Incidence matrix

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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'.

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).

An incidence matrix for a simple system (models/johnpye/fourbar.a4c)

See also