#pragma once

#include <algorithm>
#include <array>
#include <cctype>
#include <cmath>
#include <cstdint>
#include <fstream>
#include <initializer_list>
#include <limits>
#include <map>
#include <memory>
#include <optional>
#include <set>
#include <sstream>
#include <stdexcept>
#include <string>
#include <utility>
#include <vector>

namespace fesa {

using Real = double;
using GlobalId = std::int64_t;
using LocalIndex = std::int64_t;
using EquationId = std::int64_t;
using SparseIndex = std::int64_t;

enum class Severity { Info, Warning, Error };

struct SourceLocation {
  std::string file;
  LocalIndex line = 0;
  std::string keyword;
};

struct Diagnostic {
  Severity severity = Severity::Error;
  std::string code;
  std::string message;
  SourceLocation source;
};

inline bool hasError(const std::vector<Diagnostic>& diagnostics) {
  return std::any_of(diagnostics.begin(), diagnostics.end(), [](const Diagnostic& diagnostic) {
    return diagnostic.severity == Severity::Error;
  });
}

inline bool containsDiagnostic(const std::vector<Diagnostic>& diagnostics, const std::string& code) {
  return std::any_of(diagnostics.begin(), diagnostics.end(), [&](const Diagnostic& diagnostic) {
    return diagnostic.code == code;
  });
}

inline Diagnostic makeDiagnostic(Severity severity, std::string code, std::string message, std::string keyword,
                                 std::string file = "<domain>", LocalIndex line = 0) {
  return {severity, std::move(code), std::move(message), {std::move(file), line, std::move(keyword)}};
}

inline std::string trim(std::string text) {
  auto is_space = [](unsigned char c) { return std::isspace(c) != 0; };
  text.erase(text.begin(), std::find_if(text.begin(), text.end(), [&](unsigned char c) { return !is_space(c); }));
  text.erase(std::find_if(text.rbegin(), text.rend(), [&](unsigned char c) { return !is_space(c); }).base(), text.end());
  return text;
}

inline std::string lower(std::string text) {
  std::transform(text.begin(), text.end(), text.begin(), [](unsigned char c) {
    return static_cast<char>(std::tolower(c));
  });
  return text;
}

inline std::vector<std::string> splitCsv(const std::string& line) {
  std::vector<std::string> fields;
  std::string field;
  std::istringstream stream(line);
  while (std::getline(stream, field, ',')) {
    fields.push_back(trim(field));
  }
  if (!line.empty() && line.back() == ',') {
    fields.emplace_back();
  }
  return fields;
}

inline std::optional<Real> parseReal(std::string token) {
  token = trim(token);
  if (token.empty()) {
    return std::nullopt;
  }
  std::replace(token.begin(), token.end(), 'D', 'E');
  std::replace(token.begin(), token.end(), 'd', 'e');
  try {
    std::size_t used = 0;
    Real value = std::stod(token, &used);
    if (used != token.size()) {
      return std::nullopt;
    }
    return value;
  } catch (...) {
    return std::nullopt;
  }
}

inline std::optional<GlobalId> parseInt64(const std::string& token) {
  std::string value_text = trim(token);
  if (value_text.empty()) {
    return std::nullopt;
  }
  try {
    std::size_t used = 0;
    long long value = std::stoll(value_text, &used);
    if (used != value_text.size()) {
      return std::nullopt;
    }
    return static_cast<GlobalId>(value);
  } catch (...) {
    return std::nullopt;
  }
}

enum class Dof : int { UX = 0, UY = 1, UZ = 2, RX = 3, RY = 4, RZ = 5 };

inline std::array<Dof, 6> allDofs() {
  return {Dof::UX, Dof::UY, Dof::UZ, Dof::RX, Dof::RY, Dof::RZ};
}

inline int dofIndex(Dof dof) {
  return static_cast<int>(dof);
}

inline int abaqusDofNumber(Dof dof) {
  return dofIndex(dof) + 1;
}

inline std::optional<Dof> dofFromAbaqus(int dof) {
  if (dof < 1 || dof > 6) {
    return std::nullopt;
  }
  return static_cast<Dof>(dof - 1);
}

inline const char* dofLabel(Dof dof) {
  switch (dof) {
    case Dof::UX:
      return "UX";
    case Dof::UY:
      return "UY";
    case Dof::UZ:
      return "UZ";
    case Dof::RX:
      return "RX";
    case Dof::RY:
      return "RY";
    case Dof::RZ:
      return "RZ";
  }
  return "";
}

inline std::vector<std::string> displacementComponentLabels() {
  return {"UX", "UY", "UZ", "RX", "RY", "RZ"};
}

inline std::vector<std::string> reactionComponentLabels() {
  return {"RFX", "RFY", "RFZ", "RMX", "RMY", "RMZ"};
}

struct Vec3 {
  Real x = 0.0;
  Real y = 0.0;
  Real z = 0.0;
};

inline Vec3 operator+(const Vec3& a, const Vec3& b) {
  return {a.x + b.x, a.y + b.y, a.z + b.z};
}

inline Vec3 operator-(const Vec3& a, const Vec3& b) {
  return {a.x - b.x, a.y - b.y, a.z - b.z};
}

inline Vec3 operator*(Real scalar, const Vec3& value) {
  return {scalar * value.x, scalar * value.y, scalar * value.z};
}

inline Real dot(const Vec3& a, const Vec3& b) {
  return a.x * b.x + a.y * b.y + a.z * b.z;
}

inline Vec3 cross(const Vec3& a, const Vec3& b) {
  return {a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x};
}

inline Real norm(const Vec3& value) {
  return std::sqrt(dot(value, value));
}

inline bool isFinite(Real value) {
  return std::isfinite(value);
}

inline bool isFinite(const Vec3& value) {
  return isFinite(value.x) && isFinite(value.y) && isFinite(value.z);
}

inline std::optional<Vec3> normalizedIfValid(const Vec3& value, Real tolerance = 1.0e-12) {
  const Real length = norm(value);
  if (!isFinite(length) || length <= tolerance) {
    return std::nullopt;
  }
  return (1.0 / length) * value;
}

inline Vec3 normalized(const Vec3& value) {
  const Real length = norm(value);
  if (length <= std::numeric_limits<Real>::epsilon()) {
    throw std::runtime_error("zero-length vector");
  }
  return (1.0 / length) * value;
}

struct Node {
  GlobalId id = 0;
  Vec3 coordinates;
};

enum class ElementType { MITC4 };

struct Element {
  GlobalId id = 0;
  ElementType type = ElementType::MITC4;
  std::array<GlobalId, 4> node_ids{};
  std::string source_elset;
};

struct NodeSet {
  std::string name;
  std::vector<GlobalId> node_ids;
};

struct ElementSet {
  std::string name;
  std::vector<GlobalId> element_ids;
};

struct Material {
  std::string name;
  Real elastic_modulus = 0.0;
  Real poisson_ratio = 0.0;
};

struct ShellSection {
  std::string element_set;
  std::string material;
  Real thickness = 0.0;
};

struct BoundaryCondition {
  std::string target;
  int first_dof = 0;
  int last_dof = 0;
  Real magnitude = 0.0;
};

struct NodalLoad {
  std::string target;
  int dof = 0;
  Real magnitude = 0.0;
};

struct StepDefinition {
  std::string name = "Step-1";
  std::string analysis_type = "linear_static";
};

struct Domain {
  std::map<GlobalId, Node> nodes;
  std::map<GlobalId, Element> elements;
  std::map<std::string, NodeSet> node_sets;
  std::map<std::string, ElementSet> element_sets;
  std::map<std::string, Material> materials;
  std::vector<ShellSection> shell_sections;
  std::vector<BoundaryCondition> boundary_conditions;
  std::vector<NodalLoad> loads;
  std::vector<StepDefinition> steps;

  static std::string key(const std::string& label) {
    return lower(trim(label));
  }
};

inline void addUnique(std::vector<GlobalId>& values, GlobalId value) {
  if (std::find(values.begin(), values.end(), value) == values.end()) {
    values.push_back(value);
  }
}

inline std::vector<GlobalId> generatedRange(GlobalId first, GlobalId last, GlobalId increment) {
  std::vector<GlobalId> values;
  if (increment <= 0) {
    return values;
  }
  for (GlobalId value = first; value <= last; value += increment) {
    values.push_back(value);
  }
  return values;
}

struct KeywordLine {
  std::string name;
  std::map<std::string, std::string> parameters;
  std::set<std::string> flags;
};

inline KeywordLine parseKeywordLine(const std::string& line) {
  KeywordLine keyword;
  std::vector<std::string> pieces = splitCsv(line.substr(1));
  if (pieces.empty()) {
    return keyword;
  }
  keyword.name = lower(trim(pieces.front()));
  for (std::size_t i = 1; i < pieces.size(); ++i) {
    const std::string piece = trim(pieces[i]);
    if (piece.empty()) {
      continue;
    }
    const auto eq = piece.find('=');
    if (eq == std::string::npos) {
      keyword.flags.insert(lower(piece));
    } else {
      keyword.parameters[lower(trim(piece.substr(0, eq)))] = trim(piece.substr(eq + 1));
    }
  }
  return keyword;
}

struct ParseResult {
  Domain domain;
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

class AbaqusInputParser {
 public:
  ParseResult parseString(const std::string& text, const std::string& file_name = "<memory>") const {
    ParseResult result;
    std::istringstream stream(text);
    std::string line;
    KeywordLine current;
    std::string current_material_key;
    KeywordLine current_shell_section;
    LocalIndex line_number = 0;
    LocalIndex current_keyword_line = 0;

    auto add_error = [&](const std::string& code, const std::string& message) {
      const LocalIndex source_line = current_keyword_line == 0 ? line_number : current_keyword_line;
      result.diagnostics.push_back({Severity::Error, code, message, {file_name, source_line, current.name}});
    };
    auto is_allowed = [](const std::string& value, std::initializer_list<const char*> allowed_values) {
      return std::any_of(allowed_values.begin(), allowed_values.end(), [&](const char* allowed) {
        return value == allowed;
      });
    };
    auto reject_unsupported_controls = [&](std::initializer_list<const char*> allowed_parameters,
                                           std::initializer_list<const char*> allowed_flags) {
      for (const auto& [parameter, value] : current.parameters) {
        (void)value;
        if (!is_allowed(parameter, allowed_parameters)) {
          const LocalIndex source_line = current_keyword_line == 0 ? line_number : current_keyword_line;
          result.diagnostics.push_back({Severity::Error,
                                        "FESA-PARSE-UNSUPPORTED-PARAMETER",
                                        "Unsupported *" + current.name + " parameter: " + parameter,
                                        {file_name, source_line, current.name}});
        }
      }
      for (const std::string& flag : current.flags) {
        if (!is_allowed(flag, allowed_flags)) {
          const LocalIndex source_line = current_keyword_line == 0 ? line_number : current_keyword_line;
          result.diagnostics.push_back({Severity::Error,
                                        "FESA-PARSE-UNSUPPORTED-PARAMETER",
                                        "Unsupported *" + current.name + " flag: " + flag,
                                        {file_name, source_line, current.name}});
        }
      }
    };

    while (std::getline(stream, line)) {
      ++line_number;
      line = trim(line);
      if (line.empty() || line.rfind("**", 0) == 0) {
        continue;
      }
      if (!line.empty() && line.front() == '*') {
        current_keyword_line = line_number;
        std::string keyword_line = line;
        while (!keyword_line.empty() && keyword_line.back() == ',') {
          std::string continuation;
          if (!std::getline(stream, continuation)) {
            break;
          }
          ++line_number;
          continuation = trim(continuation);
          if (continuation.empty() || continuation.rfind("**", 0) == 0) {
            continue;
          }
          keyword_line += continuation;
        }
        current = parseKeywordLine(keyword_line);
        if (current.name == "node") {
          reject_unsupported_controls({}, {});
          continue;
        }
        if (current.name == "element") {
          reject_unsupported_controls({"type", "elset"}, {});
          continue;
        }
        if (current.name == "nset") {
          reject_unsupported_controls({"nset"}, {"generate"});
          continue;
        }
        if (current.name == "elset") {
          reject_unsupported_controls({"elset"}, {"generate"});
          continue;
        }
        if (current.name == "elastic") {
          reject_unsupported_controls({}, {});
          continue;
        }
        if (current.name == "shell section") {
          reject_unsupported_controls({"elset", "material"}, {});
          current_shell_section = current;
          continue;
        }
        if (current.name == "boundary" || current.name == "cload" || current.name == "static") {
          reject_unsupported_controls({}, {});
          continue;
        }
        if (current.name == "material") {
          reject_unsupported_controls({"name"}, {});
          auto name_it = current.parameters.find("name");
          if (name_it == current.parameters.end() || trim(name_it->second).empty()) {
            add_error("FESA-PARSE-MATERIAL-NAME", "*Material requires NAME");
            current_material_key.clear();
            continue;
          }
          Material material;
          material.name = trim(name_it->second);
          current_material_key = Domain::key(material.name);
          if (result.domain.materials.count(current_material_key) != 0) {
            add_error("FESA-PARSE-DUPLICATE-MATERIAL", "Duplicate material: " + material.name);
          } else {
            result.domain.materials[current_material_key] = material;
          }
          continue;
        }
        if (current.name == "step") {
          reject_unsupported_controls({"name", "nlgeom"}, {});
          auto nlgeom = current.parameters.find("nlgeom");
          if (nlgeom != current.parameters.end() && lower(trim(nlgeom->second)) == "yes") {
            add_error("FESA-PARSE-UNSUPPORTED-NLGEOM", "NLGEOM=YES is not supported in Phase 1");
          }
          StepDefinition step;
          auto name_it = current.parameters.find("name");
          if (name_it != current.parameters.end() && !trim(name_it->second).empty()) {
            step.name = trim(name_it->second);
          }
          result.domain.steps.push_back(step);
          continue;
        }
        if (current.name == "end step") {
          reject_unsupported_controls({}, {});
          continue;
        }
        add_error("FESA-PARSE-UNSUPPORTED-KEYWORD", "Unsupported keyword: *" + current.name);
        continue;
      }

      const std::vector<std::string> fields = splitCsv(line);
      if (current.name == "node") {
        parseNode(fields, result, file_name, line_number);
      } else if (current.name == "element") {
        parseElement(fields, current, result, file_name, line_number);
      } else if (current.name == "nset") {
        parseNodeSet(fields, current, result, file_name, line_number);
      } else if (current.name == "elset") {
        parseElementSet(fields, current, result, file_name, line_number);
      } else if (current.name == "elastic") {
        parseElastic(fields, current_material_key, result, file_name, line_number);
      } else if (current.name == "shell section") {
        parseShellSection(fields, current_shell_section, result, file_name, line_number);
      } else if (current.name == "boundary") {
        parseBoundary(fields, result, file_name, line_number);
      } else if (current.name == "cload") {
        parseLoad(fields, result, file_name, line_number);
      }
    }

    if (result.domain.steps.empty()) {
      result.domain.steps.push_back({"Step-1", "linear_static"});
    }
    return result;
  }

  ParseResult parseFile(const std::string& path) const {
    std::ifstream input(path);
    std::ostringstream buffer;
    buffer << input.rdbuf();
    ParseResult result = parseString(buffer.str(), path);
    if (!input.good() && buffer.str().empty()) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-FILE", "Could not read input file", {path, 0, ""}});
    }
    return result;
  }

 private:
  static std::size_t effectiveFieldCount(const std::vector<std::string>& fields) {
    std::size_t count = fields.size();
    while (count > 0 && trim(fields[count - 1]).empty()) {
      --count;
    }
    return count;
  }

  static void parseNode(const std::vector<std::string>& fields, ParseResult& result, const std::string& file_name, LocalIndex line) {
    if (effectiveFieldCount(fields) != 4) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-NODE", "*Node data requires id,x,y,z", {file_name, line, "node"}});
      return;
    }
    auto id = parseInt64(fields[0]);
    auto x = parseReal(fields[1]);
    auto y = parseReal(fields[2]);
    auto z = parseReal(fields[3]);
    if (!id || !x || !y || !z) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-NODE-NUMERIC", "Invalid node numeric field", {file_name, line, "node"}});
      return;
    }
    if (result.domain.nodes.count(*id) != 0) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-DUPLICATE-NODE", "Duplicate node id", {file_name, line, "node"}});
      return;
    }
    result.domain.nodes[*id] = {*id, {*x, *y, *z}};
  }

  static void parseElement(const std::vector<std::string>& fields, const KeywordLine& keyword, ParseResult& result, const std::string& file_name, LocalIndex line) {
    auto type_it = keyword.parameters.find("type");
    if (type_it == keyword.parameters.end()) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-ELEMENT-TYPE", "*Element requires TYPE", {file_name, line, "element"}});
      return;
    }
    const std::string type = lower(trim(type_it->second));
    if (type != "s4") {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-UNSUPPORTED-ELEMENT", "Unsupported element type: " + type_it->second, {file_name, line, "element"}});
      return;
    }
    if (effectiveFieldCount(fields) != 5) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-ELEMENT", "S4 element requires id,n1,n2,n3,n4", {file_name, line, "element"}});
      return;
    }
    auto id = parseInt64(fields[0]);
    std::array<GlobalId, 4> nodes{};
    bool ok = id.has_value();
    for (int i = 0; i < 4; ++i) {
      auto node = parseInt64(fields[1 + static_cast<std::size_t>(i)]);
      ok = ok && node.has_value();
      if (node) {
        nodes[static_cast<std::size_t>(i)] = *node;
      }
    }
    if (!ok) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-ELEMENT-NUMERIC", "Invalid element numeric field", {file_name, line, "element"}});
      return;
    }
    if (result.domain.elements.count(*id) != 0) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-DUPLICATE-ELEMENT", "Duplicate element id", {file_name, line, "element"}});
      return;
    }
    Element element;
    element.id = *id;
    element.node_ids = nodes;
    auto elset_it = keyword.parameters.find("elset");
    if (elset_it != keyword.parameters.end()) {
      element.source_elset = trim(elset_it->second);
      auto& set = result.domain.element_sets[Domain::key(element.source_elset)];
      set.name = element.source_elset;
      addUnique(set.element_ids, *id);
    }
    result.domain.elements[*id] = element;
  }

  static void parseNodeSet(const std::vector<std::string>& fields, const KeywordLine& keyword, ParseResult& result, const std::string& file_name, LocalIndex line) {
    auto name_it = keyword.parameters.find("nset");
    if (name_it == keyword.parameters.end()) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-NSET-NAME", "*Nset requires NSET", {file_name, line, "nset"}});
      return;
    }
    auto& set = result.domain.node_sets[Domain::key(name_it->second)];
    set.name = trim(name_it->second);
    parseSetData(fields, keyword.flags.count("generate") != 0, set.node_ids, result.diagnostics, file_name, line, "nset");
  }

  static void parseElementSet(const std::vector<std::string>& fields, const KeywordLine& keyword, ParseResult& result, const std::string& file_name, LocalIndex line) {
    auto name_it = keyword.parameters.find("elset");
    if (name_it == keyword.parameters.end()) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-ELSET-NAME", "*Elset requires ELSET", {file_name, line, "elset"}});
      return;
    }
    auto& set = result.domain.element_sets[Domain::key(name_it->second)];
    set.name = trim(name_it->second);
    parseSetData(fields, keyword.flags.count("generate") != 0, set.element_ids, result.diagnostics, file_name, line, "elset");
  }

  static void parseSetData(const std::vector<std::string>& fields, bool generate, std::vector<GlobalId>& output,
                           std::vector<Diagnostic>& diagnostics, const std::string& file_name, LocalIndex line, const std::string& keyword) {
    if (generate) {
      const std::size_t field_count = effectiveFieldCount(fields);
      if (field_count != 3) {
        diagnostics.push_back({Severity::Error, "FESA-PARSE-GENERATE", "Generated set requires first,last,increment", {file_name, line, keyword}});
        return;
      }
      auto first = parseInt64(fields[0]);
      auto last = parseInt64(fields[1]);
      auto increment = parseInt64(fields[2]);
      if (!first || !last || !increment || *increment <= 0) {
        diagnostics.push_back({Severity::Error, "FESA-PARSE-GENERATE", "Invalid generated set range", {file_name, line, keyword}});
        return;
      }
      for (GlobalId value : generatedRange(*first, *last, *increment)) {
        addUnique(output, value);
      }
      return;
    }
    const std::size_t field_count = effectiveFieldCount(fields);
    for (std::size_t i = 0; i < field_count; ++i) {
      const std::string& field = fields[i];
      if (trim(field).empty()) {
        continue;
      }
      auto value = parseInt64(field);
      if (!value) {
        diagnostics.push_back({Severity::Error, "FESA-PARSE-SET-NUMERIC", "Invalid set id", {file_name, line, keyword}});
        return;
      }
      addUnique(output, *value);
    }
  }

  static void parseElastic(const std::vector<std::string>& fields, const std::string& material_key, ParseResult& result, const std::string& file_name, LocalIndex line) {
    if (material_key.empty() || result.domain.materials.count(material_key) == 0) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-ELASTIC-MATERIAL", "*Elastic must follow *Material", {file_name, line, "elastic"}});
      return;
    }
    const std::size_t field_count = effectiveFieldCount(fields);
    if (field_count < 2) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-ELASTIC", "*Elastic requires E,nu", {file_name, line, "elastic"}});
      return;
    }
    if (field_count > 2) {
      result.diagnostics.push_back(
          {Severity::Error, "FESA-PARSE-ELASTIC-UNSUPPORTED", "Only isotropic E,nu elastic data is supported", {file_name, line, "elastic"}});
      return;
    }
    auto e = parseReal(fields[0]);
    auto nu = parseReal(fields[1]);
    if (!e || !nu || *e <= 0.0 || *nu <= -1.0 || *nu >= 0.5) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-ELASTIC-RANGE", "Invalid isotropic elastic constants", {file_name, line, "elastic"}});
      return;
    }
    result.domain.materials[material_key].elastic_modulus = *e;
    result.domain.materials[material_key].poisson_ratio = *nu;
  }

  static void parseShellSection(const std::vector<std::string>& fields, const KeywordLine& keyword, ParseResult& result, const std::string& file_name, LocalIndex line) {
    auto elset_it = keyword.parameters.find("elset");
    auto material_it = keyword.parameters.find("material");
    if (elset_it == keyword.parameters.end() || material_it == keyword.parameters.end()) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-SHELL-SECTION-PARAM", "*Shell Section requires ELSET and MATERIAL", {file_name, line, "shell section"}});
      return;
    }
    const std::size_t field_count = effectiveFieldCount(fields);
    if (field_count == 0) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-SHELL-SECTION", "*Shell Section requires thickness", {file_name, line, "shell section"}});
      return;
    }
    if (field_count > 1) {
      result.diagnostics.push_back({Severity::Error,
                                    "FESA-PARSE-SHELL-SECTION-UNSUPPORTED",
                                    "Only homogeneous shell thickness data is supported",
                                    {file_name, line, "shell section"}});
      return;
    }
    auto thickness = parseReal(fields[0]);
    if (!thickness || *thickness <= 0.0) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-SHELL-THICKNESS", "Shell thickness must be positive", {file_name, line, "shell section"}});
      return;
    }
    result.domain.shell_sections.push_back({trim(elset_it->second), trim(material_it->second), *thickness});
  }

  static void parseBoundary(const std::vector<std::string>& fields, ParseResult& result, const std::string& file_name, LocalIndex line) {
    const std::size_t field_count = effectiveFieldCount(fields);
    if (field_count < 2) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-BOUNDARY", "*Boundary requires target,first_dof", {file_name, line, "boundary"}});
      return;
    }
    if (field_count > 4) {
      result.diagnostics.push_back({Severity::Error,
                                    "FESA-PARSE-BOUNDARY-UNSUPPORTED",
                                    "Only direct zero-valued boundary data is supported",
                                    {file_name, line, "boundary"}});
      return;
    }
    auto first = parseInt64(fields[1]);
    auto last = field_count >= 3 && !fields[2].empty() ? parseInt64(fields[2]) : first;
    auto magnitude = field_count >= 4 && !fields[3].empty() ? parseReal(fields[3]) : std::optional<Real>(0.0);
    if (!first || !last || !magnitude || !dofFromAbaqus(static_cast<int>(*first)) || !dofFromAbaqus(static_cast<int>(*last)) || *first > *last) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-BOUNDARY-DOF", "Invalid boundary DOF range", {file_name, line, "boundary"}});
      return;
    }
    if (std::fabs(*magnitude) > 0.0) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-BOUNDARY-NONZERO", "Nonzero prescribed displacement is not supported in Phase 1", {file_name, line, "boundary"}});
      return;
    }
    result.domain.boundary_conditions.push_back({trim(fields[0]), static_cast<int>(*first), static_cast<int>(*last), *magnitude});
  }

  static void parseLoad(const std::vector<std::string>& fields, ParseResult& result, const std::string& file_name, LocalIndex line) {
    const std::size_t field_count = effectiveFieldCount(fields);
    if (field_count < 3) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-CLOAD", "*Cload requires target,dof,magnitude", {file_name, line, "cload"}});
      return;
    }
    if (field_count > 3) {
      result.diagnostics.push_back({Severity::Error,
                                    "FESA-PARSE-CLOAD-UNSUPPORTED",
                                    "Only direct concentrated load data is supported",
                                    {file_name, line, "cload"}});
      return;
    }
    auto dof = parseInt64(fields[1]);
    auto magnitude = parseReal(fields[2]);
    if (!dof || !magnitude || !dofFromAbaqus(static_cast<int>(*dof))) {
      result.diagnostics.push_back({Severity::Error, "FESA-PARSE-CLOAD-DOF", "Invalid concentrated load", {file_name, line, "cload"}});
      return;
    }
    result.domain.loads.push_back({trim(fields[0]), static_cast<int>(*dof), *magnitude});
  }
};

inline std::optional<GlobalId> numericTarget(const std::string& target) {
  return parseInt64(target);
}

inline std::vector<GlobalId> resolveNodeTarget(const Domain& domain, const std::string& target, std::vector<Diagnostic>* diagnostics = nullptr,
                                               const std::string& diagnostic_keyword = "node target") {
  if (auto node_id = numericTarget(target)) {
    if (domain.nodes.count(*node_id) == 0) {
      if (diagnostics != nullptr) {
        diagnostics->push_back(
            makeDiagnostic(Severity::Error, "FESA-VALIDATION-MISSING-NODE", "Missing node target: " + target, diagnostic_keyword));
      }
      return {};
    }
    return {*node_id};
  }
  auto set_it = domain.node_sets.find(Domain::key(target));
  if (set_it == domain.node_sets.end()) {
    if (diagnostics != nullptr) {
      diagnostics->push_back(
          makeDiagnostic(Severity::Error, "FESA-VALIDATION-MISSING-NSET", "Missing node set: " + target, diagnostic_keyword));
    }
    return {};
  }
  return set_it->second.node_ids;
}

inline const ShellSection* shellSectionForElement(const Domain& domain, GlobalId element_id) {
  for (const ShellSection& section : domain.shell_sections) {
    auto set_it = domain.element_sets.find(Domain::key(section.element_set));
    if (set_it == domain.element_sets.end()) {
      continue;
    }
    if (std::find(set_it->second.element_ids.begin(), set_it->second.element_ids.end(), element_id) != set_it->second.element_ids.end()) {
      return &section;
    }
  }
  return nullptr;
}

inline std::string dofNameOrNumber(int abaqus_dof) {
  auto dof = dofFromAbaqus(abaqus_dof);
  if (dof) {
    return dofLabel(*dof);
  }
  return "DOF " + std::to_string(abaqus_dof);
}

inline bool validAbaqusDofRange(int first, int last) {
  return dofFromAbaqus(first).has_value() && dofFromAbaqus(last).has_value() && first <= last;
}

inline std::vector<Diagnostic> validateDomain(const Domain& domain) {
  std::vector<Diagnostic> diagnostics;
  if (domain.elements.empty()) {
    diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-SINGULAR-NO-ACTIVE-ELEMENTS",
                                         "No active elements exist in the current model", "analysis model"));
  }
  if (domain.boundary_conditions.empty()) {
    diagnostics.push_back(makeDiagnostic(Severity::Warning, "FESA-SINGULAR-NO-BOUNDARY", "No boundary constraints are defined", "boundary"));
  }
  for (const auto& [set_key, set] : domain.node_sets) {
    (void)set_key;
    for (GlobalId node_id : set.node_ids) {
      if (domain.nodes.count(node_id) == 0) {
        diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-VALIDATION-NSET-MISSING-NODE",
                                             "Node set " + set.name + " references missing node " + std::to_string(node_id),
                                             "nset"));
      }
    }
  }
  for (const auto& [set_key, set] : domain.element_sets) {
    (void)set_key;
    for (GlobalId element_id : set.element_ids) {
      if (domain.elements.count(element_id) == 0) {
        diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-VALIDATION-ELSET-MISSING-ELEMENT",
                                             "Element set " + set.name + " references missing element " + std::to_string(element_id),
                                             "elset"));
      }
    }
  }
  for (const auto& [id, element] : domain.elements) {
    for (GlobalId node_id : element.node_ids) {
      if (domain.nodes.count(node_id) == 0) {
        diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-VALIDATION-ELEMENT-MISSING-NODE",
                                             "Element " + std::to_string(id) + " references missing node " + std::to_string(node_id),
                                             "element"));
      }
    }
    const ShellSection* section = shellSectionForElement(domain, id);
    if (section == nullptr) {
      diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-VALIDATION-MISSING-PROPERTY",
                                           "Element " + std::to_string(id) + " has no assigned shell section", "element"));
    }
  }
  for (const ShellSection& section : domain.shell_sections) {
    if (section.thickness <= 0.0 || !std::isfinite(section.thickness)) {
      diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-VALIDATION-NONPOSITIVE-THICKNESS",
                                           "Shell section for element set " + section.element_set + " has non-positive thickness",
                                           "shell section"));
    }
    if (domain.element_sets.count(Domain::key(section.element_set)) == 0) {
      diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-VALIDATION-MISSING-ELSET",
                                           "Shell section references missing element set: " + section.element_set, "shell section"));
    }
    auto material_it = domain.materials.find(Domain::key(section.material));
    if (material_it == domain.materials.end()) {
      diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-VALIDATION-MISSING-MATERIAL",
                                           "Shell section references missing material: " + section.material, "shell section"));
    } else if (material_it->second.elastic_modulus <= 0.0) {
      diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-VALIDATION-INCOMPLETE-MATERIAL",
                                           "Material has no valid elastic constants: " + section.material, "material"));
    }
  }
  for (const BoundaryCondition& boundary : domain.boundary_conditions) {
    if (!validAbaqusDofRange(boundary.first_dof, boundary.last_dof)) {
      diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-VALIDATION-BOUNDARY-DOF",
                                           "Boundary target " + boundary.target + " has invalid DOF range " +
                                               dofNameOrNumber(boundary.first_dof) + " to " + dofNameOrNumber(boundary.last_dof),
                                           "boundary"));
    }
    (void)resolveNodeTarget(domain, boundary.target, &diagnostics, "boundary");
  }
  for (const NodalLoad& load : domain.loads) {
    if (!dofFromAbaqus(load.dof)) {
      diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-VALIDATION-CLOAD-DOF",
                                           "Load target " + load.target + " has invalid " + dofNameOrNumber(load.dof), "cload"));
    }
    (void)resolveNodeTarget(domain, load.target, &diagnostics, "cload");
  }
  const bool any_nonzero_load = std::any_of(domain.loads.begin(), domain.loads.end(), [](const NodalLoad& load) {
    return std::fabs(load.magnitude) > 0.0;
  });
  if (!any_nonzero_load) {
    diagnostics.push_back(makeDiagnostic(Severity::Warning, "FESA-SINGULAR-NO-NONZERO-LOAD", "No nonzero load is defined", "cload"));
  }

  std::set<std::pair<GlobalId, int>> constrained_dofs;
  for (const BoundaryCondition& boundary : domain.boundary_conditions) {
    if (!validAbaqusDofRange(boundary.first_dof, boundary.last_dof)) {
      continue;
    }
    for (GlobalId node_id : resolveNodeTarget(domain, boundary.target)) {
      if (domain.nodes.count(node_id) == 0) {
        continue;
      }
      for (int dof = boundary.first_dof; dof <= boundary.last_dof; ++dof) {
        constrained_dofs.insert(std::make_pair(node_id, dof - 1));
      }
    }
  }

  std::set<GlobalId> active_connectivity_nodes;
  for (const auto& [element_id, element] : domain.elements) {
    (void)element_id;
    for (GlobalId node_id : element.node_ids) {
      if (domain.nodes.count(node_id) != 0) {
        active_connectivity_nodes.insert(node_id);
      }
    }
  }

  LocalIndex free_dof_count = 0;
  LocalIndex weak_drilling_count = 0;
  GlobalId weak_drilling_example = 0;
  for (const auto& [node_id, node] : domain.nodes) {
    (void)node;
    for (Dof dof : allDofs()) {
      const auto key = std::make_pair(node_id, dofIndex(dof));
      if (constrained_dofs.count(key) != 0) {
        continue;
      }
      ++free_dof_count;
      if (!domain.elements.empty() && active_connectivity_nodes.count(node_id) == 0) {
        diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-SINGULAR-DOF-UNTOUCHED",
                                             "Node " + std::to_string(node_id) + " DOF " + dofLabel(dof) +
                                                 " is free but is not touched by active element connectivity",
                                             "dof"));
      }
      if (!domain.elements.empty() && active_connectivity_nodes.count(node_id) != 0 && dof == Dof::RZ) {
        if (weak_drilling_count == 0) {
          weak_drilling_example = node_id;
        }
        ++weak_drilling_count;
      }
    }
  }
  if (!domain.nodes.empty() && free_dof_count == 0) {
    diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-SINGULAR-NO-FREE-DOFS",
                                         "No free DOFs exist after applying boundary constraints", "dof"));
  }
  if (weak_drilling_count > 0) {
    diagnostics.push_back(makeDiagnostic(Severity::Warning, "FESA-SINGULAR-WEAK-DRILLING-DOF",
                                         "Node " + std::to_string(weak_drilling_example) +
                                             " DOF RZ is free; drilling rotation is weakly stabilized in Phase 1 (" +
                                             std::to_string(weak_drilling_count) + " free drilling DOF(s))",
                                         "dof"));
  }
  return diagnostics;
}

struct DofAddress {
  GlobalId node_id = 0;
  Dof dof = Dof::UX;
};

class DofManager {
 public:
  explicit DofManager(const Domain& domain) {
    for (const auto& [node_id, node] : domain.nodes) {
      (void)node;
      node_ids_.push_back(node_id);
      for (Dof dof : allDofs()) {
        const LocalIndex full_index = static_cast<LocalIndex>(all_dofs_.size());
        const auto key = std::make_pair(node_id, dofIndex(dof));
        all_dofs_.push_back(key);
        full_index_by_key_[key] = full_index;
      }
    }
    for (const BoundaryCondition& boundary : domain.boundary_conditions) {
      if (!validAbaqusDofRange(boundary.first_dof, boundary.last_dof)) {
        continue;
      }
      for (GlobalId node_id : resolveNodeTarget(domain, boundary.target)) {
        for (int dof = boundary.first_dof; dof <= boundary.last_dof; ++dof) {
          constrained_.insert(std::make_pair(node_id, dof - 1));
        }
      }
    }
    for (const auto& key : all_dofs_) {
      const LocalIndex full_index = full_index_by_key_.at(key);
      if (constrained_.count(key) == 0) {
        equation_by_key_[key] = static_cast<EquationId>(free_full_indices_.size());
        free_full_indices_.push_back(full_index);
      } else {
        equation_by_key_[key] = -1;
        constrained_full_indices_.push_back(full_index);
      }
    }
  }

  LocalIndex fullDofCount() const {
    return static_cast<LocalIndex>(all_dofs_.size());
  }

  LocalIndex freeDofCount() const {
    return static_cast<LocalIndex>(free_full_indices_.size());
  }

  LocalIndex constrainedDofCount() const {
    return static_cast<LocalIndex>(constrained_full_indices_.size());
  }

  const std::vector<GlobalId>& nodeIds() const {
    return node_ids_;
  }

  const std::vector<LocalIndex>& freeFullIndices() const {
    return free_full_indices_;
  }

  const std::vector<LocalIndex>& constrainedFullIndices() const {
    return constrained_full_indices_;
  }

  DofAddress fullDof(LocalIndex full_index) const {
    const auto& key = all_dofs_.at(static_cast<std::size_t>(full_index));
    return {key.first, static_cast<Dof>(key.second)};
  }

  LocalIndex fullIndex(GlobalId node_id, Dof dof) const {
    return full_index_by_key_.at(std::make_pair(node_id, dofIndex(dof)));
  }

  EquationId equation(GlobalId node_id, Dof dof) const {
    return equation_by_key_.at(std::make_pair(node_id, dofIndex(dof)));
  }

  bool isConstrained(GlobalId node_id, Dof dof) const {
    return constrained_.count(std::make_pair(node_id, dofIndex(dof))) != 0;
  }

  std::vector<Real> reduceFullVector(const std::vector<Real>& full) const {
    std::vector<Real> reduced;
    reduced.reserve(free_full_indices_.size());
    for (LocalIndex full_index : free_full_indices_) {
      reduced.push_back(full.at(static_cast<std::size_t>(full_index)));
    }
    return reduced;
  }

  std::vector<Real> reconstructFullVector(const std::vector<Real>& reduced) const {
    std::vector<Real> full(static_cast<std::size_t>(fullDofCount()), 0.0);
    for (std::size_t i = 0; i < free_full_indices_.size(); ++i) {
      full[static_cast<std::size_t>(free_full_indices_[i])] = reduced.at(i);
    }
    return full;
  }

  std::array<LocalIndex, 24> elementFullDofIndices(const Element& element) const {
    std::array<LocalIndex, 24> indices{};
    for (LocalIndex node = 0; node < 4; ++node) {
      for (Dof dof : allDofs()) {
        const LocalIndex local = 6 * node + dofIndex(dof);
        indices[static_cast<std::size_t>(local)] = fullIndex(element.node_ids[static_cast<std::size_t>(node)], dof);
      }
    }
    return indices;
  }

  std::array<EquationId, 24> elementEquationIds(const Element& element) const {
    std::array<EquationId, 24> equations{};
    for (LocalIndex node = 0; node < 4; ++node) {
      for (Dof dof : allDofs()) {
        const LocalIndex local = 6 * node + dofIndex(dof);
        equations[static_cast<std::size_t>(local)] = equation(element.node_ids[static_cast<std::size_t>(node)], dof);
      }
    }
    return equations;
  }

 private:
  std::vector<GlobalId> node_ids_;
  std::vector<std::pair<GlobalId, int>> all_dofs_;
  std::set<std::pair<GlobalId, int>> constrained_;
  std::map<std::pair<GlobalId, int>, LocalIndex> full_index_by_key_;
  std::map<std::pair<GlobalId, int>, EquationId> equation_by_key_;
  std::vector<LocalIndex> free_full_indices_;
  std::vector<LocalIndex> constrained_full_indices_;
};

struct SparsePatternEntry {
  EquationId row = 0;
  EquationId col = 0;
};

struct SparsePattern {
  EquationId equation_count = 0;
  std::vector<SparsePatternEntry> entries;

  SparseIndex nonzeroCount() const {
    return static_cast<SparseIndex>(entries.size());
  }

  bool contains(EquationId row, EquationId col) const {
    return std::any_of(entries.begin(), entries.end(), [&](const SparsePatternEntry& entry) {
      return entry.row == row && entry.col == col;
    });
  }
};

inline SparsePattern buildReducedSparsePattern(const Domain& domain, const DofManager& dofs) {
  SparsePattern pattern;
  pattern.equation_count = dofs.freeDofCount();
  std::set<std::pair<EquationId, EquationId>> ordered_entries;
  for (const auto& [element_id, element] : domain.elements) {
    (void)element_id;
    const auto equations = dofs.elementEquationIds(element);
    for (EquationId row : equations) {
      if (row < 0) {
        continue;
      }
      for (EquationId col : equations) {
        if (col < 0) {
          continue;
        }
        ordered_entries.insert({row, col});
      }
    }
  }
  pattern.entries.reserve(ordered_entries.size());
  for (const auto& entry : ordered_entries) {
    pattern.entries.push_back({entry.first, entry.second});
  }
  return pattern;
}

class DenseMatrix {
 public:
  DenseMatrix() = default;
  DenseMatrix(LocalIndex rows, LocalIndex cols) : rows_(rows), cols_(cols), values_(static_cast<std::size_t>(rows * cols), 0.0) {}

  LocalIndex rows() const {
    return rows_;
  }

  LocalIndex cols() const {
    return cols_;
  }

  Real& operator()(LocalIndex row, LocalIndex col) {
    return values_[static_cast<std::size_t>(row * cols_ + col)];
  }

  Real operator()(LocalIndex row, LocalIndex col) const {
    return values_[static_cast<std::size_t>(row * cols_ + col)];
  }

  void add(LocalIndex row, LocalIndex col, Real value) {
    (*this)(row, col) += value;
  }

  std::vector<Real> multiply(const std::vector<Real>& x) const {
    std::vector<Real> y(static_cast<std::size_t>(rows_), 0.0);
    for (LocalIndex i = 0; i < rows_; ++i) {
      Real sum = 0.0;
      for (LocalIndex j = 0; j < cols_; ++j) {
        sum += (*this)(i, j) * x[static_cast<std::size_t>(j)];
      }
      y[static_cast<std::size_t>(i)] = sum;
    }
    return y;
  }

 private:
  LocalIndex rows_ = 0;
  LocalIndex cols_ = 0;
  std::vector<Real> values_;
};

inline std::vector<Real> recoverFullReaction(const DenseMatrix& k_full, const std::vector<Real>& u_full, const std::vector<Real>& f_full) {
  if (k_full.rows() != k_full.cols() || static_cast<LocalIndex>(u_full.size()) != k_full.cols() ||
      static_cast<LocalIndex>(f_full.size()) != k_full.rows()) {
    throw std::runtime_error("full reaction size mismatch");
  }
  std::vector<Real> reaction = k_full.multiply(u_full);
  for (std::size_t i = 0; i < reaction.size(); ++i) {
    reaction[i] -= f_full[i];
  }
  return reaction;
}

struct SolveResult {
  std::vector<Real> x;
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

class LinearSolver {
 public:
  virtual ~LinearSolver() = default;
  virtual SolveResult solve(DenseMatrix a, std::vector<Real> b) const = 0;
};

class GaussianEliminationSolver final : public LinearSolver {
 public:
  SolveResult solve(DenseMatrix a, std::vector<Real> b) const override {
    const LocalIndex n = a.rows();
    SolveResult result;
    if (a.rows() != a.cols() || static_cast<LocalIndex>(b.size()) != n) {
      result.diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-SOLVER-SIZE", "Linear system size mismatch", "solver"));
      return result;
    }
    for (LocalIndex col = 0; col < n; ++col) {
      LocalIndex pivot = col;
      Real pivot_abs = std::fabs(a(col, col));
      for (LocalIndex row = col + 1; row < n; ++row) {
        const Real candidate = std::fabs(a(row, col));
        if (candidate > pivot_abs) {
          pivot_abs = candidate;
          pivot = row;
        }
      }
      if (pivot_abs < 1.0e-12) {
        result.diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-SINGULAR-SOLVER",
                                                    "Reduced system is singular or ill-conditioned", "solver"));
        return result;
      }
      if (pivot != col) {
        for (LocalIndex j = col; j < n; ++j) {
          std::swap(a(col, j), a(pivot, j));
        }
        std::swap(b[static_cast<std::size_t>(col)], b[static_cast<std::size_t>(pivot)]);
      }
      const Real diag = a(col, col);
      for (LocalIndex row = col + 1; row < n; ++row) {
        const Real factor = a(row, col) / diag;
        a(row, col) = 0.0;
        for (LocalIndex j = col + 1; j < n; ++j) {
          a(row, j) -= factor * a(col, j);
        }
        b[static_cast<std::size_t>(row)] -= factor * b[static_cast<std::size_t>(col)];
      }
    }
    result.x.assign(static_cast<std::size_t>(n), 0.0);
    for (LocalIndex i = n; i-- > 0;) {
      Real sum = b[static_cast<std::size_t>(i)];
      for (LocalIndex j = i + 1; j < n; ++j) {
        sum -= a(i, j) * result.x[static_cast<std::size_t>(j)];
      }
      result.x[static_cast<std::size_t>(i)] = sum / a(i, i);
    }
    return result;
  }
};

struct ShapeData {
  std::array<Real, 4> n{};
  std::array<Real, 4> dr{};
  std::array<Real, 4> ds{};
};

inline ShapeData shapeFunctions(Real r, Real s) {
  return {{
              0.25 * (1.0 - r) * (1.0 - s),
              0.25 * (1.0 + r) * (1.0 - s),
              0.25 * (1.0 + r) * (1.0 + s),
              0.25 * (1.0 - r) * (1.0 + s),
          },
          {
              -0.25 * (1.0 - s),
              0.25 * (1.0 - s),
              0.25 * (1.0 + s),
              -0.25 * (1.0 + s),
          },
          {
              -0.25 * (1.0 - r),
              -0.25 * (1.0 + r),
              0.25 * (1.0 + r),
              0.25 * (1.0 - r),
          }};
}

struct LocalBasis {
  Vec3 e1;
  Vec3 e2;
  Vec3 e3;
};

struct MITC4NaturalPoint {
  Real xi = 0.0;
  Real eta = 0.0;
};

struct MITC4TyingPoint {
  std::string label;
  MITC4NaturalPoint natural;
  std::array<LocalIndex, 2> edge_node_indices{};
};

inline std::array<MITC4NaturalPoint, 4> mitc4NodeNaturalCoordinates() {
  return {{{-1.0, -1.0}, {1.0, -1.0}, {1.0, 1.0}, {-1.0, 1.0}}};
}

inline std::array<MITC4TyingPoint, 4> mitc4TyingPoints() {
  return {{{"A", {0.0, -1.0}, {0, 1}},
           {"B", {-1.0, 0.0}, {0, 3}},
           {"C", {0.0, 1.0}, {3, 2}},
           {"D", {1.0, 0.0}, {1, 2}}}};
}

struct MITC4DirectorFrame {
  Vec3 v1;
  Vec3 v2;
  Vec3 vn;
};

struct MITC4MidsurfaceDerivatives {
  ShapeData shape;
  Vec3 g1;
  Vec3 g2;
};

struct MITC4Geometry {
  std::array<Vec3, 4> coordinates{};
  Real thickness = 0.0;
  ShapeData center_shape;
  Vec3 g1_center;
  Vec3 g2_center;
  Vec3 center_normal;
  std::array<MITC4DirectorFrame, 4> nodal_frames{};
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

struct MITC4IntegrationBasis {
  ShapeData shape;
  Vec3 g1;
  Vec3 g2;
  Vec3 g3;
  Real jacobian = 0.0;
  LocalBasis local;
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

using MITC4ElementDofVector = std::array<Real, 24>;
using MITC4StrainVector = std::array<Real, 6>;
using MITC4StrainRow = std::array<Real, 24>;
using MITC4MaterialMatrix = std::array<std::array<Real, 6>, 6>;

enum class MITC4StrainComponent {
  Eps11 = 0,
  Eps22 = 1,
  Eps33 = 2,
  Gamma23 = 3,
  Gamma13 = 4,
  Gamma12 = 5
};

inline std::size_t strainComponentIndex(MITC4StrainComponent component) {
  return static_cast<std::size_t>(component);
}

inline std::array<std::string, 6> mitc4StrainComponentLabels() {
  return {"eps11", "eps22", "eps33", "gamma23", "gamma13", "gamma12"};
}

struct MITC4LocalRotations {
  Real alpha = 0.0;
  Real beta = 0.0;
  Real gamma = 0.0;
};

struct MITC4DisplacementDerivatives {
  ShapeData shape;
  Vec3 displacement;
  Vec3 du_dxi;
  Vec3 du_deta;
  Vec3 du_dzeta;
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

struct MITC4StrainEvaluation {
  MITC4StrainVector values{};
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

struct MITC4StrainRows {
  std::array<MITC4StrainRow, 6> rows{};
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

struct MITC4MaterialMatrixEvaluation {
  MITC4MaterialMatrix matrix{};
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

struct MITC4StrainTransform {
  MITC4MaterialMatrix matrix{};
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

struct MITC4IntegrationPoint {
  Real xi = 0.0;
  Real eta = 0.0;
  Real zeta = 0.0;
  Real weight = 0.0;
};

struct MITC4MaterialIntegrationSample {
  MITC4IntegrationPoint point;
  MITC4IntegrationBasis basis;
  MITC4StrainRows strain_rows;
  MITC4MaterialMatrix local_material{};
  MITC4MaterialMatrix strain_transform{};
  MITC4MaterialMatrix convected_material{};
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

struct MITC4MaterialIntegrationData {
  std::vector<MITC4MaterialIntegrationSample> samples;
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

inline Vec3 globalEX() {
  return {1.0, 0.0, 0.0};
}

inline Vec3 globalEY() {
  return {0.0, 1.0, 0.0};
}

inline Vec3 globalEZ() {
  return {0.0, 0.0, 1.0};
}

inline Diagnostic mitc4Diagnostic(std::string code, std::string message) {
  return makeDiagnostic(Severity::Error, std::move(code), std::move(message), "mitc4", "<element>", 0);
}

inline void appendDiagnostics(std::vector<Diagnostic>& target, const std::vector<Diagnostic>& source) {
  target.insert(target.end(), source.begin(), source.end());
}

inline MITC4MidsurfaceDerivatives mitc4MidsurfaceDerivatives(const std::array<Vec3, 4>& coordinates, Real xi, Real eta) {
  MITC4MidsurfaceDerivatives result;
  result.shape = shapeFunctions(xi, eta);
  for (std::size_t i = 0; i < 4; ++i) {
    result.g1 = result.g1 + result.shape.dr[i] * coordinates[i];
    result.g2 = result.g2 + result.shape.ds[i] * coordinates[i];
  }
  return result;
}

inline std::optional<Vec3> firstNormalizedCross(const std::array<Vec3, 3>& axes, const Vec3& vector, Real tolerance) {
  for (const Vec3& axis : axes) {
    auto candidate = normalizedIfValid(cross(axis, vector), tolerance);
    if (candidate) {
      return candidate;
    }
  }
  return std::nullopt;
}

inline std::optional<MITC4DirectorFrame> buildMITC4DirectorFrame(const Vec3& normal, Real tolerance) {
  auto v1 = normalizedIfValid(cross(globalEY(), normal), tolerance);
  if (!v1) {
    v1 = firstNormalizedCross({globalEZ(), globalEX(), globalEY()}, normal, tolerance);
  }
  if (!v1) {
    return std::nullopt;
  }
  auto v2 = normalizedIfValid(cross(normal, *v1), tolerance);
  if (!v2) {
    return std::nullopt;
  }
  return MITC4DirectorFrame{*v1, *v2, normal};
}

inline MITC4Geometry buildMITC4Geometry(const std::array<Vec3, 4>& coordinates, Real thickness, Real tolerance = 1.0e-12) {
  MITC4Geometry geometry;
  geometry.coordinates = coordinates;
  geometry.thickness = thickness;
  if (!isFinite(thickness) || thickness <= tolerance) {
    geometry.diagnostics.push_back(
        mitc4Diagnostic("FESA-MITC4-THICKNESS", "MITC4 shell thickness must be positive and finite"));
  }
  for (const Vec3& coordinate : coordinates) {
    if (!isFinite(coordinate)) {
      geometry.diagnostics.push_back(
          mitc4Diagnostic("FESA-MITC4-COORDINATE", "MITC4 element coordinates must be finite"));
      break;
    }
  }

  const auto center = mitc4MidsurfaceDerivatives(coordinates, 0.0, 0.0);
  geometry.center_shape = center.shape;
  geometry.g1_center = center.g1;
  geometry.g2_center = center.g2;
  const auto normal = normalizedIfValid(cross(center.g1, center.g2), tolerance);
  if (!normal) {
    geometry.diagnostics.push_back(
        mitc4Diagnostic("FESA-MITC4-SINGULAR-NORMAL", "MITC4 element center normal is near zero"));
    return geometry;
  }
  geometry.center_normal = *normal;

  const auto frame = buildMITC4DirectorFrame(*normal, tolerance);
  if (!frame) {
    geometry.diagnostics.push_back(
        mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 nodal director basis could not be constructed"));
    return geometry;
  }
  geometry.nodal_frames.fill(*frame);
  return geometry;
}

inline MITC4IntegrationBasis computeMITC4IntegrationBasis(const MITC4Geometry& geometry, Real xi, Real eta, Real zeta,
                                                          Real tolerance = 1.0e-12) {
  MITC4IntegrationBasis result;
  result.diagnostics = geometry.diagnostics;
  result.shape = shapeFunctions(xi, eta);
  for (std::size_t i = 0; i < 4; ++i) {
    const Vec3& coordinate = geometry.coordinates[i];
    const Vec3& normal = geometry.nodal_frames[i].vn;
    result.g1 = result.g1 + result.shape.dr[i] * coordinate +
                (0.5 * zeta * geometry.thickness * result.shape.dr[i]) * normal;
    result.g2 = result.g2 + result.shape.ds[i] * coordinate +
                (0.5 * zeta * geometry.thickness * result.shape.ds[i]) * normal;
    result.g3 = result.g3 + (0.5 * geometry.thickness * result.shape.n[i]) * normal;
  }

  result.jacobian = dot(cross(result.g1, result.g2), result.g3);
  if (!isFinite(result.jacobian) || std::fabs(result.jacobian) <= tolerance) {
    result.diagnostics.push_back(
        mitc4Diagnostic("FESA-MITC4-SINGULAR-JACOBIAN", "MITC4 element Jacobian is near zero"));
  }

  const auto e3 = normalizedIfValid(result.g3, tolerance);
  if (!e3) {
    result.diagnostics.push_back(
        mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 integration basis normal is near zero"));
    return result;
  }
  auto e1 = normalizedIfValid(cross(result.g2, *e3), tolerance);
  if (!e1) {
    e1 = firstNormalizedCross({globalEY(), globalEZ(), globalEX()}, *e3, tolerance);
  }
  if (!e1) {
    result.diagnostics.push_back(
        mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 integration basis tangent could not be constructed"));
    return result;
  }
  const auto e2 = normalizedIfValid(cross(*e3, *e1), tolerance);
  if (!e2) {
    result.diagnostics.push_back(
        mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 integration basis is not right-handed"));
    return result;
  }
  result.local = {*e1, *e2, *e3};
  return result;
}

inline Vec3 mitc4NodalTranslation(const MITC4ElementDofVector& values, std::size_t node) {
  const std::size_t base = 6 * node;
  return {values[base + 0], values[base + 1], values[base + 2]};
}

inline Vec3 mitc4NodalRotation(const MITC4ElementDofVector& values, std::size_t node) {
  const std::size_t base = 6 * node;
  return {values[base + 3], values[base + 4], values[base + 5]};
}

inline MITC4LocalRotations mitc4LocalRotations(const MITC4DirectorFrame& frame, const Vec3& global_rotation) {
  return {dot(global_rotation, frame.v1), dot(global_rotation, frame.v2), dot(global_rotation, frame.vn)};
}

inline Vec3 mitc4DirectorIncrement(const MITC4DirectorFrame& frame, const Vec3& global_rotation) {
  const MITC4LocalRotations rotations = mitc4LocalRotations(frame, global_rotation);
  return (-rotations.alpha) * frame.v2 + rotations.beta * frame.v1;
}

inline MITC4DisplacementDerivatives mitc4DisplacementDerivatives(const MITC4Geometry& geometry, const MITC4ElementDofVector& values,
                                                                 Real xi, Real eta, Real zeta) {
  MITC4DisplacementDerivatives result;
  result.diagnostics = geometry.diagnostics;
  result.shape = shapeFunctions(xi, eta);
  for (std::size_t node = 0; node < 4; ++node) {
    const Vec3 translation = mitc4NodalTranslation(values, node);
    const Vec3 rotation = mitc4NodalRotation(values, node);
    const Vec3 q = mitc4DirectorIncrement(geometry.nodal_frames[node], rotation);
    const Real n = result.shape.n[node];
    const Real dn_dxi = result.shape.dr[node];
    const Real dn_deta = result.shape.ds[node];
    result.displacement = result.displacement + n * translation + (0.5 * zeta * geometry.thickness * n) * q;
    result.du_dxi = result.du_dxi + dn_dxi * translation + (0.5 * zeta * geometry.thickness * dn_dxi) * q;
    result.du_deta = result.du_deta + dn_deta * translation + (0.5 * zeta * geometry.thickness * dn_deta) * q;
    result.du_dzeta = result.du_dzeta + (0.5 * geometry.thickness * n) * q;
  }
  return result;
}

inline void assignMITC4CovariantStrain(MITC4StrainVector& values, const MITC4IntegrationBasis& basis,
                                       const MITC4DisplacementDerivatives& derivatives) {
  values[strainComponentIndex(MITC4StrainComponent::Eps11)] = dot(derivatives.du_dxi, basis.g1);
  values[strainComponentIndex(MITC4StrainComponent::Eps22)] = dot(derivatives.du_deta, basis.g2);
  values[strainComponentIndex(MITC4StrainComponent::Eps33)] = 0.0;
  values[strainComponentIndex(MITC4StrainComponent::Gamma23)] = dot(derivatives.du_deta, basis.g3) + dot(derivatives.du_dzeta, basis.g2);
  values[strainComponentIndex(MITC4StrainComponent::Gamma13)] = dot(derivatives.du_dxi, basis.g3) + dot(derivatives.du_dzeta, basis.g1);
  values[strainComponentIndex(MITC4StrainComponent::Gamma12)] = dot(derivatives.du_dxi, basis.g2) + dot(derivatives.du_deta, basis.g1);
}

inline MITC4StrainEvaluation mitc4DirectCovariantStrain(const MITC4Geometry& geometry, const MITC4ElementDofVector& values,
                                                        Real xi, Real eta, Real zeta) {
  MITC4StrainEvaluation result;
  const auto basis = computeMITC4IntegrationBasis(geometry, xi, eta, zeta);
  appendDiagnostics(result.diagnostics, basis.diagnostics);
  const auto derivatives = mitc4DisplacementDerivatives(geometry, values, xi, eta, zeta);
  appendDiagnostics(result.diagnostics, derivatives.diagnostics);
  if (hasError(result.diagnostics)) {
    return result;
  }
  assignMITC4CovariantStrain(result.values, basis, derivatives);
  return result;
}

inline MITC4StrainRows mitc4DirectCovariantStrainRows(const MITC4Geometry& geometry, Real xi, Real eta, Real zeta) {
  MITC4StrainRows result;
  const auto basis = computeMITC4IntegrationBasis(geometry, xi, eta, zeta);
  appendDiagnostics(result.diagnostics, basis.diagnostics);
  if (hasError(result.diagnostics)) {
    return result;
  }
  for (std::size_t dof = 0; dof < 24; ++dof) {
    MITC4ElementDofVector unit{};
    unit.fill(0.0);
    unit[dof] = 1.0;
    const auto derivatives = mitc4DisplacementDerivatives(geometry, unit, xi, eta, zeta);
    appendDiagnostics(result.diagnostics, derivatives.diagnostics);
    if (hasError(result.diagnostics)) {
      return result;
    }
    MITC4StrainVector values{};
    assignMITC4CovariantStrain(values, basis, derivatives);
    for (std::size_t component = 0; component < 6; ++component) {
      result.rows[component][dof] = values[component];
    }
  }
  return result;
}

inline MITC4StrainEvaluation evaluateMITC4StrainRows(const MITC4StrainRows& rows, const MITC4ElementDofVector& values) {
  MITC4StrainEvaluation result;
  result.diagnostics = rows.diagnostics;
  if (hasError(result.diagnostics)) {
    return result;
  }
  for (std::size_t component = 0; component < 6; ++component) {
    for (std::size_t dof = 0; dof < 24; ++dof) {
      result.values[component] += rows.rows[component][dof] * values[dof];
    }
  }
  return result;
}

inline MITC4StrainRows mitc4TiedCovariantStrainRows(const MITC4Geometry& geometry, Real xi, Real eta, Real zeta) {
  MITC4StrainRows result = mitc4DirectCovariantStrainRows(geometry, xi, eta, zeta);
  const auto direct_a = mitc4DirectCovariantStrainRows(geometry, 0.0, -1.0, zeta);
  const auto direct_b = mitc4DirectCovariantStrainRows(geometry, -1.0, 0.0, zeta);
  const auto direct_c = mitc4DirectCovariantStrainRows(geometry, 0.0, 1.0, zeta);
  const auto direct_d = mitc4DirectCovariantStrainRows(geometry, 1.0, 0.0, zeta);
  appendDiagnostics(result.diagnostics, direct_a.diagnostics);
  appendDiagnostics(result.diagnostics, direct_b.diagnostics);
  appendDiagnostics(result.diagnostics, direct_c.diagnostics);
  appendDiagnostics(result.diagnostics, direct_d.diagnostics);
  if (hasError(result.diagnostics)) {
    return result;
  }
  const std::size_t gamma23 = strainComponentIndex(MITC4StrainComponent::Gamma23);
  const std::size_t gamma13 = strainComponentIndex(MITC4StrainComponent::Gamma13);
  for (std::size_t dof = 0; dof < 24; ++dof) {
    result.rows[gamma13][dof] = 0.5 * (1.0 - eta) * direct_a.rows[gamma13][dof] +
                                0.5 * (1.0 + eta) * direct_c.rows[gamma13][dof];
    result.rows[gamma23][dof] = 0.5 * (1.0 - xi) * direct_b.rows[gamma23][dof] +
                                0.5 * (1.0 + xi) * direct_d.rows[gamma23][dof];
  }
  return result;
}

inline std::array<MITC4IntegrationPoint, 8> mitc4GaussQuadrature2x2x2() {
  const Real gauss = 1.0 / std::sqrt(3.0);
  const std::array<Real, 2> points = {-gauss, gauss};
  std::array<MITC4IntegrationPoint, 8> integration_points{};
  std::size_t index = 0;
  for (Real xi : points) {
    for (Real eta : points) {
      for (Real zeta : points) {
        integration_points[index++] = {xi, eta, zeta, 1.0};
      }
    }
  }
  return integration_points;
}

inline MITC4MaterialMatrixEvaluation mitc4PlaneStressMaterialMatrix(Real elastic_modulus, Real poisson_ratio,
                                                                    Real shear_correction = 5.0 / 6.0,
                                                                    Real tolerance = 1.0e-12) {
  MITC4MaterialMatrixEvaluation result;
  if (!isFinite(elastic_modulus) || elastic_modulus <= tolerance) {
    result.diagnostics.push_back(
        mitc4Diagnostic("FESA-MITC4-MATERIAL", "MITC4 elastic modulus must be positive and finite"));
  }
  if (!isFinite(poisson_ratio) || poisson_ratio <= -1.0 || poisson_ratio >= 0.5) {
    result.diagnostics.push_back(
        mitc4Diagnostic("FESA-MITC4-POISSON", "MITC4 isotropic Poisson ratio must satisfy -1 < nu < 0.5"));
  }
  if (!isFinite(shear_correction) || shear_correction <= tolerance) {
    result.diagnostics.push_back(
        mitc4Diagnostic("FESA-MITC4-SHEAR-CORRECTION", "MITC4 shear correction factor must be positive and finite"));
  }
  if (hasError(result.diagnostics)) {
    return result;
  }

  const Real scale = elastic_modulus / (1.0 - poisson_ratio * poisson_ratio);
  const Real shear_modulus = elastic_modulus / (2.0 * (1.0 + poisson_ratio));
  const std::size_t eps11 = strainComponentIndex(MITC4StrainComponent::Eps11);
  const std::size_t eps22 = strainComponentIndex(MITC4StrainComponent::Eps22);
  const std::size_t gamma23 = strainComponentIndex(MITC4StrainComponent::Gamma23);
  const std::size_t gamma13 = strainComponentIndex(MITC4StrainComponent::Gamma13);
  const std::size_t gamma12 = strainComponentIndex(MITC4StrainComponent::Gamma12);

  result.matrix[eps11][eps11] = scale;
  result.matrix[eps11][eps22] = poisson_ratio * scale;
  result.matrix[eps22][eps11] = poisson_ratio * scale;
  result.matrix[eps22][eps22] = scale;
  result.matrix[gamma23][gamma23] = shear_correction * shear_modulus;
  result.matrix[gamma13][gamma13] = shear_correction * shear_modulus;
  result.matrix[gamma12][gamma12] = shear_modulus;
  return result;
}

inline MITC4StrainVector multiplyMITC4MaterialMatrix(const MITC4MaterialMatrix& matrix, const MITC4StrainVector& vector) {
  MITC4StrainVector result{};
  for (std::size_t row = 0; row < 6; ++row) {
    for (std::size_t col = 0; col < 6; ++col) {
      result[row] += matrix[row][col] * vector[col];
    }
  }
  return result;
}

inline Real dotMITC4Vector(const MITC4StrainVector& a, const MITC4StrainVector& b) {
  Real result = 0.0;
  for (std::size_t i = 0; i < 6; ++i) {
    result += a[i] * b[i];
  }
  return result;
}

inline MITC4MaterialMatrix mitc4TransformMaterialMatrix(const MITC4MaterialMatrix& local_material,
                                                        const MITC4MaterialMatrix& covariant_to_local) {
  MITC4MaterialMatrix result{};
  for (std::size_t i = 0; i < 6; ++i) {
    for (std::size_t j = 0; j < 6; ++j) {
      Real value = 0.0;
      for (std::size_t a = 0; a < 6; ++a) {
        for (std::size_t b = 0; b < 6; ++b) {
          value += covariant_to_local[a][i] * local_material[a][b] * covariant_to_local[b][j];
        }
      }
      result[i][j] = value;
    }
  }
  return result;
}

inline std::array<std::array<Real, 3>, 3> mitc4TensorFromEngineeringComponent(std::size_t component) {
  std::array<std::array<Real, 3>, 3> tensor{};
  switch (static_cast<MITC4StrainComponent>(component)) {
    case MITC4StrainComponent::Eps11:
      tensor[0][0] = 1.0;
      break;
    case MITC4StrainComponent::Eps22:
      tensor[1][1] = 1.0;
      break;
    case MITC4StrainComponent::Eps33:
      tensor[2][2] = 1.0;
      break;
    case MITC4StrainComponent::Gamma23:
      tensor[1][2] = 0.5;
      tensor[2][1] = 0.5;
      break;
    case MITC4StrainComponent::Gamma13:
      tensor[0][2] = 0.5;
      tensor[2][0] = 0.5;
      break;
    case MITC4StrainComponent::Gamma12:
      tensor[0][1] = 0.5;
      tensor[1][0] = 0.5;
      break;
  }
  return tensor;
}

inline MITC4StrainVector mitc4EngineeringVectorFromTensor(const std::array<std::array<Real, 3>, 3>& tensor) {
  MITC4StrainVector vector{};
  vector[strainComponentIndex(MITC4StrainComponent::Eps11)] = tensor[0][0];
  vector[strainComponentIndex(MITC4StrainComponent::Eps22)] = tensor[1][1];
  vector[strainComponentIndex(MITC4StrainComponent::Eps33)] = tensor[2][2];
  vector[strainComponentIndex(MITC4StrainComponent::Gamma23)] = 2.0 * tensor[1][2];
  vector[strainComponentIndex(MITC4StrainComponent::Gamma13)] = 2.0 * tensor[0][2];
  vector[strainComponentIndex(MITC4StrainComponent::Gamma12)] = 2.0 * tensor[0][1];
  return vector;
}

inline MITC4StrainTransform mitc4CovariantToLocalStrainTransform(const MITC4IntegrationBasis& basis,
                                                                 Real tolerance = 1.0e-12) {
  MITC4StrainTransform result;
  result.diagnostics = basis.diagnostics;
  const Real jacobian = dot(cross(basis.g1, basis.g2), basis.g3);
  if (!isFinite(jacobian) || std::fabs(jacobian) <= tolerance) {
    result.diagnostics.push_back(
        mitc4Diagnostic("FESA-MITC4-SINGULAR-JACOBIAN", "MITC4 material transform Jacobian is near zero"));
    return result;
  }
  if (hasError(result.diagnostics)) {
    return result;
  }

  const std::array<Vec3, 3> contravariant = {
      (1.0 / jacobian) * cross(basis.g2, basis.g3),
      (1.0 / jacobian) * cross(basis.g3, basis.g1),
      (1.0 / jacobian) * cross(basis.g1, basis.g2)};
  const std::array<Vec3, 3> local = {basis.local.e1, basis.local.e2, basis.local.e3};
  std::array<std::array<Real, 3>, 3> direction_cosines{};
  for (std::size_t local_axis = 0; local_axis < 3; ++local_axis) {
    for (std::size_t convected_axis = 0; convected_axis < 3; ++convected_axis) {
      direction_cosines[local_axis][convected_axis] = dot(local[local_axis], contravariant[convected_axis]);
    }
  }

  for (std::size_t column = 0; column < 6; ++column) {
    const auto covariant_tensor = mitc4TensorFromEngineeringComponent(column);
    std::array<std::array<Real, 3>, 3> local_tensor{};
    for (std::size_t a = 0; a < 3; ++a) {
      for (std::size_t b = 0; b < 3; ++b) {
        for (std::size_t i = 0; i < 3; ++i) {
          for (std::size_t j = 0; j < 3; ++j) {
            local_tensor[a][b] += direction_cosines[a][i] * direction_cosines[b][j] * covariant_tensor[i][j];
          }
        }
      }
    }
    const auto local_vector = mitc4EngineeringVectorFromTensor(local_tensor);
    for (std::size_t row = 0; row < 6; ++row) {
      result.matrix[row][column] = local_vector[row];
    }
  }
  return result;
}

inline MITC4MaterialIntegrationData mitc4BuildMaterialIntegrationData(const MITC4Geometry& geometry, Real elastic_modulus,
                                                                      Real poisson_ratio,
                                                                      Real shear_correction = 5.0 / 6.0) {
  MITC4MaterialIntegrationData data;
  const auto material = mitc4PlaneStressMaterialMatrix(elastic_modulus, poisson_ratio, shear_correction);
  appendDiagnostics(data.diagnostics, material.diagnostics);
  if (hasError(data.diagnostics)) {
    return data;
  }

  for (const MITC4IntegrationPoint& point : mitc4GaussQuadrature2x2x2()) {
    MITC4MaterialIntegrationSample sample;
    sample.point = point;
    sample.local_material = material.matrix;
    sample.basis = computeMITC4IntegrationBasis(geometry, point.xi, point.eta, point.zeta);
    appendDiagnostics(sample.diagnostics, sample.basis.diagnostics);
    const auto transform = mitc4CovariantToLocalStrainTransform(sample.basis);
    sample.strain_transform = transform.matrix;
    appendDiagnostics(sample.diagnostics, transform.diagnostics);
    sample.strain_rows = mitc4TiedCovariantStrainRows(geometry, point.xi, point.eta, point.zeta);
    appendDiagnostics(sample.diagnostics, sample.strain_rows.diagnostics);
    if (!hasError(sample.diagnostics)) {
      sample.convected_material = mitc4TransformMaterialMatrix(sample.local_material, sample.strain_transform);
    }
    appendDiagnostics(data.diagnostics, sample.diagnostics);
    data.samples.push_back(sample);
  }
  return data;
}

inline LocalBasis computeLocalBasis(const std::array<Vec3, 4>& coordinates) {
  const MITC4Geometry geometry = buildMITC4Geometry(coordinates, 1.0);
  if (!geometry.ok()) {
    throw std::runtime_error("invalid MITC4 geometry");
  }
  const MITC4DirectorFrame& frame = geometry.nodal_frames[0];
  return {frame.v1, frame.v2, frame.vn};
}

struct ElementStiffnessOptions {
  Real drilling_stiffness_scale = 1.0e-3;
};

struct MITC4DrillingStabilizationResult {
  DenseMatrix local_with_drilling;
  Real reference_diagonal = 0.0;
  Real drilling_stiffness = 0.0;
  Real drilling_stiffness_scale = 0.0;
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

struct MITC4ElementStiffnessResult {
  DenseMatrix local_without_drilling;
  DenseMatrix local_with_drilling;
  DenseMatrix global;
  std::size_t integration_point_count = 0;
  Real drilling_reference_diagonal = 0.0;
  Real drilling_stiffness = 0.0;
  Real drilling_stiffness_scale = 0.0;
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

inline DenseMatrix mitc4LocalDofTransform(const MITC4Geometry& geometry) {
  DenseMatrix transform(24, 24);
  for (LocalIndex node = 0; node < 4; ++node) {
    const LocalIndex base = 6 * node;
    const auto& frame = geometry.nodal_frames[static_cast<std::size_t>(node)];
    const std::array<Vec3, 3> axes = {frame.v1, frame.v2, frame.vn};
    for (LocalIndex local_axis = 0; local_axis < 3; ++local_axis) {
      const Vec3 axis = axes[static_cast<std::size_t>(local_axis)];
      transform(base + local_axis, base + 0) = axis.x;
      transform(base + local_axis, base + 1) = axis.y;
      transform(base + local_axis, base + 2) = axis.z;
      transform(base + 3 + local_axis, base + 3) = axis.x;
      transform(base + 3 + local_axis, base + 4) = axis.y;
      transform(base + 3 + local_axis, base + 5) = axis.z;
    }
  }
  return transform;
}

inline MITC4StrainRows mitc4TransformStrainRowsToLocalDofs(const MITC4StrainRows& global_rows,
                                                           const DenseMatrix& local_dof_transform) {
  MITC4StrainRows local_rows;
  local_rows.diagnostics = global_rows.diagnostics;
  if (hasError(local_rows.diagnostics)) {
    return local_rows;
  }
  for (std::size_t component = 0; component < 6; ++component) {
    for (LocalIndex local_dof = 0; local_dof < 24; ++local_dof) {
      Real value = 0.0;
      for (LocalIndex global_dof = 0; global_dof < 24; ++global_dof) {
        value += global_rows.rows[component][static_cast<std::size_t>(global_dof)] *
                 local_dof_transform(local_dof, global_dof);
      }
      local_rows.rows[component][static_cast<std::size_t>(local_dof)] = value;
    }
  }
  return local_rows;
}

inline void accumulateMITC4BtDB(DenseMatrix& stiffness, const MITC4StrainRows& rows,
                                const MITC4MaterialMatrix& material, Real factor) {
  for (LocalIndex i = 0; i < 24; ++i) {
    for (LocalIndex j = 0; j < 24; ++j) {
      Real value = 0.0;
      for (std::size_t a = 0; a < 6; ++a) {
        for (std::size_t b = 0; b < 6; ++b) {
          value += rows.rows[a][static_cast<std::size_t>(i)] * material[a][b] *
                   rows.rows[b][static_cast<std::size_t>(j)];
        }
      }
      stiffness.add(i, j, value * factor);
    }
  }
}

inline Real mitc4MinimumPositivePhysicalLocalDiagonal(const DenseMatrix& local_without_drilling,
                                                     Real tolerance = 1.0e-12) {
  Real minimum = std::numeric_limits<Real>::infinity();
  for (LocalIndex node = 0; node < 4; ++node) {
    for (LocalIndex local_dof = 0; local_dof < 5; ++local_dof) {
      const Real diagonal = local_without_drilling(6 * node + local_dof, 6 * node + local_dof);
      if (isFinite(diagonal) && diagonal > tolerance) {
        minimum = std::min(minimum, diagonal);
      }
    }
  }
  return minimum;
}

inline MITC4DrillingStabilizationResult mitc4ApplyDrillingStabilization(const DenseMatrix& local_without_drilling,
                                                                        Real drilling_stiffness_scale,
                                                                        Real tolerance = 1.0e-12) {
  MITC4DrillingStabilizationResult result;
  result.local_with_drilling = local_without_drilling;
  result.drilling_stiffness_scale = drilling_stiffness_scale;
  if (!isFinite(drilling_stiffness_scale) || drilling_stiffness_scale < 0.0) {
    result.diagnostics.push_back(
        mitc4Diagnostic("FESA-MITC4-DRILLING-SCALE", "MITC4 drilling stiffness scale must be non-negative and finite"));
    return result;
  }

  result.reference_diagonal = mitc4MinimumPositivePhysicalLocalDiagonal(local_without_drilling, tolerance);
  if (!isFinite(result.reference_diagonal)) {
    result.diagnostics.push_back(mitc4Diagnostic("FESA-MITC4-DRILLING-REFERENCE",
                                                 "MITC4 drilling stiffness reference diagonal is not positive"));
    return result;
  }

  result.drilling_stiffness = drilling_stiffness_scale * result.reference_diagonal;
  for (LocalIndex node = 0; node < 4; ++node) {
    const LocalIndex gamma = 6 * node + 5;
    result.local_with_drilling.add(gamma, gamma, result.drilling_stiffness);
  }
  return result;
}

inline DenseMatrix mitc4TransformLocalStiffnessToGlobal(const DenseMatrix& local_stiffness,
                                                        const DenseMatrix& local_dof_transform) {
  DenseMatrix global(24, 24);
  for (LocalIndex i = 0; i < 24; ++i) {
    for (LocalIndex j = 0; j < 24; ++j) {
      Real value = 0.0;
      for (LocalIndex a = 0; a < 24; ++a) {
        for (LocalIndex b = 0; b < 24; ++b) {
          value += local_dof_transform(a, i) * local_stiffness(a, b) * local_dof_transform(b, j);
        }
      }
      global(i, j) = value;
    }
  }
  return global;
}

inline MITC4ElementStiffnessResult mitc4ElementStiffness(const std::array<Vec3, 4>& coordinates,
                                                        Real elastic_modulus, Real poisson_ratio, Real thickness,
                                                        ElementStiffnessOptions options = {}) {
  MITC4ElementStiffnessResult result;
  result.local_without_drilling = DenseMatrix(24, 24);
  result.local_with_drilling = DenseMatrix(24, 24);
  result.global = DenseMatrix(24, 24);
  result.drilling_stiffness_scale = options.drilling_stiffness_scale;

  const MITC4Geometry geometry = buildMITC4Geometry(coordinates, thickness);
  appendDiagnostics(result.diagnostics, geometry.diagnostics);
  if (hasError(result.diagnostics)) {
    return result;
  }

  const MITC4MaterialIntegrationData integration =
      mitc4BuildMaterialIntegrationData(geometry, elastic_modulus, poisson_ratio);
  appendDiagnostics(result.diagnostics, integration.diagnostics);
  if (hasError(result.diagnostics)) {
    return result;
  }
  result.integration_point_count = integration.samples.size();

  const DenseMatrix local_dof_transform = mitc4LocalDofTransform(geometry);
  for (const MITC4MaterialIntegrationSample& sample : integration.samples) {
    const MITC4StrainRows local_rows =
        mitc4TransformStrainRowsToLocalDofs(sample.strain_rows, local_dof_transform);
    appendDiagnostics(result.diagnostics, local_rows.diagnostics);
    if (hasError(result.diagnostics)) {
      return result;
    }
    const Real factor = std::fabs(sample.basis.jacobian) * sample.point.weight;
    accumulateMITC4BtDB(result.local_without_drilling, local_rows, sample.convected_material, factor);
  }

  const auto drilling = mitc4ApplyDrillingStabilization(result.local_without_drilling, options.drilling_stiffness_scale);
  appendDiagnostics(result.diagnostics, drilling.diagnostics);
  result.local_with_drilling = drilling.local_with_drilling;
  result.drilling_reference_diagonal = drilling.reference_diagonal;
  result.drilling_stiffness = drilling.drilling_stiffness;
  result.drilling_stiffness_scale = drilling.drilling_stiffness_scale;
  if (hasError(result.diagnostics)) {
    return result;
  }

  result.global = mitc4TransformLocalStiffnessToGlobal(result.local_with_drilling, local_dof_transform);
  return result;
}

inline std::vector<Real> mitc4ElementInternalForce(const MITC4ElementStiffnessResult& stiffness,
                                                  const std::vector<Real>& element_displacement) {
  if (stiffness.global.rows() != static_cast<LocalIndex>(element_displacement.size())) {
    throw std::runtime_error("MITC4 internal force size mismatch");
  }
  return stiffness.global.multiply(element_displacement);
}

class MITC4ElementKernel {
 public:
  DenseMatrix stiffness(const std::array<Vec3, 4>& coordinates, Real elastic_modulus, Real poisson_ratio, Real thickness,
                        ElementStiffnessOptions options = {}) const {
    const auto result = mitc4ElementStiffness(coordinates, elastic_modulus, poisson_ratio, thickness, options);
    if (!result.ok()) {
      throw std::runtime_error(result.diagnostics.empty() ? "invalid MITC4 stiffness"
                                                          : result.diagnostics.front().message);
    }
    return result.global;
  }
};

struct AssemblyResult {
  DenseMatrix k_full;
  std::vector<Real> f_full;
  SparsePattern reduced_pattern;
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

struct ReducedSystem {
  DenseMatrix k;
  std::vector<Real> f;
  std::vector<LocalIndex> free_full_indices;
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

inline AssemblyResult assembleSystem(const Domain& domain, const DofManager& dofs, ElementStiffnessOptions options = {}) {
  AssemblyResult result;
  result.k_full = DenseMatrix(dofs.fullDofCount(), dofs.fullDofCount());
  result.f_full = std::vector<Real>(static_cast<std::size_t>(dofs.fullDofCount()), 0.0);
  result.reduced_pattern = buildReducedSparsePattern(domain, dofs);
  if (dofs.freeDofCount() > 0 && result.reduced_pattern.nonzeroCount() == 0) {
    result.diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-SINGULAR-SPARSE-PATTERN",
                                                "Reduced sparse pattern has no stiffness entries", "assembly"));
  }
  for (const auto& [element_id, element] : domain.elements) {
    const ShellSection* section = shellSectionForElement(domain, element_id);
    if (section == nullptr) {
      result.diagnostics.push_back({Severity::Error, "FESA-ASSEMBLY-MISSING-PROPERTY", "Element has no shell section", {}});
      continue;
    }
    const auto material_it = domain.materials.find(Domain::key(section->material));
    if (material_it == domain.materials.end()) {
      result.diagnostics.push_back({Severity::Error, "FESA-ASSEMBLY-MISSING-MATERIAL", "Element material is missing", {}});
      continue;
    }
    std::array<Vec3, 4> coordinates{};
    for (std::size_t i = 0; i < 4; ++i) {
      coordinates[i] = domain.nodes.at(element.node_ids[i]).coordinates;
    }
    const auto stiffness = mitc4ElementStiffness(coordinates, material_it->second.elastic_modulus,
                                                material_it->second.poisson_ratio, section->thickness, options);
    result.diagnostics.insert(result.diagnostics.end(), stiffness.diagnostics.begin(), stiffness.diagnostics.end());
    if (!stiffness.ok()) {
      continue;
    }
    const auto element_full_indices = dofs.elementFullDofIndices(element);
    for (LocalIndex a = 0; a < 24; ++a) {
      const LocalIndex ia = element_full_indices[static_cast<std::size_t>(a)];
      for (LocalIndex b = 0; b < 24; ++b) {
        const LocalIndex ib = element_full_indices[static_cast<std::size_t>(b)];
        result.k_full.add(ia, ib, stiffness.global(a, b));
      }
    }
  }
  for (const NodalLoad& load : domain.loads) {
    const auto dof = dofFromAbaqus(load.dof);
    if (!dof) {
      result.diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-ASSEMBLY-LOAD-DOF",
                                                  "Nodal load references an invalid DOF", "cload"));
      continue;
    }
    for (GlobalId node_id : resolveNodeTarget(domain, load.target, &result.diagnostics)) {
      result.f_full[static_cast<std::size_t>(dofs.fullIndex(node_id, *dof))] += load.magnitude;
    }
  }
  return result;
}

inline ReducedSystem projectToReducedSystem(const AssemblyResult& assembly, const DofManager& dofs) {
  ReducedSystem result;
  result.k = DenseMatrix(dofs.freeDofCount(), dofs.freeDofCount());
  result.f = std::vector<Real>(static_cast<std::size_t>(dofs.freeDofCount()), 0.0);
  result.free_full_indices = dofs.freeFullIndices();
  if (assembly.k_full.rows() != assembly.k_full.cols() ||
      assembly.k_full.rows() != dofs.fullDofCount() ||
      static_cast<LocalIndex>(assembly.f_full.size()) != dofs.fullDofCount()) {
    result.diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-ASSEMBLY-SIZE",
                                                "Full-space stiffness/load sizes do not match DofManager", "assembly"));
    return result;
  }
  if (dofs.freeDofCount() == 0) {
    result.diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-SINGULAR-NO-FREE-DOFS",
                                                "No free DOFs exist after applying constraints", "dof"));
    return result;
  }
  if (assembly.reduced_pattern.equation_count != dofs.freeDofCount() || assembly.reduced_pattern.nonzeroCount() == 0) {
    result.diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-SINGULAR-SPARSE-PATTERN",
                                                "Reduced sparse pattern is empty or inconsistent with free DOFs", "assembly"));
    return result;
  }
  for (LocalIndex i = 0; i < dofs.freeDofCount(); ++i) {
    const LocalIndex full_i = dofs.freeFullIndices()[static_cast<std::size_t>(i)];
    result.f[static_cast<std::size_t>(i)] = assembly.f_full[static_cast<std::size_t>(full_i)];
    for (LocalIndex j = 0; j < dofs.freeDofCount(); ++j) {
      const LocalIndex full_j = dofs.freeFullIndices()[static_cast<std::size_t>(j)];
      result.k(i, j) = assembly.k_full(full_i, full_j);
    }
  }
  return result;
}

struct FieldOutput {
  std::string name;
  std::string position = "NODAL";
  std::string entity_type = "node";
  std::string basis = "GLOBAL";
  std::string description;
  std::vector<GlobalId> entity_ids;
  std::vector<std::string> component_labels;
  std::vector<std::array<Real, 6>> values;
};

struct ResultFrame {
  LocalIndex frame_id = 0;
  LocalIndex increment = 1;
  LocalIndex iteration = 0;
  Real step_time = 1.0;
  Real total_time = 1.0;
  bool converged = true;
  std::string description = "Phase 1 linear static frame";
  std::map<std::string, FieldOutput> field_outputs;
};

struct ResultStep {
  std::string name;
  std::vector<ResultFrame> frames;
};

struct ResultFile {
  std::string schema_name = "FESA_RESULTS";
  LocalIndex schema_version = 1;
  std::string solver_name = "FESA";
  std::string dof_convention = "UX,UY,UZ,RX,RY,RZ";
  std::string sign_convention = "Abaqus-compatible";
  std::string precision = "double";
  std::string index_type = "int64";
  std::vector<GlobalId> node_ids;
  std::vector<Vec3> coordinates;
  std::vector<GlobalId> element_ids;
  std::vector<std::array<GlobalId, 4>> connectivity;
  std::vector<ResultStep> steps;
};

class InMemoryResultsWriter {
 public:
  void writeLinearStatic(const Domain& domain, const DofManager& dofs, const std::vector<Real>& u_full, const std::vector<Real>& rf_full) {
    result_ = ResultFile{};
    for (const auto& [node_id, node] : domain.nodes) {
      result_.node_ids.push_back(node_id);
      result_.coordinates.push_back(node.coordinates);
    }
    for (const auto& [element_id, element] : domain.elements) {
      result_.element_ids.push_back(element_id);
      result_.connectivity.push_back(element.node_ids);
    }
    ResultStep step;
    step.name = domain.steps.empty() ? "Step-1" : domain.steps.front().name;
    ResultFrame frame;
    frame.frame_id = 0;
    frame.field_outputs["U"] = buildNodalField("U", displacementComponentLabels(), "Nodal displacement and rotation", domain, dofs, u_full);
    frame.field_outputs["RF"] = buildNodalField("RF", reactionComponentLabels(), "Nodal reaction force and moment", domain, dofs, rf_full);
    step.frames.push_back(frame);
    result_.steps.push_back(step);
  }

  const ResultFile& result() const {
    return result_;
  }

 private:
  static FieldOutput buildNodalField(const std::string& name, const std::vector<std::string>& labels, const std::string& description,
                                     const Domain& domain, const DofManager& dofs, const std::vector<Real>& full_values) {
    FieldOutput field;
    field.name = name;
    field.position = "NODAL";
    field.entity_type = "node";
    field.basis = "GLOBAL";
    field.description = description;
    field.component_labels = labels;
    for (const auto& [node_id, node] : domain.nodes) {
      (void)node;
      field.entity_ids.push_back(node_id);
      std::array<Real, 6> values{};
      for (Dof dof : allDofs()) {
        values[static_cast<std::size_t>(dofIndex(dof))] = full_values[static_cast<std::size_t>(dofs.fullIndex(node_id, dof))];
      }
      field.values.push_back(values);
    }
    return field;
  }

  ResultFile result_;
};

struct AnalysisState {
  std::vector<Real> u_full;
  std::vector<Real> f_external_full;
  std::vector<Real> f_internal_full;
  std::vector<Real> reaction_full;
  bool converged = false;
};

struct AnalysisResult {
  AnalysisState state;
  ResultFile result_file;
  std::vector<Diagnostic> diagnostics;

  bool ok() const {
    return !hasError(diagnostics);
  }
};

class Analysis {
 public:
  virtual ~Analysis() = default;
  AnalysisResult run(const Domain& domain) const {
    AnalysisResult result;
    initialize(domain, result);
    if (hasError(result.diagnostics)) {
      return result;
    }
    solve(domain, result);
    return result;
  }

 protected:
  virtual void initialize(const Domain& domain, AnalysisResult& result) const {
    auto diagnostics = validateDomain(domain);
    result.diagnostics.insert(result.diagnostics.end(), diagnostics.begin(), diagnostics.end());
  }
  virtual void solve(const Domain& domain, AnalysisResult& result) const = 0;
};

class LinearStaticAnalysis final : public Analysis {
 public:
  explicit LinearStaticAnalysis(const LinearSolver* solver = nullptr) : solver_(solver) {}

 protected:
  void solve(const Domain& domain, AnalysisResult& result) const override {
    DofManager dofs(domain);
    if (dofs.freeDofCount() == 0) {
      result.diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-SINGULAR-NO-FREE-DOFS",
                                                  "No free DOFs exist after applying constraints", "dof"));
      return;
    }
    AssemblyResult assembly = assembleSystem(domain, dofs);
    result.diagnostics.insert(result.diagnostics.end(), assembly.diagnostics.begin(), assembly.diagnostics.end());
    if (hasError(result.diagnostics)) {
      return;
    }
    const auto reduced = projectToReducedSystem(assembly, dofs);
    result.diagnostics.insert(result.diagnostics.end(), reduced.diagnostics.begin(), reduced.diagnostics.end());
    if (hasError(result.diagnostics)) {
      return;
    }
    const LinearSolver& active_solver = solver_ == nullptr ? defaultSolver() : *solver_;
    SolveResult solved = active_solver.solve(reduced.k, reduced.f);
    result.diagnostics.insert(result.diagnostics.end(), solved.diagnostics.begin(), solved.diagnostics.end());
    if (!solved.ok()) {
      return;
    }
    if (static_cast<LocalIndex>(solved.x.size()) != dofs.freeDofCount()) {
      result.diagnostics.push_back(makeDiagnostic(Severity::Error, "FESA-SOLVER-SIZE",
                                                  "Linear solver returned a vector with the wrong size", "solver"));
      return;
    }
    result.state.u_full = dofs.reconstructFullVector(solved.x);
    result.state.f_external_full = assembly.f_full;
    result.state.f_internal_full = assembly.k_full.multiply(result.state.u_full);
    result.state.reaction_full = recoverFullReaction(assembly.k_full, result.state.u_full, result.state.f_external_full);
    result.state.converged = true;
    InMemoryResultsWriter writer;
    writer.writeLinearStatic(domain, dofs, result.state.u_full, result.state.reaction_full);
    result.result_file = writer.result();
  }

 private:
  static const LinearSolver& defaultSolver() {
    static const GaussianEliminationSolver solver;
    return solver;
  }

  const LinearSolver* solver_ = nullptr;
};

struct CsvDisplacementRow {
  GlobalId node_id = 0;
  std::array<Real, 6> values{};
};

struct CsvDisplacementTable {
  std::map<GlobalId, CsvDisplacementRow> rows;
  std::vector<Diagnostic> diagnostics;
};

inline std::vector<std::string> displacementCsvRequiredColumns() {
  return {"Node Label", "U-U1", "U-U2", "U-U3", "UR-UR1", "UR-UR2", "UR-UR3"};
}

inline CsvDisplacementTable loadDisplacementCsvFromStream(std::istream& input, const std::string& source_name) {
  CsvDisplacementTable table;
  std::string line;
  if (!std::getline(input, line)) {
    table.diagnostics.push_back({Severity::Error, "FESA-CSV-EMPTY", "Displacement CSV is empty", {source_name, 1, ""}});
    return table;
  }
  const std::vector<std::string> required = displacementCsvRequiredColumns();
  std::vector<std::string> headers = splitCsv(line);
  std::map<std::string, std::size_t> column;
  for (std::size_t i = 0; i < headers.size(); ++i) {
    column[trim(headers[i])] = i;
  }
  for (const std::string& name : required) {
    if (column.count(name) == 0) {
      table.diagnostics.push_back({Severity::Error, "FESA-CSV-MISSING-COLUMN", "Missing CSV column: " + name, {source_name, 1, ""}});
    }
  }
  if (hasError(table.diagnostics)) {
    return table;
  }
  LocalIndex line_number = 1;
  while (std::getline(input, line)) {
    ++line_number;
    if (trim(line).empty()) {
      continue;
    }
    std::vector<std::string> fields = splitCsv(line);
    auto get = [&](const std::string& name) -> std::string {
      const std::size_t index = column[name];
      return index < fields.size() ? fields[index] : "";
    };
    auto node_id = parseInt64(get("Node Label"));
    if (!node_id) {
      table.diagnostics.push_back({Severity::Error, "FESA-CSV-NODE", "Invalid node label", {source_name, line_number, ""}});
      continue;
    }
    if (table.rows.count(*node_id) != 0) {
      table.diagnostics.push_back({Severity::Error, "FESA-CSV-DUPLICATE-NODE", "Duplicate node label", {source_name, line_number, ""}});
      continue;
    }
    CsvDisplacementRow row;
    row.node_id = *node_id;
    for (std::size_t i = 0; i < 6; ++i) {
      auto value = parseReal(get(required[i + 1]));
      if (!value) {
        table.diagnostics.push_back({Severity::Error, "FESA-CSV-NUMERIC", "Invalid displacement value", {source_name, line_number, ""}});
        value = 0.0;
      }
      row.values[i] = *value;
    }
    table.rows[*node_id] = row;
  }
  return table;
}

inline CsvDisplacementTable loadDisplacementCsvFromString(const std::string& text, const std::string& source_name = "<memory>") {
  std::istringstream input(text);
  return loadDisplacementCsvFromStream(input, source_name);
}

inline CsvDisplacementTable loadDisplacementCsv(const std::string& path) {
  std::ifstream input(path);
  if (!input.good()) {
    CsvDisplacementTable table;
    table.diagnostics.push_back({Severity::Error, "FESA-CSV-READ", "Could not read displacement CSV", {path, 0, ""}});
    return table;
  }
  return loadDisplacementCsvFromStream(input, path);
}

struct ComparisonOptions {
  Real abs_tol = 1.0e-12;
  Real rel_tol = 1.0e-5;
  Real reference_scale = 1.0;
};

struct ComparisonResult {
  bool pass = false;
  Real max_abs_error = 0.0;
  Real max_rel_error = 0.0;
  std::vector<Diagnostic> diagnostics;
};

inline ComparisonResult compareDisplacements(const FieldOutput& actual, const CsvDisplacementTable& expected, ComparisonOptions options = {}) {
  ComparisonResult result;
  result.diagnostics = expected.diagnostics;
  if (hasError(result.diagnostics)) {
    return result;
  }
  if (actual.name != "U") {
    result.diagnostics.push_back({Severity::Error, "FESA-COMPARE-FIELD-NAME", "Expected FESA displacement field named U", {}});
  }
  if (actual.component_labels != displacementComponentLabels()) {
    result.diagnostics.push_back({Severity::Error, "FESA-COMPARE-COMPONENT-LABELS", "FESA U field component labels must be UX,UY,UZ,RX,RY,RZ", {}});
  }
  if (actual.position != "NODAL" || actual.entity_type != "node" || actual.basis != "GLOBAL") {
    result.diagnostics.push_back({Severity::Error, "FESA-COMPARE-FIELD-METADATA", "FESA U field must be nodal values in the global basis", {}});
  }
  if (actual.entity_ids.size() != actual.values.size()) {
    result.diagnostics.push_back({Severity::Error, "FESA-COMPARE-FIELD-SIZE", "FESA U field entity/value counts differ", {}});
  }
  std::map<GlobalId, std::array<Real, 6>> actual_by_node;
  const std::size_t actual_count = std::min(actual.entity_ids.size(), actual.values.size());
  for (std::size_t i = 0; i < actual_count; ++i) {
    if (actual_by_node.count(actual.entity_ids[i]) != 0) {
      result.diagnostics.push_back(
          {Severity::Error, "FESA-COMPARE-DUPLICATE-ACTUAL", "FESA U field contains duplicate node " + std::to_string(actual.entity_ids[i]), {}});
      continue;
    }
    actual_by_node[actual.entity_ids[i]] = actual.values[i];
  }
  for (const auto& [node_id, row] : expected.rows) {
    auto actual_it = actual_by_node.find(node_id);
    if (actual_it == actual_by_node.end()) {
      result.diagnostics.push_back({Severity::Error, "FESA-COMPARE-MISSING-ACTUAL", "FESA U field is missing node " + std::to_string(node_id), {}});
      continue;
    }
    for (std::size_t component = 0; component < 6; ++component) {
      const Real expected_value = row.values[component];
      const Real actual_value = actual_it->second[component];
      const Real abs_error = std::fabs(actual_value - expected_value);
      const Real scale = std::max(std::fabs(expected_value), std::fabs(options.reference_scale));
      const Real rel_error = scale > 0.0 ? abs_error / scale : (abs_error == 0.0 ? 0.0 : std::numeric_limits<Real>::infinity());
      result.max_abs_error = std::max(result.max_abs_error, abs_error);
      result.max_rel_error = std::max(result.max_rel_error, rel_error);
      if (!(abs_error <= options.abs_tol || rel_error <= options.rel_tol)) {
        const std::string component_label = displacementComponentLabels()[component];
        result.diagnostics.push_back({Severity::Error, "FESA-COMPARE-TOLERANCE",
                                      "Displacement comparison failed at node " + std::to_string(node_id) + " component " + component_label, {}});
      }
    }
  }
  result.pass = !hasError(result.diagnostics);
  return result;
}

}  // namespace fesa