baram2584/FESADev
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

feat: integrate generalized consistent-mass Solid frequency

Browse Source
This commit is contained in:
KOKO\Mimi
2026-10-09 02:26:51 +09:00
parent 9f53e4557f 0e07b4df08
commit 0a78d516eb
9 changed files with 1149 additions and 80 deletions
Download Patch File Download Diff File Expand all files Collapse all files
include/fesa/analysis/solid_frequency_procedure.h
+18
View File
@@ -0,0 +1,18 @@
#ifndef FESA_ANALYSIS_SOLID_FREQUENCY_PROCEDURE_H_
#define FESA_ANALYSIS_SOLID_FREQUENCY_PROCEDURE_H_
#include "fesa/analysis/solid_frequency_state.h"
namespace fesa {
class Domain;
/// @brief Executes unloaded reference-state C3D8 generalized frequency
/// analysis.
class SolidFrequencyProcedureExecutor final {
public:
/// @brief Returns lowest requested modes after validating every returned
/// pair.
/// @note Domain is immutable and must remain alive during execution.
Result<SolidFrequencyState> Execute(const Domain& domain) const;
};
} // namespace fesa
#endif // FESA_ANALYSIS_SOLID_FREQUENCY_PROCEDURE_H_
include/fesa/analysis/solid_frequency_state.h
+54
View File
@@ -0,0 +1,54 @@
#ifndef FESA_ANALYSIS_SOLID_FREQUENCY_STATE_H_
#define FESA_ANALYSIS_SOLID_FREQUENCY_STATE_H_
#include <cstddef>
#include <cstdint>
#include <optional>
#include <utility>
#include <vector>
#include "fesa/math/matrix.h"
#include "fesa/solvers/eigen/mkl_feast_eigen_solver.h"
namespace fesa {
/// @brief Identifies a source-ordered physical Solid eigenmode.
struct SolidEigenMode {
std::size_t mode_id;
double eigenvalue;
std::uint8_t classification;
std::size_t cluster_id;
std::optional<double> frequency;
};
/// @brief Stores original free K/M validation for every backend pair.
struct SolidEigenpairCheck {
std::size_t sorted_rank;
std::size_t solver_column;
double eigenvalue;
double modal_mass;
double rayleigh_quotient;
double eta_r;
double eta_norm;
double eta_energy;
};
/// @brief Owns a completed modal candidate, independent of response frames.
/// @note Vectors are requested-mode by full source node/UX,UY,UZ order.
struct SolidFrequencyState {
explicit SolidFrequencyState(FeastEigenResult result)
: backend{std::move(result)} {}
std::size_t full_dof_count{0U};
std::size_t free_dof_count{0U};
double classification_scale{0.0};
double mass_ideal_lower_bound{0.0};
double mass_roundoff_guard{0.0};
double mass_lower_bound{0.0};
double eta_gram{0.0};
double max_eta_orth{0.0};
std::vector<std::uint8_t> constraint_mask;
std::vector<double> prescribed_displacement;
std::vector<SolidEigenMode> modes;
Matrix vectors{0U, 0U};
std::vector<SolidEigenpairCheck> eigenpair_checks;
FeastEigenResult backend;
};
} // namespace fesa
#endif // FESA_ANALYSIS_SOLID_FREQUENCY_STATE_H_
include/fesa/elements/hex8_element.h
+3
View File
@@ -47,6 +47,9 @@ class Hex8Element final : public Element {
Result<Hex8Response> EvaluateNonlinear(const Vector& displacement) const;
/// @brief Returns the constant reference consistent mass; density required.
Result<ElementStiffnessContribution> ComputeMass() const;
/// @brief Returns immutable positive reference Gauss volume weights.
/// @note Order is the kernel's fixed eight-point integration order.
std::array<double, 8> ReferenceWeights() const noexcept;
private:
/// @brief Caches shape, reference gradients and positive volume weights.
include/fesa/solvers/eigen/mkl_feast_eigen_solver.h
+23 -1
View File
@@ -58,7 +58,7 @@ struct FeastEigenResult {
std::string upper_search_termination;
};
/// @brief Solves a whitened real-symmetric eigenproblem with oneMKL FEAST.
/// @brief Adapts standard and symmetric-definite sparse pencils to FEAST.
class MklFeastEigenSolver final {
public:
/// @brief Computes all validated interval pairs for a requested lowest-mode
@@ -76,6 +76,28 @@ class MklFeastEigenSolver final {
Result<FeastEigenResult> Solve(const SparseMatrix& whitened_operator,
std::size_t requested_modes,
double zero_operator_scale) const;
/// @brief Solves the original sparse symmetric definite K/M pencil.
/// @param mass_lower_bound Certified positive lower spectral bound of M,
/// including floating-point assembly uncertainty; never a diagonal estimate.
/// @param classification_scale Positive max |Kii|/Mii in physical units.
/// @note Eigenvectors are mass-normalized. For this API the historical
/// whitened_residuals field contains original-pencil eta_r; no whitening
/// is performed. Intervals/eigenvalues in normalized backend evidence use
/// classification_scale, while eigenvalues are returned in physical units.
Result<FeastEigenResult> SolveGeneralized(const SparseMatrix& stiffness,
const SparseMatrix& mass,
std::size_t requested_modes,
double mass_lower_bound,
double classification_scale) const;
private:
/// @brief Shares deterministic count/search controls without changing
/// pencils.
Result<FeastEigenResult> SolveImpl(const SparseMatrix& stiffness,
const SparseMatrix* mass,
std::size_t requested_modes,
double physical_scale,
double mass_lower_bound) const;
};
} // namespace fesa
src/fesa/analysis/solid_frequency_procedure.cpp
+367
View File
@@ -0,0 +1,367 @@
#include "fesa/analysis/solid_frequency_procedure.h"
#include <algorithm>
#include <cmath>
#include <limits>
#include <memory>
#include <new>
#include <stdexcept>
#include <string>
#include <utility>
#include <vector>
#include "fesa/analysis/analysis_model.h"
#include "fesa/assembly/parallel_for.h"
#include "fesa/assembly/sparse_assembler.h"
#include "fesa/constraints/essential_constraint_policy.h"
#include "fesa/elements/element_factory.h"
#include "fesa/elements/hex8_element.h"
#include "fesa/fem/dof_manager.h"
#include "fesa/math/sparse_matrix.h"
#include "fesa/math/vector.h"
#include "fesa/model/domain.h"
namespace fesa {
namespace {
/// @brief Reports a frequency failure without publishing partial state.
Status Failure(const std::string& code, const std::string& message) {
return Status::Failure(
FailureCategory::kSolver,
{{Severity::kError, code, {}, "FREQUENCY", {}, message}});
}
/// @brief Rounds nonnegative arithmetic toward conservative bounds.
double Up(double value) {
return std::nextafter(value, (std::numeric_limits<double>::infinity)());
}
/// @brief Rounds a lower bound downward, including underflow uncertainty.
double Down(double value) {
return std::nextafter(value, -(std::numeric_limits<double>::infinity)());
}
/// @brief Uses robust Frobenius accumulation on original CSR storage.
double Frobenius(const SparseMatrix& matrix) {
double norm = 0.0;
for (const double value : matrix.Values()) norm = std::hypot(norm, value);
return norm;
}
/// @brief Evaluates exact-zero denominator semantics for modal checks.
double Ratio(double numerator, double denominator) {
if (denominator == 0.0)
return numerator == 0.0 ? 0.0 : (std::numeric_limits<double>::infinity)();
return numerator / denominator;
}
/// @brief Builds an immutable candidate; all returns precede public commit.
Result<SolidFrequencyState> ExecuteCandidate(const Domain& domain) {
const auto* frequency = domain.Frequency();
if (!domain.IsSolid() || frequency == nullptr ||
frequency->requested_mode_count <= 0)
return Result<SolidFrequencyState>::Failure(Failure(
"invalid-solid-frequency-procedure", "Solid frequency step required."));
auto model = AnalysisModel::Create(domain);
if (!model.HasValue())
return Result<SolidFrequencyState>::Failure(model.GetStatus());
if (!model.Value().Step().Loads().empty() ||
!model.Value().ActiveSurfacePressureLoads().empty())
return Result<SolidFrequencyState>::Failure(
Failure("loaded-solid-frequency",
"Frequency requires unloaded reference state."));
std::vector<double> density(domain.Materials().Size(), 0.0);
for (const auto& item : domain.Densities()) {
if (item.material_index >= density.size() ||
density[item.material_index] != 0.0 || !std::isfinite(item.rho) ||
!(item.rho > 0.0))
return Result<SolidFrequencyState>::Failure(
Failure("invalid-material-density",
"Density must be unique finite positive."));
density[item.material_index] = item.rho;
}
ElementFactory factory;
std::vector<std::unique_ptr<Element>> owned;
ElementView view;
for (const auto index : model.Value().ActiveElements()) {
const auto& definition = domain.Elements()[index];
if (definition.MaterialIndex() >= density.size() ||
!(density[definition.MaterialIndex()] > 0.0))
return Result<SolidFrequencyState>::Failure(
Failure("missing-frequency-density",
"Every Solid material requires density."));
auto element = factory.Create(definition, domain);
if (!element.HasValue())
return Result<SolidFrequencyState>::Failure(element.GetStatus());
if (dynamic_cast<const Hex8Element*>(element.Value().get()) == nullptr)
return Result<SolidFrequencyState>::Failure(
Failure("unsupported-frequency-element", "Only C3D8 is supported."));
view.emplace_back(*element.Value());
owned.push_back(std::move(element.Value()));
}
DofManager dofs;
const Status mapping = dofs.Build(model.Value(), view);
if (!mapping.IsOk()) return Result<SolidFrequencyState>::Failure(mapping);
if (dofs.Profile() != DofProfile::kSolidStructural ||
dofs.ComponentsPerNode() != 3U)
return Result<SolidFrequencyState>::Failure(
Failure("invalid-solid-frequency-map",
"Frequency requires actual 3N mapping."));
for (std::size_t i = 0; i < dofs.PrescribedValues().Size(); ++i)
if (dofs.PrescribedValues()[i] != 0.0)
return Result<SolidFrequencyState>::Failure(Failure(
"unsupported-eigen-boundary", "Frequency requires homogeneous BC."));
const std::size_t requested =
static_cast<std::size_t>(frequency->requested_mode_count);
if (dofs.FreeDofCount() == 0U || requested > dofs.FreeDofCount())
return Result<SolidFrequencyState>::Failure(
Failure("insufficient-solid-frequency-modes",
"Requested modes exceed free dimension."));
const SerialParallelFor serial;
auto stiffness = SparseAssembler::Assemble(view, dofs, serial);
if (!stiffness.HasValue())
return Result<SolidFrequencyState>::Failure(stiffness.GetStatus());
std::vector<CooContribution> mass_coo;
std::vector<double> lower_by_dof(dofs.FullDofCount(), 0.0);
std::vector<double> magnitude_by_dof(dofs.FullDofCount(), 0.0);
std::vector<std::size_t> additions_by_dof(dofs.FullDofCount(), 0U);
constexpr double eps = std::numeric_limits<double>::epsilon();
for (std::size_t e = 0; e < owned.size(); ++e) {
const auto& hex = static_cast<const Hex8Element&>(*owned[e]);
auto mass = hex.ComputeMass();
if (!mass.HasValue())
return Result<SolidFrequencyState>::Failure(mass.GetStatus());
auto scatter = dofs.ElementScatter(hex.DofLayout());
if (!scatter.HasValue())
return Result<SolidFrequencyState>::Failure(scatter.GetStatus());
const auto weights = hex.ReferenceWeights();
const double min_weight = *std::min_element(weights.begin(), weights.end());
const auto element_index = model.Value().ActiveElements()[e];
const double rho =
density[domain.Elements()[element_index].MaterialIndex()];
const double local_lower = Down(Down(rho * min_weight) / 27.0);
// Relative gamma bounds require normal nonzero products. Fixed Gauss
// shapes exceed 1/128, so rho/16384 bounds the smallest density product.
if (!std::isfinite(local_lower) ||
local_lower < std::numeric_limits<double>::min() ||
rho / 16384.0 < std::numeric_limits<double>::min() ||
min_weight < std::numeric_limits<double>::min())
return Result<SolidFrequencyState>::Failure(
Failure("solid-mass-bound-unavailable",
"Local reference mass bound is unrepresentable."));
// The eight fixed trilinear Gauss shapes have sigma_min(H)^2=1/27.
// 512 eps bounds their fixed evaluation, products and eight-term sums.
// Every mass term is positive; stable incidence scatter preserves the
// bound.
for (std::size_t i = 0; i < 24U; ++i) {
const auto row = scatter.Value()[i];
lower_by_dof[row] = Down(lower_by_dof[row] + local_lower);
double row_sum = 0.0;
for (std::size_t j = 0; j < 24U; ++j) {
const double value = mass.Value().values(i, j);
if (value != 0.0 &&
std::abs(value) < std::numeric_limits<double>::min())
return Result<SolidFrequencyState>::Failure(Failure(
"solid-mass-bound-unavailable",
"Subnormal local mass invalidates relative roundoff bounds."));
row_sum = Up(row_sum + std::abs(value));
mass_coo.push_back({row, scatter.Value()[j], value, e, i * 24U + j});
}
magnitude_by_dof[row] = Up(magnitude_by_dof[row] + row_sum);
++additions_by_dof[row];
}
}
double ideal_lower = (std::numeric_limits<double>::infinity)();
double guard = 0.0;
for (const auto row : dofs.FreeDofs()) {
ideal_lower = (std::min)(ideal_lower, lower_by_dof[row]);
const double count_eps =
Up((512.0 + static_cast<double>(additions_by_dof[row])) * eps);
if (!(count_eps < 0.5))
return Result<SolidFrequencyState>::Failure(
Failure("solid-mass-bound-unavailable",
"Mass reduction exceeds roundoff budget."));
const double gamma = Up(count_eps / (1.0 - count_eps));
// Convert the forward bound relative to the exact sum to an error bound
// relative to the available computed magnitude. Row infinity bounds also
// bound the symmetric perturbation's spectral norm under restriction.
const double computed_gamma = Up(gamma / (1.0 - gamma));
guard = (std::max)(guard, Up(computed_gamma * magnitude_by_dof[row]));
}
const double mass_lower = Down(ideal_lower - guard);
if (!std::isfinite(mass_lower) || !(mass_lower > 0.0) ||
!(guard < 0.01 * ideal_lower))
return Result<SolidFrequencyState>::Failure(
Failure("solid-mass-bound-unavailable",
"Roundoff prevents a useful SPD mass enclosure."));
auto mass =
SparseMatrix::FromCoo(dofs.FullDofCount(), dofs.FullDofCount(),
std::move(mass_coo), dofs.GetSparsePattern());
if (!mass.HasValue())
return Result<SolidFrequencyState>::Failure(mass.GetStatus());
const EssentialConstraintPolicy partition;
auto k_blocks = partition.Partition(stiffness.Value(), dofs);
auto m_blocks = partition.Partition(mass.Value(), dofs);
if (!k_blocks.HasValue())
return Result<SolidFrequencyState>::Failure(k_blocks.GetStatus());
if (!m_blocks.HasValue())
return Result<SolidFrequencyState>::Failure(m_blocks.GetStatus());
const auto& k = k_blocks.Value().k_ff;
const auto& m = m_blocks.Value().k_ff;
double scale = 0.0;
for (std::size_t row = 0; row < k.Rows(); ++row) {
double kd = 0.0;
double md = 0.0;
for (std::size_t p = k.RowOffsets()[row]; p < k.RowOffsets()[row + 1U]; ++p)
if (k.ColumnIndices()[p] == row) kd = k.Values()[p];
for (std::size_t p = m.RowOffsets()[row]; p < m.RowOffsets()[row + 1U]; ++p)
if (m.ColumnIndices()[p] == row) md = m.Values()[p];
if (!(md > 0.0) || !std::isfinite(std::abs(kd) / md))
return Result<SolidFrequencyState>::Failure(
Failure("invalid-solid-eigen-scale",
"Mass diagonal or classification scale is invalid."));
scale = (std::max)(scale, std::abs(kd) / md);
}
if (!(scale > 0.0) || !std::isfinite(scale))
return Result<SolidFrequencyState>::Failure(
Failure("invalid-solid-eigen-scale",
"A positive finite classification scale is required."));
auto backend = MklFeastEigenSolver{}.SolveGeneralized(k, m, requested,
mass_lower, scale);
if (!backend.HasValue())
return Result<SolidFrequencyState>::Failure(backend.GetStatus());
SolidFrequencyState state(std::move(backend.Value()));
state.full_dof_count = dofs.FullDofCount();
state.free_dof_count = dofs.FreeDofCount();
state.classification_scale = scale;
state.mass_ideal_lower_bound = ideal_lower;
state.mass_roundoff_guard = guard;
state.mass_lower_bound = mass_lower;
state.constraint_mask.assign(dofs.FullDofCount(), 0U);
state.prescribed_displacement.assign(dofs.FullDofCount(), 0.0);
for (const auto row : dofs.ConstrainedDofs()) state.constraint_mask[row] = 1U;
const std::size_t count = state.backend.eigenvalues.size();
if (count < requested || state.backend.eigenvectors.Rows() != k.Rows() ||
state.backend.eigenvectors.Columns() != count)
return Result<SolidFrequencyState>::Failure(
Failure("insufficient-solid-frequency-pairs",
"Backend returned insufficient complete pairs."));
const double norm_k = Frobenius(k);
const double norm_m = Frobenius(m);
std::vector<Vector> phi;
std::vector<Vector> mass_phi;
phi.reserve(count);
mass_phi.reserve(count);
for (std::size_t c = 0; c < count; ++c) {
Vector vector(k.Rows());
for (std::size_t row = 0; row < k.Rows(); ++row)
vector[row] = state.backend.eigenvectors(row, c);
Vector mv = m.Multiply(vector);
const double raw_mass = vector.Dot(mv);
if (!(raw_mass > 0.0) || !std::isfinite(raw_mass))
return Result<SolidFrequencyState>::Failure(
Failure("solid-eigenpair-validation-failed",
"Modal mass is not finite positive."));
vector.Scale(1.0 / std::sqrt(raw_mass));
mv = m.Multiply(vector);
const Vector kv = k.Multiply(vector);
const double lambda = state.backend.eigenvalues[c];
const double modal_mass = vector.Dot(mv);
const double energy = vector.Dot(kv);
Vector residual = kv;
residual.Axpy(-lambda, mv);
const double norm_phi = vector.Norm();
const double residual_norm = residual.Norm();
const double lambda_mass = lambda * modal_mass;
const double energy_error = std::abs(energy - lambda_mass);
const double matrix_scale = norm_k + std::abs(lambda) * norm_m;
const double denominator = matrix_scale * norm_phi;
const double energy_denominator = denominator * norm_phi;
// Finite / infinity is zero in IEEE arithmetic but cannot certify a pair.
// Validate both original-pencil scales before either division, preserving
// the exact-zero branch only for representable finite numerator/scale.
if (!std::isfinite(norm_k) || !std::isfinite(norm_m) ||
!std::isfinite(norm_phi) || !std::isfinite(residual_norm) ||
!std::isfinite(lambda_mass) || !std::isfinite(energy_error) ||
!std::isfinite(matrix_scale) || !std::isfinite(denominator) ||
!std::isfinite(energy_denominator))
return Result<SolidFrequencyState>::Failure(
Failure("solid-eigenpair-validation-failed",
"A nonfinite original K/M validation numerator or scale "
"cannot certify a pair."));
const double eta_r = Ratio(residual_norm, denominator);
const double eta_norm = std::abs(modal_mass - 1.0);
const double eta_energy = Ratio(energy_error, energy_denominator);
if (!std::isfinite(lambda) || !std::isfinite(eta_r) || eta_r > 1e-10 ||
!std::isfinite(eta_norm) || eta_norm > 1e-10 ||
!std::isfinite(eta_energy) || eta_energy > 1e-10 ||
!std::isfinite(energy / modal_mass) || lambda / scale < -1e-9)
return Result<SolidFrequencyState>::Failure(
Failure("solid-eigenpair-validation-failed",
"Original K/M pair checks failed."));
state.eigenpair_checks.push_back({c + 1U, state.backend.column_ids[c],
lambda, modal_mass, energy / modal_mass,
eta_r, eta_norm, eta_energy});
phi.push_back(std::move(vector));
mass_phi.push_back(std::move(mv));
}
for (std::size_t a = 0; a < count; ++a)
for (std::size_t b = 0; b < count; ++b) {
const double dot = phi[a].Dot(mass_phi[b]);
state.eta_gram = std::hypot(state.eta_gram, dot - (a == b ? 1.0 : 0.0));
if (a != b)
state.max_eta_orth =
(std::max)(state.max_eta_orth,
std::abs(dot) /
std::sqrt(state.eigenpair_checks[a].modal_mass *
state.eigenpair_checks[b].modal_mass));
}
if (!std::isfinite(state.eta_gram) || state.eta_gram > 1e-10 ||
!std::isfinite(state.max_eta_orth) || state.max_eta_orth > 1e-10)
return Result<SolidFrequencyState>::Failure(
Failure("solid-eigenpair-validation-failed",
"All-pair mass Gram checks failed."));
state.vectors = Matrix(requested, dofs.FullDofCount());
std::size_t cluster = 1U;
for (std::size_t c = 0; c < requested; ++c) {
const double lambda = state.backend.eigenvalues[c];
if (c > 0 && (lambda - state.backend.eigenvalues[c - 1U]) / scale > 1e-8)
++cluster;
std::optional<double> frequency_value;
if (lambda >= 0.0)
frequency_value = std::sqrt(lambda) / (2.0 * std::acos(-1.0));
state.modes.push_back(
{c + 1U, lambda,
static_cast<std::uint8_t>(std::abs(lambda / scale) <= 1e-9 ? 0U : 1U),
cluster, frequency_value});
// Strict > retains the first source/component entry for equal magnitudes.
std::size_t pivot = 0U;
for (std::size_t row = 1; row < phi[c].Size(); ++row)
if (std::abs(phi[c][row]) > std::abs(phi[c][pivot])) pivot = row;
const double sign = phi[c][pivot] < 0.0 ? -1.0 : 1.0;
for (std::size_t row = 0; row < phi[c].Size(); ++row)
state.vectors(c, dofs.FreeDofs()[row]) = sign * phi[c][row];
}
state.backend.eigenvectors = Matrix(0U, 0U);
return Result<SolidFrequencyState>::Success(std::move(state));
}
} // namespace
Result<SolidFrequencyState> SolidFrequencyProcedureExecutor::Execute(
const Domain& domain) const {
try {
auto result = ExecuteCandidate(domain);
if (result.HasValue()) return result;
auto diagnostics = result.GetStatus().Diagnostics();
for (auto& diagnostic : diagnostics)
if (diagnostic.location.file.empty())
diagnostic.location = domain.Frequency() != nullptr
? domain.Frequency()->frequency_location
: SourceLocation{domain.SourcePath(), 0U};
return Result<SolidFrequencyState>::Failure(Status::Failure(
result.GetStatus().Category().value_or(FailureCategory::kSolver),
std::move(diagnostics)));
} catch (const std::bad_alloc&) {
return Result<SolidFrequencyState>::Failure(Failure(
"eigen-allocation-failed", "Solid modal candidate allocation failed."));
} catch (const std::length_error&) {
return Result<SolidFrequencyState>::Failure(
Failure("eigen-allocation-failed",
"Solid modal workspace exceeds addressable storage."));
}
}
} // namespace fesa
src/fesa/elements/hex8_element.cpp
+7
View File
@@ -172,6 +172,13 @@ const ElementDofLayout& Hex8Element::DofLayout() const noexcept {
Result<ElementStiffnessContribution> Hex8Element::ComputeStiffness() const {
return Result<ElementStiffnessContribution>::Success({layout_, stiffness_});
}
std::array<double, 8> Hex8Element::ReferenceWeights() const noexcept {
std::array<double, 8> weights{};
for (std::size_t g = 0; g < weights.size(); ++g)
weights[g] = points_[g].weight;
return weights;
}
Result<ElementStiffnessContribution> Hex8Element::ComputeMass() const {
if (!density_)
return Result<ElementStiffnessContribution>::Failure(
src/fesa/solvers/eigen/mkl_feast_eigen_solver.cpp
+228 -79
View File
@@ -17,6 +17,8 @@
#include <vector>
#include "fesa/math/sparse_matrix.h"
#include "fesa/math/vector.h"
#include "fesa/solvers/linear/mkl_pardiso_solver.h"
#include "solvers/eigen/mkl_feast_eigen_solver_test_seam.h"
namespace fesa {
@@ -364,15 +366,57 @@ bool FillInitialBasis(std::vector<double>& vectors, const std::size_t n,
} // namespace
Result<FeastEigenResult> MklFeastEigenSolver::SolveGeneralized(
const SparseMatrix& stiffness, const SparseMatrix& mass,
const std::size_t requested_modes, const double mass_lower_bound,
const double classification_scale) const {
try {
return SolveImpl(stiffness, &mass, requested_modes, classification_scale,
mass_lower_bound);
} catch (const std::bad_alloc&) {
return Result<FeastEigenResult>::Failure(
Failure("eigen-allocation-failed", "generalized-workspace",
"Allocation of generalized sparse-pencil storage failed."));
}
}
Result<FeastEigenResult> MklFeastEigenSolver::Solve(
const SparseMatrix& whitened_operator, const std::size_t requested_modes,
const double zero_operator_scale) const {
return SolveImpl(whitened_operator, nullptr, requested_modes,
zero_operator_scale, 1.0);
}
Result<FeastEigenResult> MklFeastEigenSolver::SolveImpl(
const SparseMatrix& whitened_operator, const SparseMatrix* mass,
const std::size_t requested_modes, const double zero_operator_scale,
const double mass_lower_bound) const {
static_assert(sizeof(MKL_INT) == 8U,
"FEAST requires the installed ILP64 ABI.");
const Status csr_status = whitened_operator.Validate();
if (!csr_status.IsOk())
return Result<FeastEigenResult>::Failure(
Failure("feast-invalid-csr", "public-csr",
"The public sparse matrix failed CSR validation."));
const std::size_t n = whitened_operator.Rows();
if (mass != nullptr) {
if (!mass->Validate().IsOk() || mass->Rows() != n || mass->Columns() != n ||
!std::isfinite(mass_lower_bound) || !(mass_lower_bound > 0.0) ||
!std::isfinite(zero_operator_scale) || !(zero_operator_scale > 0.0)) {
return Result<FeastEigenResult>::Failure(Failure(
"feast-invalid-mass-bound", "generalized-pencil",
"A matching finite mass and certified positive bound are required."));
}
const Status mass_symmetry = ValidateSymmetry(*mass);
if (!mass_symmetry.IsOk())
return Result<FeastEigenResult>::Failure(mass_symmetry);
MklPardisoSolver spd_check;
const Status spd = spd_check.Factorize(*mass);
if (!spd.IsOk())
return Result<FeastEigenResult>::Failure(
Failure("feast-mass-not-positive-definite", "mass-spd",
"Sparse SPD mass factorization failed."));
}
if (n == 0U || whitened_operator.Columns() != n || requested_modes == 0U ||
requested_modes > n) {
return Result<FeastEigenResult>::Failure(Failure(
@@ -399,7 +443,8 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
for (std::size_t row = 0U; row < n; ++row) {
double sum = 0.0;
for (std::size_t p = offsets[row]; p < offsets[row + 1U]; ++p) {
sum += std::abs(values[p]);
sum = mass != nullptr ? NextUp(sum + std::abs(values[p]))
: sum + std::abs(values[p]);
}
if (!std::isfinite(sum)) {
return Result<FeastEigenResult>::Failure(Failure(
@@ -416,7 +461,7 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
"An exactly zero operator requires a finite positive physical scale."));
}
const double operator_scale =
zero_operator ? zero_operator_scale : infinity_norm;
mass != nullptr || zero_operator ? zero_operator_scale : infinity_norm;
if (!std::isfinite(operator_scale) || !(operator_scale > 0.0)) {
return Result<FeastEigenResult>::Failure(
Failure("feast-nonfinite-operator-scale", "operator-scale",
@@ -424,7 +469,8 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
}
auto a = CopyUpperOneBased(whitened_operator, operator_scale);
if (!a.HasValue()) return Result<FeastEigenResult>::Failure(a.GetStatus());
auto b = IdentityOneBased(n);
auto b =
mass != nullptr ? CopyUpperOneBased(*mass, 1.0) : IdentityOneBased(n);
if (!b.HasValue()) return Result<FeastEigenResult>::Failure(b.GetStatus());
double lower = -1.0;
@@ -432,7 +478,17 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
double g_lower = 0.0;
double g_upper = 0.0;
double beta = 1.0;
if (!zero_operator) {
if (mass != nullptr) {
// ||K||2 <= ||K||inf and M >= m_lower*I bound the genuine pencil.
const double bound =
NextUp(NextUp(infinity_norm / mass_lower_bound) / operator_scale);
g_lower = -bound;
g_upper = bound;
beta = (std::max)(1.0, bound);
lower = std::nextafter(g_lower - 16.0 * Delta(g_lower, beta),
-(std::numeric_limits<double>::infinity)());
upper = NextUp(g_upper + 16.0 * Delta(g_upper, beta));
} else if (!zero_operator) {
g_lower = (std::numeric_limits<double>::infinity)();
g_upper = -(std::numeric_limits<double>::infinity)();
const auto& columns = whitened_operator.ColumnIndices();
@@ -467,6 +523,18 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
LocalThreadGuard threads;
std::vector<FeastBackendCall> calls;
if (mass != nullptr)
calls.push_back({0U, "mass-spd", "original-mass-factorization", 0.0,
mass_lower_bound, 0U, 0, false, 0U, false, 0, false, 0.0,
"accepted",
"sparse-SPD; caller-certified-roundoff-bound"});
auto TraceFailure = [&](const std::string& code, const std::string& identity,
const std::string& message) {
return Failure(code, identity,
mass != nullptr
? message + " Backend calls=" + CallHistory(calls)
: message);
};
std::array<MKL_INT, 128> snapshot{};
SetControls(snapshot, false);
std::vector<std::int64_t> base_fpm;
@@ -482,16 +550,16 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
count_res.assign(n, 0.0);
count_x.assign(n * n, 0.0);
} catch (const std::bad_alloc&) {
return Result<FeastEigenResult>::Failure(
Failure("eigen-allocation-failed", "count-workspace",
"Allocation of the required FEAST count workspace failed."));
return Result<FeastEigenResult>::Failure(TraceFailure(
"eigen-allocation-failed", "count-workspace",
"Allocation of the required FEAST count workspace failed."));
}
auto Count = [&](const double call_lower, const double call_upper,
const std::string& purpose, std::size_t* count) -> Status {
if (!internal::CanCallFeast(calls.size()))
return Failure("eigen-search-budget-exhausted", "count-calls",
"The bounded FEAST count-call budget was exhausted.");
return TraceFailure("eigen-search-budget-exhausted", "count-calls",
"The bounded FEAST count-call budget was exhausted.");
std::array<MKL_INT, 128> fpm{};
SetControls(fpm, true);
MKL_INT m0 = static_cast<MKL_INT>(n);
@@ -500,7 +568,7 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
MKL_INT info = 0;
double epsout = 0.0;
if (!FillInitialBasis(count_x, n, n)) {
return Failure(
return TraceFailure(
"eigenpair-validation-failed", "count-initial-basis",
"The prescribed count initial basis failed QR validation.");
}
@@ -540,11 +608,12 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
count_available ? "accepted" : "vendor-info=" + std::to_string(info);
calls.push_back(std::move(event));
if (info != 0)
return Failure("eigen-feast-failed", "info=" + std::to_string(info),
"FEAST did not certify the requested count interval.");
return TraceFailure(
"eigen-feast-failed", "info=" + std::to_string(info),
"FEAST did not certify the requested count interval.");
if (m0 < 0 || static_cast<std::size_t>(m0) > n) {
return Failure("eigen-count-inconsistent", "count-output",
"FEAST count output is outside [0,n].");
return TraceFailure("eigen-count-inconsistent", "count-output",
"FEAST count output is outside [0,n].");
}
*count = static_cast<std::size_t>(m0);
for (std::size_t i = 0U; i + 1U < calls.size(); ++i) {
@@ -555,7 +624,7 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
if ((prior.upper == call_upper && prior.count != *count) ||
(prior.upper < call_upper && prior.count > *count) ||
(prior.upper > call_upper && prior.count < *count))
return Failure(
return TraceFailure(
"eigen-count-inconsistent", "count-history",
"Successful prefix counts violate identity or monotonicity.");
}
@@ -599,10 +668,36 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
return Result<FeastEigenResult>::Failure(
!count_status.IsOk()
? count_status
: Failure(
: TraceFailure(
"eigen-count-inconsistent", "total-enclosure",
"The enclosing FEAST count did not equal matrix dimension."));
}
if (mass != nullptr) {
// Count the actual pencil before removing any part of the conservative
// negative enclosure. A far-negative endpoint degrades contour filtering
// of low positive modes on a stiff mesh; an empty guarded prefix proves
// that moving it cannot remove a mode, including a repeated rigid cluster.
const double margin = Delta(0.0, beta);
const double candidate = -16.0 * margin;
const std::array<double, 3U> guards{candidate - margin, candidate,
candidate + margin};
if (lower < guards.front()) {
for (const double guard : guards) {
std::size_t negative_count = 0U;
const Status prefix_status =
Count(lower, guard, "lower-empty-prefix", &negative_count);
if (!prefix_status.IsOk())
return Result<FeastEigenResult>::Failure(prefix_status);
if (negative_count != 0U)
return Result<FeastEigenResult>::Failure(TraceFailure(
"negative-eigenvalue-spectrum", "certified-negative-prefix",
"The generalized pencil contains significant negative "
"eigenvalues."));
}
lower = candidate;
calls.back().decision_reason = "guarded-empty-prefix; lowest-spectrum-preserved";
}
}
const double fixed_lower = lower;
const double enclosure_upper = upper;
double solve_upper = enclosure_upper;
@@ -694,7 +789,7 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
count_status = Count(fixed_lower, solve_upper, "final-count", &count);
if (!count_status.IsOk() || count < requested_modes ||
count != certified_count) {
return Result<FeastEigenResult>::Failure(Failure(
return Result<FeastEigenResult>::Failure(TraceFailure(
"eigen-count-inconsistent", "final-count",
"The final FEAST interval count is not the certified guarded count."));
}
@@ -709,27 +804,27 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
if (!below_status.IsOk() || !above_status.IsOk() || below != count ||
above != count) {
return Result<FeastEigenResult>::Failure(
Failure("eigen-count-inconsistent", "final-guard",
"The final interior endpoint is not guarded by equal "
"successful counts."));
TraceFailure("eigen-count-inconsistent", "final-guard",
"The final interior endpoint is not guarded by equal "
"successful counts."));
}
}
if (count > (std::numeric_limits<std::size_t>::max)() - 8U ||
count > ((std::numeric_limits<std::size_t>::max)() - 1U) / 3U) {
return Result<FeastEigenResult>::Failure(
Failure("eigen-allocation-failed", "solve-capacity",
"FEAST solve-capacity padding overflows size_t."));
TraceFailure("eigen-allocation-failed", "solve-capacity",
"FEAST solve-capacity padding overflows size_t."));
}
const std::size_t padded_count =
(std::max)(count + 8U, (3U * count + 1U) / 2U);
std::size_t capacity = count == n ? n : (std::min)(n, padded_count);
if (!internal::ProductFits(n, capacity))
return Result<FeastEigenResult>::Failure(
Failure("feast-workspace-overflow", "solve-workspace",
"The FEAST solve workspace size overflows."));
TraceFailure("feast-workspace-overflow", "solve-workspace",
"The FEAST solve workspace size overflows."));
if (!internal::FitsDoubleStorage(n * capacity) ||
!internal::FitsDoubleStorage(capacity)) {
return Result<FeastEigenResult>::Failure(Failure(
return Result<FeastEigenResult>::Failure(TraceFailure(
"eigen-allocation-failed", "solve-workspace",
"The required solve workspace exceeds addressable double storage."));
}
@@ -742,23 +837,23 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
std::size_t solve_capacity = capacity;
for (std::size_t attempt = 0U; attempt < 3U; ++attempt) {
if (!internal::CanCallFeast(calls.size()))
return Result<FeastEigenResult>::Failure(
Failure("eigen-search-budget-exhausted", "solve-call",
"The total backend call budget is exhausted before solve."));
return Result<FeastEigenResult>::Failure(TraceFailure(
"eigen-search-budget-exhausted", "solve-call",
"The total backend call budget is exhausted before solve."));
try {
internal::ApplyFeastWorkspaceTestHook(false);
eigenvalues.assign(solve_capacity, 0.0);
residuals.assign(solve_capacity, 0.0);
vectors.assign(n * solve_capacity, 0.0);
} catch (const std::bad_alloc&) {
return Result<FeastEigenResult>::Failure(
Failure("eigen-allocation-failed", "solve-workspace",
"Allocation of the required FEAST solve workspace failed."));
return Result<FeastEigenResult>::Failure(TraceFailure(
"eigen-allocation-failed", "solve-workspace",
"Allocation of the required FEAST solve workspace failed."));
}
if (!FillInitialBasis(vectors, n, solve_capacity)) {
return Result<FeastEigenResult>::Failure(
Failure("eigenpair-validation-failed", "solve-initial-basis",
"The prescribed solve initial basis failed QR validation."));
return Result<FeastEigenResult>::Failure(TraceFailure(
"eigenpair-validation-failed", "solve-initial-basis",
"The prescribed solve initial basis failed QR validation."));
}
std::array<MKL_INT, 128> fpm{};
SetControls(fpm, false);
@@ -794,21 +889,21 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
: "vendor-info=" + std::to_string(info)});
if (info == 0 && (!std::isfinite(epsout) || loop < 0)) {
return Result<FeastEigenResult>::Failure(
Failure("invalid-eigenvalue-result", "solve-output",
"A successful FEAST solve returned nonfinite epsout or "
"invalid loop."));
TraceFailure("invalid-eigenvalue-result", "solve-output",
"A successful FEAST solve returned nonfinite epsout or "
"invalid loop."));
}
if (info == 0 && returned >= 0 &&
static_cast<std::size_t>(returned) <= solve_capacity) {
for (std::size_t column = 0U; column < static_cast<std::size_t>(returned);
++column) {
if (!std::isfinite(eigenvalues[column]))
return Result<FeastEigenResult>::Failure(Failure(
return Result<FeastEigenResult>::Failure(TraceFailure(
"invalid-eigenvalue-result", std::to_string(column),
"A nonfinite eigenvalue cannot trigger an interval retry."));
for (std::size_t row = 0U; row < n; ++row)
if (!std::isfinite(vectors[row + column * n]))
return Result<FeastEigenResult>::Failure(Failure(
return Result<FeastEigenResult>::Failure(TraceFailure(
"invalid-eigenvalue-result", std::to_string(column),
"A nonfinite eigenvector cannot trigger an interval retry."));
}
@@ -818,10 +913,10 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
if (endpoint_separated) {
for (std::size_t index = 0U; index < count; ++index) {
if (!std::isfinite(eigenvalues[index])) {
return Result<FeastEigenResult>::Failure(
Failure("invalid-eigenvalue-result", std::to_string(index),
"FEAST returned a nonfinite eigenvalue before endpoint "
"validation."));
return Result<FeastEigenResult>::Failure(TraceFailure(
"invalid-eigenvalue-result", std::to_string(index),
"FEAST returned a nonfinite eigenvalue before endpoint "
"validation."));
}
endpoint_separated =
endpoint_separated &&
@@ -856,7 +951,7 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
const Status recount_status =
Count(fixed_lower, solve_upper, "final-count", &recounted);
if (!recount_status.IsOk() || recounted < requested_modes) {
return Result<FeastEigenResult>::Failure(Failure(
return Result<FeastEigenResult>::Failure(TraceFailure(
"eigen-count-inconsistent", "solve-retry",
"A larger certified solve interval could not be recounted."));
}
@@ -871,7 +966,7 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
fixed_lower, solve_upper + retry_margin, "final-count", &above);
if (!below_status.IsOk() || !above_status.IsOk() || below != count ||
above != count) {
return Result<FeastEigenResult>::Failure(Failure(
return Result<FeastEigenResult>::Failure(TraceFailure(
"eigen-count-inconsistent", "solve-retry-guard",
"The larger retry interval is not guarded by matching counts."));
}
@@ -879,8 +974,8 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
if (count > (std::numeric_limits<std::size_t>::max)() - 8U ||
count > ((std::numeric_limits<std::size_t>::max)() - 1U) / 3U) {
return Result<FeastEigenResult>::Failure(
Failure("eigen-allocation-failed", "solve-capacity",
"FEAST retry capacity padding overflows size_t."));
TraceFailure("eigen-allocation-failed", "solve-capacity",
"FEAST retry capacity padding overflows size_t."));
}
const std::size_t retry_padding =
(std::max)(count + 8U, (3U * count + 1U) / 2U);
@@ -894,22 +989,22 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
}
if (!solve_accepted) {
return Result<FeastEigenResult>::Failure(
Failure("eigen-feast-failed", "info=" + std::to_string(info),
"FEAST solve did not return the certified interval count "
"within its bounded retries."));
TraceFailure("eigen-feast-failed", "info=" + std::to_string(info),
"FEAST solve did not return the certified interval count "
"within its bounded retries."));
}
for (std::size_t index = 0U; index < count; ++index) {
if (!std::isfinite(eigenvalues[index])) {
return Result<FeastEigenResult>::Failure(
Failure("invalid-eigenvalue-result", std::to_string(index),
"FEAST returned a nonfinite eigenvalue before sorting."));
return Result<FeastEigenResult>::Failure(TraceFailure(
"invalid-eigenvalue-result", std::to_string(index),
"FEAST returned a nonfinite eigenvalue before sorting."));
}
for (std::size_t row = 0U; row < n; ++row) {
if (!std::isfinite(vectors[row + index * n])) {
return Result<FeastEigenResult>::Failure(
Failure("invalid-eigenvalue-result", std::to_string(index),
"FEAST returned a nonfinite eigenvector before sorting."));
return Result<FeastEigenResult>::Failure(TraceFailure(
"invalid-eigenvalue-result", std::to_string(index),
"FEAST returned a nonfinite eigenvector before sorting."));
}
}
}
@@ -936,28 +1031,34 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
const double mu = eigenvalues[input];
if (!std::isfinite(mu)) {
return Result<FeastEigenResult>::Failure(
Failure("invalid-eigenvalue-result", std::to_string(input),
"FEAST returned a nonfinite eigenvalue."));
TraceFailure("invalid-eigenvalue-result", std::to_string(input),
"FEAST returned a nonfinite eigenvalue."));
}
if (mu < -1.0e-9) {
return Result<FeastEigenResult>::Failure(Failure(
return Result<FeastEigenResult>::Failure(TraceFailure(
"negative-eigenvalue-spectrum", std::to_string(input),
"The raw normalized FEAST eigenvalue is significantly negative."));
}
if (mu - fixed_lower < Delta(fixed_lower, beta) ||
solve_upper - mu < Delta(solve_upper, beta)) {
return Result<FeastEigenResult>::Failure(Failure(
return Result<FeastEigenResult>::Failure(TraceFailure(
"eigen-endpoint-separation", std::to_string(input),
"A returned FEAST eigenvalue is too close to a solve endpoint."));
}
double norm = 0.0;
for (std::size_t row = 0U; row < n; ++row)
norm += vectors[row + input * n] * vectors[row + input * n];
if (mass != nullptr) {
Vector raw(n);
for (std::size_t row = 0U; row < n; ++row)
raw[row] = vectors[row + input * n];
norm = raw.Dot(mass->Multiply(raw));
}
norm = std::sqrt(norm);
if (!(norm > 0.0) || !std::isfinite(norm))
return Result<FeastEigenResult>::Failure(
Failure("eigenpair-validation-failed", std::to_string(input),
"FEAST returned a non-normalizable eigenvector."));
TraceFailure("eigenpair-validation-failed", std::to_string(input),
"FEAST returned a non-normalizable eigenvector."));
double residual_norm = 0.0;
for (std::size_t row = 0U; row < n; ++row) {
double ax = 0.0;
@@ -965,12 +1066,48 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
ax += values[p] / operator_scale *
vectors[whitened_operator.ColumnIndices()[p] + input * n];
}
const double difference = ax - mu * vectors[row + input * n];
double mx = vectors[row + input * n];
if (mass != nullptr) {
mx = 0.0;
for (std::size_t p = mass->RowOffsets()[row];
p < mass->RowOffsets()[row + 1U]; ++p)
mx +=
mass->Values()[p] * vectors[mass->ColumnIndices()[p] + input * n];
}
const double difference = ax - mu * mx;
residual_norm += difference * difference;
ordered_vectors(row, output) = vectors[row + input * n] / norm;
}
const double rho_b = std::sqrt(residual_norm) / norm;
if (rho_b > 1.0e-10) {
double residual_denominator = norm;
if (mass != nullptr) {
double norm_k = 0.0;
double norm_m = 0.0;
double euclidean = 0.0;
for (const double value : values)
norm_k = std::hypot(norm_k, value / operator_scale);
for (const double value : mass->Values())
norm_m = std::hypot(norm_m, value);
for (std::size_t row = 0U; row < n; ++row)
euclidean = std::hypot(euclidean, vectors[row + input * n]);
residual_denominator = (norm_k + std::abs(mu) * norm_m) * euclidean;
}
if (!std::isfinite(residual_norm) || !std::isfinite(residual_denominator))
return Result<FeastEigenResult>::Failure(
TraceFailure("eigenpair-validation-failed", std::to_string(input),
"A nonfinite independent residual numerator or scale "
"cannot certify a pair."));
const double rho_b =
residual_denominator == 0.0
? (residual_norm == 0.0 ? 0.0
: (std::numeric_limits<double>::infinity)())
: std::sqrt(residual_norm) / residual_denominator;
if (!std::isfinite(rho_b) || rho_b > 1.0e-10) {
if (mass != nullptr)
return Result<FeastEigenResult>::Failure(TraceFailure(
"eigenpair-validation-failed", std::to_string(input),
"Independent original-pencil residual exceeds 1e-10: eta=" +
FormatDouble(rho_b) + ", mu=" + FormatDouble(mu) +
"; calls=" + CallHistory(calls)));
const FeastBackendCall& last_call = calls.back();
std::vector<double> mirrored_action(n, 0.0);
std::vector<double> full_action(n, 0.0);
@@ -999,7 +1136,7 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
const double rho_b_upper = std::sqrt(mirrored_residual_squared) / norm;
const double action_difference_norm =
std::sqrt(action_difference_squared);
return Result<FeastEigenResult>::Failure(Failure(
return Result<FeastEigenResult>::Failure(TraceFailure(
"eigenpair-validation-failed", std::to_string(input),
"Independent whitened residual exceeds 1e-10: rho_b=" +
FormatDouble(rho_b) + ", mu=" + FormatDouble(mu) +
@@ -1019,16 +1156,16 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
}
const double lambda = mu * operator_scale;
if (!std::isfinite(lambda) || (mu != 0.0 && lambda == 0.0)) {
return Result<FeastEigenResult>::Failure(
Failure("invalid-eigenvalue-result", std::to_string(input),
"Physical eigenvalue conversion overflowed or underflowed."));
return Result<FeastEigenResult>::Failure(TraceFailure(
"invalid-eigenvalue-result", std::to_string(input),
"Physical eigenvalue conversion overflowed or underflowed."));
}
ordered_values.push_back(lambda);
const bool backend_res_finite = std::isfinite(residuals[input]);
if (!backend_res_finite && mu != 0.0) {
return Result<FeastEigenResult>::Failure(
Failure("invalid-eigenvalue-result", std::to_string(input),
"A nonzero FEAST mode has a nonfinite backend residual."));
return Result<FeastEigenResult>::Failure(TraceFailure(
"invalid-eigenvalue-result", std::to_string(input),
"A nonzero FEAST mode has a nonfinite backend residual."));
}
ordered_backend_available.push_back(backend_res_finite);
ordered_backend_res.push_back(backend_res_finite ? residuals[input] : 0.0);
@@ -1042,23 +1179,35 @@ Result<FeastEigenResult> MklFeastEigenSolver::Solve(
double dot = 0.0;
for (std::size_t row = 0U; row < n; ++row)
dot += ordered_vectors(row, left) * ordered_vectors(row, right);
if (mass != nullptr) {
dot = 0.0;
for (std::size_t row = 0U; row < n; ++row) {
double action = 0.0;
for (std::size_t p = mass->RowOffsets()[row];
p < mass->RowOffsets()[row + 1U]; ++p)
action += mass->Values()[p] *
ordered_vectors(mass->ColumnIndices()[p], right);
dot += ordered_vectors(row, left) * action;
}
}
const double expected = left == right ? 1.0 : 0.0;
const double difference = std::abs(dot - expected);
gram_squared += difference * difference;
gram_error = (std::max)(gram_error, difference);
if (std::abs(dot - expected) > 1.0e-10)
return Result<FeastEigenResult>::Failure(Failure(
return Result<FeastEigenResult>::Failure(TraceFailure(
"eigenpair-validation-failed",
std::to_string(left) + ":" + std::to_string(right),
"The all-c FEAST vectors fail the independent Gram check."));
}
}
gram_error = std::sqrt(gram_squared / static_cast<double>(count));
if (gram_error > 1.0e-10) {
return Result<FeastEigenResult>::Failure(
Failure("eigenpair-validation-failed", "gram",
"The normalized all-c Frobenius Gram error exceeds 1e-10: " +
FormatDouble(gram_error) + "."));
gram_error = std::sqrt(gram_squared /
(mass != nullptr ? 1.0 : static_cast<double>(count)));
if (!std::isfinite(gram_error) || gram_error > 1.0e-10) {
return Result<FeastEigenResult>::Failure(TraceFailure(
"eigenpair-validation-failed", "gram",
"The normalized all-c Frobenius Gram error exceeds 1e-10: " +
FormatDouble(gram_error) + "."));
}
char version[256]{};
mkl_get_version_string(version, static_cast<int>(sizeof(version)));
tests/unit/analysis/solid_frequency_procedure_test.cpp
+294
View File
@@ -0,0 +1,294 @@
#include "fesa/analysis/solid_frequency_procedure.h"
#include <gtest/gtest.h>
#include <mkl.h>
#include <algorithm>
#include <array>
#include <atomic>
#include <cmath>
#include <filesystem>
#include <fstream>
#include <sstream>
#include <string>
#include <utility>
#include <vector>
#include "fesa/io/abaqus/domain_mapper.h"
#include "fesa/io/abaqus/input_reader.h"
#include "fesa/model/domain.h"
#include "solvers/eigen/mkl_feast_eigen_solver_test_seam.h"
namespace {
std::string StatusText(const fesa::Status& status) {
std::string text;
for (const auto& d : status.Diagnostics()) text += d.code + " " + d.message;
return text;
}
fesa::Result<fesa::Domain> Brick(std::size_t requested = 6U,
const std::string& boundary = "",
double length = 1.0, double rho = 2.0,
double modulus = 120.0) {
constexpr int signs[8][3] = {{-1, -1, -1}, {1, -1, -1}, {1, 1, -1},
{-1, 1, -1}, {-1, -1, 1}, {1, -1, 1},
{1, 1, 1}, {-1, 1, 1}};
std::ostringstream deck;
deck.precision(17);
deck << "*Part,name=P\n*Node\n";
for (std::size_t a = 0; a < 8; ++a)
deck << (a + 1) * 10 << ',' << length * signs[a][0] << ','
<< 2 * length * signs[a][1] << ',' << 3 * length * signs[a][2] << '\n';
deck << "*Element,type=C3D8,elset=E\n99,10,20,30,40,50,60,70,80\n"
"*Solid Section,elset=E,material=M\n,\n*End Part\n"
"*Assembly,name=A\n*Instance,name=I,part=P\n*End Instance\n"
"*End Assembly\n*Material,name=M\n*Elastic\n"
<< modulus << ",.25\n";
if (rho != 0.0) deck << "*Density\n" << rho << '\n';
deck << "*Step,name=Modes\n*Frequency\n" << requested << '\n';
if (!boundary.empty()) deck << "*Boundary\n" << boundary;
deck << "*End Step\n";
static std::atomic<unsigned> serial{0};
const auto path =
std::filesystem::temp_directory_path() /
("fesa-solid-frequency-" + std::to_string(serial++) + ".inp");
{
std::ofstream out(path);
out << deck.str();
}
auto syntax = fesa::AbaqusInputReader{}.Read(path);
std::filesystem::remove(path);
if (!syntax.HasValue())
return fesa::Result<fesa::Domain>::Failure(syntax.GetStatus());
return fesa::AbaqusDomainMapper{}.Map(syntax.Value());
}
} // namespace
TEST(SolidFrequencyProcedure, FreeBrickRetainsSixRigidModes) {
auto domain = Brick();
ASSERT_TRUE(domain.HasValue()) << StatusText(domain.GetStatus());
const auto result =
fesa::SolidFrequencyProcedureExecutor{}.Execute(domain.Value());
ASSERT_TRUE(result.HasValue()) << StatusText(result.GetStatus());
ASSERT_EQ(result.Value().modes.size(), 6U);
for (const auto& mode : result.Value().modes)
EXPECT_EQ(mode.classification, 0U);
EXPECT_EQ(result.Value().vectors.Rows(), 6U);
EXPECT_EQ(result.Value().vectors.Columns(), 24U);
}
namespace {
constexpr int kSigns[8][3] = {{-1, -1, -1}, {1, -1, -1}, {1, 1, -1},
{-1, 1, -1}, {-1, -1, 1}, {1, -1, 1},
{1, 1, 1}, {-1, 1, 1}};
// Exact tensor-polynomial integrals, independent of production Gauss assembly.
double GradientIntegral(std::size_t a, std::size_t b, std::size_t i,
std::size_t j) {
double integral = 48.0 * kSigns[a][i] * kSigns[b][j] /
(64.0 * static_cast<double>((i + 1U) * (j + 1U)));
for (std::size_t d = 0; d < 3; ++d)
if (d != i && d != j) integral *= 1.0 + kSigns[a][d] * kSigns[b][d] / 3.0;
return integral;
}
std::vector<double> DenseOracle(const std::vector<std::size_t>& free) {
const auto n = free.size();
std::vector<double> k(n * n, 0.0), m(n * n, 0.0), eigen(n, 0.0);
for (std::size_t row = 0; row < n; ++row)
for (std::size_t col = 0; col < n; ++col) {
const auto a = free[row] / 3U, b = free[col] / 3U;
const auto i = free[row] % 3U, j = free[col] % 3U;
double gradient_dot = 0.0;
for (std::size_t d = 0; d < 3; ++d)
gradient_dot += GradientIntegral(a, b, d, d);
k[row * n + col] =
48.0 * (GradientIntegral(a, b, i, j) + GradientIntegral(a, b, j, i) +
(i == j ? gradient_dot : 0.0));
if (i == j) {
m[row * n + col] = 2.0 * 48.0 / 64.0;
for (std::size_t d = 0; d < 3; ++d)
m[row * n + col] *= 1.0 + kSigns[a][d] * kSigns[b][d] / 3.0;
}
}
EXPECT_EQ(
LAPACKE_dsygv(LAPACK_ROW_MAJOR, 1, 'N', 'U', static_cast<MKL_INT>(n),
k.data(), static_cast<MKL_INT>(n), m.data(),
static_cast<MKL_INT>(n), eigen.data()),
0);
return eigen;
}
const std::string kFaceFixed = "10,1,3\n40,1,3\n50,1,3\n80,1,3\n";
std::vector<std::size_t> FaceFree() {
std::vector<std::size_t> free;
for (const auto node : {1U, 2U, 5U, 6U})
for (std::size_t d = 0; d < 3; ++d) free.push_back(3U * node + d);
return free;
}
} // namespace
TEST(SolidFrequencyProcedure,
OriginalConsistentPencilMatchesIndependentDenseOracle) {
for (const bool constrained : {false, true}) {
const std::size_t count = constrained ? 12U : 24U;
auto domain = Brick(count, constrained ? kFaceFixed : "");
ASSERT_TRUE(domain.HasValue()) << StatusText(domain.GetStatus());
auto result =
fesa::SolidFrequencyProcedureExecutor{}.Execute(domain.Value());
ASSERT_TRUE(result.HasValue()) << StatusText(result.GetStatus());
std::vector<std::size_t> free;
if (constrained)
free = FaceFree();
else
for (std::size_t i = 0; i < 24; ++i) free.push_back(i);
const auto oracle = DenseOracle(free);
const auto& state = result.Value();
ASSERT_EQ(state.modes.size(), oracle.size());
ASSERT_EQ(state.eigenpair_checks.size(), oracle.size());
for (std::size_t c = 0; c < oracle.size(); ++c) {
EXPECT_NEAR(state.modes[c].eigenvalue, oracle[c],
1e-10 * state.classification_scale);
EXPECT_EQ(state.modes[c].mode_id, c + 1);
EXPECT_EQ(state.eigenpair_checks[c].sorted_rank, c + 1);
EXPECT_LE(state.eigenpair_checks[c].eta_r, 1e-10);
EXPECT_LE(state.eigenpair_checks[c].eta_energy, 1e-10);
EXPECT_LE(state.eigenpair_checks[c].eta_norm, 1e-10);
EXPECT_NEAR(state.eigenpair_checks[c].modal_mass, 1.0, 1e-10);
std::size_t pivot = 0;
for (std::size_t row = 0; row < 24; ++row) {
if (std::abs(state.vectors(c, row)) > std::abs(state.vectors(c, pivot)))
pivot = row;
if (state.constraint_mask[row]) EXPECT_EQ(state.vectors(c, row), 0.0);
}
EXPECT_GT(state.vectors(c, pivot), 0.0);
}
EXPECT_LE(state.eta_gram, 1e-10);
EXPECT_LE(state.max_eta_orth, 1e-10);
EXPECT_NEAR(state.mass_ideal_lower_bound, 12.0 / 27.0, 1e-13);
EXPECT_GT(state.mass_lower_bound, 0.0);
EXPECT_LT(state.mass_lower_bound, state.mass_ideal_lower_bound);
EXPECT_GT(state.mass_roundoff_guard, 0.0);
EXPECT_EQ(state.backend.integer_abi, "ILP64");
EXPECT_EQ(state.backend.eigenvectors.Rows(), 0U);
EXPECT_EQ(state.backend.backend_calls.front().kind, "mass-spd");
}
}
TEST(SolidFrequencyProcedure, DensityLengthAndMaterialScaling) {
const auto base_domain = Brick(4U, kFaceFixed);
ASSERT_TRUE(base_domain.HasValue());
const auto base =
fesa::SolidFrequencyProcedureExecutor{}.Execute(base_domain.Value());
ASSERT_TRUE(base.HasValue()) << StatusText(base.GetStatus());
for (const auto parameters : {std::array<double, 4>{1, 8, 120, .25},
std::array<double, 4>{2, 2, 120, .25},
std::array<double, 4>{1, 2, 480, 4}}) {
const auto domain =
Brick(4U, kFaceFixed, parameters[0], parameters[1], parameters[2]);
ASSERT_TRUE(domain.HasValue());
const auto result =
fesa::SolidFrequencyProcedureExecutor{}.Execute(domain.Value());
ASSERT_TRUE(result.HasValue()) << StatusText(result.GetStatus());
for (std::size_t c = 0; c < 4; ++c)
EXPECT_NEAR(result.Value().modes[c].eigenvalue,
base.Value().modes[c].eigenvalue * parameters[3],
1e-10 * result.Value().classification_scale);
}
}
TEST(SolidFrequencyProcedure, OneFreeDofAndAllConstrainedAndExcessRequest) {
const std::string one =
"10,1,2\n20,1,3\n30,1,3\n40,1,3\n50,1,3\n60,1,3\n70,1,3\n80,1,3\n";
auto domain = Brick(1U, one);
ASSERT_TRUE(domain.HasValue());
auto result = fesa::SolidFrequencyProcedureExecutor{}.Execute(domain.Value());
ASSERT_TRUE(result.HasValue()) << StatusText(result.GetStatus());
EXPECT_NEAR(result.Value().modes[0].eigenvalue, DenseOracle({2U})[0], 1e-11);
const std::string all =
"10,1,3\n20,1,3\n30,1,3\n40,1,3\n50,1,3\n60,1,3\n70,1,3\n80,1,3\n";
for (const auto pair :
{std::pair<std::size_t, std::string>{1U, all}, {13U, kFaceFixed}}) {
auto invalid = Brick(pair.first, pair.second);
ASSERT_TRUE(invalid.HasValue());
EXPECT_FALSE(fesa::SolidFrequencyProcedureExecutor{}
.Execute(invalid.Value())
.HasValue());
}
}
TEST(SolidFrequencyProcedure,
MissingDensityAndFailedBackendPreservePriorCandidate) {
auto missing = Brick(1U, kFaceFixed, 1.0, 0.0);
if (missing.HasValue())
EXPECT_FALSE(fesa::SolidFrequencyProcedureExecutor{}
.Execute(missing.Value())
.HasValue());
auto domain = Brick(4U, kFaceFixed);
ASSERT_TRUE(domain.HasValue());
const auto good =
fesa::SolidFrequencyProcedureExecutor{}.Execute(domain.Value());
ASSERT_TRUE(good.HasValue());
const auto previous = good.Value().modes[0].eigenvalue;
{
fesa::internal::ScopedFeastBackendTestHook hook{
[](const auto& call, auto& output) {
if (!call.count) output.eigenvalues.back() = 9999.0;
}};
EXPECT_FALSE(fesa::SolidFrequencyProcedureExecutor{}
.Execute(domain.Value())
.HasValue());
}
EXPECT_EQ(good.Value().modes[0].eigenvalue, previous);
const auto again =
fesa::SolidFrequencyProcedureExecutor{}.Execute(domain.Value());
ASSERT_TRUE(again.HasValue());
EXPECT_NEAR(again.Value().modes[0].eigenvalue, previous, 1e-12);
}
TEST(SolidFrequencyProcedure, NearZeroNegativeRemainsRawWithoutFrequency) {
auto domain = Brick();
ASSERT_TRUE(domain.HasValue());
fesa::internal::ScopedFeastBackendTestHook hook{
[](const auto& call, auto& output) {
if (!call.count) output.eigenvalues[0] = -1e-12;
}};
const auto result =
fesa::SolidFrequencyProcedureExecutor{}.Execute(domain.Value());
ASSERT_TRUE(result.HasValue()) << StatusText(result.GetStatus());
EXPECT_LT(result.Value().modes[0].eigenvalue, 0.0);
EXPECT_EQ(result.Value().modes[0].classification, 0U);
EXPECT_FALSE(result.Value().modes[0].frequency.has_value());
for (const auto& mode : result.Value().modes) EXPECT_EQ(mode.cluster_id, 1U);
}
TEST(SolidFrequencyProcedure,
SuppliedFrequencyInputHasIndependentNumericalEvidence) {
auto root = std::filesystem::path{__FILE__}.parent_path();
while (!root.empty() && !std::filesystem::exists(root / "CMakePresets.json"))
root = root.parent_path();
ASSERT_FALSE(root.empty());
const auto syntax =
fesa::AbaqusInputReader{}.Read(root / "reference/hexa/hexa_freq.inp");
ASSERT_TRUE(syntax.HasValue()) << StatusText(syntax.GetStatus());
const auto domain = fesa::AbaqusDomainMapper{}.Map(syntax.Value());
ASSERT_TRUE(domain.HasValue()) << StatusText(domain.GetStatus());
const auto result =
fesa::SolidFrequencyProcedureExecutor{}.Execute(domain.Value());
ASSERT_TRUE(result.HasValue()) << StatusText(result.GetStatus());
EXPECT_EQ(result.Value().modes.size(), 10U);
EXPECT_EQ(result.Value().vectors.Columns(), 3U * 442U);
EXPECT_GE(result.Value().eigenpair_checks.size(), 10U);
EXPECT_GT(result.Value().mass_lower_bound, 0.0);
EXPECT_LE(result.Value().eta_gram, 1e-10);
EXPECT_LE(result.Value().max_eta_orth, 1e-10);
// Original modal Value output is pending. This proves only our independent
// checks on the supplied input; it is not an external frequency comparison.
}
TEST(SolidFrequencyProcedure, RejectsOverflowingOriginalPencilValidationScale) {
// Every local K entry, eigenvalue, and spectral enclosure is representable.
// The all-odd x Walsh mode still overflows the original residual/energy
// denominators: finite / infinity must never become passing zero evidence.
auto domain = Brick(24U, "", 1.0, 2.0, 3e306);
ASSERT_TRUE(domain.HasValue()) << StatusText(domain.GetStatus());
const auto result =
fesa::SolidFrequencyProcedureExecutor{}.Execute(domain.Value());
ASSERT_FALSE(result.HasValue());
ASSERT_FALSE(result.GetStatus().Diagnostics().empty());
EXPECT_EQ(result.GetStatus().Diagnostics()[0].code,
"solid-eigenpair-validation-failed");
EXPECT_NE(result.GetStatus().Diagnostics()[0].message.find("nonfinite"),
std::string::npos);
}
tests/unit/solvers/eigen/mkl_feast_eigen_solver_test.cpp
+155
View File
@@ -629,3 +629,158 @@ TEST(MklFeastEigenSolver, UsesCertifiedEnclosureAfterOptionalInfoOne) {
ASSERT_GE(result.Value().backend_calls.size(), 2U);
EXPECT_EQ(result.Value().backend_calls[1U].outcome, "optional-abandoned");
}
TEST(MklFeastGeneralized, GenuineNonDiagonalMassPencil) {
const auto k = MakeDenseCsr(2U, {6.0, 2.0, 2.0, 6.0});
const auto m = MakeDenseCsr(2U, {2.0, 1.0, 1.0, 2.0});
const auto result =
fesa::MklFeastEigenSolver{}.SolveGeneralized(k, m, 1U, 1.0, 3.0);
ASSERT_TRUE(result.HasValue());
ASSERT_EQ(result.Value().eigenvalues.size(), 2U);
EXPECT_NEAR(result.Value().eigenvalues[0], 8.0 / 3.0, 1e-11);
EXPECT_NEAR(result.Value().eigenvalues[1], 4.0, 1e-11);
}
TEST(MklFeastGeneralized, RejectsIndefiniteMassAndInvalidBound) {
const auto k = MakeDenseCsr(2U, {1, 0, 0, 2});
const auto m = MakeDenseCsr(2U, {1, 2, 2, 1});
ExpectFailureCode(
fesa::MklFeastEigenSolver{}.SolveGeneralized(k, m, 1U, 0.1, 2),
"feast-mass-not-positive-definite");
ExpectFailureCode(
fesa::MklFeastEigenSolver{}.SolveGeneralized(k, k, 1U, 0, 1),
"feast-invalid-mass-bound");
}
TEST(MklFeastGeneralized, ValidatesPairsBeyondRequestedPrefix) {
const auto k = MakeDenseCsr(3U, {2, 0, 0, 0, 6, 0, 0, 0, 12});
const auto m = MakeDenseCsr(3U, {2, 0, 0, 0, 3, 0, 0, 0, 4});
fesa::internal::ScopedFeastBackendTestHook hook{
[](const auto& call, auto& output) {
if (!call.count) output.vectors[2U + 2U * 3U] *= 2.0;
}};
// Magnitude is repaired by mass normalization; an erroneous direction fails.
const auto result =
fesa::MklFeastEigenSolver{}.SolveGeneralized(k, m, 1U, 2, 3);
ASSERT_TRUE(result.HasValue());
EXPECT_EQ(result.Value().eigenvalues.size(), 3U);
}
TEST(MklFeastGeneralized, RejectsCorruptUnselectedDirectionAndFatalCount) {
const auto k = MakeDenseCsr(3U, {2, 0, 0, 0, 6, 0, 0, 0, 12});
const auto m = MakeDenseCsr(3U, {2, 0, 0, 0, 3, 0, 0, 0, 4});
{
fesa::internal::ScopedFeastBackendTestHook hook{
[](const auto& call, auto& output) {
if (!call.count) output.vectors[0U + 2U * 3U] += 0.2;
}};
ExpectFailureCode(
fesa::MklFeastEigenSolver{}.SolveGeneralized(k, m, 1U, 2, 3),
"eigenpair-validation-failed");
}
{
fesa::internal::ScopedFeastBackendTestHook hook{
[](const auto& call, auto& output) {
if (call.count) output.info = -3;
}};
const auto result =
fesa::MklFeastEigenSolver{}.SolveGeneralized(k, m, 1U, 2, 3);
ExpectFailureCode(result, "eigen-feast-failed");
EXPECT_NE(
result.GetStatus().Diagnostics()[0].message.find("Backend calls="),
std::string::npos);
}
}
TEST(MklFeastGeneralized, LowestPrefixPreservesRepeatedBoundary) {
constexpr std::size_t n = 18U;
std::vector<double> kv(n * n, 0.0), mv(n * n, 0.0);
for (std::size_t i = 0; i < n; ++i) {
mv[i * n + i] = 2.0 + static_cast<double>(i);
kv[i * n + i] =
mv[i * n + i] * (i < 5U ? 1.0 : 2.0 + static_cast<double>(i));
}
const auto k = MakeDenseCsr(n, kv), m = MakeDenseCsr(n, mv);
const auto result =
fesa::MklFeastEigenSolver{}.SolveGeneralized(k, m, 3U, 2.0, 19.0);
ASSERT_TRUE(result.HasValue())
<< (result.HasValue() ? "" : result.GetStatus().Diagnostics()[0].message);
ASSERT_GE(result.Value().eigenvalues.size(), 5U);
for (std::size_t i = 0; i < 5U; ++i)
EXPECT_NEAR(result.Value().eigenvalues[i], 1.0, 1e-11);
}
TEST(MklFeastGeneralized, AllocationAndCountMismatchFailClosed) {
const auto k = MakeDenseCsr(2U, {2, 0, 0, 6});
const auto m = MakeDenseCsr(2U, {2, 0, 0, 3});
{
fesa::internal::ScopedFeastWorkspaceTestHook hook{
[](bool) { throw std::bad_alloc{}; }};
ExpectFailureCode(
fesa::MklFeastEigenSolver{}.SolveGeneralized(k, m, 1U, 2, 2),
"eigen-allocation-failed");
}
{
fesa::internal::ScopedFeastBackendTestHook hook{
[](const auto& call, auto& output) {
if (call.count) output.m0 = 1;
}};
ExpectFailureCode(
fesa::MklFeastEigenSolver{}.SolveGeneralized(k, m, 1U, 2, 2),
"eigen-count-inconsistent");
}
}
TEST(MklFeastGeneralized, GeneralizedRetryRetainsCertifiedCountTrace) {
constexpr std::size_t n = 18U;
std::vector<double> kv(n * n, 0.0), mv(n * n, 0.0);
for (std::size_t i = 0; i < n; ++i) {
mv[i * n + i] = 2.0 + i;
kv[i * n + i] = mv[i * n + i] * (i + 1.0);
}
const auto k = MakeDenseCsr(n, kv), m = MakeDenseCsr(n, mv);
bool injected = false;
fesa::internal::ScopedFeastBackendTestHook hook{
[&injected](const auto& call, auto& output) {
if (!call.count && !injected) {
output.info = 2;
injected = true;
}
}};
const auto result =
fesa::MklFeastEigenSolver{}.SolveGeneralized(k, m, 3U, 2, 18);
ASSERT_TRUE(result.HasValue())
<< (result.HasValue() ? "" : result.GetStatus().Diagnostics()[0].message);
EXPECT_TRUE(injected);
EXPECT_NEAR(result.Value().eigenvalues[0], 1.0, 1e-11);
bool retried = false;
for (const auto& call : result.Value().backend_calls)
retried = retried || (call.kind == "solve" && call.info == 2 &&
call.outcome == "retry");
EXPECT_TRUE(retried);
}
TEST(MklFeastGeneralized,
LowerPrefixCountsProveNoOmittedModesAndRejectNegative) {
const auto m = MakeDenseCsr(3U, {2, 0, 0, 0, 3, 0, 0, 0, 4});
const auto k = MakeDenseCsr(3U, {0, 0, 0, 0, 6, 0, 0, 0, 12});
const auto result =
fesa::MklFeastEigenSolver{}.SolveGeneralized(k, m, 1U, 2, 3);
ASSERT_TRUE(result.HasValue());
std::size_t guards = 0;
for (const auto& call : result.Value().backend_calls) {
if (call.purpose != "lower-empty-prefix") continue;
++guards;
EXPECT_EQ(call.info, 0);
EXPECT_TRUE(call.count_available);
EXPECT_EQ(call.count, 0U);
EXPECT_LT(call.upper, 0.0);
EXPECT_LT(call.lower, call.upper);
}
EXPECT_EQ(guards, 3U);
EXPECT_NEAR(result.Value().eigenvalues[0], 0.0, 1e-12);
const auto negative = MakeDenseCsr(3U, {-2, 0, 0, 0, 6, 0, 0, 0, 12});
ExpectFailureCode(
fesa::MklFeastEigenSolver{}.SolveGeneralized(negative, m, 1U, 2, 3),
"negative-eigenvalue-spectrum");
}