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Document the unit test hierarchy in here.
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‎TEST_HIERARCHY.md‎

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This is the order in which new units tests for VMEC++ shall be implemented.
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When running them, progress in a depth-first manner - make sure all minor steps of a given major step pass before progressing towards the next major step.
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1. `//vmecpp/common/vmec_indata` - parsing of input file
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2. `//vmecpp/common/sizes` - sizes of arrays
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3. `//vmecpp/common/fourier_basis_fast_poloidal` - Fourier basis functions for (inv-)DFTs
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4. `//vmecpp/common/fourier_basis_fast_toroidal` - Fourier basis functions for (inv-)DFTs
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5. `//vmecpp/vmec/boundaries` - convert the INDATA rbc, …, zbc boundary representation into the VMEC-internal rbcc, …, zbcc format (Ptolemy’s identity)
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6. `//vmecpp/vmec/ideal_mhd_model` - go through the forward model step by step
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1. `CheckSpectralConstraint` - static computation of the arrays related to the spectral constraint
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7. `//vmecpp/vmec/radial_profiles` - evaluation of static radial profiles
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8. `//vmecpp/vmec/fourier_geometry` - get an initial guess for the geometry of the flux surfaces by interpolation between the axis and the boundary from the INDATA
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9. `//vmecpp/vmec/ideal_mhd_model` - go through the forward model step by step
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1. `CheckFourierGeometryToStartWith` - check inputs to inv-DFT - first iteration
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2. `CheckInverseFourierTransformGeometry` - checks output of inv-DFT - first iteration
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3. `CheckJacobian` - Jacobian calculation - first iteration
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4. `CheckMetric` - metric coefficients - first iteration
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5. `CheckVolume` - plasma volume (differential and total) - first iteration
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6. `CheckContravariantMagneticField` - toroidal current constraint and contravariant B - first iteration
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7. `CheckCovariantMagneticField` - covariant magnetic field components - first iteration
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8. `CheckTotalPressureAndEnergies` - total pressure, thermal energy, magnetic energy - first iteration
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9. `CheckRadialForceBalance` - radial force balance - first iteration
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10. `CheckHybridLambdaForce` - hybrid lambda force (covariant B on full-grid) - first iteration
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11. `CheckUpdateRadialPreconditioner` - compute preconditioning matrix elements - first iteration
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12. `CheckForceNorms` - force normalization - first iteration
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13. `CheckConstraintForceMultiplier` - constraint force re-scaling - first iteration
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14. All the Nestor tests have to be run here in case of a free-boundary case, since Nestor is executed at this point along the forward model evaluation. - (likely) not in first iteration
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1. `//vmecpp/nestor/nestor`
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1. `CheckInputsToNestorCall`
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2. `//vmecpp/nestor/surface_geometry`
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1. `CheckSurfaceGeometry`
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3. `//vmecpp/nestor/mgrid_provider`
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1. `CheckLoadMGrid`
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4. `//vmecpp/nestor/external_magnetic_field`
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1. `CheckExternalMagneticField`
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5. `//vmecpp/nestor/singular_integrals`
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1. `CheckConstants`
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2. `CheckCmns`
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3. `CheckAnalyt`
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This maybe requires swapping `slp`/`slm` and `tlp`/`tlm` in `analyt` when passed to `analysum2`.
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6. `//vmecpp/nestor/regularized_integrals`
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1. `CheckTanuTanv`
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2. `CheckGreenF`
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7. `//vmecpp/nestor/laplace_solver`
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1. `CheckFourP`
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2. `CheckFourISymm`
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3. `CheckFourIAccumulateGrpmn`
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4. `CheckFourIKvDft`
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5. `CheckFourIKuDft`
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6. `CheckSolverInputs`
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7. `CheckLinearSolver`
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8. `//vmecpp/nestor/nestor`
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1. `CheckBsqVac`
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15. `CheckRBsq` - free-boundary force contribution
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16. `CheckAlias` - de-alias constraint force - first iteration
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17. `CheckRealspaceForces` - MHD forces on R and Z - first iteration
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18. `CheckForwardTransformForces` - forward DFT of forces - first iteration
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19. `CheckPhysicalForces` - re-scaled force coefficients - first iteration
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20. `CheckInvariantResiduals` - invariant force residuals - first iteration
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21. `CheckApplyM1Preconditioner` - apply the m=1 preconditioner - first iteration
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22. `CheckAssembleRZPreconditioner` - assemble preconditioning matrix for R and Z - first iteration
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23. `CheckApplyPreconditioner` - tri-diagonal solver used to apply radial preconditioner for R and Z - first iteration
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24. `CheckPreconditionedResiduals` - preconditioned force residuals - first iteration
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10. `//vmecpp/vmec/vmec` - iterative solver
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1. `CheckPrintout` - check screen printout quantities, like <M> etc.
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2. `CheckEvolve` - evolve Fourier coefficients to next iteration - first iteration
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11. `//vmecpp/vmec/ideal_mhd_model` - go through the forward model step by step all tests as above again, but now for second iteration
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12. `//vmecpp/vmec/vmec` - iterative solver
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1. `CheckEvolve` - evolve Fourier coefficients to next iteration - second iteration
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2. `CheckMultigridResult` - run a multi-grid step until convergence - first multi-grid step
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3. `CheckInterp` - interpolation to next multi-grid resolution - first to second multi-grid step
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13. `//vmecpp/vmec/output_quantities` - final output quantities computation
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1. `CheckGatherDataFromThreads` - gather data from multiple threads
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2. `CheckBSSRoutineOutputs` - compute remaining metric elements, B_s and cylindrical components of B
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3. `CheckLowpassFilterBSubsS` low-pass filtering in tangential Fourier space of covariant B components
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4. `CheckExtrapolateBSubsS` - extrapolate B_s onto axis and boundary
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5. `CheckJxBOutputContents` - compute quantities that normally end up in the jxbout file
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6. `CheckMercierStability` - compute ideal-MHD Mercier stability→ mercier output file
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7. `CheckThreed1FirstTable` - first table that appears in the threed1 output file
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8. `CheckThreed1GeometricMagneticQuantities` - table on “more geometric and magnetic quantities” in threed1 output file
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9. `CheckThreed1Volumetrics` - volumetric quantities that appear in the threed1 file
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10. `CheckThreed1Axis` - Fourier coefficients of magnetic axis, as they appear in the threed1 output file
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11. `CheckThreed1Betas` - table of beta values in threed1 file
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12. `CheckThreed1ShafranovIntegrals` - Shafranov integrals in threed1 output file
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13. `CheckWOutFileContents` - main VMEC output file wout

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