Add documentation for all Keyword arguments

src/bicgstab.jl

@@ -62,17 +62,17 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `c`:
-* `M`:
-* `N`:
-* `ldiv`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `c`: the second initial vector of length `n` required by the Lanczos biorthogonalization process;
+* `M`: linear operator that models a nonsingular matrix of size `n` used for left preconditioning;
+* `N`: linear operator that models a nonsingular matrix of size `n` used for right preconditioning;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 

src/bilq.jl

@@ -48,15 +48,15 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `c`:
-* `transfer_to_bicg`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `c`: the second initial vector of length `n` required by the Lanczos biorthogonalization process;
+* `transfer_to_bicg`: transfer from the BiLQ point to the BiCG point, when it exists. The transfer is based on the residual norm;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 

src/bilqr.jl

@@ -54,14 +54,14 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `transfer_to_bicg`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `transfer_to_bicg`: transfer from the BiLQ point to the BiCG point, when it exists. The transfer is based on the residual norm;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 

src/cg.jl

@@ -54,17 +54,17 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `ldiv`:
-* `radius`:
-* `linesearch`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning;
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `radius`: add the trust-region constraint ‖x‖ ≤ `radius` if `radius > 0`. Useful to compute a step in a trust-region method for optimization;
+* `linesearch`: if `true`, indicate that the solution is to be used in an inexact Newton method with linesearch. If negative curvature is detected at iteration k > 0, the solution of iteration k-1 is returned. If negative curvature is detected at iteration 0, the right-hand side is returned (i.e., the negative gradient);
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 

src/cg_lanczos.jl

@@ -49,16 +49,16 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `ldiv`:
-* `check_curvature`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning;
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `check_curvature`: if `true`, check that the curvature of the quadratic along the search direction is positive, and abort if not, unless `linesearch` is also `true`;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 

src/cg_lanczos_shift.jl

@@ -45,16 +45,16 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `ldiv`:
-* `check_curvature`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning;
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `check_curvature`: if `true`, check that the curvature of the quadratic along the search direction is positive, and abort if not, unless `linesearch` is also `true`;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 

src/cgls.jl

@@ -63,17 +63,17 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `ldiv`:
-* `radius`:
-* `λ`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `N`: linear operator that models a Hermitian positive-definite matrix of size `n` used for preconditioning;
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `radius`: add the trust-region constraint ‖x‖ ≤ `radius` if `radius > 0`. Useful to compute a step in a trust-region method for optimization;
+* `λ`: regularization parameter;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 

src/cgne.jl

@@ -74,15 +74,15 @@ and `false` otherwise.
 #### Keyword arguments
 
 * `N`:
-* `ldiv`:
-* `λ`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `λ`: regularization parameter;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 

src/cgs.jl

@@ -60,17 +60,17 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `c`:
-* `M`:
-* `N`:
-* `ldiv`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `c`: the second initial vector of length `n` required by the Lanczos biorthogonalization process;
+* `M`: linear operator that models a nonsingular matrix of size `n` used for left preconditioning;
+* `N`: linear operator that models a nonsingular matrix of size `n` used for right preconditioning;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 

src/cr.jl

@@ -54,18 +54,18 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `ldiv`:
-* `radius`:
-* `linesearch`:
-* `γ`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning;
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `radius`: add the trust-region constraint ‖x‖ ≤ `radius` if `radius > 0`. Useful to compute a step in a trust-region method for optimization;
+* `linesearch`: if `true`, indicate that the solution is to be used in an inexact Newton method with linesearch. If negative curvature is detected at iteration k > 0, the solution of iteration k-1 is returned. If negative curvature is detected at iteration 0, the right-hand side is returned (i.e., the negative gradient);
+* `γ`: tolerance to determine that the curvature of the quadratic model is nonpositive;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 

src/craig.jl

@@ -98,21 +98,21 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `N`:
-* `ldiv`:
-* `transfer_to_lsqr`:
-* `sqd`:
-* `λ`:
-* `btol`:
-* `conlim`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `m` used for centered preconditioning of the augmented system;
+* `N`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning of the augmented system;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `transfer_to_lsqr`: transfer from the LSLQ point to the LSQR point, when it exists. The transfer is based on the residual norm;
+* `sqd`: if `true`, set `λ=1` for Hermitian quasi-definite systems;
+* `λ`: regularization parameter;
+* `btol`: stopping tolerance used to detect zero-residual problems;
+* `conlim`: limit on the estimated condition number of `A` beyond which the solution will be abandoned;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 

src/craigmr.jl

@@ -93,18 +93,18 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `N`:
-* `ldiv`:
-* `sqd`:
-* `λ`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `m` used for centered preconditioning of the augmented system;
+* `N`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning of the augmented system;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `sqd`: if `true`, set `λ=1` for Hermitian quasi-definite systems;
+* `λ`: regularization parameter;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 

src/crls.jl

@@ -55,17 +55,17 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `ldiv`:
-* `radius`:
-* `λ`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `N`: linear operator that models a Hermitian positive-definite matrix of size `n` used for preconditioning;
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `radius`: add the trust-region constraint ‖x‖ ≤ `radius` if `radius > 0`. Useful to compute a step in a trust-region method for optimization;
+* `λ`: regularization parameter;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 

src/crmr.jl

@@ -72,15 +72,15 @@ and `false` otherwise.
 #### Keyword arguments
 
 * `N`:
-* `ldiv`:
-* `λ`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `λ`: regularization parameter;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments