PITCON - The Continuation Method

PITCON is an implementation of the continuation method for systems of nonlinear equations. The program is designed for problems in which N variables are constrained by N-1 nonlinear equations. Generally, there is an entire family of solutions to such a problem, which can be thought of as a curve in N-dimensional space. Given one solution, PITCON attempts to determine the curve of solutions through that point, and to produce further solutions along the curve.

An earlier version of PITCON is available as an ACM TOMS algorithm 596, through the NETLIB web site.

Files you may copy include:

• PITCON.F90, the source code;
• PCPRB1.F90, sample program 1;
• PCPRB1.OUT, output from sample program 1;
• PCPRB2.F90, sample program 2;
• PCPRB2.OUT, output from sample program 2;
• PCPRB3.F90, sample program 3;
• PCPRB3.OUT, output from sample program 3;
• PCPRB4.F90, sample program 4;
• PCPRB4.OUT, output from sample program 4;
• PCPRB5.F90, sample program 5;
• PCPRB5.OUT, output from sample program 5;
• PCPRB6.F90, sample program 6;
• PCPRB6.OUT, output from sample program 6;
• PCPRB7.F90, sample program 7;
• PCPRB7.OUT, output from sample program 7;
• PCPRB8.F90, sample program 8;
• PCPRB8.OUT, output from sample program 8;

The list of routines includes:

• PITCON is the user-interface routine for the continuation code.
• DGB_JAC approximates a banded jacobian matrix.
• DGB_SLV solves a linear system of the form
• DGE_JAC approximates a dense jacobian matrix.
• DGE_SLV solves the NVAR by NVAR dense linear system
• DGE_TRF computes the PLU factorization of a general M by N matrix.
• DGE_TRS solves a system of linear equations factored by DGE_TRF.
• CHECKW checks the entries of IWORK and RWORK on the first call.
• COQUAL computes the factor QUAL which is based on the 'quality' of
• CORECT performs the Newton correction of an approximate solution X of
• DGB_DET computes the determinant of a band matrix factored by SGB_FA.
• DGE_DET computes the determinant of a matrix factored by DGE_TRF.
• LIMIT seeks a limit point between two continuation points.
• REPS tries to compute the machine relative precision.
• ROOT seeks a root of the scalar equation F(X)=0.0.
• SETSTP computes the stepsize to be used by the Euler prediction step.
• STAJAC is used to generate and factor the jacobian the very
• START makes sure that, on the first call, the input point XR
• TANGNT computes a tangent vector to the solution curve.
• TANPAR computes the next tangent vector and continuation index.
• TARGET controls the computation of a target point.
• TRYSTP tries to carry out a continuation step.
• UPDATE updates information after a successful continuation step.
• DGB_TRF performs a PLU factorization of an M by N band matrix.
• DGBTRS solves a linear system factored by DGB_TRF.

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