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oblas
oblas
 
 
README.md
README.md
 
 
blas1.go
blas1.go
 
 
blas2.go
blas2.go
 
 
blas3.go
blas3.go
 
 
densesol.go
densesol.go
 
 
eigen.go
eigen.go
 
 
equations.go
equations.go
 
 
flags.go
flags.go
 
 
jacobi.go
jacobi.go
 
 
matrix.go
matrix.go
 
 
matrix_ops.go
matrix_ops.go
 
 
sparse_blas.go
sparse_blas.go
 
 
sparse_config.go
sparse_config.go
 
 
sparse_conversions.go
sparse_conversions.go
 
 
sparse_matrix.go
sparse_matrix.go
 
 
sparse_solver.go
sparse_solver.go
 
 
sparse_solver_mumps.go
sparse_solver_mumps.go
 
 
sparse_solver_umfpack.go
sparse_solver_umfpack.go
 
 
t_blas1_test.go
t_blas1_test.go
 
 
t_blas2_test.go
t_blas2_test.go
 
 
t_blas3_test.go
t_blas3_test.go
 
 
t_densesol_test.go
t_densesol_test.go
 
 
t_eigen_test.go
t_eigen_test.go
 
 
t_equations_test.go
t_equations_test.go
 
 
t_init_test.go
t_init_test.go
 
 
t_jacobi_test.go
t_jacobi_test.go
 
 
t_matrix_ops_test.go
t_matrix_ops_test.go
 
 
t_matrix_test.go
t_matrix_test.go
 
 
t_sp_blas_test.go
t_sp_blas_test.go
 
 
t_sp_conversions_test.go
t_sp_conversions_test.go
 
 
t_sp_matrix_test.go
t_sp_matrix_test.go
 
 
t_sp_solver_mumps_test.go
t_sp_solver_mumps_test.go
 
 
t_sp_solver_test.go
t_sp_solver_test.go
 
 
t_sp_solver_umfpack_test.go
t_sp_solver_umfpack_test.go
 
 
t_vector_test.go
t_vector_test.go
 
 
testing.go
testing.go
 
 
vector.go
vector.go
 
 

README.md

Gosl. la. Linear Algebra: vector, matrix, efficient sparse solvers, eigenvalues, decompositions, etc.

Go Reference

The la sub-package implements functions to perform linear algebra operations such as vector addition or matrix-vector multiplications. It also wraps some efficient sparse linear systems solvers such as Umfpack and MUMPS (not the parotitis disease!).

Both Umfpack and MUMPS solvers are very efficient!

Sometimes, we call the lower level functions in la/oblas to improve performance.

Structures for sparse problems

In la, there are two types of structures to hold data for solving a sparse linear system: triplet and column-compressed matrix. Both have a complex version and are named as follows:

  1. Triplet and TripletC (complex)
  2. CCMatrix and CCMatrixC (complex)

The Triplet is more convenient for data input; e.g. during the assemblage step in a finite element code. The CCMatrix is better (faster) for computations and is the structure used by Umfpack.

Triplets are initialized by giving the size of the corresponding matrix and the number of non-zero entries (components). Thus, only space for the non-zero entries is allocated. Afterwards, each component can be set by calling the Put method after calling the Start method. The Start method can be called several times. Therefore, this structure helps with the efficient implementation of codes requiring multiple solutions of linear systems as in finite element analyses.

To convert the Triplet into a Column-Compressed Matrix, call the ToMatrix method of Triplet. And to convert the sparse matrix to a dense version (e.g. for reporting/printing), call the ToDense method of CCMatrix.

The Triplet has also a very convenient method to copy the contents of another Triplet (i.e. sparse matrix) into the positions starting with the maximum number of columns of this second matrix and the positions starting with the maximum number of rows of this second matrix. This is done with the method PutMatAndMatT. This operation is particularly common when solving mechanical problems with Lagrange multipliers and can be illustrated as follows:

[... ... ... a00 a10 ...] 0
[... ... ... a01 a11 ...] 1
[... ... ... a02 a12 ...] 2      [. at  .]
[a00 a01 a02 ... ... ...] 3  =>  [a  .  .]
[a10 a11 a12 ... ... ...] 4      [.  .  .]
[... ... ... ... ... ...] 5

The version in which the second matrix is a column-compressed matrix is named PutCCMatAndMatT.

Linear solvers for sparse problems

SparseSolver defines an interface for linear solvers in la. Two implementations satisfying this interface are:

  1. Umfpack wrapper to Umfpack; and
  2. Mumps wrapper to MUMPS

There are also high level functions to solve linear systems with Umfpack:

  1. SpSolve; and
  2. SpSolveC with complex numbers

Note however that the high level functions shouldn't be used for repeated executions because memory would be constantly allocated and released.

Examples

Vectors and matrices

BLAS1, 2 and 3 functions

General dense solver and Cholesky decomposition

Eigenvalues and eigenvectors of general matrix

Eigenvalues of symmetric (3 x 3) matrix

Sparse BLAS functions

Conversions related to sparse matrices

Sparse Triplet and Matrix

Sparse linear solver using MUMPS

Sparse linear solver using UMFPACK

Solutions using sparse solvers

API

Please see the documentation here