The LSQR pane is on the PEST Properties dialog box.
Singular Value Decomposition and LSQR can not both be used together so activating one deactivates the other. If both are deactivated, PEST’s default solver is used.
The variables specified on the LSQR pane are described in the PEST User Manual, Part I, Section 4.5. More extensive descriptions of these variables are in the PEST user manual. The variables specified on this pane appear in the LSQR section of the PEST control file.
LSQR can be used interchangeably with singular value decomposition and with PEST’s default solver.
The LSQR solution process is similar in many respects to that forthcoming from singular value decomposition. Parameter space is subdivided into estimable and inestimable subspaces. Estimates are calculated only for linear combinations of parameters comprising the former; other combinations remain unchanged from the initial values of these combinations. The process is thus numerically stable, regardless of how ill-posed the inverse problem is. In practice, in order to promulgate not just numerical stability, but also sensibility of estimated parameters, Tikhonov regularization should also be introduced to an ill-posed inverse problem.
A benefit of LSQR over singular value decomposition is its speed. If parameters number more than a couple of thousand, singular value decomposition can become very slow. This is not the case for LSQR which can happily handle tens of thousands of parameters and hundreds of thousands of observations. The cost of this speed is a slight approximation in separating solution and null subspaces; but this rarely matters.
LSQRMODE is used to activate or deactivate the LSQR solution process.
LSQR_ATOL is an estimate of the relative error in the data defining the matrix A. For example, if A is accurate to about 6 digits, set atol to 1.0e-6. An ATOL value of 1E-4 generally works well.
LSQR_BTOL is an estimate of the relative error in the data defining the right-hand side vector b. For example, if b is accurate to about 6 digits, set btol to 1.0e-6. A value of 1E-4 generally works well.
LSQR_CONLIM is an upper limit on cond(A), the apparent condition number of the matrix A. Iterations will be terminated if a computed estimate of cond(A) exceeds LSQR_CONLIM. This is intended to prevent certain small or zero singular values of A or A from coming into effect and causing unwanted growth in the computed solution. A value of 1000.0 generally works well.
LSQR_ITNLIM is an upper limit on the number of iterations. If LSQR_ITNLIM is specified as zero, ModelMuse will automatically export LSQR_ITNLIM as four times the number of parameters.
LSQRWRITE is used to activate or deactivate and output file from the LSQR process.
