Procedures

Given a square linear operator $A$, find matrices $X$ and $H$ such that

This interface provides methods to assert tha thte shape of its input vector or matrix is as expected. It throws an error if not.

In-place addition of two arrays of extended abstract_vector.

Given a general linear operator $A$, find matrices $U$, $V$ and $B$ such that

Given a symmetric (positive definite) matrix $A$, solves the linear system

Constant tolerance scheduler for the Newton iteration

Constant tolerance scheduler for the Newton iteration

This interface provides methods to copy an array X of abstract_vector into another array Y. Note that Y needs to be pre-allocated.

Given an array $X$ of abstract_vector and an abstract_vector (or array of abstract_vectors) $y$, this subroutine returns a modified vector $y$ orthogonal to all columns of $X$, i.e.

Dynamic tolerance scheduler for the Newton iteration setting tol based on the current residual tol

Dynamic tolerance scheduler for the Newton iteration setting tol based on the current residual tol

Computes the eigenvalue decomposition of a general square matrix.

Computes the leading eigenpairs of a symmetric operator $A$ using the Lanczos iterative process. Given a square linear operator $A$, it finds the leading eigvalues and eigvectors such that:

Computes the leading eigenpairs of a square linear operator $A$ using the Arnoldi iterative process. Given a square linear operator $A$, it finds the leading eigvalues and eigvectorss such that:

Evaluate the exponential of a dense matrix using Pade approximations.

Solve a square linear system of equations

Utility function to get the dimension of the communicator known to LightKrylov.

Utility function to get the rank of the current MPI process.

Solve a square linear system of equations

Compute the Gram matrix $\mathbf{G} = \mathbf{X}^H \mathbf{X}$.

Utility function to initialize a basis for a Krylov subspace.

Compute the inner product vector $\mathbf{v} = \mathbf{X}^H \mathbf{y}$ or matrix $\mathbf{M} = \mathbf{X}^H \mathbf{Y}$.

Given a permutation vector $p$, this function computes the vector representation of the inverse permutation matrix.

Utility function to determine whether the current MPI process can do I/O.

Utility function returning a logical .true. if the set of vectors stored in $X$ form an orthonormal set of vectors and .false. otherwise.

This interface provides methods to evaluate the matrix-vector product $c = \exp(\tau A) b$ based on the Arnoldi method.

Utility function to evaluate the matrix-exponential times vector.

Given a partial Krylov decomposition

Given a symmetric or Hermitian linear operator $A$, find matrices $X$ and $T$ such that

Given a set of extended abstract_vectors and coefficients, return the corresponding linear combinations.

Utility function to compute the base-2 logarithm of a real number.

Wrapper to set up MPI if needed and initialize log files

Implements the simple Newton-Krylov method for finding roots (fixed points) of a nonlinear vector-valued function $F(\mathbf{X})$, i.e. solutions $\mathbf{X}^*$ such that $F(\mathbf{X}^*) - \mathbf{X}^* = \mathbf{0}$ starting from an initial guess via successive solution increments based on local linearization $\mathbf{J}_\mathbf{X}$ (the Jacobian) of the nonlinear function in the vicinity of the current solution.

Given the Schur factorization and basis of a matrix, reorders it to have the selected eigenvalues in the upper left block.

Given an array $X$ of vectors, it computes an orthonormal basis for its column-span using the double_gram_schmidt process. All computations are done in-place.

Given an array $X$ and a permutation vector $p$, this function computes in-place the column-permuted matrix

Given an array $X$ of types derived from abstract_vector, it computes the in-place QR factorization of $X$, i.e.

This interface provides methods to create an array X of random abstract_vector. It is a simple wrapper around X(i)%rand(ifnorm).

Utility function to save the eigenspectrum computed from the Arnoldi factorization. It outpost a .npy file.

Utility function to inform LightKrylov of the MPI-communicator's dimension.

Utility function to set the rank of the process doing I/O.

Utility function to set the rank of an MPI process.

Computes the non-negative square root of a symmetric positive definite matrix using its singular value decomposition.

Computes the leading singular triplets of an arbitrary linear operator $A$ using the Lanczos iterative process. Given a linear operator $A$, it finds the leading singular values and singular vectors such that:

Prints the intermediate results of iterative eigenvalue/singular value decompositions

Prints the intermediate results of iterative eigenvalue/singular value decompositions

Prints the intermediate results of iterative eigenvalue/singular value decompositions

Prints the intermediate results of iterative eigenvalue/singular value decompositions

This interface provides methods to zero-out a collection of abstract_vector X. It is a simple wrapper around X(i)%zero().