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XPRSbasisstability (BASISSTABILITY)

Purpose
Calculates various measures for the stability of the current basis, including the basis condition number.
Topic areas
Linear Algebra, LP
Synopsis
int XPRS_CC XPRSbasisstability(XPRSprob prob, int type, int norm, int scaled, double *p_value);
BASISSTABILITY [-flags]
Arguments
prob 
The current problem.
type 
0 
Condition number of the basis.
1 
Stability measure for the solution relative to the current basis.
2 
Stability measure for the duals relative to the current basis.
3 
Stability measure for the right hand side relative to the current basis.
4 
Stability measure for the basic part of the objective relative to the current basis.
norm 
0 
Use the infinity norm.
1 
Use the 1 norm.
2 
Use the Euclidian norm for vectors, and the Frobenius norm for matrices.
scaled 
If the stability values are to be calculated in the scaled, or the unscaled matrix.
p_value 
Pointer to a double, where the calculated value is to be returned.
flags 
x 
Stability measure for the solution and right–hand side values relative to the current basis.
d 
Stability measure for the duals and the basic part of the objective relative to the current basis.
c 
Condition number of the basis (default).
i 
Use the infinity norm (default).
o 
Use the one norm.
e 
Use the Euclidian norm for vectors, and the Frobenius norm for matrices.
u 
Calculate values in the unscaled matrix.
Further information
1. The Console Optimizer command BASISSTABILITY uses 0 as the default value for type and norm, and calculates the values in the scaled matrix.
2. The condition number ( type = 0) of an invertible matrix is the norm of the matrix multiplied with the norm of its inverse. This number is an indication of how accurate the solution can be calculated and how sensitive it is to small changes in the data. The larger the condition number is, the less accurate the solution is likely to become.
3. The stability measures ( type = 1...4) are using the original matrix and the basis to recalculate the various vectors related to the solution and the duals. The returned stability measure is the norm of the difference of the recalculated vector to the original one.

Parent Topic Console and Library Functions

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