Simbody
3.7
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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... | |
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)