raisim::Mat

class · #include <raisim/math/Matrix.hpp>

Inherits: raisim::MatExpr< Mat< n, m > >

template <size_t n, size_t m>
class Mat

Fixed-size n x m matrix of doubles, stored column-major: element (i, j) is v[i + j * n]. Vec<n> is the column-vector alias Mat<n, 1>.

The default constructor leaves the elements uninitialized. Arithmetic on Mat objects and other raisim matrix expressions (+, -, *, /, also with scalars) builds expression templates that hold their operands by reference and are evaluated when assigned, so do not store an expression that refers to temporaries (e.g. with auto). Assignment evaluates the expression element by element into the destination: element-wise expressions that read the destination (a = a + b) are fine, but a product or transpose that reads it (a = a * b, a = a.transpose()) gives wrong results; the 4x4 by 4x4 product is evaluated eagerly and is the exception. e() returns an Eigen map of the same memory.

In addition to the members listed here, Mat provides (through a shared macro that is not shown in this reference) norm(), sum(), squaredNorm(), dot(), setZero(), setConstant(), scalar *=, /=, += and -=, assignment from any matrix-like object of the same dimensions, cross() and skew() for 3D vectors, and an implicit conversion to double that returns element (0, 0).

Public types

EigenMat

typedef Eigen::Map<Eigen::Matrix<ScalarType, n, m>> EigenMat

Mutable Eigen map type returned by e().

ConstEigenMat

typedef Eigen::Map<const Eigen::Matrix<ScalarType, n, m>> ConstEigenMat

Read-only Eigen map type returned by e() const.

SelfType

typedef Mat<n, m> SelfType

This type (used by the shared expression machinery).

Constructors & destructor

Mat

Mat() = default

Leaves the elements uninitialized.

Mat(std::initializer_list<ScalarType> init)

Constructs from values listed in column-major order. The list may not exceed n*m elements (fatal otherwise); missing trailing elements are zero-filled.

Parameters

Parameter	Description
init (in)	element values, column-major

template <class scalarType>
Mat(const Eigen::Matrix<scalarType, n, m> &eigen)

Copies an Eigen matrix with the same dimensions.

Parameters

Parameter	Description
eigen (in)	source matrix

template <class T2>
Mat(const T2 &rhs)

Constructs from any matrix-like object with rows(), cols() and operator()(i, j), such as a raisim matrix expression or an Eigen object. Mismatched dimensions are a compile-time error for raisim types and fatal at run time otherwise.

Parameters

Parameter	Description
rhs (in)	source

Public member functions

operator=

template <class T2>
Mat<n, m> &operator=(const MatExpr<T2> &expr)

Evaluates an expression with identical dimensions into this matrix (see the class description for aliasing).

Parameters

Parameter	Description
expr (in)	expression to evaluate

Returns *this

template <size_t n2, size_t m2>
Mat<n, m> &operator=(const Mat<n2, m2> &expr)

Copies a Mat with identical dimensions (checked at compile time).

Parameters

Parameter	Description
expr (in)	matrix to copy

Returns *this

ptr

ScalarType *ptr()

Returns pointer to the first element.

const ScalarType *ptr() const

Returns pointer to the first element.

data

ScalarType *data()

Returns pointer to the first element (Eigen-compatible name).

const ScalarType *data() const

Returns pointer to the first element (Eigen-compatible name).

operator[]

double operator[](size_t i) const

Parameters

Parameter	Description
i (in)	column-major linear index

Returns element i (no bounds check)

double &operator[](size_t i)

Parameters

Parameter	Description
i (in)	column-major linear index

Returns reference to element i (no bounds check)

operator()

double operator()(size_t i) const

Parameters

Parameter	Description
i (in)	column-major linear index

Returns element i (no bounds check)

double &operator()(size_t i)

Parameters

Parameter	Description
i (in)	column-major linear index

Returns reference to element i (no bounds check)

double operator()(size_t i, size_t j) const

Parameters

Parameter	Description
i (in)	row index
j (in)	column index

Returns element (i, j) (no bounds check)

double &operator()(size_t i, size_t j)

Parameters

Parameter	Description
i (in)	row index
j (in)	column index

Returns reference to element (i, j) (no bounds check)

operator-

Mat<n, m> operator-()

Returns the negated matrix.

e

EigenMat e()

Returns Eigen map aliasing this matrix's memory (writes go to this matrix).

ConstEigenMat e() const

Returns read-only Eigen map aliasing this matrix's memory.

operator<<

ElementRef<Mat<n, m>> operator<<(ScalarType a)

Comma-initializer entry point (Eigen-style): v << 1.0, 2.0, 3.0;. Elements are written in column-major order; writing past the last element is fatal.

Parameters

Parameter	Description
a (in)	value of the first element

Returns proxy that receives the following elements

normalize

void normalize()

Eigen-like vector normalization (vectors only). A zero vector is left unchanged.

operator-=

void operator-=(const Mat<n, m> &val)

Element-wise subtraction.

Parameters

Parameter	Description
val (in)	matrix to subtract

operator+=

void operator+=(const Mat<n, m> &val)

Element-wise addition.

Parameters

Parameter	Description
val (in)	matrix to add

operator/=

void operator/=(const Mat<n, m> &val)

Element-wise division.

Parameters

Parameter	Description
val (in)	element-wise divisors

setIdentity

void setIdentity()

Sets this square matrix to the identity.

determinant

ScalarType determinant() const

Returns the determinant, computed by Eigen (square matrices only).

inverse

Mat<n, n> inverse() const

Returns the inverse, computed by Eigen (square matrices only). Singularity is not checked.

transpose

Transpose<Mat<n, m>> transpose()

Returns lazy transpose expression referencing this matrix.

const Transpose<Mat<n, m>> transpose() const

Returns lazy transpose expression referencing this matrix.

row

RowRef<Mat<n, m>, m> row(size_t r)

Parameters

Parameter	Description
r (in)	row index

Returns proxy referencing row r; writes go to this matrix.

RowRef<const Mat<n, m>, m> row(size_t r) const

Parameters

Parameter	Description
r (in)	row index

Returns read-only proxy referencing row r.

col

ColRef<Mat<n, m>, n> col(size_t r)

Parameters

Parameter	Description
r (in)	column index

Returns proxy referencing column r; writes go to this matrix.

ColRef<const Mat<n, m>, n> col(size_t r) const

Parameters

Parameter	Description
r (in)	column index

Returns read-only proxy referencing column r.

segment

template <size_t sizeRow, size_t sizeCol>
BlockRef<Mat<n, m>, sizeRow, sizeCol> segment(
    size_t startRow,
    size_t startCol)

Block of size sizeRow x sizeCol (template arguments) starting at a run-time position. No bounds check.

Parameters

Parameter	Description
startRow (in)	row of the block's top-left element
startCol (in)	column of the block's top-left element

Returns proxy referencing the block; writes go to this matrix.

template <size_t sizeRow, size_t sizeCol>
BlockRef<const Mat<n, m>, sizeRow, sizeCol> segment(
    size_t startRow,
    size_t startCol) const

Read-only block of size sizeRow x sizeCol starting at a run-time position. No bounds check.

Parameters

Parameter	Description
startRow (in)	row of the block's top-left element
startCol (in)	column of the block's top-left element

Returns read-only proxy referencing the block.

head

template <size_t sizeRow>
BlockRef<Mat<n, m>, sizeRow, 1> head()

Returns proxy referencing the first sizeRow elements (vectors only).

template <size_t sizeRow>
BlockRef<const Mat<n, m>, sizeRow, 1> head() const

Returns read-only proxy referencing the first sizeRow elements (vectors only).

tail

template <size_t sizeRow>
BlockRef<Mat<n, m>, sizeRow, 1> tail()

Returns proxy referencing the last sizeRow elements (vectors only).

template <size_t sizeRow>
BlockRef<const Mat<n, m>, sizeRow, 1> tail() const

Returns read-only proxy referencing the last sizeRow elements (vectors only).

topLeftCorner

template <size_t sizeRow, size_t sizeCol>
BlockRef<const Mat<n, m>, sizeRow, sizeCol> topLeftCorner() const

Returns read-only proxy referencing the top-left sizeRow x sizeCol block.

template <size_t sizeRow, size_t sizeCol>
BlockRef<Mat<n, m>, sizeRow, sizeCol> topLeftCorner()

Returns proxy referencing the top-left sizeRow x sizeCol block.

topRightCorner

template <size_t sizeRow, size_t sizeCol>
BlockRef<const Mat<n, m>, sizeRow, sizeCol> topRightCorner() const

Returns read-only proxy referencing the top-right sizeRow x sizeCol block.

template <size_t sizeRow, size_t sizeCol>
BlockRef<Mat<n, m>, sizeRow, sizeCol> topRightCorner()

Returns proxy referencing the top-right sizeRow x sizeCol block.

bottomRightCorner

template <size_t sizeRow, size_t sizeCol>
BlockRef<const Mat<n, m>, sizeRow, sizeCol> bottomRightCorner() const

Returns read-only proxy referencing the bottom-right sizeRow x sizeCol block.

template <size_t sizeRow, size_t sizeCol>
BlockRef<Mat<n, m>, sizeRow, sizeCol> bottomRightCorner()

Returns proxy referencing the bottom-right sizeRow x sizeCol block.

bottomLeftCorner

template <size_t sizeRow, size_t sizeCol>
BlockRef<const Mat<n, m>, sizeRow, sizeCol> bottomLeftCorner() const

Returns read-only proxy referencing the bottom-left sizeRow x sizeCol block.

template <size_t sizeRow, size_t sizeCol>
BlockRef<Mat<n, m>, sizeRow, sizeCol> bottomLeftCorner()

Returns proxy referencing the bottom-left sizeRow x sizeCol block.

block

template <size_t sizeRow, size_t sizeCol, size_t startRow, size_t startCol>
BlockRef<const Mat<n, m>, sizeRow, sizeCol> block() const

Returns read-only proxy referencing the sizeRow x sizeCol block at (startRow, startCol), all given as template arguments.

template <size_t sizeRow, size_t sizeCol, size_t startRow, size_t startCol>
BlockRef<Mat<n, m>, sizeRow, sizeCol> block()

Returns proxy referencing the sizeRow x sizeCol block at (startRow, startCol), all given as template arguments.

Static member functions

size static

static constexpr size_t size()

Returns number of elements, n * m.

rows static

static constexpr size_t rows()

Returns number of rows, n.

cols static

static constexpr size_t cols()

Returns number of columns, m.

getIdentity static

static Mat<n, n> getIdentity()

Returns the n x n identity matrix (square matrices only).

Identity static

static Mat<n, n> Identity()

Returns the n x n identity matrix (Eigen-style name for getIdentity()).

getZeros static

static Mat<n, m> getZeros()

Returns a matrix of zeros.

Zero static

static Mat<n, m> Zero()

Returns a matrix of zeros (Eigen-style name for getZeros()).

Public attributes

alignment_only

std::aligned_storage<n *m *sizeof(ScalarType), 32> alignment_only

v

double v[n *m]

(anonymous union)

An anonymous union: its members are listed with the other attributes and share storage.