Procedures

Returns the values of the Jacobi elliptic functions evaluated at real or complex argument u and parameter $M = \exp(-2 \pi L)$, $0 < L < \infty$. For $M = K^2$, and $K$ the elliptic modulus.

Complete elliptic integral of the first kind, with complement. Returns the value of the complete elliptic integral of the first kind, evaluated at $M=\exp(-2\pi L)$, $0 < L < \infty$, and the complementarity parameter $1-M$.

Function to integrate

Get iteration parameters from the command line

Get iteration parameters from the command line

This subroutine reads the parameters needed to run the arnolditest program from standard input

This subroutine reads the parameters needed to run the lanczostest program from standard input

This subroutine reads the parameters needed to run the serialtest program from standard input

Method 1 of Hale, Nicholas; Higham, Nicholas J.; Trefethen, Lloyd N. Computing $\mathbf{A}^\alpha,\ \log(\mathbf{A})$, and related matrix functions by contour integrals. SIAM J. Numer. Anal. 46 (2008), no. 5, 2505--2523.

Apply Horner rule to evaluate a polynomial

Prints out information on incorrected program usage

Prints out information on incorrected program usage

Prints out information on incorrected program usage

We add the methods for the shifted system to the same interfaces in PSBLAS it is a lazy way to avoid modifying all the Krylov methods in PSBLAS to allow for the solution of shifted linear systems

Simple polynomial method based on the Arnoldi orthogonalization procedure, the method builds a basis $V_k$ for the Krylov subspace

Simple polynomial method based on the Lanczos orthogonalization procedure, the method builds a basis $V_k$ for the Krylov subspace

This is the generic function for applying every implemented Krylov method. The general iteration parameters (like the number of iteration, the stop criterion to be used, and the verbosity of the trace) can be passed directly to this routine. All the constitutive parameters of the actual method, and the information relative to the function are instead contained in the meth and fun objects. The Descriptor object `desc_a' contains the properties of the parallel environment.

This function plots the convergence history of the Krylov method

This function builds the AMG4PSBLAS preconditioner for the inner solve in a Rational Krylov method

This function performs the init of the preconditioner for the inner solve in the rational Krylov method

Plots on the complex plane the quadrature poles, and plots the weights of the formula

This interface contains the Shift-and-Invert method based on Arnoldi orthogonalization.

This is the core of the function apply on a serial matrix to compute $y = f(\alpha A) x$. It calls on the specific routines implementing the different functions. It is the function to modify if ones want to interface a new function that was not previously available or a new algorithm (variant) for an already existing function.

This is the core of the function apply on a serial matrix to compute $y = f(\alpha*A) x$ when A is memorized in a sparse storage. In this case the routine converts it to a dense storage and then calls the array version of itself. That is the one implementing the different functions. It is the function to modify if ones want to interface a new function that was not previously available or a new algorithm (variant) for an already existing function.

Preconditioned Conjugate Gradient for shifted system $(\eta A + \zeta I)x = b$

Apply Krylov method to $(\eta A + \zeta I)x = b$ on distributed vectors

Compute the poles for a given combination of quadrature rule and quadrature formula

Plots on the complex plane the quadrature poles, and plots the weights of the formula

Set the matrix $A$ for $f(A)x$

Set the preconditioner to use for the given quadrature formula