GaussDLL JINRLIB

JOINT INSTITUTE FOR NUCLEAR RESEARCH

PROGRAM LIBRARY JINRLIB

GaussDLL - program complex of matrix-vector operations and solution of Slae with real coefficients

Author: I.N.Kiyan

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Language: C++
Environment: MS Visual C++ 7.0

GaussDLL is a C++ program complex written in MS Visual C++ 7.0 programming environment on the base of use of Microsoft Foundation Classes (MFC). It is intended for realization of matrix-vector operations and for decision of systems of the linear algebraic equations (SLAE) with real coefficients by a method of Gauss without and with pivoting. GaussDLL could be used if calling application makes calls to the MFC library at run time.

User data type:: CMatrix (arrays.h); CVector (arrays.h)

Function return type: enum MatErrType { matErr_None, matErr_Size, matErr_Singular, matErr_IllConditioned, matErr_IterLimit, matErr_QNAN }; (arrays.h).: matErr_None - correct solution,; matErr_Size - error of size,; matErr_Singular - error of singular,; matErr_IllConditioned - error of ill conditionality,; matErr_IterLimit - error of excess of limit of iteration number,; matErr_QNAN - error of division by zero.

Exported functions:

The functions, exported from GaussDLL library, allow to make account of norm of a vector, norm of a matrix, number of conditionality of system, left and right of rearrangement matrixes, sum and difference of two matrixes, products of a matrix on a vector and matrixes on a matrix, inverse matrix and determinant of a matrix. Besides they allow to make copying a vector, copying a matrix, and also transposition and Low / Up decomposition of the matrixes. Three functions are intended for the decision of systems of the linear algebraic equations with real coefficients by a method of Gauss, method of Gauss with column pivoting and method of Gauss with matrix pivoting accordingly. Left rearrangement matrix is used for rearrangement of rows in a matrix of coefficients and in a vector of the free members. Right rearrangement matrix is used for rearrangement columns in a matrix of coefficients and rows in a vector of the solution. The absolute value of the determinant of a matrix of coefficients should be more than e-15 (machine 0).

Norm of vector:
void NormVec(double& norm, CVector& VecA, int numRowsA);

Input parameters:

VecA - source vector,

numRowsA - number of rows of source vector.

Output parameters:

norm - norm of source vector.
Norm of matrix:
void NormMat(double& norm, CMatrix& MatA, int numRowsA, int numColsA);

Input parameters:

MatA - source matrix,

numRowsA - number of rows of source matrix,

numColsA - number of columns of source matrix.

Output parameters:

norm - norm of source matrix.
Condition number of system:
void SystCond(double normMat, double normInvMat, double& cond);

Input parameters:

normMat - norm of source matrix,

normInvMat - norm of inverse matrix.

Output parameters:

cond - condition number of system.
Left rearrangement matrix:
MatErrType RrrMatL(CMatrix& MatRes, int numRowsA, int rowInd, int colInd);

Input parameters:

numRowsA - number of rows of source matrix,

rowInd - ziro based index of row of main element,

colInd - ziro based index of column of main element.

Output parameters:

MatRes - left rearrangement matrix.
Right rearrangement matrix:
MatErrType RrrMatR(CMatrix& MatRes, int numColsA, int rowInd, int colInd);

Input parameters:

numColsA - number of columns of source matrix,

rowInd - ziro based index of row of main element,

colInd - ziro based index of column of main element.

Output parameters:

MatRes - right rearrangement matrix.
Copying of vector:
void CopyVec(CVector& VecA, CVector& VecB, int numRowsB);

Input parameters:

VecB - source vector,

numRowsB - number of rows of source vector.

Output parameters:

VecA - destination vector.
Copying of matrix:
void CopyMat(CMatrix& MatA, CMatrix& MatB, int numRowsB, int numColsB);

Input parameters:

MatB - source matrix,

numRowsB - number of rows of source matrix,

numColsB - number of columns of source matrix.

Output parameters:

MatA - destination matrix.
Addition of matrixes:
MatErrType AddMat(CMatrix& MatA, CMatrix& MatB, CMatrix& MatC,
int numRowsA, int numColsA, int numRowsB, int numColsB);

Input parameters:

MatA - first source matrix,

MatB - second source matrix,

numRowsA - number of rows of first source matrix,

numColsA - number of columns of first source matrix,

numRowsB - number of rows of second source matrix,

numColsB - number of columns of second source matrix.

Output parameters:

MatC - sum of source matrixes.
Subtraction of matrixes:
MatErrType SubMat(CMatrix& MatA, CMatrix& MatB, CMatrix& MatC,
int numRowsA, int numColsA, int numRowsB, int numColsB);

Input parameters:

MatA - reduced matrix,

MatB - deducted matrix,

numRowsA - number of rows of reduced matrix,

numColsA - number of columns of reduced matrix,

numRowsB - number of rows of deducted matrix,

numColsB - number of columns of deducted matrix.

Output parameters:

MatC - difference of two matrixes.
Transposition of matrix:
void TransMat(CMatrix& MatA, CMatrix& MatRes, int numRowsA, int numColsA);

Input parameters:

MatA - source matrix,

numRowsA - number of rows of source matrix,

numColsA - number of columns of source matrix.

Output parameters:

MatRes - transposed matrix.
Multiplication of matrix and vector:
MatErrType MulMatVec(CMatrix& MatA, CVector& VecB, CVector& VecC,
int numRowsA, int numColsA, int numRowsB);

Input parameters:

MatA - source matrix,

VecB - source vector,

numRowsA - number of rows of source matrix,

numColsA - number of columns of source matrix,

numRowsB - number of rows of source vector.

Output parameters:

VecC - product.
Multiplication of two matrixes:
MatErrType MulMatMat(CMatrix& MatA, CMatrix& MatB, CMatrix& MatC,
int numRowsA, int numColsA, int numRowsB, int numColsB);

Input parameters:

MatA - left matrix,

MatB - right matrix,

numRowsA - number of rows of left matrix,

numColsA - number of columns of left matrix,

numRowsB - number of rows of right matrix,

numColsB - number of columns of right matrix.

Output parameters:

MatC - product.
Low/Up decomposition:
MatErrType LowUp(CMatrix& MatA, CMatrix& MatLow, CMatrix& MatUp,
int numRowsA, int numColsA);

Input parameters:

MatA - source matrix,

numRowsA - number of rows of source matrix,

numColsA - number of columns of source matrix.

Output parameters:

MatLow - bottom triangular matrix,

MatUp - top triangular matrix.
Determinant of matrix:
MatErrType DetMat(CMatrix& MatA, double& det, int numRowsA, int numColsA);

Input parameters:

MatA - source matrix,

numRowsA - number of rows of source matrix,

numColsA - number of columns of source matrix.

Output parameters:

det - determinant.
Inverse matrix:
MatErrType InverseMat(CMatrix& MatA, CMatrix& MatRes, int numRowsA, int numColsA);

Input parameters:

MatA - source matrix,

numRowsA - number of rows of source matrix,

numColsA - number of columns of source matrix.

Output parameters:

MatRes - inverse matrix.
Gauss method:
MatErrType Gauss(CMatrix& MatLow, CMatrix& MatUp, CVector& VecIn, CVector& VecOut,
int numRowsLow, int numColsLow, int numRowsUp, int numColsUp, int numRowsIn);

Input parameters:

MatLow - bottom triangular matrix,

MatUp - top triangular matrix,

VecIn - vector of free members,

numRowsLow - number of rows of bottom triangular matrix,

numColsLow -number of columns of bottom triangular matrix,

numRowsUp - number of rows of top triangular matrix,

numColsUp - number of columns of top triangular matrix,

numRowsIn - number of rows of vector of free members.

Output parameters:

VecOut - vector of solution.
Gauss method with pivoting by column:
MatErrType GaussPivCol(CMatrix& MatA, CVector& VecIn, CVector& VecOut,
int numRowsA, int numColsA, int numRowsIn);

Input parameters:

MatA - source matrix,

VecIn - vector of free members,

numRowsA - number of rows of source matrix,

numColsA - number of columns of source matrix,

numRowsIn - number of rows of vector of free members.

Output parameters:

VecOut - vector of solution.
Gauss method with pivoting by table:
MatErrType GaussPivTbl(CMatrix& MatA, CVector& VecIn, CVector& VecOut,
int numRowsA, int numColsA, int numRowsIn);

Input parameters:

MatA - source matrix,

VecIn - vector of free members,

numRowsA - number of rows of source matrix,

numColsA - number of columns of source matrix,

numRowsIn - number of rows of vector of free members.

Output parameters:

VecOut - vector of solution.

DLL function call (MS Visual C++ X.X):

Declaring the global variable of handle to the module:: HMODULE gGaussDLL;
Definition of type of pointer to the function:: typedef MatErrType (*GAUSSPIVTBL)(CMatrix& MatA, CVector& VecIn, CVector& VecOut, int numRowsA, int numColsA, int numRowsIn);
Declaring the global pointer to the function:: GAUSSPIVTBL pGaussPivTbl;
Loading the DLL (in constructor):: gGaussDLL = LoadLibrary("GaussDLL");
Retrieving the address of an function exported by DLL (in constructor):: pGaussPivTbl = (GAUSSPIVTBL)GetProcAddress(gGaussDLL, "GaussPivTbl");
Declaring the local variable and call of the exported function:: MatErrType ErrCode;; ErrCode = pGaussPivTbl(MatA, VecIn, VecOut, MatA.getRows(),; MatA.getCols(), VecIn.getSize());
Unloading the DLL (in destructor):: FreeLibrary(gGaussDLL);

Archive GaussDLL (GaussDLL.dll, mfc70.dll, ARRAYS.H, test, example and description) are submitted.