org.opensourcephysics.numerics.dde_solvers.rk.irk
Class IRKLinearAlgebra
java.lang.Object
org.opensourcephysics.numerics.dde_solvers.rk.irk.IRKLinearAlgebra
public class IRKLinearAlgebra
- extends java.lang.Object
Non objective software for solving linear equations
see org.opensourcephysics.numerics.LUPdecomposition
Method Summary |
int |
dec(int N,
int NDIM,
double[][] A,
int[] IP)
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MATRIX TRIANGULARIZATION BY GAUSSIAN ELIMINATION. |
int |
decc(int N,
int NDIM,
double[][] AR,
double[][] AI,
int[] IP)
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MATRIX TRIANGULARIZATION BY GAUSSIAN ELIMINATION
------ MODIFICATION FOR COMPLEX MATRICES --------
INPUT.. |
void |
sol(int N,
int NDIM,
double[][] A,
double[] B,
int[] IP)
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SOLUTION OF LINEAR SYSTEM, A * X = B . |
void |
solc(int N,
int NDIM,
double[][] AR,
double[][] AI,
double[] BR,
double[] BI,
int[] IP)
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SOLUTION OF LINEAR SYSTEM, A * X = B . |
Methods inherited from class java.lang.Object |
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
IRKLinearAlgebra
public IRKLinearAlgebra()
dec
public int dec(int N,
int NDIM,
double[][] A,
int[] IP)
- -----------------------------------------------------------------------
MATRIX TRIANGULARIZATION BY GAUSSIAN ELIMINATION.
INPUT..
N = ORDER OF MATRIX.
NDIM = DECLARED DIMENSION OF ARRAY A .
A = MATRIX TO BE TRIANGULARIZED.
OUTPUT..
A[I][J], I <= J = UPPER TRIANGULAR FACTOR, U .
A[I][J], I > J = MULTIPLIERS = LOWER TRIANGULAR FACTOR, I - L.
IP[K], K < N - 1 = INDEX OF K-TH PIVOT ROW.
IP[N - 1] = (-1)**(NUMBER OF INTERCHANGES) OR O .
IER = -1 IF MATRIX A IS NONSINGULAR, OR K IF FOUND TO BE
SINGULAR AT STAGE K.
USE SOL TO OBTAIN SOLUTION OF LINEAR SYSTEM.
DETERM(A) = IP[N - 1] * A[0][0] * A[1][1] * ... * A[N - 1][N - 1].
IF IP[N - 1] = O, A IS SINGULAR, SOL WILL DIVIDE BY ZERO.
REFERENCE..
C. B. MOLER, ALGORITHM 423, LINEAR EQUATION SOLVER,
C.A.C.M. 15 (1972), P. 274.
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sol
public void sol(int N,
int NDIM,
double[][] A,
double[] B,
int[] IP)
- -----------------------------------------------------------------------
SOLUTION OF LINEAR SYSTEM, A * X = B .
INPUT..
N = ORDER OF MATRIX.
NDIM = DECLARED DIMENSION OF ARRAY A .
A = TRIANGULARIZED MATRIX OBTAINED FROM DEC.
B = RIGHT HAND SIDE VECTOR.
IP = PIVOT VECTOR OBTAINED FROM DEC.
DO NOT USE IF DEC HAS SET IER != -1.
OUTPUT..
B = SOLUTION VECTOR, X .
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decc
public int decc(int N,
int NDIM,
double[][] AR,
double[][] AI,
int[] IP)
- -----------------------------------------------------------------------
MATRIX TRIANGULARIZATION BY GAUSSIAN ELIMINATION
------ MODIFICATION FOR COMPLEX MATRICES --------
INPUT..
N = ORDER OF MATRIX.
NDIM = DECLARED DIMENSION OF ARRAYS AR AND AI .
(AR, AI) = MATRIX TO BE TRIANGULARIZED.
OUTPUT..
AR[I][J], I <= J = UPPER TRIANGULAR FACTOR, U ; REAL PART.
AI[I][J], I <= J = UPPER TRIANGULAR FACTOR, U ; IMAGINARY PART.
AR[I][J], I > J = MULTIPLIERS = LOWER TRIANGULAR FACTOR, I - L ; REAL PART.
AI[I][J], I > J = MULTIPLIERS = LOWER TRIANGULAR FACTOR, I - L ; IMAGINARY PART.
IP[K], K <= N - 1 = INDEX OF K-TH PIVOT ROW.
IP[N - 1] = (-1)**(NUMBER OF INTERCHANGES) OR O .
IER = -1 IF MATRIX A IS NONSINGULAR, OR K IF FOUND TO BE
SINGULAR AT STAGE K.
USE SOLC TO OBTAIN SOLUTION OF LINEAR SYSTEM.
IF IP[N - 1] = O, A IS SINGULAR, SOLC WILL DIVIDE BY ZERO.
REFERENCE..
C. B. MOLER, ALGORITHM 423, LINEAR EQUATION SOLVER,
C.A.C.M. 15 (1972), P. 274.
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solc
public void solc(int N,
int NDIM,
double[][] AR,
double[][] AI,
double[] BR,
double[] BI,
int[] IP)
- -----------------------------------------------------------------------
SOLUTION OF LINEAR SYSTEM, A * X = B .
INPUT..
N = ORDER OF MATRIX.
NDIM = DECLARED DIMENSION OF ARRAYS AR AND AI.
(AR,AI) = TRIANGULARIZED MATRIX OBTAINED FROM DEC.
(BR,BI) = RIGHT HAND SIDE VECTOR.
IP = PIVOT VECTOR OBTAINED FROM DEC.
DO NOT USE IF DECC HAS SET IER != -1.
OUTPUT..
(BR,BI) = SOLUTION VECTOR, X .
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