Difference: MathCore (4 vs. 5)

Revision 52005-10-04 - unknown

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META TOPICPARENT name="LHCbPhysicsEventModelTaskForce"

LHCb Physics Event Model Comments on the MathCore Vector and the Root Linear Algebra Classes

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 There are a few small problems that can be easily fixed:
  • We found an inconsistency in the behaviour of the typedefs for Vector3Ds and LorentzVectors. If Ione includes MathCore/Vector3D.h in the code, this includes MathCore/Vector3Dfwd.h, so one gets the typedefs XYZVector, XYZVectorF, etc. However, if one includes MathCore/LorentzVector.h, one does not get access to the typedefs as this file does not include MathCore/LorentzVectorfwd.h.
  • A XYZTPoint is missing. That would be nice to have for MC truth.
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  • The Vec() method in XYZTVector is not const
 
  • There is an Eta() method in the LorentzVector, but no Gamma() and Beta().

Root Linear Algebra Classes

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  • We would like to be able to get a sub-matrix by reference. This is presently implemented, but the interface of the method is quite strange.
  • The linear algebra classes seem not to be compatible with the mathcore classes. There is no way to multiply a matrix and a vector. (?)
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Use case for linear algebra package presented to SEAL/ROOT group

The minimal algebra package is to be optimised for small (typically < 10) size matrices and vectors. In what follows, is is assumed that the software must be fast and efficient. This use-case has been compiled from communications between Patrick K., Vanya, Matt N., Juan and Lorenzo Moneta.

Main requirements

  • Square matrices up to at least 7x7 dimension
  • Row and column vectors up to 7x1
  • Matrix inversion with defined failure indication
  • Calculation of matrix determinant
  • Basic matrix operations: *, +, +=, -, transpose
  • Specialisations for the case of symmetric matrices and their operations
    • Important: symmetric matrix similarity specialisation: M*S*M^T is faster for symmetric matrices than for standard ones. This is used extensively in the track fit.
  • Easy construction of identity and zero matrices
  • Assignment without temporaries (generaliseable to = operator?)
  • Access to individual elements
  • Access to size (rows, columns)
  • Access by reference to rows and columns
  • Access by reference to matrix sub-blocks (with clear syntax!)
    • Diagonal sub-blocks of symmetric matrices returned as symmetric matrices
    • Off-diagonal sub-blocks returned as standard matrices
  • Easy coupling to MathCore 3D and 4D vectors and points (with compile time dimentionality check?)
    • Multiplication operations
    • Vectors to matrix columns or rows
    • Matrix columns or rows to vectors

Other requirements

These are requirements where speed might not be of the escence, since they relate to operations not needed in typical reconstruction algorithms
  • Evaluation of eigenvalues and eigenvectors
  • Decompositions
  • Conversion to GSL matrices? This would allow to use the GSL eigenvalues and decompositions for free.

Open questions

Which of the operations above should be non-mutating? Should inverse and transpose return a new matrix, or perform the operation on itself?

-- JuanPalacios - 04 Oct 2005

 

What do we expect from a Linear Algebra package?

First brain dump by PK at the LHCb Software week (slides) summarized by Juan:
 
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