PETSc version 3.15.5
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# KSPComputeRitz

Computes the Ritz or harmonic Ritz pairs associated to the smallest or largest in modulus, for the preconditioned operator. Called after KSPSolve().

### Synopsis

    #include "petscksp.h"
    #include "petscmat.h"
    PetscErrorCode  KSPComputeRitz(KSP ksp,PetscBool ritz,PetscBool small,PetscInt *nrit,Vec S[],PetscReal tetar[],PetscReal tetai[])

Not Collective

### Input Parameters

| ksp | - iterative context obtained from KSPCreate()
| ritz | - PETSC_TRUE or PETSC_FALSE for ritz pairs or harmonic Ritz pairs, respectively
| small | - PETSC_TRUE or PETSC_FALSE for smallest or largest (harmonic) Ritz values, respectively
| nrit | - number of (harmonic) Ritz pairs to compute

### Output Parameters

| nrit | - actual number of computed (harmonic) Ritz pairs
| S | - multidimensional vector with Ritz vectors
| tetar | - real part of the Ritz values
| tetai | - imaginary part of the Ritz values

### Notes

-For GMRES, the (harmonic) Ritz pairs are computed from the Hessenberg matrix obtained during the last complete cycle, or obtained at the end of the solution if the method is stopped before a restart. Then, the number of actual (harmonic) Ritz pairs computed is less or equal to the restart parameter for GMRES if a complete cycle has been performed or less or equal to the number of GMRES iterations. -Moreover, for real matrices, the (harmonic) Ritz pairs are possibly complex-valued. In such a case, the routine selects the complex (harmonic) Ritz value and its conjugate, and two successive columns of S are equal to the real and the imaginary parts of the associated vectors. -the (harmonic) Ritz pairs are given in order of increasing (harmonic) Ritz values in modulus -this is currently not implemented when PETSc is built with complex numbers

One must call KSPSetComputeRitz() before calling KSPSetUp() in order for this routine to work correctly.

### See Also

KSPSetComputeRitz(), KSP

### Level

advanced

### Location

src/ksp/ksp/interface/itfunc.c

### Implementations

KSPComputeRitz_GMRES in src/ksp/ksp/impls/gmres/gmreig.c
Index of all KSP routines
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