SparseGenColLinSOE

#include \(<\tilde{ }\)/system_of_eqn/linearSOE/sparseGen/SparseGenColLinSOE.h\(>\)

class SparseGenColLinSOE: public LinearSOE

MovableObject
SystemOfEqn
LinearSOE

SparseGenColLinSOE is class which is used to store the matrix equation \(Ax=b\) of order \(size\) using a sparse column-compacted storage scheme for \(A\). The \(A\) matrix is stored in a 1d double array with \(nnz\) elements, where \(nnz\) is the number of non-zeroes in the matrix \(A\). Two additional 1d integer arrays \(rowA\) and \(colStartA\) are used to store information about the location of the coefficients, with \(colStartA(i)\) storing the location in the 1d double array of the start of column \(i\) and \(rowA(j)\) identifying the row in \(A\) to which the \(j'th\) component in the 1d double array. \(colStartA\) is of dimension \(size+1\) and \(rowA\) of dimension \(nnz\). For example

\[\left[ \begin{array}{ccccc} a_{0,0} & 0 & a_{0,2} & a_{0,3} & 0 \\ a_{1,0} & a_{1,1} & 0 & 0 & 0 \\ 0 & a_{2,1} & a_{2,2} & 0 & 0 \\ 0 & 0 & 0 & a_{3,3} & a_{3,4} \\ a_{4,0} & a_{4,1} & 0 & 0 & a_{4,4} \end{array} \right]\]

is stored in:

\[\left[ \begin{array}{cccccccccccccc} a_{0,0} & a_{1,0} & a_{4,0} & a_{1,1} & a_{2,1} & a_{4,1} & a_{0,2} & a_{2,2} & a_{0,3} & a_{3,3} & a_{3,4} & a_{4,4} \\ \end{array} \right]\]

with

\[colStartA = \left[ \begin{array}{cccccccccccccc} 0 & 3 & 6 & 8 & 10 & 12 \end{array} \right]\]

and

\[rowA = \left[ \begin{array}{cccccccccccccc} 0 & 1 & 4 & 1 & 2 & 4 & 0 & 2 & 0 & 3 & 3 & 4 \end{array} \right]\] The \(x\) and \(b\) vectors are stored in 1d double arrays of length \(n\).

The solver and a unique class tag (defined in \(<\)classTags.h\(>\)) are passed to the LinearSOE constructor. The system size is set to \(0\) and the matrix \(A\) is marked as not having been factored. Invokes setLinearSOE(*this) on the solver. No memory is allocated for the 3 1d arrays. SparseGenColLinSOE(int N, int NNZ, int *colStartA, int *rowA, SparseGenColLinSolver &theSolver);
The solver and a unique class tag (defined in \(<\)classTags.h\(>\)) are passed to the LinearSOE constructor. The system size is set to \(N\), the number of non-zeros is set to \(NNZ\) and the matrix \(A\) is marked as not having been factored. Obtains memory from the heap for the 1d arrays storing the data for \(A\), \(x\) and \(b\) and stores the size of these arrays. If not enough memory is available for these arrays a warning message is printed and the system size is set to \(0\). Invokes setLinearSOE(*this) and setSize() on solver, printing a warning message if setSize() returns a negative number. Also creates Vector objects for \(x\) and \(b\) using the (double \*,int) Vector constructor. It is up to the user to ensure that colStartA and rowA are of the correct size and contain the correct data.

Calls delete on any arrays created.

Invokes setLinearSOE(\*this) on newSolver. If the system size is not equal to \(0\), it also invokes setSize() on newSolver, printing a warning and returning \(-1\) if this method returns a number less than \(0\). Finally it returns the result of invoking the LinearSOE classes setSolver() method.

A method which returns the current size of the system.

The size of the system is determined from the Graph object theGraph, which must contain size vertices labelled \(0\) through \(size-1\), the adjacency list for each vertex containing the associated vertices in a column of the matrix \(A\). The size is determined by invoking getNumVertex() on theGraph and the number of non-zeros is determined by looking at the size of the adjacenecy list of each vertex in the graph, allowing space for the diagonal term. If the old space allocated for the 1d arrays is not big enough, it the old space is returned to the heap and new space is allocated from the heap. Prints a warning message, sets size to \(0\) and returns a \(-1\), if not enough memory is available on the heap for the 1d arrays. If memory is available, the components of the arrays are zeroed and \(A\) is marked as being unfactored. If the system size has increased, new Vector objects for \(x\) and \(b\) using the (double *,int) Vector constructor are created. The \(colStartA\) and \(rowA\) are then determined by looping through the vertices, setting \(colStartA(i) = colStartA(i-1) + 1 +\)the size of Vertices \(i\) adjacency list and placing the contents of \(i\) and the adjacency list into \(rowA\) in ascending order. Finally, the result of invoking setSize() on the associated Solver object is returned.

First tests that loc and M are of compatible sizes; if not a warning message is printed and a \(-1\) is returned. The LinearSOE object then assembles fact times the Matrix M into the matrix \(A\). The Matrix is assembled into \(A\) at the locations given by the ID object loc, i.e. \(a_{loc(i),loc(j)} += fact * M(i,j)\). If the location specified is outside the range, i.e. \((-1,-1)\) the corrseponding entry in M is not added to \(A\). If fact is equal to \(0.0\) or \(1.0\), more efficient steps are performed. Returns \(0\).

int addB(const Vector & V, const ID & loc, double fact = 1.0) =0;

First tests that loc and V are of compatible sizes; if not a warning message is printed and a \(-1\) is returned. The LinearSOE object then assembles fact times the Vector V into the vector \(b\). The Vector is assembled into \(b\) at the locations given by the ID object loc, i.e. \(b_{loc(i)} += fact * V(i)\). If a location specified is outside the range, e.g. \(-1\), the corresponding entry in V is not added to \(b\). If fact is equal to \(0.0\), \(1.0\) or \(-1.0\), more efficient steps are performed. Returns \(0\).

int setB(const Vector & V, double fact = 1.0) =0;

First tests that V and the size of the system are of compatible sizes; if not a warning message is printed and a \(-1\) is returned. The LinearSOE object then sets the vector b to be fact times the Vector V. If fact is equal to \(0.0\), \(1.0\) or \(-1.0\), more efficient steps are performed. Returns \(0\).

void zeroA(void) =0;

Zeros the entries in the 1d array for \(A\) and marks the system as not having been factored.

void zeroB(void) =0;

Zeros the entries in the 1d array for \(b\).

const Vector &getX(void) = 0;

Returns the Vector object created for \(x\).

const Vector &getB(void) = 0;

Returns the Vector object created for \(b\).

double normRHS(void) =0;

Returns the 2-norm of the vector \(x\).

void setX(int loc, double value) =0;

If loc is within the range of \(x\), sets \(x(loc) = value\).

Returns \(0\). The object does not send any data or connectivity information as this is not needed in the finite element design.

Returns \(0\). The object does not receive any data or connectivity information as this is not needed in the finite element design.