Incidence matrix: Difference between revisions
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The '''incidence matrix''' (or '''sparsity matrix''') is a matrix of ones and zeros. The rows correspond to equations in your model, and the columns correspond to the variables in your model. At points where the variable corresponding to the current column is present in the equation corresponding to the current row, there will be a '1', otherwise there will be a '0'. | The '''incidence matrix''' (or '''sparsity matrix''') is a matrix of ones and zeros. The rows correspond to equations in your model, and the columns correspond to the variables in your model. At points where the variable corresponding to the current column is present in the equation corresponding to the current row, there will be a '1', otherwise there will be a '0'. | ||
When incidence matrices are shown graphically in ASCEND PyGTK, a green mark is used to indicate '''fixed''' variables, and blue is used to indicate '''free''' variables (ie those that are being solved for). | When incidence matrices are shown graphically in ASCEND PyGTK, a green mark is used to indicate '''fixed''' variables, and blue is used to indicate '''free''' variables (ie those that are being solved for). | ||
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The incidence matrix shows the variables and equations after they have been reordered to minimise iterative solving. As a result, when the blue part of the incidence matrix is in lower-triangular shape, it means that there are no simultaneous equations: all variables can be solved for explicitly, in order. In other cases, as here, there are some variables that need to be solved; ASCEND uses Newton's method in these cases (see [[QRSlv]]). | The incidence matrix shows the variables and equations after they have been reordered to minimise iterative solving. As a result, when the blue part of the incidence matrix is in lower-triangular shape, it means that there are no simultaneous equations: all variables can be solved for explicitly, in order. In other cases, as here, there are some variables that need to be solved; ASCEND uses Newton's method in these cases (see [[QRSlv]]). | ||
[[Image:sparsity-4bar.png|400px|thumb|none|An incidence matrix for a simple system ({{src|models/johnpye/fourbar.a4c}}) | [[Image:sparsity-4bar.png|400px|thumb|none|An incidence matrix for a simple system ({{src|models/johnpye/fourbar.a4c}})]] | ||
== See also == | == See also == | ||
You can also generate an [[Incidence Graph]] of your system. | * You can also generate an [[Incidence Graph]] of your system. | ||
* [[Block partitioning]] | |||
[[Category:Documentation]] | [[Category:Documentation]] | ||
Latest revision as of 05:18, 3 February 2011
The incidence matrix (or sparsity matrix) is a matrix of ones and zeros. The rows correspond to equations in your model, and the columns correspond to the variables in your model. At points where the variable corresponding to the current column is present in the equation corresponding to the current row, there will be a '1', otherwise there will be a '0'.
When incidence matrices are shown graphically in ASCEND PyGTK, a green mark is used to indicate fixed variables, and blue is used to indicate free variables (ie those that are being solved for).
The incidence matrix shows the variables and equations after they have been reordered to minimise iterative solving. As a result, when the blue part of the incidence matrix is in lower-triangular shape, it means that there are no simultaneous equations: all variables can be solved for explicitly, in order. In other cases, as here, there are some variables that need to be solved; ASCEND uses Newton's method in these cases (see QRSlv).
See also
- You can also generate an Incidence Graph of your system.
- Block partitioning