SmallMatrix.h File Reference

This file is the user-includeable header to be included in user programs to provide fixed-length Vec & Mat classes. More...

Go to the source code of this file.

Namespaces
	SimTK
	This is the top-level SimTK namespace into which all SimTK names are placed to avoid collision with other symbols.

Typedefs
typedef Vec< 2 >	SimTK::Vec2
	This is the most common 2D vector type: a column of 2 Real values stored consecutively in memory (packed). More...
typedef Vec< 3 >	SimTK::Vec3
	This is the most common 3D vector type: a column of 3 Real values stored consecutively in memory (packed). More...
typedef Vec< 4 >	SimTK::Vec4
	This is the most common 4D vector type: a column of 4 Real values stored consecutively in memory (packed). More...
typedef Mat< 2, 2 >	SimTK::Mat22
	This is the most common 2x2 matrix type: two packed columns of 2 Real values each. More...
typedef Mat< 3, 3 >	SimTK::Mat33
	This is the most common 3x3 matrix type: three packed columns of 3 Real values each. More...
typedef Mat< 4, 4 >	SimTK::Mat44
	This is the most common 4x4 matrix type: four packed columns of 4 Real values each. More...
typedef SymMat< 2 >	SimTK::SymMat22
	A compact, 2x2 Real symmetric matrix; only 3 elements are stored. More...
typedef SymMat< 3 >	SimTK::SymMat33
	A compact, 3x3 Real symmetric matrix; only 6 elements are stored. More...
typedef SymMat< 4 >	SimTK::SymMat44
	A compact, 2x2 Real symmetric matrix; only 10 elements are stored. More...
typedef Row< 2 >	SimTK::Row2
	Packed, 2-element row of Real values. More...
typedef Row< 3 >	SimTK::Row3
	Packed, 3-element row of Real values. More...
typedef Row< 4 >	SimTK::Row4
	Packed, 4-element row of Real values. More...
typedef Vec< 1 >	SimTK::Vec1
	A vector of just one Real element (not too useful). More...
typedef Vec< 5 >	SimTK::Vec5
	Packed, 5-element vector of Real values. More...
typedef Vec< 6 >	SimTK::Vec6
	Packed, 6-element vector of Real values. More...
typedef Vec< 7 >	SimTK::Vec7
	Packed, 7-element vector of Real values. More...
typedef Vec< 8 >	SimTK::Vec8
	Packed, 8-element vector of Real values. More...
typedef Vec< 9 >	SimTK::Vec9
	Packed, 9-element vector of Real values. More...
typedef Mat< 1, 1 >	SimTK::Mat11
	1x1 Real matrix, that is, a scalar. More...
typedef Mat< 1, 2 >	SimTK::Mat12
	1x2 Real row matrix. More...
typedef Mat< 1, 3 >	SimTK::Mat13
	1x3 Real row matrix. More...
typedef Mat< 1, 4 >	SimTK::Mat14
	1x4 Real row matrix. More...
typedef Mat< 1, 5 >	SimTK::Mat15
	1x5 Real row matrix. More...
typedef Mat< 1, 6 >	SimTK::Mat16
	1x6 Real row matrix. More...
typedef Mat< 1, 7 >	SimTK::Mat17
	1x7 Real row matrix. More...
typedef Mat< 1, 8 >	SimTK::Mat18
	1x8 Real row matrix. More...
typedef Mat< 1, 9 >	SimTK::Mat19
	1x9 Real row matrix. More...
typedef Mat< 2, 1 >	SimTK::Mat21
	2x1 Real column matrix. More...
typedef Mat< 2, 3 >	SimTK::Mat23
	2x3 Real matrix, packed by columns. More...
typedef Mat< 2, 4 >	SimTK::Mat24
	2x4 Real matrix, packed by columns. More...
typedef Mat< 2, 5 >	SimTK::Mat25
	2x5 Real matrix, packed by columns. More...
typedef Mat< 2, 6 >	SimTK::Mat26
	2x6 Real matrix, packed by columns. More...
typedef Mat< 2, 7 >	SimTK::Mat27
	2x7 Real matrix, packed by columns. More...
typedef Mat< 2, 8 >	SimTK::Mat28
	2x8 Real matrix, packed by columns. More...
typedef Mat< 2, 9 >	SimTK::Mat29
	2x9 Real matrix, packed by columns. More...
typedef Mat< 3, 1 >	SimTK::Mat31
	3x1 Real column matrix. More...
typedef Mat< 3, 2 >	SimTK::Mat32
	3x2 Real matrix, packed by columns. More...
typedef Mat< 3, 4 >	SimTK::Mat34
	3x4 Real matrix, packed by columns. More...
typedef Mat< 3, 5 >	SimTK::Mat35
	3x5 Real matrix, packed by columns. More...
typedef Mat< 3, 6 >	SimTK::Mat36
	3x6 Real matrix, packed by columns. More...
typedef Mat< 3, 7 >	SimTK::Mat37
	3x7 Real matrix, packed by columns. More...
typedef Mat< 3, 8 >	SimTK::Mat38
	3x8 Real matrix, packed by columns. More...
typedef Mat< 3, 9 >	SimTK::Mat39
	3x9 Real matrix, packed by columns. More...
typedef Mat< 4, 1 >	SimTK::Mat41
	4x1 Real column matrix. More...
typedef Mat< 4, 2 >	SimTK::Mat42
	4x2 Real matrix, packed by columns. More...
typedef Mat< 4, 3 >	SimTK::Mat43
	4x3 Real matrix, packed by columns. More...
typedef Mat< 4, 5 >	SimTK::Mat45
	4x5 Real matrix, packed by columns. More...
typedef Mat< 4, 6 >	SimTK::Mat46
	4x6 Real matrix, packed by columns. More...
typedef Mat< 4, 7 >	SimTK::Mat47
	4x7 Real matrix, packed by columns. More...
typedef Mat< 4, 8 >	SimTK::Mat48
	4x8 Real matrix, packed by columns. More...
typedef Mat< 4, 9 >	SimTK::Mat49
	4x9 Real matrix, packed by columns. More...
typedef Mat< 5, 1 >	SimTK::Mat51
	5x1 Real column matrix. More...
typedef Mat< 5, 2 >	SimTK::Mat52
	5x2 Real matrix, packed by columns. More...
typedef Mat< 5, 3 >	SimTK::Mat53
	5x3 Real matrix, packed by columns. More...
typedef Mat< 5, 4 >	SimTK::Mat54
	5x4 Real matrix, packed by columns. More...
typedef Mat< 5, 5 >	SimTK::Mat55
	5x5 Real matrix, packed by columns. More...
typedef Mat< 5, 6 >	SimTK::Mat56
	5x6 Real matrix, packed by columns. More...
typedef Mat< 5, 7 >	SimTK::Mat57
	5x7 Real matrix, packed by columns. More...
typedef Mat< 5, 8 >	SimTK::Mat58
	5x8 Real matrix, packed by columns. More...
typedef Mat< 5, 9 >	SimTK::Mat59
	5x9 Real matrix, packed by columns. More...
typedef Mat< 6, 1 >	SimTK::Mat61
	6x1 Real column matrix. More...
typedef Mat< 6, 2 >	SimTK::Mat62
	6x2 Real matrix, packed by columns. More...
typedef Mat< 6, 3 >	SimTK::Mat63
	6x3 Real matrix, packed by columns. More...
typedef Mat< 6, 4 >	SimTK::Mat64
	6x4 Real matrix, packed by columns. More...
typedef Mat< 6, 5 >	SimTK::Mat65
	6x5 Real matrix, packed by columns. More...
typedef Mat< 6, 6 >	SimTK::Mat66
	6x6 Real matrix, packed by columns. More...
typedef Mat< 6, 7 >	SimTK::Mat67
	6x7 Real matrix, packed by columns. More...
typedef Mat< 6, 8 >	SimTK::Mat68
	6x8 Real matrix, packed by columns. More...
typedef Mat< 6, 9 >	SimTK::Mat69
	6x9 Real matrix, packed by columns. More...
typedef Mat< 7, 1 >	SimTK::Mat71
	7x1 Real column matrix. More...
typedef Mat< 7, 2 >	SimTK::Mat72
	7x2 Real matrix, packed by columns. More...
typedef Mat< 7, 3 >	SimTK::Mat73
	7x3 Real matrix, packed by columns. More...
typedef Mat< 7, 4 >	SimTK::Mat74
	7x4 Real matrix, packed by columns. More...
typedef Mat< 7, 5 >	SimTK::Mat75
	7x5 Real matrix, packed by columns. More...
typedef Mat< 7, 6 >	SimTK::Mat76
	7x6 Real matrix, packed by columns. More...
typedef Mat< 7, 7 >	SimTK::Mat77
	7x7 Real matrix, packed by columns. More...
typedef Mat< 7, 8 >	SimTK::Mat78
	7x8 Real matrix, packed by columns. More...
typedef Mat< 7, 9 >	SimTK::Mat79
	7x9 Real matrix, packed by columns. More...
typedef Mat< 8, 1 >	SimTK::Mat81
	8x1 Real column matrix. More...
typedef Mat< 8, 2 >	SimTK::Mat82
	8x2 Real matrix, packed by columns. More...
typedef Mat< 8, 3 >	SimTK::Mat83
	8x3 Real matrix, packed by columns. More...
typedef Mat< 8, 4 >	SimTK::Mat84
	8x4 Real matrix, packed by columns. More...
typedef Mat< 8, 5 >	SimTK::Mat85
	8x5 Real matrix, packed by columns. More...
typedef Mat< 8, 6 >	SimTK::Mat86
	8x6 Real matrix, packed by columns. More...
typedef Mat< 8, 7 >	SimTK::Mat87
	8x7 Real matrix, packed by columns. More...
typedef Mat< 8, 8 >	SimTK::Mat88
	8x8 Real matrix, packed by columns. More...
typedef Mat< 8, 9 >	SimTK::Mat89
	8x9 Real matrix, packed by columns. More...
typedef Mat< 9, 1 >	SimTK::Mat91
	9x1 Real column matrix. More...
typedef Mat< 9, 2 >	SimTK::Mat92
	9x2 Real matrix, packed by columns. More...
typedef Mat< 9, 3 >	SimTK::Mat93
	9x3 Real matrix, packed by columns. More...
typedef Mat< 9, 4 >	SimTK::Mat94
	9x4 Real matrix, packed by columns. More...
typedef Mat< 9, 5 >	SimTK::Mat95
	9x5 Real matrix, packed by columns. More...
typedef Mat< 9, 6 >	SimTK::Mat96
	9x6 Real matrix, packed by columns. More...
typedef Mat< 9, 7 >	SimTK::Mat97
	9x7 Real matrix, packed by columns. More...
typedef Mat< 9, 8 >	SimTK::Mat98
	9x8 Real matrix, packed by columns. More...
typedef Mat< 9, 9 >	SimTK::Mat99
	9x9 Real matrix, packed by columns. More...
typedef SymMat< 1 >	SimTK::SymMat11
	1x1 Real symmetric matrix, that is, a scalar. More...
typedef SymMat< 5 >	SimTK::SymMat55
	5x5 compact Real symmetric matrix. More...
typedef SymMat< 6 >	SimTK::SymMat66
	6x6 compact Real symmetric matrix. More...
typedef SymMat< 7 >	SimTK::SymMat77
	7x7 compact Real symmetric matrix. More...
typedef SymMat< 8 >	SimTK::SymMat88
	8x8 compact Real symmetric matrix. More...
typedef SymMat< 9 >	SimTK::SymMat99
	9x9 compact Real symmetric matrix. More...
typedef Row< 1 >	SimTK::Row1
	A row vector of one Real element (not too useful). More...
typedef Row< 5 >	SimTK::Row5
	Packed, 5-element row of Real values. More...
typedef Row< 6 >	SimTK::Row6
	Packed, 6-element row of Real values. More...
typedef Row< 7 >	SimTK::Row7
	Packed, 7-element row of Real values. More...
typedef Row< 8 >	SimTK::Row8
	Packed, 8-element row of Real values. More...
typedef Row< 9 >	SimTK::Row9
	Packed, 9-element row of Real values. More...
typedef Vec< 1, float >	SimTK::fVec1
	A vector of one float element (not too useful). More...
typedef Vec< 2, float >	SimTK::fVec2
	Packed, 2-element vector of float values. More...
typedef Vec< 3, float >	SimTK::fVec3
	Packed, 3-element vector of float values. More...
typedef Vec< 4, float >	SimTK::fVec4
	Packed, 4-element vector of float values. More...
typedef Vec< 5, float >	SimTK::fVec5
	Packed, 5-element vector of float values. More...
typedef Vec< 6, float >	SimTK::fVec6
	Packed, 6-element vector of float values. More...
typedef Vec< 7, float >	SimTK::fVec7
	Packed, 7-element vector of float values. More...
typedef Vec< 8, float >	SimTK::fVec8
	Packed, 8-element vector of float values. More...
typedef Vec< 9, float >	SimTK::fVec9
	Packed, 9-element vector of float values. More...
typedef Mat< 1, 1, float >	SimTK::fMat11
	1x1 float matrix, that is, a scalar. More...
typedef Mat< 2, 2, float >	SimTK::fMat22
	2x2 float matrix, packed by columns. More...
typedef Mat< 3, 3, float >	SimTK::fMat33
	3x3 float matrix, packed by columns. More...
typedef Mat< 3, 4, float >	SimTK::fMat34
	3x4 float matrix, packed by columns. More...
typedef Mat< 4, 3, float >	SimTK::fMat43
	4x3 float matrix, packed by columns. More...
typedef Mat< 4, 4, float >	SimTK::fMat44
	4x4 float matrix, packed by columns. More...
typedef Mat< 5, 5, float >	SimTK::fMat55
	5x5 float matrix, packed by columns. More...
typedef Mat< 6, 6, float >	SimTK::fMat66
	6x6 float matrix, packed by columns. More...
typedef Mat< 7, 7, float >	SimTK::fMat77
	7x7 float matrix, packed by columns. More...
typedef Mat< 8, 8, float >	SimTK::fMat88
	8x8 float matrix, packed by columns. More...
typedef Mat< 9, 9, float >	SimTK::fMat99
	9x9 float matrix, packed by columns. More...
typedef SymMat< 1, float >	SimTK::fSymMat11
	A 1x1 float symmetric matrix, that is, a scalar. More...
typedef SymMat< 2, float >	SimTK::fSymMat22
	2x2 compact float symmetric matrix. More...
typedef SymMat< 3, float >	SimTK::fSymMat33
	3x3 compact float symmetric matrix. More...
typedef SymMat< 4, float >	SimTK::fSymMat44
	4x4 compact float symmetric matrix. More...
typedef SymMat< 5, float >	SimTK::fSymMat55
	5x5 compact float symmetric matrix. More...
typedef SymMat< 6, float >	SimTK::fSymMat66
	6x6 compact float symmetric matrix. More...
typedef SymMat< 7, float >	SimTK::fSymMat77
	7x7 compact float symmetric matrix. More...
typedef SymMat< 8, float >	SimTK::fSymMat88
	8x8 compact float symmetric matrix. More...
typedef SymMat< 9, float >	SimTK::fSymMat99
	9x9 compact float symmetric matrix. More...
typedef Row< 1, float >	SimTK::fRow1
	A row vector of one float element (not too useful). More...
typedef Row< 2, float >	SimTK::fRow2
	Packed, 2-element row vector of float values. More...
typedef Row< 3, float >	SimTK::fRow3
	Packed, 3-element row vector of float values. More...
typedef Row< 4, float >	SimTK::fRow4
	Packed, 4-element row vector of float values. More...
typedef Row< 5, float >	SimTK::fRow5
	Packed, 5-element row vector of float values. More...
typedef Row< 6, float >	SimTK::fRow6
	Packed, 6-element row vector of float values. More...
typedef Row< 7, float >	SimTK::fRow7
	Packed, 7-element row vector of float values. More...
typedef Row< 8, float >	SimTK::fRow8
	Packed, 8-element row vector of float values. More...
typedef Row< 9, float >	SimTK::fRow9
	Packed, 9-element row vector of float values. More...

Detailed Description

This file is the user-includeable header to be included in user programs to provide fixed-length Vec & Mat classes.

The included internal headers declare templates needed for zero-overhead handling of small vectors and matrices. The idea is to convey all needed information, including the size, at compile time through the templatized types. These classes have well-defined minimal storage layouts and can be easily interconverted to/from arrays of scalar types, with zero conversion overhead.

There are three generic types required: a column vector Vec, a row vector (a.k.a. "covector") Row, and a matrix Mat. Real and Complex elements at single, double, and quad precision are supported. Almost all operations are inline – this package is intended to provide performance as good as one could achieve by special-purpose C code.

When the element type is a "basic numerical type" then the resulting Vec, Row or Mat is also a basic numerical type, so these can be built up with structured elements so that Vec< 2,Vec<3> > for example is a 2-element vector whose elements are Vec<3>'s.

These classes are designed so that many operations that look like computations are free. These include: negation, conjugation, extraction of real and imaginary parts from complex numerical types, and hermitian or positional transpose. These are performed by type casting rather than computation. That is, these operations can be viewed as a change in perspective rather than an actual computation.

To achieve zero overhead, separate types are needed to convey special matrix structure, although appropriate interconversions are defined. So symmetric matrices are SymMat's and diagonal matrices are DiagMat's. Note that symmetric matrices are more properly called Hermitian in that the reflected elements are conjugates of one another.

Supported operations

Class member functions for Vec<M>: Unary: -, +, ~ (Hermitian transpose) Assignment: copy assignment of identical object elementwise assignment from any M-row Vec or Mat scalar assignment to each element TODO

Global operations involving only Vecs or Vec and scalar, yielding a vector result. (Row has the same set.) v+s, s+v, v+v v-s, s-v, v-v v*s, s*v (can't multiply a vector by another vector) v/s v==s, s==v, v==v (same for !=)

Global operations mixing Row, Vec, Mat s=r*v (dot product) m=v*r (outer product) v=m*v, r=r*m m=m*m (with compatible dimensions)