Simbody
3.6

This file is the userincludeable header to be included in user programs to provide fixedlength Vec & Mat classes. More...
Go to the source code of this file.
Namespaces  
SimTK  
This is the toplevel 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, 2element row of Real values. More...  
typedef Row< 3 >  SimTK::Row3 
Packed, 3element row of Real values. More...  
typedef Row< 4 >  SimTK::Row4 
Packed, 4element 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, 5element vector of Real values. More...  
typedef Vec< 6 >  SimTK::Vec6 
Packed, 6element vector of Real values. More...  
typedef Vec< 7 >  SimTK::Vec7 
Packed, 7element vector of Real values. More...  
typedef Vec< 8 >  SimTK::Vec8 
Packed, 8element vector of Real values. More...  
typedef Vec< 9 >  SimTK::Vec9 
Packed, 9element 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, 5element row of Real values. More...  
typedef Row< 6 >  SimTK::Row6 
Packed, 6element row of Real values. More...  
typedef Row< 7 >  SimTK::Row7 
Packed, 7element row of Real values. More...  
typedef Row< 8 >  SimTK::Row8 
Packed, 8element row of Real values. More...  
typedef Row< 9 >  SimTK::Row9 
Packed, 9element 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, 2element vector of float values. More...  
typedef Vec< 3, float >  SimTK::fVec3 
Packed, 3element vector of float values. More...  
typedef Vec< 4, float >  SimTK::fVec4 
Packed, 4element vector of float values. More...  
typedef Vec< 5, float >  SimTK::fVec5 
Packed, 5element vector of float values. More...  
typedef Vec< 6, float >  SimTK::fVec6 
Packed, 6element vector of float values. More...  
typedef Vec< 7, float >  SimTK::fVec7 
Packed, 7element vector of float values. More...  
typedef Vec< 8, float >  SimTK::fVec8 
Packed, 8element vector of float values. More...  
typedef Vec< 9, float >  SimTK::fVec9 
Packed, 9element 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, 2element row vector of float values. More...  
typedef Row< 3, float >  SimTK::fRow3 
Packed, 3element row vector of float values. More...  
typedef Row< 4, float >  SimTK::fRow4 
Packed, 4element row vector of float values. More...  
typedef Row< 5, float >  SimTK::fRow5 
Packed, 5element row vector of float values. More...  
typedef Row< 6, float >  SimTK::fRow6 
Packed, 6element row vector of float values. More...  
typedef Row< 7, float >  SimTK::fRow7 
Packed, 7element row vector of float values. More...  
typedef Row< 8, float >  SimTK::fRow8 
Packed, 8element row vector of float values. More...  
typedef Row< 9, float >  SimTK::fRow9 
Packed, 9element row vector of float values. More...  
This file is the userincludeable header to be included in user programs to provide fixedlength Vec & Mat classes.
The included internal headers declare templates needed for zerooverhead 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 welldefined 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 specialpurpose 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 2element 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 Mrow 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 vs, sv, vv 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)