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79 lines
3.7 KiB
Plaintext
79 lines
3.7 KiB
Plaintext
Things that need to be done for 2.0:
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The Core modules is essentially ready. Now we need more modules:
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- QR decomposition
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-> ANY VOLUNTEER? I can provide a scanned copy of Golub&vanLoan.
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-> investigate various algorithms, balance numerical stability vs. speed,
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maybe go for a different algos for fixed-size (small) vs. dynamic-size
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(typically bigger).
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-> applications: eigenvalues, eigenspaces, operator norm...
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-> more applications: by computing eigenvalues of a companion matrix,
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we can provide a general polynomial solver. I can explain that to
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a potential volunteer... also this is optional.
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- SVD decomposition
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-> ANY VOLUNTEER?
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-> Same remarks as for QR.
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-> applications include pseudo-inverse and linear regression (in Eigen1 we
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did linear regression with LU but that was not very good).
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- Array
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-> ANY VOLUNTEER?
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-> We should group in this module all the functionality that consists in
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abusing a matrix as an array. Many people have asked for such
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functionality:
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-> coefficient-wise product (a.k.a. "Schur product" of matrices).
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This should return a new expression. Look at Core/Sum.h for a starting
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point.
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-> Apply some function (such as "exp") to every coefficient of a matrix.
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This should return a new expression. Look at Core/Conjugate.h for a
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starting point.
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-> stack matrices horizontally and vertically to form larger matrix
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expressions. Look at Core/Block.h, Core/Minor.h for a starting point.
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-> sum over the elements of a vector (look at Core/Trace.h to get
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a starting point).
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-> Given a matrix, return a vector whose i-th coefficient is the sum
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of the coefficients in the i-th column of that matrix. Same for rows.
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-> This should return an actual vector (i.e. evaluate immediately),
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not an expression, because a loop is involved.
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-> Yes, this can be done as "matrix * VectorType::ones()" but we
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should implement it separately so as to not be too hard on the
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compiler.
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- Gaussian elimination
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-> LEAVE IT TO ME as I did something similar in Eigen1.
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-> I don't call this module LU because I want to code certain operations
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such as inverse in an optimized way that bypasses the LU decomposition.
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But yes, LU is one of the things that will be provided by this module.
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-> Other things to do here: determinant, basis of kernel, basis of range,
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antecedent etc...
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-> Should be do a "simple linear solver" like in eigen1? Did anybody
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use it?
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-> linear regression should use SVD instead. However as a temporary
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solution we could borrow the implementation from eigen1, using gaussian
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elimination.
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- Geometry
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-> LEAVE IT TO ME as I did something similar in Eigen1.
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->low-dimensional geometry (quaternions, cross product, rotations)
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->projective geometry(opengl matrices, Qt matrices)
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->euclidean geometry (Gram-Schmidt)
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- Sparse objects support, by wrapping GMM++
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-> ANY VOLUNTEER? I'm looking at the folks already used to GMM++. I will
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provide support but am not used to GMM++ so wouldn't like to have to do
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all that alone.
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-> Goal: provide a nice wrapper around GMM++ with Qt-style copy-on-write
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(I can code the copy-on-write part if you don't want to do it)
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-> Very important for Krita 2.1 and Step
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-> No expression templates here. So the API won't be quite identical to the
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rest of Eigen. Should be release under a different name? "Speisen" comes
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to mind ;)
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-> No need to wrap all of GMM++. Only sparse objects. Only what's useful
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for KOffice 2.1 and Step (if you want more, do it).
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-> Step uses:
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-gmm::cg, constrained_cg
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-dantzig algorithm
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-types: gmm::row_matrix, col_matrix, rsvector, array1D_reference
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-> What is needed for Krita?
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