#System of equations solver 6x6 update
#System of equations solver 6x6 manual

Here is my sympy input: from sympy import Matrix, symbols, pprint, Eq, linsolveДЇrom import lambdastr In theory, it should be solvable, however, linsolve takes forever (roughly a day so far) to calculate a solution. The equation system has 3 unknowns and 24 input variables. Otherwise a linker error will be created.ДЇurthermore, it is important to note that it is not possible to use any kind of view on the expression object returned by the two-argument solve() functions.I have a linear equation system consisting of 3 equations as a result of a matrix multiplication. Thus the functions can only be used if a fitting LAPACK library is available and linked to the executable. The attempt to call the function with matrices of any other element type or with a sparse matrix results in a compile time error!ДЄlso note that the functions may make use of LAPACK kernels. Note that the solve() functions can only be used for dense matrices with float, double, complex or complex element type. In all failure cases either a compilation error is created if the failure can be predicted at compile time or a std::invalid_argument exception is thrown. the given matrix is singular and not invertible. the number of rows of the right-hand side matrix doesn't match the dimensions of the system matrix the size of the right-hand side vector doesn't match the dimensions of the system matrix Resizing and initialization blaze :: DynamicVector x // The solution vector solve ( declsym ( A ), x, b ) // Solving the LSE with a symmetric system matrix solve ( declherm ( A ), x, b ) // Solving the LSE with an Hermitian system matrix solve ( decllow ( A ), x, b ) // Solving the LSE with a lower system matrix solve ( declunilow ( A ), x, b ) // Solving the LSE with an unilower system matrix solve ( declupp ( A ), x, b ) // Solving the LSE with an upper system matrix solve ( decluniupp ( A ), x, b ) // Solving the LSE with an uniupper system matrix solve ( decldiag ( A ), x, b ) // Solving the LSE with a diagonal system matrixДЇor both solve() functions the computation fails if. It is highly appreciated.Д«laze :: DynamicMatrix A // The square lower system matrix blaze :: DynamicVector b // The right-hand side vector //. Still, thanks a lot for your offer to provide us with a fast implementation of the LU decomposition.

#System of equations solver 6x6 manual

We would need manual implementations for all LAPACK functions, including the according substitution, inversion, and solver routines, to be independent of LAPACK. Replacing a single of these functions by a manual implementation would not help to get rid of the dependency to LAPACK. Blaze is currently using more than 30 LAPACK functions (starting from the upcoming 2.6 release), among these the functions for the LU, LLH, LDLT, LDLH, QR, RQ, QL, and LQ decomposition.

Thus using LAPACK provides parallel implementations of all these algorithms without additional effort.

#System of equations solver 6x6 update

As the vendors update their LAPACK implementation it is to be expected that also the parallelization is improved.

This effort is only justifiable if the manual implementation initially outperforms the LAPACK implementation.

Replacing the LAPACK implementation with a manual implementation of the same performance would thus not increase performance (the user experience), but introduces a high initial implementation effort and a constant maintenance effort (for continuous modernization).

As noted by you, the LAPACK implementations are constantly updated and expected to run at maximum performance.

However, it appears that integrating your LU implementation would not have many benefits for Blaze: