SimTK::Mat< M, N, ELT, CS, RS > Class Template Reference

This class represents a small matrix whose size is known at compile time, containing elements of any Composite Numerical Type (CNT) and engineered to have no runtime overhead whatsoever. More...

Inheritance diagram for SimTK::Mat< M, N, ELT, CS, RS >:

Classes
struct	EltResult
struct	Result
struct	SubMat
struct	Substitute

Public Types
enum	{   NRows = M,   NCols = N,   MinDim,   RowSpacing = RS,   ColSpacing = CS,   NPackedElements = M * N,   NActualElements = (N-1)*CS + (M-1)*RS + 1,   NActualScalars = CNT<E>::NActualScalars * NActualElements,   ImagOffset = NTraits<ENumber>::ImagOffset,   RealStrideFactor = 1,   ArgDepth,   IsScalar = 0,   IsULessScalar = 0,   IsNumber = 0,   IsStdNumber = 0,   IsPrecision = 0,   SignInterpretation = CNT<E>::SignInterpretation }
	Every Composite Numerical Type (CNT) must define these values. More...
typedef Mat< M, N, E, CS, RS >	T
typedef Mat< M, N, ENeg, CS, RS >	TNeg
typedef Mat< M, N, EWithoutNegator, CS, RS >	TWithoutNegator
typedef Mat< M, N, EReal, CS *CNT< E >::RealStrideFactor, RS *CNT< E >::RealStrideFactor >	TReal
typedef Mat< M, N, EImag, CS *CNT< E >::RealStrideFactor, RS *CNT< E >::RealStrideFactor >	TImag
typedef Mat< M, N, EComplex, CS, RS >	TComplex
typedef Mat< N, M, EHerm, RS, CS >	THerm
typedef Mat< N, M, E, RS, CS >	TPosTrans
typedef E	TElement
typedef Row< N, E, CS >	TRow
typedef Vec< M, E, RS >	TCol
typedef Vec< MinDim, E, RS+CS >	TDiag
typedef Mat< M, N, ESqrt, M, 1 >	TSqrt
typedef Mat< M, N, EAbs, M, 1 >	TAbs
typedef Mat< M, N, EStandard, M, 1 >	TStandard
typedef Mat< N, M, EInvert, N, 1 >	TInvert
typedef Mat< M, N, ENormalize, M, 1 >	TNormalize
typedef SymMat< N, ESqHermT >	TSqHermT
typedef SymMat< M, ESqTHerm >	TSqTHerm
typedef Mat< M, N, E, M, 1 >	TPacked
typedef Mat< M-1, N, E, M-1, 1 >	TDropRow
typedef Mat< M, N-1, E, M, 1 >	TDropCol
typedef Mat< M-1, N-1, E, M-1, 1 >	TDropRowCol
typedef Mat< M+1, N, E, M+1, 1 >	TAppendRow
typedef Mat< M, N+1, E, M, 1 >	TAppendCol
typedef Mat< M+1, N+1, E, M+1, 1 >	TAppendRowCol
typedef EScalar	Scalar
typedef EULessScalar	ULessScalar
typedef ENumber	Number
typedef EStdNumber	StdNumber
typedef EPrecision	Precision
typedef EScalarNormSq	ScalarNormSq
typedef THerm	TransposeType

Public Member Functions
ScalarNormSq	scalarNormSqr () const
	Scalar norm square is the sum of squares of all the scalars that comprise the value of this Mat. More...
TSqrt	sqrt () const
	Elementwise square root; that is, the return value has the same dimensions as this Mat but with each element replaced by whatever it thinks its square root is. More...
TAbs	abs () const
	Elementwise absolute value; that is, the return value has the same dimensions as this Mat but with each element replaced by whatever it thinks its absolute value is. More...
TStandard	standardize () const
	Mat ()
	Default construction initializes to NaN when debugging but is left uninitialized otherwise to ensure that there is no overhead. More...
	Mat (const Mat &src)
	Copy constructor copies only the elements that are present and does not touch any unused memory space between them if they are not packed. More...
Mat &	operator= (const Mat &src)
	Copy assignment copies only the elements that are present and does not touch any unused memory space between them if they are not packed. More...
	Mat (const SymMat< M, ELT > &src)
	Explicit construction of a Mat from a SymMat (symmetric/Hermitian matrix). More...
template<int CSS, int RSS>
	Mat (const Mat< M, N, E, CSS, RSS > &src)
	This provides an implicit conversion from a Mat of the same dimensions and element type but with different element spacing. More...
template<int CSS, int RSS>
	Mat (const Mat< M, N, ENeg, CSS, RSS > &src)
	This provides an implicit conversion from a Mat of the same dimensions and negated element type, possibly with different element spacing. More...
template<class EE , int CSS, int RSS>
	Mat (const Mat< M, N, EE, CSS, RSS > &mm)
	Explicit construction of a Mat from a source Mat of the same dimensions and an assignment-compatible element type, with any element spacing allowed. More...
	Mat (const E &e)
	Explicit construction from a single element e of this Mat's element type E sets all the main diagonal elements to e but sets the rest of the elements to zero. More...
	Mat (const ENeg &e)
	Explicit construction from a single element e whose type is negator<E> (abbreviated ENeg here) where E is this Mat's element type sets all the main diagonal elements to e but sets the rest of the elements to zero. More...
	Mat (int i)
	Explicit construction from an int value means we convert the int into an object of this Mat's element type E, and then apply the single-element constructor above which sets the Mat to zero except for its main diagonal elements which will all be set to the given value. More...
	Mat (const E &e0, const E &e1)
	Mat (const E &e0, const E &e1, const E &e2)
	Mat (const E &e0, const E &e1, const E &e2, const E &e3)
	Mat (const E &e0, const E &e1, const E &e2, const E &e3, const E &e4)
	Mat (const E &e0, const E &e1, const E &e2, const E &e3, const E &e4, const E &e5)
	Mat (const E &e0, const E &e1, const E &e2, const E &e3, const E &e4, const E &e5, const E &e6)
	Mat (const E &e0, const E &e1, const E &e2, const E &e3, const E &e4, const E &e5, const E &e6, const E &e7)
	Mat (const E &e0, const E &e1, const E &e2, const E &e3, const E &e4, const E &e5, const E &e6, const E &e7, const E &e8)
	Mat (const E &e0, const E &e1, const E &e2, const E &e3, const E &e4, const E &e5, const E &e6, const E &e7, const E &e8, const E &e9)
	Mat (const E &e0, const E &e1, const E &e2, const E &e3, const E &e4, const E &e5, const E &e6, const E &e7, const E &e8, const E &e9, const E &e10)
	Mat (const E &e0, const E &e1, const E &e2, const E &e3, const E &e4, const E &e5, const E &e6, const E &e7, const E &e8, const E &e9, const E &e10, const E &e11)
	Mat (const E &e0, const E &e1, const E &e2, const E &e3, const E &e4, const E &e5, const E &e6, const E &e7, const E &e8, const E &e9, const E &e10, const E &e11, const E &e12)
	Mat (const E &e0, const E &e1, const E &e2, const E &e3, const E &e4, const E &e5, const E &e6, const E &e7, const E &e8, const E &e9, const E &e10, const E &e11, const E &e12, const E &e13)
	Mat (const E &e0, const E &e1, const E &e2, const E &e3, const E &e4, const E &e5, const E &e6, const E &e7, const E &e8, const E &e9, const E &e10, const E &e11, const E &e12, const E &e13, const E &e14)
	Mat (const E &e0, const E &e1, const E &e2, const E &e3, const E &e4, const E &e5, const E &e6, const E &e7, const E &e8, const E &e9, const E &e10, const E &e11, const E &e12, const E &e13, const E &e14, const E &e15)
	Mat (const TRow &r0)
	Mat (const TRow &r0, const TRow &r1)
	Mat (const TRow &r0, const TRow &r1, const TRow &r2)
	Mat (const TRow &r0, const TRow &r1, const TRow &r2, const TRow &r3)
	Mat (const TRow &r0, const TRow &r1, const TRow &r2, const TRow &r3, const TRow &r4)
	Mat (const TRow &r0, const TRow &r1, const TRow &r2, const TRow &r3, const TRow &r4, const TRow &r5)
template<class EE , int SS>
	Mat (const Row< N, EE, SS > &r0)
template<class EE , int SS>
	Mat (const Row< N, EE, SS > &r0, const Row< N, EE, SS > &r1)
template<class EE , int SS>
	Mat (const Row< N, EE, SS > &r0, const Row< N, EE, SS > &r1, const Row< N, EE, SS > &r2)
template<class EE , int SS>
	Mat (const Row< N, EE, SS > &r0, const Row< N, EE, SS > &r1, const Row< N, EE, SS > &r2, const Row< N, EE, SS > &r3)
template<class EE , int SS>
	Mat (const Row< N, EE, SS > &r0, const Row< N, EE, SS > &r1, const Row< N, EE, SS > &r2, const Row< N, EE, SS > &r3, const Row< N, EE, SS > &r4)
template<class EE , int SS>
	Mat (const Row< N, EE, SS > &r0, const Row< N, EE, SS > &r1, const Row< N, EE, SS > &r2, const Row< N, EE, SS > &r3, const Row< N, EE, SS > &r4, const Row< N, EE, SS > &r5)
	Mat (const TCol &r0)
	Mat (const TCol &r0, const TCol &r1)
	Mat (const TCol &r0, const TCol &r1, const TCol &r2)
	Mat (const TCol &r0, const TCol &r1, const TCol &r2, const TCol &r3)
	Mat (const TCol &r0, const TCol &r1, const TCol &r2, const TCol &r3, const TCol &r4)
	Mat (const TCol &r0, const TCol &r1, const TCol &r2, const TCol &r3, const TCol &r4, const TCol &r5)
template<class EE , int SS>
	Mat (const Vec< M, EE, SS > &r0)
template<class EE , int SS>
	Mat (const Vec< M, EE, SS > &r0, const Vec< M, EE, SS > &r1)
template<class EE , int SS>
	Mat (const Vec< M, EE, SS > &r0, const Vec< M, EE, SS > &r1, const Vec< M, EE, SS > &r2)
template<class EE , int SS>
	Mat (const Vec< M, EE, SS > &r0, const Vec< M, EE, SS > &r1, const Vec< M, EE, SS > &r2, const Vec< M, EE, SS > &r3)
template<class EE , int SS>
	Mat (const Vec< M, EE, SS > &r0, const Vec< M, EE, SS > &r1, const Vec< M, EE, SS > &r2, const Vec< M, EE, SS > &r3, const Vec< M, EE, SS > &r4)
template<class EE , int SS>
	Mat (const Vec< M, EE, SS > &r0, const Vec< M, EE, SS > &r1, const Vec< M, EE, SS > &r2, const Vec< M, EE, SS > &r3, const Vec< M, EE, SS > &r4, const Vec< M, EE, SS > &r5)
template<class EE >
	Mat (const EE *p)
template<class EE , int CSS, int RSS>
Mat &	operator= (const Mat< M, N, EE, CSS, RSS > &mm)
template<class EE >
Mat &	operator= (const EE *p)
template<class EE , int CSS, int RSS>
Mat &	operator+= (const Mat< M, N, EE, CSS, RSS > &mm)
template<class EE , int CSS, int RSS>
Mat &	operator+= (const Mat< M, N, negator< EE >, CSS, RSS > &mm)
template<class EE , int CSS, int RSS>
Mat &	operator-= (const Mat< M, N, EE, CSS, RSS > &mm)
template<class EE , int CSS, int RSS>
Mat &	operator-= (const Mat< M, N, negator< EE >, CSS, RSS > &mm)
template<class EE , int CSS, int RSS>
Mat &	operator*= (const Mat< N, N, EE, CSS, RSS > &mm)
template<class E2 , int CS2, int RS2>
Result< Mat< M, N, E2, CS2, RS2 > >::Add	conformingAdd (const Mat< M, N, E2, CS2, RS2 > &r) const
template<class E2 , int CS2, int RS2>
Result< Mat< M, N, E2, CS2, RS2 > >::Sub	conformingSubtract (const Mat< M, N, E2, CS2, RS2 > &r) const
template<class E2 , int CS2, int RS2>
Mat< M, N, E2, CS2, RS2 > ::template Result< Mat >::Sub	conformingSubtractFromLeft (const Mat< M, N, E2, CS2, RS2 > &l) const
template<class E2 , int CS2, int RS2>
EltResult< E2 >::Mul	elementwiseMultiply (const Mat< M, N, E2, CS2, RS2 > &r) const
template<class E2 , int CS2, int RS2>
EltResult< E2 >::Dvd	elementwiseDivide (const Mat< M, N, E2, CS2, RS2 > &r) const
template<class E2 , int RS2>
Result< SymMat< M, E2, RS2 > >::Add	conformingAdd (const SymMat< M, E2, RS2 > &sy) const
template<class E2 , int RS2>
Result< SymMat< M, E2, RS2 > >::Sub	conformingSubtract (const SymMat< M, E2, RS2 > &sy) const
template<class E2 , int RS2>
SymMat< M, E2, RS2 >::template Result< Mat >::Sub	conformingSubtractFromLeft (const SymMat< M, E2, RS2 > &sy) const
template<int N2, class E2 , int CS2, int RS2>
Result< Mat< N, N2, E2, CS2, RS2 > >::Mul	conformingMultiply (const Mat< N, N2, E2, CS2, RS2 > &m) const
template<int M2, class E2 , int CS2, int RS2>
Mat< M2, M, E2, CS2, RS2 > ::template Result< Mat >::Mul	conformingMultiplyFromLeft (const Mat< M2, M, E2, CS2, RS2 > &m) const
template<int M2, class E2 , int CS2, int RS2>
Result< Mat< M2, N, E2, CS2, RS2 > >::Dvd	conformingDivide (const Mat< M2, N, E2, CS2, RS2 > &m) const
template<int M2, class E2 , int CS2, int RS2>
Mat< M2, N, E2, CS2, RS2 > ::template Result< Mat >::Dvd	conformingDivideFromLeft (const Mat< M2, N, E2, CS2, RS2 > &m) const
const TRow &	operator[] (int i) const
TRow &	operator[] (int i)
const TCol &	operator() (int j) const
TCol &	operator() (int j)
const E &	operator() (int i, int j) const
E &	operator() (int i, int j)
ScalarNormSq	normSqr () const
CNT< ScalarNormSq >::TSqrt	norm () const
TNormalize	normalize () const
TInvert	invert () const
const Mat &	operator+ () const
const TNeg &	operator- () const
TNeg &	operator- ()
const THerm &	operator~ () const
THerm &	operator~ ()
const TNeg &	negate () const
TNeg &	updNegate ()
const THerm &	transpose () const
THerm &	updTranspose ()
const TPosTrans &	positionalTranspose () const
TPosTrans &	updPositionalTranspose ()
const TReal &	real () const
TReal &	real ()
const TImag &	imag () const
TImag &	imag ()
const TWithoutNegator &	castAwayNegatorIfAny () const
TWithoutNegator &	updCastAwayNegatorIfAny ()
const TRow &	row (int i) const
TRow &	row (int i)
const TCol &	col (int j) const
TCol &	col (int j)
const E &	elt (int i, int j) const
E &	elt (int i, int j)
const TDiag &	diag () const
	Select main diagonal (of largest leading square if rectangular) and return it as a read-only view (as a Vec) of the diagonal elements of this Mat. More...
TDiag &	updDiag ()
	Select main diagonal (of largest leading square if rectangular) and return it as a writable view (as a Vec) of the diagonal elements of this Mat. More...
TDiag &	diag ()
	This non-const version of diag() is an alternate name for updDiag() available for historical reasons. More...
EStandard	trace () const
template<class EE >
Mat< M, N, typename CNT< E > ::template Result< EE >::Mul >	scalarMultiply (const EE &e) const
template<class EE >
Mat< M, N, typename CNT< EE > ::template Result< E >::Mul >	scalarMultiplyFromLeft (const EE &e) const
template<class EE >
Mat< M, N, typename CNT< E > ::template Result< EE >::Dvd >	scalarDivide (const EE &e) const
template<class EE >
Mat< M, N, typename CNT< EE > ::template Result< E >::Dvd >	scalarDivideFromLeft (const EE &e) const
template<class EE >
Mat< M, N, typename CNT< E > ::template Result< EE >::Add >	scalarAdd (const EE &e) const
template<class EE >
Mat< M, N, typename CNT< E > ::template Result< EE >::Sub >	scalarSubtract (const EE &e) const
template<class EE >
Mat< M, N, typename CNT< EE > ::template Result< E >::Sub >	scalarSubtractFromLeft (const EE &e) const
template<class EE >
Mat &	operator= (const EE &e)
template<class EE >
Mat &	operator+= (const EE &e)
template<class EE >
Mat &	operator-= (const EE &e)
template<class EE >
Mat &	operator*= (const EE &e)
template<class EE >
Mat &	operator/= (const EE &e)
template<class EE >
Mat &	scalarEq (const EE &ee)
template<class EE >
Mat &	scalarPlusEq (const EE &ee)
template<class EE >
Mat &	scalarMinusEq (const EE &ee)
template<class EE >
Mat &	scalarMinusEqFromLeft (const EE &ee)
template<class EE >
Mat &	scalarTimesEq (const EE &ee)
template<class EE >
Mat &	scalarTimesEqFromLeft (const EE &ee)
template<class EE >
Mat &	scalarDivideEq (const EE &ee)
template<class EE >
Mat &	scalarDivideEqFromLeft (const EE &ee)
void	setToNaN ()
void	setToZero ()
template<int MM, int NN>
const SubMat< MM, NN >::Type &	getSubMat (int i, int j) const
template<int MM, int NN>
SubMat< MM, NN >::Type &	updSubMat (int i, int j)
template<int MM, int NN>
void	setSubMat (int i, int j, const typename SubMat< MM, NN >::Type &value)
TDropRow	dropRow (int i) const
	Return a matrix one row smaller than this one by dropping row i. More...
TDropCol	dropCol (int j) const
	Return a matrix one column smaller than this one by dropping column j. More...
TDropRowCol	dropRowCol (int i, int j) const
	Return a matrix one row and one column smaller than this one by dropping row i and column j. More...
template<class EE , int SS>
TAppendRow	appendRow (const Row< N, EE, SS > &row) const
	Return a matrix one row larger than this one by adding a row to the end. More...
template<class EE , int SS>
TAppendCol	appendCol (const Vec< M, EE, SS > &col) const
	Return a matrix one column larger than this one by adding a column to the end. More...
template<class ER , int SR, class EC , int SC>
TAppendRowCol	appendRowCol (const Row< N+1, ER, SR > &row, const Vec< M+1, EC, SC > &col) const
	Return a matrix one row and one column larger than this one by adding a row to the bottom and a column to the right. More...
template<class EE , int SS>
TAppendRow	insertRow (int i, const Row< N, EE, SS > &row) const
	Return a matrix one row larger than this one by inserting a row *before* row i. More...
template<class EE , int SS>
TAppendCol	insertCol (int j, const Vec< M, EE, SS > &col) const
	Return a matrix one column larger than this one by inserting a column *before* column j. More...
template<class ER , int SR, class EC , int SC>
TAppendRowCol	insertRowCol (int i, int j, const Row< N+1, ER, SR > &row, const Vec< M+1, EC, SC > &col) const
	Return a matrix one row and one column larger than this one by inserting a row *before* row i and a column *before* column j. More...
bool	isNaN () const
	Return true if any element of this Mat contains a NaN anywhere. More...
bool	isInf () const
	Return true if any element of this Mat contains a +Inf or -Inf somewhere but no element contains a NaN anywhere. More...
bool	isFinite () const
	Return true if no element contains an Infinity or a NaN. More...
template<class E2 , int CS2, int RS2>
bool	isNumericallyEqual (const Mat< M, N, E2, CS2, RS2 > &m, double tol) const
	Test whether this matrix is numerically equal to some other matrix with the same shape, using a specified tolerance. More...
template<class E2 , int CS2, int RS2>
bool	isNumericallyEqual (const Mat< M, N, E2, CS2, RS2 > &m) const
	Test whether this matrix is numerically equal to some other matrix with the same shape, using a default tolerance which is the looser of the default tolerances of the two objects being compared. More...
bool	isNumericallyEqual (const ELT &e, double tol=getDefaultTolerance()) const
	Test whether this is numerically a "scalar" matrix, meaning that it is a diagonal matrix in which each diagonal element is numerically equal to the same scalar, using either a specified tolerance or the matrix's default tolerance (which is always the same or looser than the default tolerance for one of its elements). More...
bool	isNumericallySymmetric (double tol=getDefaultTolerance()) const
	A Matrix is symmetric (actually Hermitian) if it is square and each element (i,j) is the Hermitian transpose of element (j,i). More...
bool	isExactlySymmetric () const
	A Matrix is symmetric (actually Hermitian) if it is square and each element (i,j) is the Hermitian (conjugate) transpose of element (j,i). More...
TRow	colSum () const
	Returns a row vector (Row) containing the column sums of this matrix. More...
TRow	sum () const
	This is an alternate name for colSum(); behaves like the Matlab function of the same name. More...
TCol	rowSum () const
	Returns a column vector (Vec) containing the row sums of this matrix. More...
std::string	toString () const
	toString() returns a string representation of the Mat. More...
const ELT &	get (int i, int j) const
	Variant of indexing operator that's scripting friendly to get entry (i, j) More...
void	set (int i, int j, const ELT &value)
	Variant of indexing operator that's scripting friendly to set entry (i, j) More...

Static Public Member Functions
static int	size ()
	Return the total number of elements M*N contained in this Mat. More...
static int	nrow ()
	Return the number of rows in this Mat, echoing the value supplied for the template paramter M. More...
static int	ncol ()
	Return the number of columns in this Mat, echoing the value supplied for the template paramter N. More...
static const Mat &	getAs (const ELT *p)
static Mat &	updAs (ELT *p)
static Mat< M, N, ELT, M, 1 >	getNaN ()
static double	getDefaultTolerance ()
	For approximate comparisions, the default tolerance to use for a matrix is its shortest dimension times its elements' default tolerance. More...

Related Functions
(Note that these are not member functions.)
template<int M, int N, class E , int CS, int RS>
void	writeUnformatted (std::ostream &o, const Mat< M, N, E, CS, RS > &v)
	Specialize for Mat<M,N,E,CS,RS> delegating to Row<N,E,RS> with newlines separating the rows, but no final newline. More...
template<int M, int N, class E , int CS, int RS>
bool	readUnformatted (std::istream &in, Mat< M, N, E, CS, RS > &v)
	Specialize for Mat<M,N,E,CS,RS> delegating to Row<N,E,RS>. More...

Detailed Description

template<int M, int N, class ELT, int CS, int RS>
class SimTK::Mat< M, N, ELT, CS, RS >

This class represents a small matrix whose size is known at compile time, containing elements of any Composite Numerical Type (CNT) and engineered to have no runtime overhead whatsoever.

Memory layout defaults to packed, column-ordered storage but can be specified to have any regular row and column spacing. A Mat object is itself a Composite Numerical Type and can thus be the element type for other matrix and vector types. Some common use cases are provided below.

Template Parameters

M	The number of rows in this matrix (no default).
N	The number of columns in this matrix (no default).
ELT	The element type; default is Real.
CS	Column spacing in memory as a multiple of element size (default M).
RS	Row spacing in memory as a multiple of element size (default 1).

Construction

A 3x3 identity matrix can be constructed in the following ways:

Mat<3,3,Real>(1,0,0, 0,1,0, 0,0,1);          //row-major
Mat33(1,0,0,0,1,0,0,0,1);
Mat33(Vec3(1,0,0),Vec3(0,1,0),Vec3(0,0,1));  //column-by-column
Mat33(1);

Note that the default element type is Real, and that Mat33 is a typedef for Mat<3,3>; analogous typedefs exist for matrices of up to 9x9 elements.

Manipulation

Standard arithmetic operators can be used, as well as methods like trace() and transpose(). Here are some usage examples, each of which prints a 2x2 identity matrix:

Mat23 myMat(2,1,0, 3,0,1);
std::cout << myMat.getSubMat<2,2>(0,1) << std::endl;
std::cout << myMat.dropCol(0) << std::endl;
std::cout << Mat12(1,0).appendRow(~Vec2(0,1)) << std::endl;
std::cout << Mat21(0,1).insertCol(0,Vec2(1,0)) << std::endl;

Conversion

It may be necessary to convert between a Mat and a Matrix (to interface with FactorQTZ, for instance). In the example below, we print a Mat33 created from a 3x3 Matrix:

Matrix myMatrix(3,3);
for (int i=0; i<9; ++i) myMatrix[i/3][i%3] = i+1;
Mat33 myMat33 = Mat33(&myMatrix[0][0]).transpose();
std::cout << myMat33 << std::endl;

Converting from a Mat33 to a Matrix is straightforward:

Mat33 myMat33(1,2,3, 4,5,6, 7,8,9);
std::cout << Matrix(myMat33) << std::endl;

See also

Matrix_ for handling of large or variable-sized matrices.

SymMat, Vec, Row

Member Typedef Documentation

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M,N,E,CS,RS> SimTK::Mat< M, N, ELT, CS, RS >::T

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M,N,ENeg,CS,RS> SimTK::Mat< M, N, ELT, CS, RS >::TNeg

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M,N,EWithoutNegator,CS,RS> SimTK::Mat< M, N, ELT, CS, RS >::TWithoutNegator

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M,N,EReal,CS*CNT<E>::RealStrideFactor,RS*CNT<E>::RealStrideFactor> SimTK::Mat< M, N, ELT, CS, RS >::TReal

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M,N,EImag,CS*CNT<E>::RealStrideFactor,RS*CNT<E>::RealStrideFactor> SimTK::Mat< M, N, ELT, CS, RS >::TImag

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M,N,EComplex,CS,RS> SimTK::Mat< M, N, ELT, CS, RS >::TComplex

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<N,M,EHerm,RS,CS> SimTK::Mat< M, N, ELT, CS, RS >::THerm

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<N,M,E,RS,CS> SimTK::Mat< M, N, ELT, CS, RS >::TPosTrans

template<int M, int N, class ELT, int CS, int RS>

typedef E SimTK::Mat< M, N, ELT, CS, RS >::TElement

template<int M, int N, class ELT, int CS, int RS>

typedef Row<N,E,CS> SimTK::Mat< M, N, ELT, CS, RS >::TRow

template<int M, int N, class ELT, int CS, int RS>

typedef Vec<M,E,RS> SimTK::Mat< M, N, ELT, CS, RS >::TCol

template<int M, int N, class ELT, int CS, int RS>

typedef Vec<MinDim,E,RS+CS> SimTK::Mat< M, N, ELT, CS, RS >::TDiag

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M,N,ESqrt,M,1> SimTK::Mat< M, N, ELT, CS, RS >::TSqrt

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M,N,EAbs,M,1> SimTK::Mat< M, N, ELT, CS, RS >::TAbs

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M,N,EStandard,M,1> SimTK::Mat< M, N, ELT, CS, RS >::TStandard

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<N,M,EInvert,N,1> SimTK::Mat< M, N, ELT, CS, RS >::TInvert

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M,N,ENormalize,M,1> SimTK::Mat< M, N, ELT, CS, RS >::TNormalize

template<int M, int N, class ELT, int CS, int RS>

typedef SymMat<N,ESqHermT> SimTK::Mat< M, N, ELT, CS, RS >::TSqHermT

template<int M, int N, class ELT, int CS, int RS>

typedef SymMat<M,ESqTHerm> SimTK::Mat< M, N, ELT, CS, RS >::TSqTHerm

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M,N,E,M,1> SimTK::Mat< M, N, ELT, CS, RS >::TPacked

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M-1,N,E,M-1,1> SimTK::Mat< M, N, ELT, CS, RS >::TDropRow

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M,N-1,E,M,1> SimTK::Mat< M, N, ELT, CS, RS >::TDropCol

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M-1,N-1,E,M-1,1> SimTK::Mat< M, N, ELT, CS, RS >::TDropRowCol

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M+1,N,E,M+1,1> SimTK::Mat< M, N, ELT, CS, RS >::TAppendRow

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M,N+1,E,M,1> SimTK::Mat< M, N, ELT, CS, RS >::TAppendCol

template<int M, int N, class ELT, int CS, int RS>

typedef Mat<M+1,N+1,E,M+1,1> SimTK::Mat< M, N, ELT, CS, RS >::TAppendRowCol

template<int M, int N, class ELT, int CS, int RS>

typedef EScalar SimTK::Mat< M, N, ELT, CS, RS >::Scalar

template<int M, int N, class ELT, int CS, int RS>

typedef EULessScalar SimTK::Mat< M, N, ELT, CS, RS >::ULessScalar

template<int M, int N, class ELT, int CS, int RS>

typedef ENumber SimTK::Mat< M, N, ELT, CS, RS >::Number

template<int M, int N, class ELT, int CS, int RS>

typedef EStdNumber SimTK::Mat< M, N, ELT, CS, RS >::StdNumber

template<int M, int N, class ELT, int CS, int RS>

typedef EPrecision SimTK::Mat< M, N, ELT, CS, RS >::Precision

template<int M, int N, class ELT, int CS, int RS>

typedef EScalarNormSq SimTK::Mat< M, N, ELT, CS, RS >::ScalarNormSq

template<int M, int N, class ELT, int CS, int RS>

typedef THerm SimTK::Mat< M, N, ELT, CS, RS >::TransposeType

Constructor & Destructor Documentation

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( )

inline

Default construction initializes to NaN when debugging but is left uninitialized otherwise to ensure that there is no overhead.

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Mat< M, N, ELT, CS, RS > &  src )

inline

Copy constructor copies only the elements that are present and does not touch any unused memory space between them if they are not packed.

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const SymMat< M, ELT > &  src )

inlineexplicit

Explicit construction of a Mat from a SymMat (symmetric/Hermitian matrix).

Note that a SymMat is a Hermitian matrix when the elements are complex, so in that case the resulting Mat's upper triangle values are complex conjugates of the lower triangle ones.

template<int M, int N, class ELT, int CS, int RS>

template<int CSS, int RSS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Mat< M, N, E, CSS, RSS > &  src )

inline

This provides an implicit conversion from a Mat of the same dimensions and element type but with different element spacing.

Template Parameters

CSS	Column spacing of the source Mat.
RSS	Row spacing of the source Mat.

template<int M, int N, class ELT, int CS, int RS>

template<int CSS, int RSS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Mat< M, N, ENeg, CSS, RSS > &  src )

inline

This provides an implicit conversion from a Mat of the same dimensions and negated element type, possibly with different element spacing.

Template Parameters

CSS	Column spacing of the source Mat.
RSS	Row spacing of the source Mat.

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int CSS, int RSS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Mat< M, N, EE, CSS, RSS > &  mm )

inlineexplicit

Explicit construction of a Mat from a source Mat of the same dimensions and an assignment-compatible element type, with any element spacing allowed.

Template Parameters

EE	The element type of the source Mat; must be assignment compatible with element type E of this Mat.
CSS	Column spacing of the source Mat.
RSS	Row spacing of the source Mat.

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e )

inlineexplicit

Explicit construction from a single element e of this Mat's element type E sets all the main diagonal elements to e but sets the rest of the elements to zero.

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const ENeg &  e )

inlineexplicit

Explicit construction from a single element e whose type is negator<E> (abbreviated ENeg here) where E is this Mat's element type sets all the main diagonal elements to e but sets the rest of the elements to zero.

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( int  i )

inlineexplicit

Explicit construction from an int value means we convert the int into an object of this Mat's element type E, and then apply the single-element constructor above which sets the Mat to zero except for its main diagonal elements which will all be set to the given value.

To convert an int to an element, we first turn it into the appropriate-precision floating point number, and then call E's constructor that takes a single scalar.

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e0, const E &  e1  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e0, const E &  e1, const E &  e2  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e0, const E &  e1, const E &  e2, const E &  e3  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e0, const E &  e1, const E &  e2, const E &  e3, const E &  e4  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e0, const E &  e1, const E &  e2, const E &  e3, const E &  e4, const E &  e5  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e0, const E &  e1, const E &  e2, const E &  e3, const E &  e4, const E &  e5, const E &  e6  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e0, const E &  e1, const E &  e2, const E &  e3, const E &  e4, const E &  e5, const E &  e6, const E &  e7  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e0, const E &  e1, const E &  e2, const E &  e3, const E &  e4, const E &  e5, const E &  e6, const E &  e7, const E &  e8  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e0, const E &  e1, const E &  e2, const E &  e3, const E &  e4, const E &  e5, const E &  e6, const E &  e7, const E &  e8, const E &  e9  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e0, const E &  e1, const E &  e2, const E &  e3, const E &  e4, const E &  e5, const E &  e6, const E &  e7, const E &  e8, const E &  e9, const E &  e10  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e0, const E &  e1, const E &  e2, const E &  e3, const E &  e4, const E &  e5, const E &  e6, const E &  e7, const E &  e8, const E &  e9, const E &  e10, const E &  e11  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e0, const E &  e1, const E &  e2, const E &  e3, const E &  e4, const E &  e5, const E &  e6, const E &  e7, const E &  e8, const E &  e9, const E &  e10, const E &  e11, const E &  e12  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e0, const E &  e1, const E &  e2, const E &  e3, const E &  e4, const E &  e5, const E &  e6, const E &  e7, const E &  e8, const E &  e9, const E &  e10, const E &  e11, const E &  e12, const E &  e13  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e0, const E &  e1, const E &  e2, const E &  e3, const E &  e4, const E &  e5, const E &  e6, const E &  e7, const E &  e8, const E &  e9, const E &  e10, const E &  e11, const E &  e12, const E &  e13, const E &  e14  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const E &  e0, const E &  e1, const E &  e2, const E &  e3, const E &  e4, const E &  e5, const E &  e6, const E &  e7, const E &  e8, const E &  e9, const E &  e10, const E &  e11, const E &  e12, const E &  e13, const E &  e14, const E &  e15  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const TRow &  r0 )

inlineexplicit

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const TRow &  r0, const TRow &  r1  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const TRow &  r0, const TRow &  r1, const TRow &  r2  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const TRow &  r0, const TRow &  r1, const TRow &  r2, const TRow &  r3  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const TRow &  r0, const TRow &  r1, const TRow &  r2, const TRow &  r3, const TRow &  r4  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const TRow &  r0, const TRow &  r1, const TRow &  r2, const TRow &  r3, const TRow &  r4, const TRow &  r5  )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Row< N, EE, SS > &  r0 )

inlineexplicit

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Row< N, EE, SS > &  r0, const Row< N, EE, SS > &  r1  )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Row< N, EE, SS > &  r0, const Row< N, EE, SS > &  r1, const Row< N, EE, SS > &  r2  )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Row< N, EE, SS > &  r0, const Row< N, EE, SS > &  r1, const Row< N, EE, SS > &  r2, const Row< N, EE, SS > &  r3  )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Row< N, EE, SS > &  r0, const Row< N, EE, SS > &  r1, const Row< N, EE, SS > &  r2, const Row< N, EE, SS > &  r3, const Row< N, EE, SS > &  r4  )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Row< N, EE, SS > &  r0, const Row< N, EE, SS > &  r1, const Row< N, EE, SS > &  r2, const Row< N, EE, SS > &  r3, const Row< N, EE, SS > &  r4, const Row< N, EE, SS > &  r5  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const TCol &  r0 )

inlineexplicit

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const TCol &  r0, const TCol &  r1  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const TCol &  r0, const TCol &  r1, const TCol &  r2  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const TCol &  r0, const TCol &  r1, const TCol &  r2, const TCol &  r3  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const TCol &  r0, const TCol &  r1, const TCol &  r2, const TCol &  r3, const TCol &  r4  )

inline

template<int M, int N, class ELT, int CS, int RS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const TCol &  r0, const TCol &  r1, const TCol &  r2, const TCol &  r3, const TCol &  r4, const TCol &  r5  )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Vec< M, EE, SS > &  r0 )

inlineexplicit

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Vec< M, EE, SS > &  r0, const Vec< M, EE, SS > &  r1  )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Vec< M, EE, SS > &  r0, const Vec< M, EE, SS > &  r1, const Vec< M, EE, SS > &  r2  )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Vec< M, EE, SS > &  r0, const Vec< M, EE, SS > &  r1, const Vec< M, EE, SS > &  r2, const Vec< M, EE, SS > &  r3  )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Vec< M, EE, SS > &  r0, const Vec< M, EE, SS > &  r1, const Vec< M, EE, SS > &  r2, const Vec< M, EE, SS > &  r3, const Vec< M, EE, SS > &  r4  )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const Vec< M, EE, SS > &  r0, const Vec< M, EE, SS > &  r1, const Vec< M, EE, SS > &  r2, const Vec< M, EE, SS > &  r3, const Vec< M, EE, SS > &  r4, const Vec< M, EE, SS > &  r5  )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

SimTK::Mat< M, N, ELT, CS, RS >::Mat ( const EE *  p )

inlineexplicit

Member Function Documentation

template<int M, int N, class ELT, int CS, int RS>

static int SimTK::Mat< M, N, ELT, CS, RS >::size ( )

inlinestatic

Return the total number of elements M*N contained in this Mat.

template<int M, int N, class ELT, int CS, int RS>

static int SimTK::Mat< M, N, ELT, CS, RS >::nrow ( )

inlinestatic

Return the number of rows in this Mat, echoing the value supplied for the template paramter M.

template<int M, int N, class ELT, int CS, int RS>

static int SimTK::Mat< M, N, ELT, CS, RS >::ncol ( )

inlinestatic

Return the number of columns in this Mat, echoing the value supplied for the template paramter N.

template<int M, int N, class ELT, int CS, int RS>

ScalarNormSq SimTK::Mat< M, N, ELT, CS, RS >::scalarNormSqr ( ) const

inline

Scalar norm square is the sum of squares of all the scalars that comprise the value of this Mat.

For Mat objects with composite element types, this is defined recursively as the sum of the scalar norm squares of all the elements, where the scalar norm square of a scalar is just that scalar squared.

template<int M, int N, class ELT, int CS, int RS>

TSqrt SimTK::Mat< M, N, ELT, CS, RS >::sqrt ( ) const

inline

Elementwise square root; that is, the return value has the same dimensions as this Mat but with each element replaced by whatever it thinks its square root is.

template<int M, int N, class ELT, int CS, int RS>

TAbs SimTK::Mat< M, N, ELT, CS, RS >::abs ( ) const

inline

Elementwise absolute value; that is, the return value has the same dimensions as this Mat but with each element replaced by whatever it thinks its absolute value is.

template<int M, int N, class ELT, int CS, int RS>

TStandard SimTK::Mat< M, N, ELT, CS, RS >::standardize ( ) const

inline

template<int M, int N, class ELT, int CS, int RS>

Mat& SimTK::Mat< M, N, ELT, CS, RS >::operator= ( const Mat< M, N, ELT, CS, RS > &  src )

inline

Copy assignment copies only the elements that are present and does not touch any unused memory space between them if they are not packed.

Works correctly even if source and destination are the same object.

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int CSS, int RSS>

Mat& SimTK::Mat< M, N, ELT, CS, RS >::operator= ( const Mat< M, N, EE, CSS, RSS > &  mm )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat& SimTK::Mat< M, N, ELT, CS, RS >::operator= ( const EE *  p )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int CSS, int RSS>

Mat& SimTK::Mat< M, N, ELT, CS, RS >::operator+= ( const Mat< M, N, EE, CSS, RSS > &  mm )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int CSS, int RSS>

Mat& SimTK::Mat< M, N, ELT, CS, RS >::operator+= ( const Mat< M, N, negator< EE >, CSS, RSS > &  mm )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int CSS, int RSS>

Mat& SimTK::Mat< M, N, ELT, CS, RS >::operator-= ( const Mat< M, N, EE, CSS, RSS > &  mm )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int CSS, int RSS>

Mat& SimTK::Mat< M, N, ELT, CS, RS >::operator-= ( const Mat< M, N, negator< EE >, CSS, RSS > &  mm )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int CSS, int RSS>

Mat& SimTK::Mat< M, N, ELT, CS, RS >::operator*= ( const Mat< N, N, EE, CSS, RSS > &  mm )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class E2 , int CS2, int RS2>

Result<Mat<M,N,E2,CS2,RS2> >::Add SimTK::Mat< M, N, ELT, CS, RS >::conformingAdd ( const Mat< M, N, E2, CS2, RS2 > &  r ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<class E2 , int CS2, int RS2>

Result<Mat<M,N,E2,CS2,RS2> >::Sub SimTK::Mat< M, N, ELT, CS, RS >::conformingSubtract ( const Mat< M, N, E2, CS2, RS2 > &  r ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<class E2 , int CS2, int RS2>

Mat<M,N,E2,CS2,RS2>::template Result<Mat>::Sub SimTK::Mat< M, N, ELT, CS, RS >::conformingSubtractFromLeft ( const Mat< M, N, E2, CS2, RS2 > &  l ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<class E2 , int CS2, int RS2>

EltResult<E2>::Mul SimTK::Mat< M, N, ELT, CS, RS >::elementwiseMultiply ( const Mat< M, N, E2, CS2, RS2 > &  r ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<class E2 , int CS2, int RS2>

EltResult<E2>::Dvd SimTK::Mat< M, N, ELT, CS, RS >::elementwiseDivide ( const Mat< M, N, E2, CS2, RS2 > &  r ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<class E2 , int RS2>

Result<SymMat<M,E2,RS2> >::Add SimTK::Mat< M, N, ELT, CS, RS >::conformingAdd ( const SymMat< M, E2, RS2 > &  sy ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<class E2 , int RS2>

Result<SymMat<M,E2,RS2> >::Sub SimTK::Mat< M, N, ELT, CS, RS >::conformingSubtract ( const SymMat< M, E2, RS2 > &  sy ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<class E2 , int RS2>

SymMat<M,E2,RS2>::template Result<Mat>::Sub SimTK::Mat< M, N, ELT, CS, RS >::conformingSubtractFromLeft ( const SymMat< M, E2, RS2 > &  sy ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<int N2, class E2 , int CS2, int RS2>

Result<Mat<N,N2,E2,CS2,RS2> >::Mul SimTK::Mat< M, N, ELT, CS, RS >::conformingMultiply ( const Mat< N, N2, E2, CS2, RS2 > &  m ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<int M2, class E2 , int CS2, int RS2>

Mat<M2,M,E2,CS2,RS2>::template Result<Mat>::Mul SimTK::Mat< M, N, ELT, CS, RS >::conformingMultiplyFromLeft ( const Mat< M2, M, E2, CS2, RS2 > &  m ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<int M2, class E2 , int CS2, int RS2>

Result<Mat<M2,N,E2,CS2,RS2> >::Dvd SimTK::Mat< M, N, ELT, CS, RS >::conformingDivide ( const Mat< M2, N, E2, CS2, RS2 > &  m ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<int M2, class E2 , int CS2, int RS2>

Mat<M2,N,E2,CS2,RS2>::template Result<Mat>::Dvd SimTK::Mat< M, N, ELT, CS, RS >::conformingDivideFromLeft ( const Mat< M2, N, E2, CS2, RS2 > &  m ) const

inline

template<int M, int N, class ELT, int CS, int RS>

const TRow& SimTK::Mat< M, N, ELT, CS, RS >::operator[] ( int  i ) const

inline

template<int M, int N, class ELT, int CS, int RS>

TRow& SimTK::Mat< M, N, ELT, CS, RS >::operator[] ( int  i )

inline

template<int M, int N, class ELT, int CS, int RS>

const TCol& SimTK::Mat< M, N, ELT, CS, RS >::operator() ( int  j ) const

inline

template<int M, int N, class ELT, int CS, int RS>

TCol& SimTK::Mat< M, N, ELT, CS, RS >::operator() ( int  j )

inline

template<int M, int N, class ELT, int CS, int RS>

const E& SimTK::Mat< M, N, ELT, CS, RS >::operator() ( int  i, int  j  ) const

inline

template<int M, int N, class ELT, int CS, int RS>

E& SimTK::Mat< M, N, ELT, CS, RS >::operator() ( int  i, int  j  )

inline

template<int M, int N, class ELT, int CS, int RS>

ScalarNormSq SimTK::Mat< M, N, ELT, CS, RS >::normSqr ( ) const

inline

template<int M, int N, class ELT, int CS, int RS>

CNT<ScalarNormSq>::TSqrt SimTK::Mat< M, N, ELT, CS, RS >::norm ( ) const

inline

template<int M, int N, class ELT, int CS, int RS>

TNormalize SimTK::Mat< M, N, ELT, CS, RS >::normalize ( ) const

inline

template<int M, int N, class ELT , int CS, int RS>

Mat< M, N, ELT, CS, RS >::TInvert SimTK::Mat< M, N, ELT, CS, RS >::invert ( ) const

inline

template<int M, int N, class ELT, int CS, int RS>

const Mat& SimTK::Mat< M, N, ELT, CS, RS >::operator+ ( ) const

inline

template<int M, int N, class ELT, int CS, int RS>

const TNeg& SimTK::Mat< M, N, ELT, CS, RS >::operator- ( ) const

inline

template<int M, int N, class ELT, int CS, int RS>

TNeg& SimTK::Mat< M, N, ELT, CS, RS >::operator- ( )

inline

template<int M, int N, class ELT, int CS, int RS>

const THerm& SimTK::Mat< M, N, ELT, CS, RS >::operator~ ( ) const

inline

template<int M, int N, class ELT, int CS, int RS>

THerm& SimTK::Mat< M, N, ELT, CS, RS >::operator~ ( )

inline

template<int M, int N, class ELT, int CS, int RS>

const TNeg& SimTK::Mat< M, N, ELT, CS, RS >::negate ( ) const

inline

template<int M, int N, class ELT, int CS, int RS>

TNeg& SimTK::Mat< M, N, ELT, CS, RS >::updNegate ( )

inline

template<int M, int N, class ELT, int CS, int RS>

const THerm& SimTK::Mat< M, N, ELT, CS, RS >::transpose ( ) const

inline

template<int M, int N, class ELT, int CS, int RS>

THerm& SimTK::Mat< M, N, ELT, CS, RS >::updTranspose ( )

inline

template<int M, int N, class ELT, int CS, int RS>

const TPosTrans& SimTK::Mat< M, N, ELT, CS, RS >::positionalTranspose ( ) const

inline

template<int M, int N, class ELT, int CS, int RS>

TPosTrans& SimTK::Mat< M, N, ELT, CS, RS >::updPositionalTranspose ( )

inline

template<int M, int N, class ELT, int CS, int RS>

const TReal& SimTK::Mat< M, N, ELT, CS, RS >::real ( ) const

inline

template<int M, int N, class ELT, int CS, int RS>

TReal& SimTK::Mat< M, N, ELT, CS, RS >::real ( )

inline

template<int M, int N, class ELT, int CS, int RS>

const TImag& SimTK::Mat< M, N, ELT, CS, RS >::imag ( ) const

inline

template<int M, int N, class ELT, int CS, int RS>

TImag& SimTK::Mat< M, N, ELT, CS, RS >::imag ( )

inline

template<int M, int N, class ELT, int CS, int RS>

const TWithoutNegator& SimTK::Mat< M, N, ELT, CS, RS >::castAwayNegatorIfAny ( ) const

inline

template<int M, int N, class ELT, int CS, int RS>

TWithoutNegator& SimTK::Mat< M, N, ELT, CS, RS >::updCastAwayNegatorIfAny ( )

inline

template<int M, int N, class ELT, int CS, int RS>

const TRow& SimTK::Mat< M, N, ELT, CS, RS >::row ( int  i ) const

inline

template<int M, int N, class ELT, int CS, int RS>

TRow& SimTK::Mat< M, N, ELT, CS, RS >::row ( int  i )

inline

template<int M, int N, class ELT, int CS, int RS>

const TCol& SimTK::Mat< M, N, ELT, CS, RS >::col ( int  j ) const

inline

template<int M, int N, class ELT, int CS, int RS>

TCol& SimTK::Mat< M, N, ELT, CS, RS >::col ( int  j )

inline

template<int M, int N, class ELT, int CS, int RS>

const E& SimTK::Mat< M, N, ELT, CS, RS >::elt ( int  i, int  j  ) const

inline

template<int M, int N, class ELT, int CS, int RS>

E& SimTK::Mat< M, N, ELT, CS, RS >::elt ( int  i, int  j  )

inline

template<int M, int N, class ELT, int CS, int RS>

const TDiag& SimTK::Mat< M, N, ELT, CS, RS >::diag ( ) const

inline

Select main diagonal (of largest leading square if rectangular) and return it as a read-only view (as a Vec) of the diagonal elements of this Mat.

template<int M, int N, class ELT, int CS, int RS>

TDiag& SimTK::Mat< M, N, ELT, CS, RS >::updDiag ( )

inline

Select main diagonal (of largest leading square if rectangular) and return it as a writable view (as a Vec) of the diagonal elements of this Mat.

template<int M, int N, class ELT, int CS, int RS>

TDiag& SimTK::Mat< M, N, ELT, CS, RS >::diag ( )

inline

This non-const version of diag() is an alternate name for updDiag() available for historical reasons.

template<int M, int N, class ELT, int CS, int RS>

EStandard SimTK::Mat< M, N, ELT, CS, RS >::trace ( ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat<M,N, typename CNT<E>::template Result<EE>::Mul> SimTK::Mat< M, N, ELT, CS, RS >::scalarMultiply ( const EE &  e ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat<M,N, typename CNT<EE>::template Result<E>::Mul> SimTK::Mat< M, N, ELT, CS, RS >::scalarMultiplyFromLeft ( const EE &  e ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat<M,N, typename CNT<E>::template Result<EE>::Dvd> SimTK::Mat< M, N, ELT, CS, RS >::scalarDivide ( const EE &  e ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat<M,N, typename CNT<EE>::template Result<E>::Dvd> SimTK::Mat< M, N, ELT, CS, RS >::scalarDivideFromLeft ( const EE &  e ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat<M,N, typename CNT<E>::template Result<EE>::Add> SimTK::Mat< M, N, ELT, CS, RS >::scalarAdd ( const EE &  e ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat<M,N, typename CNT<E>::template Result<EE>::Sub> SimTK::Mat< M, N, ELT, CS, RS >::scalarSubtract ( const EE &  e ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat<M,N, typename CNT<EE>::template Result<E>::Sub> SimTK::Mat< M, N, ELT, CS, RS >::scalarSubtractFromLeft ( const EE &  e ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat& SimTK::Mat< M, N, ELT, CS, RS >::operator= ( const EE &  e )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat& SimTK::Mat< M, N, ELT, CS, RS >::operator+= ( const EE &  e )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat& SimTK::Mat< M, N, ELT, CS, RS >::operator-= ( const EE &  e )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat& SimTK::Mat< M, N, ELT, CS, RS >::operator*= ( const EE &  e )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat& SimTK::Mat< M, N, ELT, CS, RS >::operator/= ( const EE &  e )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat& SimTK::Mat< M, N, ELT, CS, RS >::scalarEq ( const EE &  ee )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat& SimTK::Mat< M, N, ELT, CS, RS >::scalarPlusEq ( const EE &  ee )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat& SimTK::Mat< M, N, ELT, CS, RS >::scalarMinusEq ( const EE &  ee )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat& SimTK::Mat< M, N, ELT, CS, RS >::scalarMinusEqFromLeft ( const EE &  ee )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat& SimTK::Mat< M, N, ELT, CS, RS >::scalarTimesEq ( const EE &  ee )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat& SimTK::Mat< M, N, ELT, CS, RS >::scalarTimesEqFromLeft ( const EE &  ee )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat& SimTK::Mat< M, N, ELT, CS, RS >::scalarDivideEq ( const EE &  ee )

inline

template<int M, int N, class ELT, int CS, int RS>

template<class EE >

Mat& SimTK::Mat< M, N, ELT, CS, RS >::scalarDivideEqFromLeft ( const EE &  ee )

inline

template<int M, int N, class ELT, int CS, int RS>

void SimTK::Mat< M, N, ELT, CS, RS >::setToNaN ( )

inline

template<int M, int N, class ELT, int CS, int RS>

void SimTK::Mat< M, N, ELT, CS, RS >::setToZero ( )

inline

template<int M, int N, class ELT, int CS, int RS>

template<int MM, int NN>

const SubMat<MM,NN>::Type& SimTK::Mat< M, N, ELT, CS, RS >::getSubMat ( int  i, int  j  ) const

inline

template<int M, int N, class ELT, int CS, int RS>

template<int MM, int NN>

SubMat<MM,NN>::Type& SimTK::Mat< M, N, ELT, CS, RS >::updSubMat ( int  i, int  j  )

inline

template<int M, int N, class ELT, int CS, int RS>

template<int MM, int NN>

void SimTK::Mat< M, N, ELT, CS, RS >::setSubMat ( int  i, int  j, const typename SubMat< MM, NN >::Type &  value  )

inline

template<int M, int N, class ELT, int CS, int RS>

TDropRow SimTK::Mat< M, N, ELT, CS, RS >::dropRow ( int  i ) const

inline

Return a matrix one row smaller than this one by dropping row i.

The result is packed but has same element type as this one.

template<int M, int N, class ELT, int CS, int RS>

TDropCol SimTK::Mat< M, N, ELT, CS, RS >::dropCol ( int  j ) const

inline

Return a matrix one column smaller than this one by dropping column j.

The result is packed but has same element type as this one.

template<int M, int N, class ELT, int CS, int RS>

TDropRowCol SimTK::Mat< M, N, ELT, CS, RS >::dropRowCol ( int  i, int  j  ) const

inline

Return a matrix one row and one column smaller than this one by dropping row i and column j.

The result is packed but has same element type as this one.

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

TAppendRow SimTK::Mat< M, N, ELT, CS, RS >::appendRow ( const Row< N, EE, SS > &  row ) const

inline

Return a matrix one row larger than this one by adding a row to the end.

The result is packed but has same element type as this one. Works for any assignment compatible row.

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

TAppendCol SimTK::Mat< M, N, ELT, CS, RS >::appendCol ( const Vec< M, EE, SS > &  col ) const

inline

Return a matrix one column larger than this one by adding a column to the end.

The result is packed but has same element type as this one. Works for any assignment compatible column.

template<int M, int N, class ELT, int CS, int RS>

template<class ER , int SR, class EC , int SC>

TAppendRowCol SimTK::Mat< M, N, ELT, CS, RS >::appendRowCol ( const Row< N+1, ER, SR > &  row, const Vec< M+1, EC, SC > &  col  ) const

inline

Return a matrix one row and one column larger than this one by adding a row to the bottom and a column to the right.

The final element of the row is ignored; that value is taken from the final element of the column instead. The result is packed but has same element type as this one. Works for any assignment compatible row and column.

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

TAppendRow SimTK::Mat< M, N, ELT, CS, RS >::insertRow ( int  i, const Row< N, EE, SS > &  row  ) const

inline

Return a matrix one row larger than this one by inserting a row *before* row i.

The result is packed but has same element type as this one. Works for any assignment compatible row. The index can be one greater than normally allowed in which case the row is appended.

template<int M, int N, class ELT, int CS, int RS>

template<class EE , int SS>

TAppendCol SimTK::Mat< M, N, ELT, CS, RS >::insertCol ( int  j, const Vec< M, EE, SS > &  col  ) const

inline

Return a matrix one column larger than this one by inserting a column *before* column j.

The result is packed but has same element type as this one. Works for any assignment compatible column. The index can be one greater than normally allowed in which case the column is appended.

template<int M, int N, class ELT, int CS, int RS>

template<class ER , int SR, class EC , int SC>

TAppendRowCol SimTK::Mat< M, N, ELT, CS, RS >::insertRowCol ( int  i, int  j, const Row< N+1, ER, SR > &  row, const Vec< M+1, EC, SC > &  col  ) const

inline

Return a matrix one row and one column larger than this one by inserting a row *before* row i and a column *before* column j.

The intersecting element of the row is ignored; that element is taken from the column. The result is packed but has same element type as this one. Works for any assignment compatible row and column. The indices can be one greater than normally allowed in which case the row or column is appended.

template<int M, int N, class ELT, int CS, int RS>

static const Mat& SimTK::Mat< M, N, ELT, CS, RS >::getAs ( const ELT *  p )

inlinestatic

template<int M, int N, class ELT, int CS, int RS>

static Mat& SimTK::Mat< M, N, ELT, CS, RS >::updAs ( ELT *  p )

inlinestatic

template<int M, int N, class ELT, int CS, int RS>

static Mat<M,N,ELT,M,1> SimTK::Mat< M, N, ELT, CS, RS >::getNaN ( )

inlinestatic

template<int M, int N, class ELT, int CS, int RS>

bool SimTK::Mat< M, N, ELT, CS, RS >::isNaN ( ) const

inline

Return true if any element of this Mat contains a NaN anywhere.

template<int M, int N, class ELT, int CS, int RS>

bool SimTK::Mat< M, N, ELT, CS, RS >::isInf ( ) const

inline

Return true if any element of this Mat contains a +Inf or -Inf somewhere but no element contains a NaN anywhere.

template<int M, int N, class ELT, int CS, int RS>

bool SimTK::Mat< M, N, ELT, CS, RS >::isFinite ( ) const

inline

Return true if no element contains an Infinity or a NaN.

template<int M, int N, class ELT, int CS, int RS>

static double SimTK::Mat< M, N, ELT, CS, RS >::getDefaultTolerance ( )

inlinestatic

For approximate comparisions, the default tolerance to use for a matrix is its shortest dimension times its elements' default tolerance.

template<int M, int N, class ELT, int CS, int RS>

template<class E2 , int CS2, int RS2>

bool SimTK::Mat< M, N, ELT, CS, RS >::isNumericallyEqual ( const Mat< M, N, E2, CS2, RS2 > &  m, double  tol  ) const

inline

Test whether this matrix is numerically equal to some other matrix with the same shape, using a specified tolerance.

template<int M, int N, class ELT, int CS, int RS>

template<class E2 , int CS2, int RS2>

bool SimTK::Mat< M, N, ELT, CS, RS >::isNumericallyEqual ( const Mat< M, N, E2, CS2, RS2 > &  m ) const

inline

Test whether this matrix is numerically equal to some other matrix with the same shape, using a default tolerance which is the looser of the default tolerances of the two objects being compared.

template<int M, int N, class ELT, int CS, int RS>

bool SimTK::Mat< M, N, ELT, CS, RS >::isNumericallyEqual ( const ELT &  e, double  tol = getDefaultTolerance()  ) const

inline

Test whether this is numerically a "scalar" matrix, meaning that it is a diagonal matrix in which each diagonal element is numerically equal to the same scalar, using either a specified tolerance or the matrix's default tolerance (which is always the same or looser than the default tolerance for one of its elements).

template<int M, int N, class ELT, int CS, int RS>

bool SimTK::Mat< M, N, ELT, CS, RS >::isNumericallySymmetric ( double  tol = getDefaultTolerance() ) const

inline

A Matrix is symmetric (actually Hermitian) if it is square and each element (i,j) is the Hermitian transpose of element (j,i).

Here we are testing for numerical symmetry, meaning that the symmetry condition is satisified to within a tolerance (supplied or default). This is a relatively expensive test since all elements must be examined but can be very useful in Debug mode to check assumptions.

See also

isExactlySymmetric() for a rarely-used exact equality test

template<int M, int N, class ELT, int CS, int RS>

bool SimTK::Mat< M, N, ELT, CS, RS >::isExactlySymmetric ( ) const

inline

A Matrix is symmetric (actually Hermitian) if it is square and each element (i,j) is the Hermitian (conjugate) transpose of element (j,i).

This method tests for exact (bitwise) equality and is too stringent for most purposes; don't use it unless you know that the corresponding elements should be bitwise conjugates, typically because you put them there directly.

See also

isNumericallySymmetric() for a more useful method

template<int M, int N, class ELT, int CS, int RS>

TRow SimTK::Mat< M, N, ELT, CS, RS >::colSum ( ) const

inline

Returns a row vector (Row) containing the column sums of this matrix.

template<int M, int N, class ELT, int CS, int RS>

TRow SimTK::Mat< M, N, ELT, CS, RS >::sum ( ) const

inline

This is an alternate name for colSum(); behaves like the Matlab function of the same name.

template<int M, int N, class ELT, int CS, int RS>

TCol SimTK::Mat< M, N, ELT, CS, RS >::rowSum ( ) const

inline

Returns a column vector (Vec) containing the row sums of this matrix.

template<int M, int N, class ELT, int CS, int RS>

std::string SimTK::Mat< M, N, ELT, CS, RS >::toString ( ) const

inline

toString() returns a string representation of the Mat.

Please refer to operator<< for details.

template<int M, int N, class ELT, int CS, int RS>

const ELT& SimTK::Mat< M, N, ELT, CS, RS >::get ( int  i, int  j  ) const

inline

Variant of indexing operator that's scripting friendly to get entry (i, j)

template<int M, int N, class ELT, int CS, int RS>

void SimTK::Mat< M, N, ELT, CS, RS >::set ( int  i, int  j, const ELT &  value  )

inline

Variant of indexing operator that's scripting friendly to set entry (i, j)

---

The documentation for this class was generated from the following files:

• SimTKcommon/include/SimTKcommon/internal/common.h
• Mat.h
• Serialize.h
• SmallMatrixMixed.h