![\[ M= \left[\begin{array}{ccccc} d_{(1)} & u_{(1)} \\ l_{(1)} & d_{(2)} & u_{(2)} \\ & \ddots & \ddots & \ddots \\ & & l_{(n-2)} & d_{(n-1)} & u_{(n-1)} \\ & & & l_{(n-1)} & d_{(n)} \end{array}\right]. \]](form_27.png)
#include <MPITridiagLinearOp.hpp>
Inheritance diagram for MPITridiagLinearOp< Scalar >:
Public Member Functions | |
| MPITridiagLinearOp () | |
| Construct to uninitialized. | |
| MPITridiagLinearOp (MPI_Comm mpiComm, const Thyra::Index localDim, const Scalar lower[], const Scalar diag[], const Scalar upper[]) | |
Calls initialize(). | |
| void | initialize (MPI_Comm mpiComm, const Thyra::Index localDim, const Scalar lower[], const Scalar diag[], const Scalar upper[]) |
This subclass represents a linear operator for tridiagonal matrices of the global form:
If there is only 
processor the arrays lower[], diag[], and upper[] of dimension localDim-1, localDim and localDim-1 respectively are stored (see initialize()).
If there 
processors then locally this class stores slightly different arrays of data depending on which processor this is and processor-to-processor communication is required.
local vector elements the following sub-matrix is stored:
![\[ \left[\begin{array}{cccccc} d_{(1)} & u_{(1)} \\ l_{(1)} & d_{(2)} & u_{(2)} \\ & \ddots & \ddots & \ddots \\ & & l_{(n_0-2)} & d_{(n_0-1)} & u_{(n_0-1)} \\ & & & l_{(n_0-1)} & d_{(n_0)} & u_{(n_0)} \end{array}\right]. \]](form_31.png)
In this case, arrays lower[], diag[], and upper[] of dimension localDim-1, localDim and localDim respectively are stored (see initialize()).
, where 
, with local offset 
and 
local vector elements the following sub-matrix is stored:
![\[ \left[\begin{array}{cccccc} l_{(g_i)} & d_{(g_i+1)} & u_{(g_i+1)} \\ & \ddots & \ddots & \ddots \\ & & & l_{(g_i+n_i-1)} & d_{(g_i+n_i)} & u_{(g_i+n_i)} \end{array}\right]. \]](form_36.png)
In this case, arrays lower[], diag[], and upper[] of dimension localDim, localDim and localDim respectively are stored (see initialize()).
with local offset 
and 
local vector elements the following sub-matrix is stored:
![\[ \left[\begin{array}{cccccc} l_{(g_{N-1})} & d_{(g_{N-1}+1)} & u_{(g_{N-1}+1)} \\ & \ddots & \ddots & \ddots \\ & & & l_{(g_{N-1}+n_{N-1}-1)} & d_{(g_{N-1}+n_{N-1})} \end{array}\right]. \]](form_40.png)
In this case, arrays lower[], diag[], and upper[] of dimension localDim, localDim and localDim-1 respectively are stored (see initialize()).
Note, this is just an example class and for the sake of simplified presentation the private members are listed first and in-class declarations are used which are not a good idea in production code. However, in this case, they make the example code easier to read and maintaining encapsulation and a well defined interface are unnecessary here.
See the source code for this simple example by clicking on the link to the definition below.
Definition at line 134 of file MPITridiagLinearOp.hpp.
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Construct to uninitialized.
Definition at line 153 of file MPITridiagLinearOp.hpp. |
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Calls
Definition at line 156 of file MPITridiagLinearOp.hpp. |
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Initialize given lower, diagonal and upper arrays of data.
Postconditions:
Definition at line 176 of file MPITridiagLinearOp.hpp. |
1.3.9.1