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perf(shell): route local products through MKL and reduce Hessian storage work

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This commit is contained in:
KOKO\Mimi
2026-10-14 18:07:16 +09:00
parent 8c7c41729e
commit f9e0df66dc
9 changed files with 758 additions and 179 deletions
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src/fesa/analysis/hht_dynamic_algebra.cpp
+124 -45
View File
@@ -2,9 +2,11 @@
#include <array>
#include <cmath>
#include <cstddef>
#include <exception>
#include <iomanip>
#include <limits>
#include <sstream>
#include <stdexcept>
#include <string>
#include <utility>
#include <vector>
@@ -13,6 +15,7 @@
#include "fesa/math/matrix.h"
#include "fesa/solvers/linear/linear_solver.h"
#include "fesa/solvers/linear/tangent_solver.h"
#include "math/dense_blas_internal.h"
namespace fesa {
namespace hht_internal {
@@ -132,13 +135,13 @@ Status CheckLocalMass(const Domain& domain, const SparseMatrix& matrix,
const std::size_t begin, const std::size_t end) {
if (begin == end) return Status::Ok();
const std::size_t size = end - begin;
std::array<std::array<double, 6>, 6> block{};
std::array<std::array<double, 6>, 6> lower{};
const dense_blas_internal::ScopedLocalDenseThreads local_threads{};
Matrix block{size, size};
double scale = 0.0;
for (std::size_t i = 0; i < size; ++i) {
for (std::size_t j = 0; j < size; ++j) {
block[i][j] = Entry(matrix, begin + i, begin + j);
scale = std::max(scale, std::abs(block[i][j]));
block(i, j) = Entry(matrix, begin + i, begin + j);
scale = std::max(scale, std::abs(block(i, j)));
}
}
if (!std::isfinite(scale) || !(scale > 0.0)) {
@@ -149,36 +152,34 @@ Status CheckLocalMass(const Domain& domain, const SparseMatrix& matrix,
for (std::size_t i = 0; i < size; ++i) {
double sum = 0.0;
for (std::size_t j = 0; j < size; ++j) {
block[i][j] /= scale;
sum += std::abs(block[i][j]);
block(i, j) /= scale;
sum += std::abs(block(i, j));
}
norm = std::max(norm, sum);
for (std::size_t j = 0; j <= i; ++j) {
double value = block[i][j];
for (std::size_t k = 0; k < j; ++k) value -= lower[i][k] * lower[j][k];
if (!std::isfinite(value) || (i == j && !(value > 0.0))) {
return Failure(
domain, "dynamic-positive-mass",
"Physical mass requires strictly positive Cholesky pivots.");
}
lower[i][j] = i == j ? std::sqrt(value) : value / lower[j][j];
}
}
Matrix lower{size, size};
Matrix inverse_lower{size, size};
auto factor_failure = dense_blas_internal::CholeskyFailure::kNone;
try {
if (!dense_blas_internal::CholeskyLowerAndInverse(
block, lower, inverse_lower, &factor_failure)) {
if (factor_failure == dense_blas_internal::CholeskyFailure::kInverse)
return Failure(
domain, "dynamic-positive-mass-conditioning",
"A nodal free physical block reciprocal condition is below 2^-32.");
return Failure(
domain, "dynamic-positive-mass",
"Physical mass requires strictly positive Cholesky pivots.");
}
} catch (const std::exception& error) {
return Failure(domain, "dynamic-positive-mass", error.what());
}
const Matrix inverse =
dense_blas_internal::MultiplyTransposeLeft(inverse_lower, inverse_lower);
std::array<double, 6> sums{};
for (std::size_t column = 0; column < size; ++column) {
std::array<double, 6> solution{};
for (std::size_t i = 0; i < size; ++i) {
double value = i == column ? 1.0 : 0.0;
for (std::size_t k = 0; k < i; ++k) value -= lower[i][k] * solution[k];
solution[i] = value / lower[i][i];
}
for (std::size_t reverse = size; reverse > 0U; --reverse) {
const std::size_t i = reverse - 1U;
double value = solution[i];
for (std::size_t k = i + 1U; k < size; ++k)
value -= lower[k][i] * solution[k];
solution[i] = value / lower[i][i];
sums[i] += std::abs(solution[i]);
sums[i] += std::abs(inverse(i, column));
}
}
const double inverse_norm = *std::max_element(sums.begin(), sums.end());
@@ -212,19 +213,33 @@ Result<PhysicalSpace> BuildPhysicalSpace(
double symmetry_error = 0.0;
double null_error = 0.0;
if (mass_scale > 0.0) {
Vector normalized_mass{mass.Values().size()};
Vector null_coefficients{mass.Values().size()};
for (std::size_t index = 0U; index < mass.Values().size(); ++index) {
normalized_mass[index] = mass.Values()[index] / mass_scale;
const auto full = dofs.FreeDofs()[mass.ColumnIndices()[index]];
if (full % 6U >= 3U && node_null[full / 6U] != no_null)
null_coefficients[index] =
assembly.rotations[full / 6U].drill_null[full % 6U - 3U];
}
Vector null_products{0U};
{
const dense_blas_internal::ScopedLocalDenseThreads local_threads{};
null_products = dense_blas_internal::MultiplyDiagonal(normalized_mass,
null_coefficients);
}
for (std::size_t row = 0; row < mass.Rows(); ++row) {
std::vector<double> action(null_nodes.size(), 0.0);
for (std::size_t index = mass.RowOffsets()[row];
index < mass.RowOffsets()[row + 1U]; ++index) {
const std::size_t column = mass.ColumnIndices()[index];
const double entry = mass.Values()[index] / mass_scale;
const double entry = normalized_mass[index];
mass_norm = std::hypot(mass_norm, entry);
symmetry_error = std::hypot(
symmetry_error, entry - Entry(mass, column, row) / mass_scale);
const std::size_t full = dofs.FreeDofs()[column];
if (full % 6U >= 3U && node_null[full / 6U] != no_null) {
action[node_null[full / 6U]] +=
entry * assembly.rotations[full / 6U].drill_null[full % 6U - 3U];
action[node_null[full / 6U]] += null_products[index];
}
}
for (const double value : action)
@@ -291,6 +306,7 @@ Result<PhysicalSpace> BuildPhysicalSpace(
}
}
std::vector<CooContribution> entries;
std::vector<std::pair<double, double>> mass_factors;
node_starts.push_back(dimension);
double complement_gram_error = 0.0;
double null_gram_error = 0.0;
@@ -350,8 +366,10 @@ Result<PhysicalSpace> BuildPhysicalSpace(
domain, "dynamic-invalid-analytic-null",
"The scaled physical and analytic null Gram identities failed."));
}
for (std::size_t i = 0; i < dimension; ++i)
for (std::size_t i = 0; i < dimension; ++i) {
entries.push_back({i, i, 0.0, 0U, entries.size()});
mass_factors.push_back({0.0, 0.0});
}
for (std::size_t row = 0; row < mass.Rows(); ++row) {
const auto& left = rows[dofs.FreeDofs()[row]];
for (std::size_t index = mass.RowOffsets()[row];
@@ -359,13 +377,54 @@ Result<PhysicalSpace> BuildPhysicalSpace(
const auto& right = rows[dofs.FreeDofs()[mass.ColumnIndices()[index]]];
for (const auto& a : left) {
for (const auto& b : right) {
entries.push_back({a.first, b.first,
a.second * mass.Values()[index] * b.second, 0U,
entries.size()});
entries.push_back({a.first, b.first, a.second, 0U, entries.size()});
mass_factors.push_back({mass.Values()[index], b.second});
}
}
}
}
Vector coefficients{entries.size()};
Vector mass_values{entries.size()};
Vector right_values{entries.size()};
for (std::size_t i = 0U; i < entries.size(); ++i) {
coefficients[i] = entries[i].value;
mass_values[i] = mass_factors[i].first;
right_values[i] = mass_factors[i].second;
}
Vector projected{0U};
{
const dense_blas_internal::ScopedLocalDenseThreads local_threads{};
projected =
dense_blas_internal::MultiplyDiagonal(coefficients, mass_values);
bool finite = true;
for (std::size_t i = 0U; i < projected.Size(); ++i) {
entries[i].value = projected[i];
finite = finite && std::isfinite(projected[i]);
}
// A rejected intermediate cannot produce a finite original contribution.
// Still compute the remaining finite entries so an earlier final-product
// overflow keeps its diagnostic priority. No invalid operand reaches MKL.
if (!finite) {
std::vector<std::size_t> valid_positions;
for (std::size_t i = 0U; i < projected.Size(); ++i)
if (std::isfinite(projected[i])) valid_positions.push_back(i);
Vector valid_left{valid_positions.size()};
Vector valid_right{valid_positions.size()};
for (std::size_t i = 0U; i < valid_positions.size(); ++i) {
valid_left[i] = projected[valid_positions[i]];
valid_right[i] = right_values[valid_positions[i]];
}
const Vector valid_products =
dense_blas_internal::MultiplyDiagonal(valid_left, valid_right);
for (std::size_t i = 0U; i < valid_positions.size(); ++i)
entries[valid_positions[i]].value = valid_products[i];
auto rejected = MakeSparse(dimension, dimension, std::move(entries));
return Result<PhysicalSpace>::Failure(rejected.GetStatus());
}
projected = dense_blas_internal::MultiplyDiagonal(projected, right_values);
}
for (std::size_t i = 0U; i < entries.size(); ++i)
entries[i].value = projected[i];
auto block = MakeSparse(dimension, dimension, std::move(entries));
if (!block.HasValue())
return Result<PhysicalSpace>::Failure(block.GetStatus());
@@ -436,15 +495,20 @@ Result<Regularity> CheckRegularity(const Domain& domain,
for (std::size_t i = 0; i < nodes.size(); ++i) {
node_null[nodes[i]] = i;
const auto& n = assembly.rotations[nodes[i]].drill_null;
double stiffness = 0.0;
Matrix metric{3U, 3U};
Vector direction{3U};
for (std::size_t a = 0; a < 3; ++a) {
direction[a] = n[a];
for (std::size_t b = 0; b < 3; ++b) {
stiffness += n[a] *
Entry(assembly.drilling_metric, 6U * nodes[i] + 3U + a,
6U * nodes[i] + 3U + b) *
n[b];
metric(a, b) = Entry(assembly.drilling_metric, 6U * nodes[i] + 3U + a,
6U * nodes[i] + 3U + b);
}
}
double stiffness = 0.0;
{
const dense_blas_internal::ScopedLocalDenseThreads local_threads{};
stiffness = direction.Dot(metric.Multiply(direction));
}
if (!std::isfinite(stiffness) || !(stiffness > 0.0)) {
return Result<Regularity>::Failure(
Failure(domain, "dynamic-algebraic-regularity",
@@ -454,22 +518,37 @@ Result<Regularity> CheckRegularity(const Domain& domain,
weights[i] = std::sqrt(stiffness);
}
std::vector<CooContribution> entries;
std::vector<double> null_coefficients;
for (std::size_t row = 0; row < nodes.size(); ++row) {
entries.push_back({row, row, 0.0, 0U, entries.size()});
null_coefficients.push_back(0.0);
for (std::size_t index = gradient.RowOffsets()[row];
index < gradient.RowOffsets()[row + 1U]; ++index) {
const std::size_t full = gradient.ColumnIndices()[index];
if (full % 6U >= 3U && node_null[full / 6U] != no_null) {
const std::size_t column = node_null[full / 6U];
entries.push_back(
{row, column,
gradient.Values()[index] *
assembly.rotations[full / 6U].drill_null[full % 6U - 3U] /
weights[row] / weights[column],
0U, entries.size()});
{row, column, gradient.Values()[index], 0U, entries.size()});
null_coefficients.push_back(
assembly.rotations[full / 6U].drill_null[full % 6U - 3U]);
}
}
}
Vector gradient_values{entries.size()};
Vector null_values{entries.size()};
for (std::size_t i = 0U; i < entries.size(); ++i) {
gradient_values[i] = entries[i].value;
null_values[i] = null_coefficients[i];
}
Vector products{0U};
{
const dense_blas_internal::ScopedLocalDenseThreads local_threads{};
products =
dense_blas_internal::MultiplyDiagonal(gradient_values, null_values);
}
for (std::size_t i = 0U; i < entries.size(); ++i)
entries[i].value =
products[i] / weights[entries[i].row] / weights[entries[i].column];
auto matrix = MakeSparse(nodes.size(), nodes.size(), std::move(entries));
if (!matrix.HasValue())
return Result<Regularity>::Failure(matrix.GetStatus());
src/fesa/analysis/hht_reduced_operators.cpp
+40 -9
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@@ -6,10 +6,12 @@
#include <limits>
#include <map>
#include <sstream>
#include <stdexcept>
#include <string>
#include <utility>
#include "fesa/solvers/linear/tangent_solver.h"
#include "math/dense_blas_internal.h"
#include "math/high_low_arithmetic.h"
namespace fesa::hht_reduced_internal {
@@ -614,10 +616,33 @@ Matrix PhysicalJacobian(const ConstraintOperators& operators,
Vector ContractConstraintHessian(const ConstraintOperators& operators,
const Vector& left, const Vector& right) {
const dense_blas_internal::ScopedLocalDenseThreads local_threads{};
Vector result{operators.rows.size()};
for (std::size_t row = 0U; row < operators.rows.size(); ++row)
for (const auto& entry : operators.rows[row].hessian)
result[row] += entry.value * left[entry.row] * right[entry.column];
for (std::size_t row = 0U; row < operators.rows.size(); ++row) {
const auto& hessian = operators.rows[row].hessian;
Vector coefficients{hessian.size()};
Vector left_values{hessian.size()};
Vector right_values{hessian.size()};
for (std::size_t i = 0U; i < hessian.size(); ++i) {
coefficients[i] = hessian[i].value;
left_values[i] = left[hessian[i].row];
right_values[i] = right[hessian[i].column];
}
try {
const Vector first =
dense_blas_internal::MultiplyDiagonal(coefficients, left_values);
const Vector products =
dense_blas_internal::MultiplyDiagonal(first, right_values);
// Retain the original entry order and left-associated products; only
// ordinary products move to MKL. This is failure-only replay evidence.
for (std::size_t i = 0U; i < products.Size(); ++i)
result[row] += products[i];
} catch (const std::invalid_argument&) {
// A nonfinite input/intermediate cannot yield a finite original sum.
// Keep the existing caller's finite failure without a scalar fallback.
result[row] = std::numeric_limits<double>::quiet_NaN();
}
}
return result;
}
@@ -1186,13 +1211,19 @@ Result<double> CheckGraphRegularity(
Failure("Reduced graph regularity node is invalid.",
"dynamic-mass-regularity"));
const auto& null = assembly.rotations[node].drill_null;
double metric = 0.0;
for (std::size_t i = 0U; i < 3U; ++i)
Matrix metric_block{3U, 3U};
Vector direction{3U};
for (std::size_t i = 0U; i < 3U; ++i) {
direction[i] = null[i];
for (std::size_t j = 0U; j < 3U; ++j)
metric += null[i] *
SparseEntry(assembly.drilling_metric, 6U * node + 3U + i,
6U * node + 3U + j) *
null[j];
metric_block(i, j) = SparseEntry(
assembly.drilling_metric, 6U * node + 3U + i, 6U * node + 3U + j);
}
double metric = 0.0;
{
const dense_blas_internal::ScopedLocalDenseThreads local_threads{};
metric = direction.Dot(metric_block.Multiply(direction));
}
if (!std::isfinite(metric) || !(metric > 0.0))
return Result<double>::Failure(Failure(
"Reduced graph requires a positive finite null drilling metric.",
src/fesa/elements/mitc4_shell.cpp
+12 -23
View File
@@ -8,6 +8,7 @@
#include <utility>
#include "fesa/model/model_types.h"
#include "math/dense_blas_internal.h"
namespace fesa {
@@ -223,28 +224,18 @@ Matrix ScaledMatrix(const Matrix& source, double factor) {
return result;
}
/// @brief Lifts a local matrix by a deterministic serial congruence product.
/// @note The loop and accumulation order are part of reproducible stiffness.
/// @brief Lifts a local matrix through MKL and mirrors the upper triangle.
Matrix Congruence(const Matrix& local, const Matrix& transformation) {
if (local.Rows() != local.Columns() ||
local.Rows() != transformation.Rows()) {
throw std::invalid_argument{
"MITC4 congruence dimensions are incompatible."};
}
Matrix result{transformation.Columns(), transformation.Columns()};
Matrix result = dense_blas_internal::MultiplyTransposeLeft(
transformation, local.Multiply(transformation));
for (std::size_t row = 0U; row < result.Rows(); ++row) {
for (std::size_t column = row; column < result.Columns(); ++column) {
double value = 0.0;
for (std::size_t local_row = 0U; local_row < local.Rows(); ++local_row) {
for (std::size_t local_column = 0U; local_column < local.Columns();
++local_column) {
value += transformation(local_row, row) *
local(local_row, local_column) *
transformation(local_column, column);
}
}
result(row, column) = value;
result(column, row) = value;
result(column, row) = result(row, column);
}
}
return result;
@@ -611,7 +602,8 @@ Matrix Mitc4Shell::TransverseShearSectionMatrix() const {
return result;
}
Result<Mitc4Stiffness> Mitc4Shell::Stiffness() const {
Result<Mitc4Stiffness> Mitc4Shell::Stiffness() const try {
const dense_blas_internal::ScopedLocalDenseThreads local_threads{};
const Matrix constitutive = MaterialConstitutive5();
const Matrix tying_samples = CovariantTyingShearSamples20();
Matrix physical_local{kPhysicalDofCount, kPhysicalDofCount};
@@ -627,17 +619,12 @@ Result<Mitc4Stiffness> Mitc4Shell::Stiffness() const {
const Matrix strain = StrainDisplacement(
point.natural_coordinates[0], point.natural_coordinates[1],
point.natural_coordinates[2], &tying_samples);
const Matrix integrand = dense_blas_internal::MultiplyTransposeLeft(
strain, constitutive.Multiply(strain));
for (std::size_t row = 0U; row < kPhysicalDofCount; ++row) {
for (std::size_t column = row; column < kPhysicalDofCount; ++column) {
double integrand = 0.0;
for (std::size_t first = 0U; first < 5U; ++first) {
for (std::size_t second = 0U; second < 5U; ++second) {
integrand += strain(first, row) * constitutive(first, second) *
strain(second, column);
}
}
const double contribution =
integrand * geometry.jacobian * point.weight;
integrand(row, column) * geometry.jacobian * point.weight;
physical_local(row, column) += contribution;
if (row != column) {
physical_local(column, row) += contribution;
@@ -714,6 +701,8 @@ Result<Mitc4Stiffness> Mitc4Shell::Stiffness() const {
Mitc4Stiffness{std::move(physical_local), std::move(physical_global),
std::move(drilling_global), std::move(stabilized_global),
drilling_stiffness});
} catch (const std::exception& error) {
return StiffnessFailure(source_location_, identity_, error.what());
}
Result<Mitc4Mass> Mitc4Shell::Mass(const double density) const {
src/fesa/elements/nonlinear_mitc4_inertia.cpp
+92 -73
View File
@@ -4,11 +4,13 @@
#include <array>
#include <cmath>
#include <cstddef>
#include <exception>
#include <limits>
#include <string>
#include <utility>
#include "fesa/elements/finite_rotation.h"
#include "math/dense_blas_internal.h"
namespace fesa {
namespace {
@@ -35,6 +37,16 @@ class InertiaSum {
double correction_ = 0.0;
};
/// @brief Contracts two nodal 6-by-3 coefficient blocks through dense MKL.
/// @note Nonfinite coefficients remain failures of the final inertia gate.
void DotBlocks(const std::array<double, 18U>& left,
const std::array<double, 18U>& right,
std::array<double, 36U>& result) {
if (!dense_blas_internal::MultiplyTransposeRight(
left.data(), 6U, right.data(), 6U, 3U, result.data()))
result.fill(std::numeric_limits<double>::quiet_NaN());
}
Vector3 WeightedSum(const std::array<double, kNodes>& weights,
const std::array<Vector3, kNodes>& values) {
Vector3 result{};
@@ -442,12 +454,11 @@ Status CheckPhysicalMass(const Matrix& mass,
}
double gram_error = 0.0;
double orthogonality_error = 0.0;
const Matrix gram =
dense_blas_internal::MultiplyTransposeLeft(complement, complement);
for (std::size_t row = 0U; row < kPhysical; ++row) {
for (std::size_t column = 0U; column < kPhysical; ++column) {
double entry = row == column ? -1.0 : 0.0;
for (std::size_t inner = 0U; inner < kDofs; ++inner) {
entry += complement(inner, row) * complement(inner, column);
}
const double entry = gram(row, column) - (row == column ? 1.0 : 0.0);
gram_error = std::hypot(gram_error, entry);
}
for (std::size_t node = 0U; node < kNodes; ++node) {
@@ -472,55 +483,42 @@ Status CheckPhysicalMass(const Matrix& mass,
return fail("invalid-nonlinear-inertia-null",
"Scaled mass symmetry and analytic null identities failed.");
}
Matrix block{kPhysical, kPhysical};
Matrix mass_complement{kDofs, kPhysical};
for (std::size_t row = 0U; row < kDofs; ++row) {
for (std::size_t column = 0U; column < kPhysical; ++column) {
for (std::size_t inner = 0U; inner < kDofs; ++inner) {
mass_complement(row, column) +=
scaled(row, inner) * complement(inner, column);
}
}
}
const Matrix mass_complement = scaled.Multiply(complement);
const Matrix block =
dense_blas_internal::MultiplyTransposeLeft(complement, mass_complement);
double block_norm = 0.0;
for (std::size_t row = 0U; row < kPhysical; ++row) {
double row_sum = 0.0;
for (std::size_t column = 0U; column < kPhysical; ++column) {
for (std::size_t inner = 0U; inner < kDofs; ++inner) {
block(row, column) +=
complement(inner, row) * mass_complement(inner, column);
}
row_sum += std::abs(block(row, column));
}
block_norm = std::max(block_norm, row_sum);
}
Matrix lower{kPhysical, kPhysical};
for (std::size_t row = 0U; row < kPhysical; ++row) {
for (std::size_t column = 0U; column <= row; ++column) {
double entry = block(row, column);
for (std::size_t inner = 0U; inner < column; ++inner) {
entry -= lower(row, inner) * lower(column, inner);
}
if (!std::isfinite(entry) || (row == column && !(entry > 0.0))) {
return fail(
"invalid-nonlinear-inertia-positive-mass",
"Physical mass requires strictly positive Cholesky pivots.");
}
lower(row, column) =
row == column ? std::sqrt(entry) : entry / lower(column, column);
}
Matrix inverse_lower{kPhysical, kPhysical};
auto factor_failure = dense_blas_internal::CholeskyFailure::kNone;
if (!dense_blas_internal::CholeskyLowerAndInverse(block, lower, inverse_lower,
&factor_failure)) {
if (factor_failure == dense_blas_internal::CholeskyFailure::kInverse)
return fail(
"ill-conditioned-nonlinear-inertia-positive-mass",
"Physical mass reciprocal infinity condition is below 2^-32.");
return fail("invalid-nonlinear-inertia-positive-mass",
"Physical mass requires strictly positive Cholesky pivots.");
}
std::array<double, kPhysical> inverse_row_sums{};
double reconstruction_error = 0.0;
double block_frobenius = 0.0;
Matrix transpose{kPhysical, kPhysical};
for (std::size_t row = 0U; row < kPhysical; ++row)
for (std::size_t column = 0U; column < kPhysical; ++column)
transpose(row, column) = lower(column, row);
const Matrix reconstructed = lower.Multiply(transpose);
for (std::size_t row = 0U; row < kPhysical; ++row) {
for (std::size_t column = 0U; column < kPhysical; ++column) {
double reconstructed = 0.0;
for (std::size_t inner = 0U; inner <= std::min(row, column); ++inner) {
reconstructed += lower(row, inner) * lower(column, inner);
}
reconstruction_error =
std::hypot(reconstruction_error, reconstructed - block(row, column));
std::hypot(reconstruction_error,
reconstructed(row, column) - block(row, column));
block_frobenius = std::hypot(block_frobenius, block(row, column));
}
}
@@ -528,25 +526,11 @@ Status CheckPhysicalMass(const Matrix& mass,
return fail("invalid-nonlinear-inertia-positive-mass",
"Physical mass Cholesky reconstruction failed.");
}
for (std::size_t column = 0U; column < kPhysical; ++column) {
std::array<double, kPhysical> solution{};
for (std::size_t row = 0U; row < kPhysical; ++row) {
double rhs = row == column ? 1.0 : 0.0;
for (std::size_t inner = 0U; inner < row; ++inner) {
rhs -= lower(row, inner) * solution[inner];
}
solution[row] = rhs / lower(row, row);
}
for (std::size_t reverse = kPhysical; reverse > 0U; --reverse) {
const std::size_t row = reverse - 1U;
double rhs = solution[row];
for (std::size_t inner = row + 1U; inner < kPhysical; ++inner) {
rhs -= lower(inner, row) * solution[inner];
}
solution[row] = rhs / lower(row, row);
inverse_row_sums[row] += std::abs(solution[row]);
}
}
const Matrix inverse =
dense_blas_internal::MultiplyTransposeLeft(inverse_lower, inverse_lower);
for (std::size_t column = 0U; column < kPhysical; ++column)
for (std::size_t row = 0U; row < kPhysical; ++row)
inverse_row_sums[row] += std::abs(inverse(row, column));
const double inverse_norm =
*std::max_element(inverse_row_sums.begin(), inverse_row_sums.end());
const double reciprocal_condition = 1.0 / block_norm / inverse_norm;
@@ -712,6 +696,7 @@ Result<NonlinearMitc4Inertia> NonlinearMitc4Inertia::Create(
Result<NonlinearMitc4InertiaEvaluation> NonlinearMitc4Inertia::Evaluate(
const NonlinearMitc4TrialDofs& trial, const Vector& velocity,
const Vector& acceleration) const {
const dense_blas_internal::ScopedLocalDenseThreads local_threads{};
if (velocity.Size() != kDofs || acceleration.Size() != kDofs ||
!IsFinite(velocity) || !IsFinite(acceleration)) {
return Failure<NonlinearMitc4InertiaEvaluation>(
@@ -899,6 +884,42 @@ Result<NonlinearMitc4InertiaEvaluation> NonlinearMitc4Inertia::Evaluate(
result.momentum_rate_scale += scale * acceleration_point.Norm();
result.angular_momentum_rate_scale +=
scale * position.Cross(acceleration_point).Norm();
std::array<double, 18U> h_block;
std::array<double, 18U> velocity_block;
std::array<double, 18U> position_block;
for (std::size_t local = 0U; local < 6U; ++local) {
const auto field = 6U * mass_node + local;
for (std::size_t axis = 0U; axis < 3U; ++axis) {
h_block[3U * local + axis] = h[field][axis];
velocity_block[3U * local + axis] =
velocity_derivative[field][axis];
position_block[3U * local + axis] =
position_derivative[field][axis];
}
}
std::array<double, 36U> mass_block;
std::array<double, 36U> velocity_product;
std::array<double, 36U> position_product;
DotBlocks(h_block, h_block, mass_block);
DotBlocks(h_block, velocity_block, velocity_product);
DotBlocks(h_block, position_block, position_product);
std::array<std::array<double, 36U>, 3U> mass_variation;
for (std::size_t direction = 0U; direction < 3U; ++direction) {
std::array<double, 18U> derivative_block;
for (std::size_t local = 0U; local < 6U; ++local) {
const Vector3 derivative =
local < 3U ? Vector3{}
: z * rotations[mass_node]
.director_second[local - 3U][direction];
for (std::size_t axis = 0U; axis < 3U; ++axis)
derivative_block[3U * local + axis] = derivative[axis];
}
std::array<double, 36U> reverse;
DotBlocks(derivative_block, h_block, mass_variation[direction]);
DotBlocks(h_block, derivative_block, reverse);
for (std::size_t index = 0U; index < 36U; ++index)
mass_variation[direction][index] += reverse[index];
}
for (std::size_t row = 6U * mass_node; row < 6U * (mass_node + 1U);
++row) {
// Keep c independent of a; subtracting M*a destroys small c values.
@@ -906,10 +927,11 @@ Result<NonlinearMitc4InertiaEvaluation> NonlinearMitc4Inertia::Evaluate(
scale * h[row].Dot(convective_point);
for (std::size_t column = 6U * mass_node;
column < 6U * (mass_node + 1U); ++column) {
result.mass(row, column) += scale * h[row].Dot(h[column]);
const auto local_index = 6U * (row % 6U) + column % 6U;
result.mass(row, column) += scale * mass_block[local_index];
result.velocity_tangent(row, column) +=
scale * h[row].Dot(velocity_derivative[column]);
double position_entry = h[row].Dot(position_derivative[column]);
scale * velocity_product[local_index];
double position_entry = position_product[local_index];
if (row / 6U == column / 6U && row % 6U >= 3U &&
column % 6U >= 3U) {
const std::size_t node = row / 6U;
@@ -922,20 +944,10 @@ Result<NonlinearMitc4InertiaEvaluation> NonlinearMitc4Inertia::Evaluate(
result.position_tangent(row, column) += scale * position_entry;
if (column % 6U >= 3U) {
const auto direction = column % 6U - 3U;
const Vector3 dh_row =
row % 6U < 3U
? Vector3{}
: z * rotations[mass_node]
.director_second[row % 6U - 3U][direction];
for (std::size_t local = 0U; local < 6U; ++local) {
const auto field = 6U * mass_node + local;
const Vector3 dh_field =
local < 3U
? Vector3{}
: z * rotations[mass_node]
.director_second[local - 3U][direction];
mass_derivative[mass_node][direction][row % 6U][local] +=
scale * (dh_row.Dot(h[field]) + h[row].Dot(dh_field));
scale *
mass_variation[direction][6U * (row % 6U) + local];
}
}
}
@@ -1004,8 +1016,15 @@ Result<NonlinearMitc4InertiaEvaluation> NonlinearMitc4Inertia::Evaluate(
"invalid-nonlinear-inertia-evaluation", source_location_, identity_,
"Nonlinear MITC4 inertia evaluation must remain finite.");
}
const Status physical_mass = CheckPhysicalMass(result.mass, nulls, length,
source_location_, identity_);
Status physical_mass = Status::Ok();
try {
physical_mass = CheckPhysicalMass(result.mass, nulls, length,
source_location_, identity_);
} catch (const std::exception& error) {
return Failure<NonlinearMitc4InertiaEvaluation>(
"invalid-nonlinear-inertia-positive-mass", source_location_, identity_,
error.what());
}
if (!physical_mass.IsOk()) {
return Result<NonlinearMitc4InertiaEvaluation>::Failure(physical_mass);
}
src/fesa/elements/nonlinear_mitc4_shell.cpp
+104 -23
View File
@@ -10,6 +10,7 @@
#include <utility>
#include "fesa/elements/finite_rotation.h"
#include "math/dense_blas_internal.h"
namespace fesa {
namespace {
@@ -394,22 +395,63 @@ constexpr std::size_t kHessianSize = kGlobalDofCount * kGlobalDofCount;
/// @brief Carries exact first and second trial-coordinate variations.
class Hessian {
public:
Hessian() : values_{std::make_shared<std::array<double, kHessianSize>>()} {}
Hessian() = default;
double& operator[](const std::size_t index) { return (*values_)[index]; }
double& operator[](const std::size_t index) { return Data()[index]; }
const double& operator[](const std::size_t index) const {
return (*values_)[index];
return Storage()[index];
}
auto begin() const { return values_->begin(); }
auto begin() const { return Storage().begin(); }
auto end() const { return values_->end(); }
auto end() const { return Storage().end(); }
double* Data() {
if (!values_) {
values_ = std::make_shared<Values>();
values_->entries.fill(0.0);
}
return values_->entries.data();
}
const double* ReadData() const { return Storage().data(); }
/// @brief Gets fresh output storage without redundant zero initialization.
/// @note Only fresh operator results use this pointer; all 576 entries must
/// be written before any read or copy of the result.
double* OverwriteData() {
if (!values_) values_ = std::make_shared<Values>();
return values_->entries.data();
}
private:
std::shared_ptr<std::array<double, kHessianSize>> values_;
struct Values {
// User-provided construction leaves entries uninitialized for a complete
// output overwrite while make_shared retains the single allocation.
Values() noexcept {}
std::array<double, kHessianSize> entries;
};
const std::array<double, kHessianSize>& Storage() const {
// Constants borrow only this immutable zero. Mutable coefficients retain
// the existing shared ownership; no trial-dependent cache is introduced.
static const std::array<double, kHessianSize> kZero{};
return values_ ? values_->entries : kZero;
}
std::shared_ptr<Values> values_;
};
/// @brief Forms an ordinary derivative outer product without a Matrix copy.
/// @note Rejected nonfinite operands propagate to the existing Jet finite gate.
void Outer(const std::array<double, kGlobalDofCount>& left,
const std::array<double, kGlobalDofCount>& right, double* result) {
if (!dense_blas_internal::OuterProduct(left.data(), left.size(), right.data(),
right.size(), result))
std::fill_n(result, kHessianSize, std::numeric_limits<double>::quiet_NaN());
}
/// @brief Carries exact first and second trial-coordinate variations.
struct Jet {
double value{};
@@ -455,8 +497,11 @@ Jet operator+(const Jet& left, const Jet& right) {
result.mixed_second[index] =
left.mixed_second[index] + right.mixed_second[index];
}
const double* left_second = left.second.ReadData();
const double* right_second = right.second.ReadData();
double* result_second = result.second.OverwriteData();
for (std::size_t index = 0U; index < kHessianSize; ++index) {
result.second[index] = left.second[index] + right.second[index];
result_second[index] = left_second[index] + right_second[index];
}
return result;
}
@@ -475,8 +520,11 @@ Jet operator-(const Jet& left, const Jet& right) {
result.mixed_second[index] =
left.mixed_second[index] - right.mixed_second[index];
}
const double* left_second = left.second.ReadData();
const double* right_second = right.second.ReadData();
double* result_second = result.second.OverwriteData();
for (std::size_t index = 0U; index < kHessianSize; ++index) {
result.second[index] = left.second[index] - right.second[index];
result_second[index] = left_second[index] - right_second[index];
}
return result;
}
@@ -506,13 +554,18 @@ Jet operator*(const Jet& left, const Jet& right) {
2.0 * left.directional_first * right.mixed_first[index] +
left.value * right.mixed_second[index];
}
const double* left_second = left.second.ReadData();
const double* right_second = right.second.ReadData();
double* result_second = result.second.OverwriteData();
Outer(left.first, right.first, result_second);
std::array<double, kHessianSize> reverse;
Outer(right.first, left.first, reverse.data());
for (std::size_t row = 0U; row < kGlobalDofCount; ++row) {
for (std::size_t column = 0U; column < kGlobalDofCount; ++column) {
const std::size_t index = row * kGlobalDofCount + column;
result.second[index] = left.second[index] * right.value +
left.first[row] * right.first[column] +
left.first[column] * right.first[row] +
left.value * right.second[index];
result_second[index] = left_second[index] * right.value +
result_second[index] + reverse[index] +
left.value * right_second[index];
}
}
return result;
@@ -529,8 +582,10 @@ Jet operator*(const double scalar, const Jet& value) {
result.mixed_first[index] = scalar * value.mixed_first[index];
result.mixed_second[index] = scalar * value.mixed_second[index];
}
const double* value_second = value.second.ReadData();
double* result_second = result.second.OverwriteData();
for (std::size_t index = 0U; index < kHessianSize; ++index) {
result.second[index] = scalar * value.second[index];
result_second[index] = scalar * value_second[index];
}
return result;
}
@@ -559,11 +614,16 @@ Jet Compose(const Jet& input, const double value, const double first,
input.first[index] * input.directional_second) +
first * input.mixed_second[index];
}
std::array<double, kGlobalDofCount> scaled_first{};
for (std::size_t row = 0U; row < kGlobalDofCount; ++row)
scaled_first[row] = second * input.first[row];
const double* input_second = input.second.ReadData();
double* result_second = result.second.OverwriteData();
Outer(scaled_first, input.first, result_second);
for (std::size_t row = 0U; row < kGlobalDofCount; ++row) {
for (std::size_t column = 0U; column < kGlobalDofCount; ++column) {
const std::size_t index = row * kGlobalDofCount + column;
result.second[index] = first * input.second[index] +
second * input.first[row] * input.first[column];
result_second[index] = first * input_second[index] + result_second[index];
}
}
return result;
@@ -613,19 +673,32 @@ Jet Atan2(const Jet& y, const Jet& x) {
const double derivative_yx =
(y.value * y.value - x.value * x.value) / radius_fourth;
const double derivative_xx = 2.0 * x.value * y.value / radius_fourth;
std::array<double, kGlobalDofCount> scaled_y{};
std::array<double, kGlobalDofCount> scaled_x{};
for (std::size_t i = 0U; i < kGlobalDofCount; ++i) {
scaled_y[i] = derivative_yy * y.first[i];
scaled_x[i] = derivative_xx * x.first[i];
}
std::array<std::array<double, kHessianSize>, 4U> products;
Outer(scaled_y, y.first, products[0U].data());
Outer(y.first, x.first, products[1U].data());
Outer(x.first, y.first, products[2U].data());
Outer(scaled_x, x.first, products[3U].data());
for (std::size_t index = 0U; index < kGlobalDofCount; ++index) {
result.first[index] =
derivative_y * y.first[index] + derivative_x * x.first[index];
}
const double* y_second = y.second.ReadData();
const double* x_second = x.second.ReadData();
double* result_second = result.second.OverwriteData();
for (std::size_t row = 0U; row < kGlobalDofCount; ++row) {
for (std::size_t column = 0U; column < kGlobalDofCount; ++column) {
const std::size_t index = row * kGlobalDofCount + column;
result.second[index] = derivative_y * y.second[index] +
derivative_x * x.second[index] +
derivative_yy * y.first[row] * y.first[column] +
derivative_yx * (y.first[row] * x.first[column] +
x.first[row] * y.first[column]) +
derivative_xx * x.first[row] * x.first[column];
result_second[index] =
derivative_y * y_second[index] + derivative_x * x_second[index] +
products[0U][index] +
derivative_yx * (products[1U][index] + products[2U][index]) +
products[3U][index];
}
}
// Use a bounded ratio for the directional third derivative only. Retain
@@ -1181,10 +1254,14 @@ Jet DrillingEnergy(const std::array<Vector3, kNodeCount>& coordinates,
DrillSpinRate(trial.rotation[node], initial_directors[node]) * gamma;
}
energy = energy + 0.5 * drilling_stiffness * gamma * gamma;
std::array<double, kGlobalDofCount> scaled_gradient{};
for (std::size_t row = 0U; row < kGlobalDofCount; ++row)
scaled_gradient[row] = drilling_stiffness * gamma.first[row];
std::array<double, kHessianSize> contribution;
Outer(scaled_gradient, gamma.first, contribution.data());
for (std::size_t row = 0U; row < kGlobalDofCount; ++row) {
for (std::size_t column = 0U; column < kGlobalDofCount; ++column) {
(*metric)(row, column) +=
drilling_stiffness * gamma.first[row] * gamma.first[column];
(*metric)(row, column) += contribution[row * kGlobalDofCount + column];
}
}
}
@@ -1505,6 +1582,7 @@ NonlinearMitc4Shell::EvaluateExternalDrillingConstraint(
const std::size_t node, const Vector3& phi, const Vector3& phi_dot,
const Vector3& force, const Vector3& force_rate,
const Vector3& force_acceleration) const {
const dense_blas_internal::ScopedLocalDenseThreads local_threads{};
if (node >= kNodeCount || !phi_dot.IsFinite() || !force.IsFinite() ||
!force_rate.IsFinite() || !force_acceleration.IsFinite()) {
return Failure<NonlinearMitc4ExternalDrillingConstraint>(
@@ -1594,6 +1672,9 @@ NonlinearMitc4Shell::EvaluateExternalDrillingConstraint(
Result<NonlinearMitc4InternalEquilibrium> EvaluateInternalResidualAndTangent(
const NonlinearMitc4Shell& element, const NonlinearMitc4TrialDofs& trial,
const Vector* coordinate_direction) {
// Element-local MKL work uses one worker only when the caller has no TLS
// override. The guard restores that request before returning to global solve.
const dense_blas_internal::ScopedLocalDenseThreads local_threads{};
if (coordinate_direction != nullptr) {
if (coordinate_direction->Size() != kGlobalDofCount) {
return Failure<NonlinearMitc4InternalEquilibrium>(
src/fesa/math/dense_blas_internal.cpp
+68 -5
View File
@@ -1,5 +1,6 @@
#include "math/dense_blas_internal.h"
#include <algorithm>
#include <cmath>
#include <limits>
#include <stdexcept>
@@ -26,8 +27,22 @@ ScopedSingleEquationThreads::~ScopedSingleEquationThreads() {
if (restore_default_) static_cast<void>(mkl_set_num_threads_local(0));
}
ScopedLocalDenseThreads::ScopedLocalDenseThreads() noexcept {
const int previous = mkl_set_num_threads_local(1);
if (previous == 0) {
restore_default_ = true;
} else {
static_cast<void>(mkl_set_num_threads_local(previous));
}
}
ScopedLocalDenseThreads::~ScopedLocalDenseThreads() {
if (restore_default_) static_cast<void>(mkl_set_num_threads_local(0));
}
bool CholeskyLowerAndInverse(const Matrix& matrix, Matrix& lower,
Matrix& inverse_lower) {
Matrix& inverse_lower, CholeskyFailure* failure) {
if (failure != nullptr) *failure = CholeskyFailure::kNone;
if (matrix.Rows() != matrix.Columns())
throw std::invalid_argument{"Cholesky requires a square matrix."};
const auto size = ToMklSize(matrix.Rows());
@@ -48,17 +63,30 @@ bool CholeskyLowerAndInverse(const Matrix& matrix, Matrix& lower,
values[row * matrix.Columns() + column] = matrix(row, column);
}
if (LAPACKE_dpotrf(LAPACK_ROW_MAJOR, 'L', size.Value(), values.data(),
size.Value()) != 0) return false;
size.Value()) != 0) {
if (failure != nullptr) *failure = CholeskyFailure::kPivot;
return false;
}
for (std::size_t row = 0; row < matrix.Rows(); ++row)
for (std::size_t column = 0; column <= row; ++column)
for (std::size_t column = 0; column <= row; ++column) {
candidate_lower(row, column) = values[row * matrix.Columns() + column];
if (!std::isfinite(candidate_lower(row, column))) {
if (failure != nullptr) *failure = CholeskyFailure::kPivot;
return false;
}
}
if (LAPACKE_dtrtri(LAPACK_ROW_MAJOR, 'L', 'N', size.Value(), values.data(),
size.Value()) != 0) return false;
size.Value()) != 0) {
if (failure != nullptr) *failure = CholeskyFailure::kInverse;
return false;
}
for (std::size_t row = 0; row < matrix.Rows(); ++row)
for (std::size_t column = 0; column <= row; ++column) {
const auto value = values[row * matrix.Columns() + column];
if (!std::isfinite(candidate_lower(row, column)) || !std::isfinite(value))
if (!std::isfinite(value)) {
if (failure != nullptr) *failure = CholeskyFailure::kInverse;
return false;
}
candidate_inverse(row, column) = value;
}
lower = std::move(candidate_lower);
@@ -96,6 +124,41 @@ Matrix MultiplyTransposeLeft(const Matrix& left, const Matrix& right) {
return transposed.Multiply(right);
}
bool OuterProduct(const double* left, const std::size_t rows,
const double* right, const std::size_t columns,
double* destination) {
return MultiplyTransposeRight(left, rows, right, columns, 1U, destination);
}
bool MultiplyTransposeRight(const double* left, const std::size_t rows,
const double* right, const std::size_t columns,
const std::size_t inner, double* destination) {
const auto m = ToMklSize(rows);
const auto n = ToMklSize(columns);
const auto k = ToMklSize(inner);
const auto maximum = std::numeric_limits<std::size_t>::max() / sizeof(double);
if (!m.HasValue() || !n.HasValue() || !k.HasValue() ||
(columns != 0U && rows > maximum / columns) ||
(inner != 0U && (rows > maximum / inner || columns > maximum / inner)))
throw std::length_error{"Dense product dimensions exceed backend limits."};
if (rows == 0U || columns == 0U) return true;
if (destination == nullptr ||
(inner != 0U && (left == nullptr || right == nullptr)))
throw std::invalid_argument{"Dense product requires nonnull storage."};
if (inner == 0U) {
std::fill_n(destination, rows * columns, 0.0);
return true;
}
for (std::size_t i = 0U; i < rows * inner; ++i)
if (!std::isfinite(left[i])) return false;
for (std::size_t i = 0U; i < columns * inner; ++i)
if (!std::isfinite(right[i])) return false;
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasTrans, m.Value(), n.Value(),
k.Value(), 1.0, left, k.Value(), right, k.Value(), 0.0,
destination, n.Value());
return true;
}
Result<MKL_INT> ToMklSize(const std::size_t size) {
if (size > static_cast<std::size_t>((std::numeric_limits<MKL_INT>::max)())) {
return Result<MKL_INT>::Failure(Status::Failure(
src/fesa/math/dense_blas_internal.h
+40 -1
View File
@@ -26,6 +26,20 @@ class ScopedSingleEquationThreads {
bool restore_default_{false};
};
/// @brief Limits element-local dense work under the caller's default policy.
/// @note Positive caller TLS overrides are retained. Default requests are
/// restored on success and unwind; process-wide settings are never changed.
class ScopedLocalDenseThreads {
public:
ScopedLocalDenseThreads() noexcept;
ScopedLocalDenseThreads(const ScopedLocalDenseThreads&) = delete;
ScopedLocalDenseThreads& operator=(const ScopedLocalDenseThreads&) = delete;
~ScopedLocalDenseThreads();
private:
bool restore_default_{false};
};
/// @brief Converts a dense storage length to the private MKL integer type.
/// @return The converted length or an uncategorized overflow failure.
Result<MKL_INT> ToMklSize(std::size_t size);
@@ -39,13 +53,38 @@ Matrix MultiplyTransposeLeft(const Matrix& left, const Matrix& right);
/// @throws std::length_error if the size exceeds the backend integer range.
Vector MultiplyDiagonal(const Vector& diagonal, const Vector& rhs);
/// @brief Writes one row-major outer product through MKL without allocation.
/// @note Source arrays and destination must not alias. A nonfinite input
/// returns false before writing; finite product overflow remains for the
/// owner's gate. A zero dimension accepts null pointers and performs no backend
/// call.
/// @throws std::invalid_argument for null storage of a nonempty product.
/// @throws std::length_error for dimensions outside the backend integer range.
bool OuterProduct(const double* left, std::size_t rows, const double* right,
std::size_t columns, double* destination);
/// @brief Writes left times right-transpose to nonaliased contiguous storage.
/// @note Inputs are row-major rows-by-inner and columns-by-inner. Nonfinite
/// input returns false before writing. Finite output overflow is not hidden.
/// Zero output dimensions accept null pointers; inner zero writes exact zeros.
/// @throws std::invalid_argument for missing nonempty storage.
/// @throws std::length_error for dimension or storage-size overflow.
bool MultiplyTransposeRight(const double* left, std::size_t rows,
const double* right, std::size_t columns,
std::size_t inner, double* destination);
/// @brief Distinguishes positive-factor failure from inverse failure.
enum class CholeskyFailure { kNone, kPivot, kInverse };
/// @brief Computes a lower Cholesky factor and its inverse with MKL LAPACK.
/// @return False for a nonpositive pivot or nonfinite factor/inverse.
/// @note Outputs are replaced only after both finite candidates succeed.
/// The optional failure output is initialized even when validation throws.
/// @throws std::invalid_argument for a nonsquare or nonfinite input.
/// @throws std::length_error for a backend size overflow.
bool CholeskyLowerAndInverse(const Matrix& matrix, Matrix& lower,
Matrix& inverse_lower);
Matrix& inverse_lower,
CholeskyFailure* failure = nullptr);
/// @brief Copies contiguous double values through the private BLAS backend.
/// @param source Readable storage for size values when size is nonzero.