(self: pydrake.symbolic.Variables) → bool¶
-
EqualTo
(self: pydrake.symbolic.Variables, arg0: pydrake.symbolic.Variables) → bool¶
-
erase
(*args, **kwargs)¶ Overloaded function.
- erase(self: pydrake.symbolic.Variables, arg0: pydrake.symbolic.Variable) -> int
Erases
key
from a set. Return number of erased elements (0 or 1).- erase(self: pydrake.symbolic.Variables, arg0: pydrake.symbolic.Variables) -> int
Erases variables in
vars
from a set. Return number of erased elements ([0, vars.size()]).
-
include
(self: pydrake.symbolic.Variables, arg0: pydrake.symbolic.Variable) → bool¶ Return true if
key
is included in the Variables.
-
insert
(*args, **kwargs)¶ Overloaded function.
- insert(self: pydrake.symbolic.Variables, arg0: pydrake.symbolic.Variable) -> None
Inserts a variable
var
into a set.- insert(self: pydrake.symbolic.Variables, arg0: pydrake.symbolic.Variables) -> None
Inserts variables in
vars
into a set.
-
IsStrictSubsetOf
(self: pydrake.symbolic.Variables, arg0: pydrake.symbolic.Variables) → bool¶ Return true if
vars
is a strict subset of the Variables.
-
IsStrictSupersetOf
(self: pydrake.symbolic.Variables, arg0: pydrake.symbolic.Variables) → bool¶ Return true if
vars
is a strict superset of the Variables.
-
IsSubsetOf
(self: pydrake.symbolic.Variables, arg0: pydrake.symbolic.Variables) → bool¶ Return true if
vars
is a subset of the Variables.
-
IsSupersetOf
(self: pydrake.symbolic.Variables, arg0: pydrake.symbolic.Variables) → bool¶ Return true if
vars
is a superset of the Variables.
-
size
(self: pydrake.symbolic.Variables) → int¶ Returns the number of elements.
-
to_string
(self: pydrake.symbolic.Variables) → str¶ Returns string representation of Variables.
-


'The Newton Boys'
A movie review by Walter Frith
Member of the 'Internet Movie Critic's Association' http://www.geocities.com/Hollywood/Studio/5713/index.html
'The Newton Boys' does something clever. It draws you in slowly after a more than mediocre beginning and eventually has you rooting for a group of wild west American outlaws who never killed anyone in their rampage of robbing somewhere in the neighbourhood of 200 banks between 1919 and 1924. Using a Robin Hood mentality of robbing from the rich to pay the poor (in this case, however, they pay themselves), Matthew McConaughey (Willis Newton) Ethan Hawke (Jess Newton) Skeet Ulrich (Joe Newton), and Vincent D'Onofrio (Dock Newton) are featured as the four brothers who are loyal to each other and to their profession. Dwight Yoakam is an explosives expert who hooks up with the brothers and his specialty is using a nitro mix in blowing safes. Rounding out the leading players is Julianna Margulies who plays Louise, a cigar store clerk who becomes Willis' girlfriend.
As the brothers plot each robbery, there is a hint of detail reminiscent of a documentary style approach by director Richard Linklater ('Dazed and Confused', 'Before Sunrise') and the visual style the film projects is very impressive and candidly entertaining. Matthew McConaughey is a charismatic leading man and he is truly one of this generation's most under rated actors and has a power capable of carrying an entire film on his back. His portrayal of Willis Newton, a man raised dirt poor who had a tough life and claims to have went to prison as an innocent man, is someone many people can generate sympathy for and these factors fuel his desire to rob banks as we see him at the start of the film as an ex-con as someone asks him: "How was prison?", to which he replies: "How was the war?"
Despite the unusual place in history the Newton brothers have found, they remain virtually unknown compared to the likes of John Dillinger, Bonnie and Clyde and "Baby Face" Nelson. Perhaps because the Newton brothers weren't as cold blooded as their criminal peers and not just the American but the human fascination with violence is something that propels the most violent criminals to the top of the list in terms of historical documentation. It's a constant pleasure to watch the creators of film pick up on a part of history that is relatively unknown because the research proves to be more difficult and when you succeed, it is a greater testament to your endeavour as a creative artist.
Everything is meticulously crafted in 'The Newton' Boys'. From the clothes, to the sets, to the music, even the dialogue and wild west attitude are nailed down as impressively as any I've ever seen. The most interesting footage of the film comes in two places. First is a trip to Canada where they try and rob banks in Ottawa and Toronto and find Canadian safes better built and harder to crack so they decide to rob banks in broad daylight on the street as they witness bank employees, in a more civilized and less dangerous society, openly carry large bags of cash on the streets for transfer and delivery and as the boys hold them up, they do what they can to get away without killing anyone in the process. Secondly is the film's closing credits which are accompanied by footage of the Johnny Carson show where the real Willis Newton is interviewed by Carson and we see the real Joe Newton in clips of home movies and they tell how the brothers always viewed banks and insurance companies as cheats themselves and that his gang was just one thief robbing from another.
Not a great justification of their profession, and while some may criticize the film as a glorification of bank robberies, it's captivating simplicity and depth of academic focus make it entertaining as an alternative form of social commentary and the film does something rare. It only uses violence when necessary to make its intended points.
OUT OF 5 > * * * 1/2
Visit FILM FOLLOW-UP by Walter Frith http://home.netinc.ca/~wfrith/movies.htm
The review above was posted to the
rec.arts.movies.reviews newsgroup (de.rec.film.kritiken for German reviews).
The Internet Movie Database accepts no responsibility for the contents of the
review and has no editorial control. Unless stated otherwise, the copyright
belongs to the author.
Please direct comments/criticisms of the review to relevant newsgroups.
Broken URLs inthe reviews are the responsibility of the author.
The formatting of the review is likely to differ from the original due
to ASCII to HTML conversion.
Related links: index of all rec.arts.movies.reviews reviews


Hydra http-post-form https-post-form only needs the post data from the body
<Login_page_url>:<postdata>:<invalid string>
hydra -L <wordlist> -P<password list> <IP_ADDRESS> http-post-form "/dvwa/login.php:username=^USER^&password=^PASS^&Login=Login:Login failed"


EBD - Easton Bible DIctionary
Nergal
NERGAL
"NERGAL "the great dog; that is, lion, one of the chief gods of the Assyrians and Babylonians (
2 Kings 17:30
), the God of war and hunting.
He is connected with Cutha as its tutelary deity.
"NERGAL "the great dog; that is, lion, one of the chief gods of the Assyrians and Babylonians (2 Kings 17:30), the God of war and hunting.
He is connected with Cutha as its tutelary deity.


ExportOutput
Represents an output of a model that can be served.
tf.compat.v1.estimator.export.ExportOutput
tf.compat.v2.estimator.export.ExportOutput
These typically correspond to model heads.
as_signature_def
as_signature_def(receiver_tensors)
Generate a SignatureDef proto for inclusion in a MetaGraphDef.
The SignatureDef will specify outputs as described in this ExportOutput, and will use the provided receiver_tensors as inputs.
receiver_tensors
: a Tensor
, or a dict of string to Tensor
, specifying
input nodes that will be fed.


Wondering how to get started with that one skill you always wanted to learn? Then this is the perfect place for you to explore and get the best tips and insights on how and where to begin. This series tackles all the information that you need as a beginner to master the skill you always wanted to. We have the best articles and videos to help you get started with. So come join us on this journey to unleash the best in you.


| Figure 1 |
The global distribution of differences in the maximum tree f ... |
| Figure 2 |
Comparison of the change in ecosystem gross primary producti ... |
| Figure 3 |
Comparison of the global area change (ΔΩ; ×10 3 km 2) for se ... |
| Figure 4 |
Global distribution of changes in tree fractional coverage ( ... |
| Figure 5 |
The dependence of the change in tree fractional coverage (Δ ... |
| Figure 6 |
Dependence of the standard deviation of Δ F tree (σ; %) on t ... |
| Figure 7 |
Global distribution of changes in tree fractional coverage ( ... |
| Figure 8 |
The dependence of the change in tree fractional coverage (Δ ... |
| Figure 9 |
Dependence of the standard deviation of Δ F tree (σ; %) on t ... |
| Figure 10 |
The relationship between tree fractional coverage ( F tree,c ... |
| Figure 11 |
The global distribution of the optimal temperature change (r ... |


The October 2005 PWG/P2600 meeting will be at the Radisson in downtown Chicago
October meeting schedule
|
Day |
Date |
Morning |
Afternoon |
Evening |
|
Monday |
Oct – 24 |
P2600 |
P2600 |
-- |
|
Tuesday |
Oct – 25 |
P2600 |
P2600 |
-- |
|
Wednesday |
Oct – 26 |
Plenary |
Port Mon |
-- |
|
Thursday |
Oct – 27 |
DMTF/CIM |
WIMS Protocol |
-- |
|
Friday |
Oct – 28 |
Display/Projector MIB |
N/A |
-- |
All
meetings begin at
There will be a meeting fee of USD$84.00 per participant per day.
Please REGISTER online at the following link
https://www.ieee-isto.org/pwg/pwg_meeting_chicago.asp
You are responsible for you own hotel reservation. A limited room block has been reserved. Please indicate that you are with the PWG or ISTO when making your reservation.


For this next challenge, we’re going to take a look at the murky world of encryption.
People have been trying to hide messages for centuries - the earliest known use of cryptography is found in non-standard hieroglyphs carved into the wall of a tomb from the Old Kingdom of Egypt circa 1900 BCE.
These are not thought to be serious attempts at secret communications, however, but rather to have been attempts at mystery, intrigue, or even amusement for literate onlookers.
One of the simplest ciphers is a Caesar Cipher, where each letter in the alphabet is replaced by a letter a fixed number of positions down the alphabet, so with a right shift of 3, ‘a’ becomes ‘d’, ‘b’ becomes ‘e’ and so forth.
So, “I love you” becomes, “L oryi brx”
Don’t worry … we’re going to go with something even simpler!
Challenge #2
Write a program that:
Pick your favorite language?


Kamala Harris called a Pete Buttigieg comment 'naive' — and Buttigieg agreed
by Tim O'DonnellSen. Kamala Harris (D-Calif.) had a good laugh at her fellow Democratic presidential candidate South Bendia, Indiana Mayor, Pete Buttigieg's comments that the race was "getting to be" a two-person showdown between Buttigieg and Sen. Elizabeth Warren (D-Mass.)
In an interview with CBS that aired Sunday, Harris called the suggestion "naive" and said the mayor should review some history books to remind himself of the fact that elections generally aren't decided this early.
Buttigieg was later asked about Harris' response to his comments and he couldn't help but agree. He said he couldn't remember the exact context that led to his answer, but he thinks "we all know that this is a fluid race, that it's a very competitive race, and that anything could happen."


This intention merges two
if
statements into one, if the second is located inside the then-branch of the first.


lighbox plugin use to view images,videos,iframes with slide option on bootstrap modal
1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It with


The debugger has a built-in C/C++ expression interpreter that can be used to invoke functions defined inside the debugged program.
From the menu bar, select Tools -> Evaluate. The Evaluate dialog pops up; type the name of the function, with its parameters, then hit the Evaluate button.
When invoking a method on an object from within another method of the same object, you must prefix the method with this->.Static methods must be fully-qualified, as in MyClass::some_method()
Note: Some functions such as constructors and user-defined conversion operators may be called behind the scenes when static_cast or C-style cast expressions are evaluated.
Note: The C calling convention is the only one supported at this time. (Parameters are pushed onto the stack starting from the right-most, and the caller is responsible for cleaning up the stack after the function returns).
Other limitations of the expression evaluator:
Note: If a function invoked from the debugger causes a signal (such as SIGSEGV) to be raised inside the debugged program, the debugger will do its best to restore the CPU registers and rewind the stack; however, side-effects such as modifications of the memory, or I/O operations cannot be undone.


PYTHON FLASK APPLICATION
Upload
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Version Number
Last Modified
{% for document in documents %}
{{document['file_name']}}
{{document['version_number']}}
{{document['lastModifiedDate']}}
Download
Delete
{% endfor %}


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--- layout: post title: Episode 077 | Daniel Marbach - Geeking Out link: http://traffic.libsyn.com/developeronfire/DeveloperOnFire-77-DanielMarbach.mp3 length: 38797312 speaker: Dave Rael duration: '40:28' subtitle: 'Developer On Fire: Daniel Marbach' guest_name: Daniel Marbach image: /assets/images/DanielMarbach.jpg guest_blog: http://www.planetgeek.ch/ guest_twitter: danielmarbach disqus_url: http://developeronfire.com/Podcast/Episodes/daniel-marbach-geeking-out episode_number: 77 book_recommendations: - { url: "http://www.amazon.com/dp/0321717295/?tag=devonfir-20", title: "12 Essential Skills for Software Architects", author: "Dave Hendricksen"} - { url: "http://www.amazon.com/dp/0201741571/?tag=devonfir-20", title: "Fearless Change: Patterns for Introducing New Ideas", author: "Mary Lynn Manns Ph.D., Linda Rising Ph.D."} tags: - { url: "http://www.amazon.com/dp/0321717295/?tag=devonfir-20", title: "12 Essential Skills for Software Architects", author: "Dave Hendricksen"} - { url: "http://www.amazon.com/dp/0201741571/?tag=devonfir-20", title: "Fearless Change: Patterns for Introducing New Ideas", author: "Mary Lynn Manns Ph.D., Linda Rising Ph.D."} redirect_from: - "/77/" - "/077/" - "/0077/" - "/daniel-marbach-geeking-out/" - "/Daniel-Marbach/" - "/DanielMarbach/" - "/Podcast/Episodes/77/" - "/Podcast/Episodes/077/" - "/Podcast/Episodes/0077/" - "/Podcast/Episodes/daniel-marbach-geeking-out/" - "/Podcast/Episodes/Daniel-Marbach/" - "/Podcast/Episodes/DanielMarbach/" guid: http://developeronfire.com:80/Podcast/Episodes/daniel-marbach-geeking-out ---
Daniel Marbach is a Solution Architect at Particular Software Ltd and the CEO of Tracelight GmbH in Switzerland. His experience spreads from client and server development to building distributed systems. Daniel has extensive knowledge in the .NET ecosystem including NoSQL databases, asynchronous programming, open-source software development and much more. He is a Microsoft MVP for Integration, a frequent speaker, coach and passionate blog writer. Daniel co-founded the .NET Usergroup Central Switzerland and continues his journey of software development with passion. Quote: Evolvable and maintainable architecture is not created in an ivory tower. It is a result of continuous improvements of targeted pragmatism and cooperation in a team with a common vision.
1. Recognize that everyone has potential, particularly that you have potential.
2. Surround yourself with people that bring you forward.
3. If you achieve something, share it with you friends and coworkers and family.


Modern Programming for Data Analytics - pandas
What is pandas?
- a Python package that provides fast, flexible and expressive data structures
- designed to work with relational and labeled data
- it is suited to work with:
- tabular data with heterogenous types
- ordered and unordered times series data
- arbitrary matrix data
- observational /statistical data sets
- pandas is fast, many high-performance algorithms under the hood
pandas does well:
- handling of missing
- mutable data structures (inserting and deleting data)
- automatic and explicit data alignment
- flexible groupby functionality and advanced data querying
- high interperability with NumPy and SciPy
- easy and intelligent slicing, indexing and subsetting of large data sets
- intuiting merging and joining of data
- hierarchical and multilevel datasets
- robust i/o operations to read and write multiple data formats
- time series specific functionality
pandas Data Structures
- Series - 1-D labeled homogeneously-typed array (that type may be object)
- DataFrame - General 2D labeled, size mutable tabular structure with potentially
heterogenous-typed columns
pandas DataFrame


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