MATH_Linalg_Core

This package contains classes for solving linear problems. More...

This package contains classes for solving linear problems.

This package is based on blas/lapack routines:

• blas ( http://www.netlib.org/blas/ )
• lapack ( http://www.netlib.org/lapack/ )

It contains :

• the general super classes:
  • LAP_Object describes the general interface which is the base of all classes
  • LAP_Exception describes an exception error
• the vector classes:
  • LAP_View describes a view of a vector.
  • LAP_Vector describes a general vector whose values can be modified
  • LAP_DoubleVector describes a double vector whose values can be modified
  • LAP_IntegerVector describes an integer (lapack integer) whose values can be modified
  • LAP_ConstVector describes a general vector whose values can not be modified
  • LAP_ConstDoubleVector describes a double vector whose values can not be modified
• the general matrix interface classes:
  • LAP_2DView describes a mask for viewing general matrix
  • LAP_Matrix describes a general type of matrix interface
  • LAP_SymmetricMatrix describes a general type of symmetric matrix interface
  • LAP_UpperMatrix describes a general type of upper matrix interface
  • LAP_DoubleMatrix describes a double matrix interface
  • LAP_DoubleSymmetricMatrix describes a double symmetric matrix interface
  • LAP_DoubleUpperMatrix describes a double uppermatrix interface
• a different kind of storage for value sof the matrices
  • LAP_DoubleFullMatrix describes a matrix in full storage.
  • LAP_DoublePackedMatrix describes a matrix in packed storage
  • LAP_DoubleBandedMatrix describes a matrix in banded storage.
• a different type of matrices:
  • LAP_DoubleFullGeneralMatrix describes a double general matrix in full storage.
  • LAP_DoubleFullSymmetricMatrix describes a double symmetric matrix in full storage.
  • LAP_DoubleFullUpperMatrix describes a double upper matrix in full storage
  • LAP_DoubleBandedSymmetricMatrix describes a double symmetrix matrix in banded storage.
  • LAP_DoubleBandedUpperMatrix describes a double upper matrix in banded storage.
  • LAP_DoublePackedSymmetricMatrix describes a double symmetrix matrix in packed storage.
  • LAP_DoublePackedUpperMatrix describes a double upper matrix in packed storage.
• the c++ driver routines of lapak routines written in fortran:
  • lapack_types.h describes the corresponding c++ type for fortran type
  • lapack_functions.h describes a c++ drivers for general lapack function
  • dvector_functions.h desribes the c++ drivers for blas routines
  • dfullmatrix_functions.h describes the c++ drivers for blas /lapack routines concerning double full general matrix
  • dfullsymmatrix_functions.h describes the c++ drivers for blas /lapack routines concerning double full symmetric matrix
  • dfulluppermatrix_functions.h describes the c++ drivers for blas /lapack routines concerning double full upper matrix
  • dpackedsymmatrix_functions.h describes the c++ drivers for blas /lapack routines concerning double packed symmetric matrix
  • dpackeduppermatrix_functions.h describes the c++ drivers for blas /lapack routines concerning double packed upper matrix
  • dbandedsymmatrix_functions.h describes the c++ drivers for blas /lapack routines concerning double banded symmetric matrix
  • dbandeduppermatrix_functions.h describes the c++ drivers for blas /lapack routines concerning double banded upper matrix
• primary test classes for the different kinds of matrices in different kind of storage:
  • LAP_Test is the main driver for primary tests
  • LAP_VectorTest describes the primary test for vector
  • LAP_FullMatrixTest describes the primary tests for general matrix in full storage
  • LAP_FullSymmetricMatrixTest describes the primary tests for symmetric matrix in full storage
  • LAP_FullUpperMatrixTest describes the primary tests for upper matrix in full storage
  • LAP_PackedSymmetricMatrixTest describes the primary tests for symmetric matrix in packed storage
  • LAP_PackedUpperMatrixTest describes the primary tests for upper matrix in packed storage
  • LAP_BandedSymmetricMatrixTest describes the primary tests for symmetric matrix in banded storage
  • LAP_BandedUpperMatrixTest describes the primary test for upper matrix in banded storage

LAP_EfficiencyTest describes a test to compare efficiency of linear methods in different matrix storage

The organization of this package is as follow:

The test case consists in building a cube discretized in each direction by N segments and to compute an exchange matrix : 6 on the diagonal at position (i,i) and -1 for all cubes j connected to it. It leads to a matrix A of size . The test consists in computing the times to compute the cholesky factorization A=tU.U , to make the product Y=tU.U.X and to solve U.X=Y. The cpu times are as follow in ms:

For Cholesky factorization: A=tU.U

N / Storage	Full	Packed	banded
2	0	0	0
8	20	40	02
16	1845	9628	36
32	887980	5444598	3442
64	X	X	437900

*

For rank product: Y=tU.U X

N / Storage	Full	Packed	banded
2	0	0	0 (#bands=5)
8	0	1	0 (#bands=65)
16	12	13	1 (#bands=257)
32	763	896	53 (#bands=1025)
64	memory error	memory error	1603

*

For solver: U.X=Y

N / Storage	Full	Packed	banded
2	0	0	0
8	1	0	0
16	8	6	1
32	452	432	27
64	X	X	782

*