最小二乘-矩阵运算
This commit is contained in:
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using System.Collections.Generic;
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namespace kcsj.Models
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{
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public class LeastSquaresResult
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{
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public int ObservationCount { get; set; }
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public int UnknownCount { get; set; }
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public int Redundancy { get; set; }
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/// <summary>
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/// 单位权中误差
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/// </summary>
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public double Sigma0 { get; set; }
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/// <summary>
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/// 未知点平差高程
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/// </summary>
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public Dictionary<string, double> UnknownElevations { get; } = new();
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/// <summary>
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/// 所有点平差后高程，包括已知点和未知点
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/// </summary>
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public Dictionary<string, double> AdjustedElevations { get; } = new();
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/// <summary>
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/// 未知点高程中误差
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/// </summary>
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public Dictionary<string, double> UnknownElevationErrors { get; } = new();
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/// <summary>
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/// 每条观测的改正数 v
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/// </summary>
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public List<double> Residuals { get; } = new();
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/// <summary>
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/// 每条观测的平差后高差
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/// </summary>
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public List<double> AdjustedHeightDiffs { get; } = new();
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/// <summary>
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/// 每条观测的详细结果
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/// </summary>
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public List<ObservationAdjustmentResult> ObservationResults { get; } = new();
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}
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public class ObservationAdjustmentResult
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{
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public int Index { get; set; }
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public string FromPoint { get; set; } = "";
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public string ToPoint { get; set; } = "";
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public double ObservedHeightDiff { get; set; }
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public double Distance { get; set; }
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public double Weight { get; set; }
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/// <summary>
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/// 改正数 v
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/// </summary>
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public double Residual { get; set; }
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/// <summary>
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/// 平差后高差 h + v
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/// </summary>
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public double AdjustedHeightDiff { get; set; }
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}
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}
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@@ -0,0 +1,297 @@
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using System;
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using System.Collections.Generic;
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using System.Linq;
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using kcsj.Models;
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namespace kcsj.Services
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{
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public class DataCheckResult
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{
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public List<string> Errors { get; } = new();
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public List<string> Warnings { get; } = new();
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public List<string> Infos { get; } = new();
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public bool IsValid => Errors.Count == 0;
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public string ToLogText()
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{
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var lines = new List<string>();
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lines.Add("========== 数据检查结果 ==========");
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foreach (string info in Infos)
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{
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lines.Add("[信息] " + info);
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}
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foreach (string warning in Warnings)
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{
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lines.Add("[警告] " + warning);
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}
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foreach (string error in Errors)
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{
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lines.Add("[错误] " + error);
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}
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lines.Add(IsValid ? "数据检查通过。" : "数据检查未通过。");
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lines.Add("================================");
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return string.Join(Environment.NewLine, lines);
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}
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}
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public static class DataCheck
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{
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public static DataCheckResult Check(
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List<KnownPoint> knownPoints,
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List<Observation> observations)
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{
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var result = new DataCheckResult();
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if (knownPoints == null || knownPoints.Count == 0)
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{
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result.Errors.Add("未导入已知点数据。");
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}
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else
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{
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result.Infos.Add($"已知点数量：{knownPoints.Count}");
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}
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if (observations == null || observations.Count == 0)
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{
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result.Errors.Add("未导入观测数据。");
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}
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else
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{
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result.Infos.Add($"观测数据数量：{observations.Count}");
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}
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if (!result.IsValid)
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{
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return result;
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}
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CheckKnownPoints(knownPoints, result);
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CheckObservations(observations, result);
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CheckNetwork(knownPoints, observations, result);
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CheckRedundancy(knownPoints, observations, result);
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return result;
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}
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private static void CheckKnownPoints(
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List<KnownPoint> knownPoints,
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DataCheckResult result)
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{
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var names = new HashSet<string>(StringComparer.OrdinalIgnoreCase);
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for (int i = 0; i < knownPoints.Count; i++)
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{
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KnownPoint point = knownPoints[i];
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if (string.IsNullOrWhiteSpace(point.Name))
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{
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result.Errors.Add($"第 {i + 1} 个已知点点名为空。");
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continue;
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}
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string name = point.Name.Trim();
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if (!names.Add(name))
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{
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result.Errors.Add($"已知点点名重复：{name}");
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}
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if (double.IsNaN(point.Elevation) || double.IsInfinity(point.Elevation))
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{
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result.Errors.Add($"已知点 {name} 的高程不是有效数字。");
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}
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}
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}
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private static void CheckObservations(
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List<Observation> observations,
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DataCheckResult result)
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{
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var edges = new HashSet<string>(StringComparer.OrdinalIgnoreCase);
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for (int i = 0; i < observations.Count; i++)
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{
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Observation obs = observations[i];
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if (string.IsNullOrWhiteSpace(obs.FromPoint))
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{
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result.Errors.Add($"第 {i + 1} 条观测起点为空。");
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continue;
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}
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if (string.IsNullOrWhiteSpace(obs.ToPoint))
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{
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result.Errors.Add($"第 {i + 1} 条观测终点为空。");
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continue;
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}
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string from = obs.FromPoint.Trim();
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string to = obs.ToPoint.Trim();
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if (string.Equals(from, to, StringComparison.OrdinalIgnoreCase))
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{
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result.Errors.Add($"第 {i + 1} 条观测起点和终点相同：{from}");
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}
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if (double.IsNaN(obs.HeightDiff) || double.IsInfinity(obs.HeightDiff))
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{
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result.Errors.Add($"第 {i + 1} 条观测高差不是有效数字。");
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}
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if (double.IsNaN(obs.Distance) || double.IsInfinity(obs.Distance))
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{
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result.Errors.Add($"第 {i + 1} 条观测距离不是有效数字。");
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}
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else if (obs.Distance <= 0)
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{
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result.Errors.Add($"第 {i + 1} 条观测距离必须大于 0。");
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}
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string edge1 = from + "-" + to;
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string edge2 = to + "-" + from;
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if (edges.Contains(edge1) || edges.Contains(edge2))
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{
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result.Warnings.Add($"第 {i + 1} 条观测边可能重复：{from} - {to}");
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}
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else
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{
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edges.Add(edge1);
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}
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}
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}
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private static void CheckNetwork(
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List<KnownPoint> knownPoints,
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List<Observation> observations,
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DataCheckResult result)
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{
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if (!result.IsValid)
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{
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return;
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}
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var knownNames = new HashSet<string>(
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knownPoints.Select(p => p.Name.Trim()),
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StringComparer.OrdinalIgnoreCase);
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var allNames = new HashSet<string>(StringComparer.OrdinalIgnoreCase);
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foreach (KnownPoint point in knownPoints)
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{
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allNames.Add(point.Name.Trim());
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}
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foreach (Observation obs in observations)
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{
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allNames.Add(obs.FromPoint.Trim());
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allNames.Add(obs.ToPoint.Trim());
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}
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var graph = new Dictionary<string, List<string>>(StringComparer.OrdinalIgnoreCase);
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foreach (string name in allNames)
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{
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graph[name] = new List<string>();
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}
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foreach (Observation obs in observations)
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{
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string from = obs.FromPoint.Trim();
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string to = obs.ToPoint.Trim();
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graph[from].Add(to);
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graph[to].Add(from);
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}
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var visited = new HashSet<string>(StringComparer.OrdinalIgnoreCase);
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var queue = new Queue<string>();
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foreach (string knownName in knownNames)
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{
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if (graph.ContainsKey(knownName))
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{
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visited.Add(knownName);
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queue.Enqueue(knownName);
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}
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}
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while (queue.Count > 0)
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{
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string current = queue.Dequeue();
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foreach (string next in graph[current])
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{
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if (!visited.Contains(next))
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{
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visited.Add(next);
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queue.Enqueue(next);
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}
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}
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}
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foreach (string name in allNames)
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{
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if (!visited.Contains(name))
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{
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result.Errors.Add($"点 {name} 没有与任何已知点连通。");
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}
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}
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int unknownCount = allNames.Count(name => !knownNames.Contains(name));
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result.Infos.Add($"总点数：{allNames.Count}");
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result.Infos.Add($"未知点数：{unknownCount}");
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}
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private static void CheckRedundancy(
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List<KnownPoint> knownPoints,
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List<Observation> observations,
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DataCheckResult result)
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{
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if (!result.IsValid)
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{
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return;
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}
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var knownNames = new HashSet<string>(
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knownPoints.Select(p => p.Name.Trim()),
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StringComparer.OrdinalIgnoreCase);
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var allNames = new HashSet<string>(StringComparer.OrdinalIgnoreCase);
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foreach (KnownPoint point in knownPoints)
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{
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allNames.Add(point.Name.Trim());
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}
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foreach (Observation obs in observations)
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{
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allNames.Add(obs.FromPoint.Trim());
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allNames.Add(obs.ToPoint.Trim());
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}
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int unknownCount = allNames.Count(name => !knownNames.Contains(name));
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int observationCount = observations.Count;
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int redundancy = observationCount - unknownCount;
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result.Infos.Add($"多余观测数：r = {observationCount} - {unknownCount} = {redundancy}");
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if (observationCount < unknownCount)
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{
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result.Errors.Add("观测数少于未知点数，无法平差。");
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}
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else if (redundancy == 0)
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{
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result.Warnings.Add("多余观测数为 0，无法进行精度评定。");
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}
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}
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}
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}
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@@ -0,0 +1,56 @@
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using System;
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using System.Collections.Generic;
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using System.Linq;
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using kcsj.Models;
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namespace kcsj.Services
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{
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public static class DataStore
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{
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public static List<KnownPoint> KnownPoints { get; private set; } = new();
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public static List<Observation> Observations { get; private set; } = new();
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public static string DataSource { get; private set; } = "";
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public static bool HasData
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{
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get
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{
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return KnownPoints.Count > 0 && Observations.Count > 0;
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}
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}
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public static void SetData(
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List<KnownPoint> knownPoints,
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List<Observation> observations,
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string dataSource)
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{
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if (knownPoints == null || knownPoints.Count == 0)
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{
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throw new ArgumentException("已知点数据为空，不能保存数据。");
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}
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if (observations == null || observations.Count == 0)
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{
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throw new ArgumentException("观测数据为空，不能保存数据。");
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}
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KnownPoints = knownPoints.ToList();
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Observations = observations.ToList();
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DataSource = dataSource;
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LogService.AddLog($"数据已更新，来源：{dataSource}");
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LogService.AddLog($"已知点数量：{KnownPoints.Count}");
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LogService.AddLog($"观测数据数量：{Observations.Count}");
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}
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public static void Clear()
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{
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KnownPoints.Clear();
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Observations.Clear();
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DataSource = "";
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LogService.AddLog("数据已清空。");
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}
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}
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}
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@@ -0,0 +1,242 @@
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using System;
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using System.Collections.Generic;
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using System.Linq;
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using kcsj.Models;
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namespace kcsj.Services
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{
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public static class LeastSquaresAdjustmentService
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{
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/// <summary>
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/// 水准网间接平差
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///
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/// 观测关系：
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/// h_AB = H_B - H_A
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///
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/// 误差方程：
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/// v = Bx - L
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///
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/// 法方程：
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/// N x = W
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/// N = B^T P B
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/// W = B^T P L
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/// x = N^-1 W
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/// </summary>
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public static LeastSquaresResult Adjust(
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List<KnownPoint> knownPoints,
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List<Observation> observations)
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{
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if (knownPoints == null || knownPoints.Count == 0)
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{
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throw new ArgumentException("已知点不能为空。");
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}
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if (observations == null || observations.Count == 0)
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{
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throw new ArgumentException("观测数据不能为空。");
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}
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Dictionary<string, double> knownElevations =
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knownPoints.ToDictionary(
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p => p.Name.Trim(),
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p => p.Elevation,
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StringComparer.OrdinalIgnoreCase);
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|
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HashSet<string> allPointNames = new(StringComparer.OrdinalIgnoreCase);
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|
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foreach (Observation obs in observations)
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{
|
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if (string.IsNullOrWhiteSpace(obs.FromPoint) ||
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string.IsNullOrWhiteSpace(obs.ToPoint))
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{
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throw new ArgumentException("观测数据中存在空点名。");
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}
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allPointNames.Add(obs.FromPoint.Trim());
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allPointNames.Add(obs.ToPoint.Trim());
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}
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List<string> unknownNames = allPointNames
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.Where(name => !knownElevations.ContainsKey(name))
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.OrderBy(name => name)
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.ToList();
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if (unknownNames.Count == 0)
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{
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throw new InvalidOperationException("没有未知点，不需要进行间接平差。");
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}
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int observationCount = observations.Count;
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int unknownCount = unknownNames.Count;
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if (observationCount < unknownCount)
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{
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throw new InvalidOperationException("观测数小于未知数，无法进行最小二乘平差。");
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}
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Dictionary<string, int> unknownIndex = new(StringComparer.OrdinalIgnoreCase);
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for (int i = 0; i < unknownNames.Count; i++)
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{
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unknownIndex[unknownNames[i]] = i;
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}
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MatrixOperations B = new MatrixOperations(observationCount, unknownCount);
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MatrixOperations L = new MatrixOperations(observationCount, 1);
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MatrixOperations P = new MatrixOperations(observationCount, observationCount);
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double[] weights = new double[observationCount];
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for (int i = 0; i < observationCount; i++)
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{
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Observation obs = observations[i];
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string from = obs.FromPoint.Trim();
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string to = obs.ToPoint.Trim();
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// h_AB = H_B - H_A
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// FromPoint 是未知点，系数为 -1
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if (unknownIndex.ContainsKey(from))
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{
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B[i, unknownIndex[from]] = -1.0;
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}
|
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|
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// ToPoint 是未知点，系数为 +1
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if (unknownIndex.ContainsKey(to))
|
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{
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B[i, unknownIndex[to]] = 1.0;
|
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}
|
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|
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// 已知点贡献：H_B(已知) - H_A(已知)
|
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double knownContribution = 0.0;
|
||||
|
||||
if (knownElevations.ContainsKey(to))
|
||||
{
|
||||
knownContribution += knownElevations[to];
|
||||
}
|
||||
|
||||
if (knownElevations.ContainsKey(from))
|
||||
{
|
||||
knownContribution -= knownElevations[from];
|
||||
}
|
||||
|
||||
// L = h观测 - 已知点贡献
|
||||
L[i, 0] = obs.HeightDiff - knownContribution;
|
||||
|
||||
// 水准测量常用定权：p = 1 / S
|
||||
// 距离越长，权越小
|
||||
double weight;
|
||||
|
||||
if (obs.Distance <= 0)
|
||||
{
|
||||
weight = 1.0;
|
||||
}
|
||||
else
|
||||
{
|
||||
weight = 1.0 / obs.Distance;
|
||||
}
|
||||
|
||||
P[i, i] = weight;
|
||||
weights[i] = weight;
|
||||
}
|
||||
|
||||
MatrixOperations Bt = B.Transpose();
|
||||
|
||||
MatrixOperations N = Bt.Multiply(P).Multiply(B);
|
||||
MatrixOperations W = Bt.Multiply(P).Multiply(L);
|
||||
|
||||
MatrixOperations Qxx = N.Inverse();
|
||||
MatrixOperations X = Qxx.Multiply(W);
|
||||
|
||||
// v = Bx - L
|
||||
MatrixOperations V = B.Multiply(X).Sub(L);
|
||||
|
||||
// V^T P V
|
||||
MatrixOperations VtPV = V.Transpose().Multiply(P).Multiply(V);
|
||||
|
||||
int redundancy = observationCount - unknownCount;
|
||||
|
||||
double sigma0;
|
||||
|
||||
if (redundancy > 0)
|
||||
{
|
||||
sigma0 = Math.Sqrt(VtPV[0, 0] / redundancy);
|
||||
}
|
||||
else
|
||||
{
|
||||
sigma0 = double.NaN;
|
||||
}
|
||||
|
||||
LeastSquaresResult result = new LeastSquaresResult
|
||||
{
|
||||
ObservationCount = observationCount,
|
||||
UnknownCount = unknownCount,
|
||||
Redundancy = redundancy,
|
||||
Sigma0 = sigma0
|
||||
};
|
||||
|
||||
foreach (KnownPoint point in knownPoints)
|
||||
{
|
||||
result.AdjustedElevations[point.Name.Trim()] = point.Elevation;
|
||||
}
|
||||
|
||||
for (int i = 0; i < unknownCount; i++)
|
||||
{
|
||||
string pointName = unknownNames[i];
|
||||
double elevation = X[i, 0];
|
||||
|
||||
result.UnknownElevations[pointName] = elevation;
|
||||
result.AdjustedElevations[pointName] = elevation;
|
||||
|
||||
if (double.IsNaN(sigma0))
|
||||
{
|
||||
result.UnknownElevationErrors[pointName] = double.NaN;
|
||||
}
|
||||
else
|
||||
{
|
||||
result.UnknownElevationErrors[pointName] =
|
||||
sigma0 * Math.Sqrt(Math.Abs(Qxx[i, i]));
|
||||
}
|
||||
}
|
||||
|
||||
for (int i = 0; i < observationCount; i++)
|
||||
{
|
||||
Observation obs = observations[i];
|
||||
|
||||
double residual = V[i, 0];
|
||||
double adjustedHeightDiff = obs.HeightDiff + residual;
|
||||
|
||||
result.Residuals.Add(residual);
|
||||
result.AdjustedHeightDiffs.Add(adjustedHeightDiff);
|
||||
|
||||
result.ObservationResults.Add(new ObservationAdjustmentResult
|
||||
{
|
||||
Index = i + 1,
|
||||
FromPoint = obs.FromPoint,
|
||||
ToPoint = obs.ToPoint,
|
||||
ObservedHeightDiff = obs.HeightDiff,
|
||||
Distance = obs.Distance,
|
||||
Weight = weights[i],
|
||||
Residual = residual,
|
||||
AdjustedHeightDiff = adjustedHeightDiff
|
||||
});
|
||||
}
|
||||
|
||||
LogService.AddLog("间接平差计算完成。");
|
||||
LogService.AddLog($"观测数：{observationCount}");
|
||||
LogService.AddLog($"未知点数：{unknownCount}");
|
||||
LogService.AddLog($"多余观测数：{redundancy}");
|
||||
|
||||
if (double.IsNaN(sigma0))
|
||||
{
|
||||
LogService.AddLog("单位权中误差：无法计算，多余观测数为 0。");
|
||||
}
|
||||
else
|
||||
{
|
||||
LogService.AddLog($"单位权中误差：{sigma0:F6}");
|
||||
}
|
||||
|
||||
return result;
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,197 @@
|
||||
using System;
|
||||
using System.Collections.Generic;
|
||||
using System.Linq;
|
||||
using System.Text;
|
||||
using System.Threading.Tasks;
|
||||
|
||||
namespace kcsj.Services
|
||||
{
|
||||
public class MatrixOperations
|
||||
{
|
||||
private const double eps = 1e-2;
|
||||
private readonly double[,] values;
|
||||
|
||||
private int RowCount { get; }
|
||||
private int ColumnCount { get; }
|
||||
|
||||
public double this[int row, int column]
|
||||
{
|
||||
get => values[row, column];
|
||||
set => values[row, column] = value;
|
||||
}
|
||||
|
||||
// 初始化矩阵大小
|
||||
public MatrixOperations(int rowCount, int columnCount)
|
||||
{
|
||||
if (rowCount <= 0 || columnCount <= 0)
|
||||
{
|
||||
throw new ArgumentException("矩阵行列数必须大于 0。");
|
||||
}
|
||||
|
||||
RowCount = rowCount;
|
||||
ColumnCount = columnCount;
|
||||
values = new double[rowCount, columnCount];
|
||||
}
|
||||
|
||||
// 从二维数组初始化矩阵
|
||||
public MatrixOperations(double[,] source)
|
||||
{
|
||||
RowCount = source.GetLength(0);
|
||||
ColumnCount = source.GetLength(1);
|
||||
values = new double[RowCount, ColumnCount];
|
||||
|
||||
for (int i = 0; i < RowCount; i++)
|
||||
{
|
||||
for (int j = 0; j < ColumnCount; j++)
|
||||
{
|
||||
values[i, j] = source[i, j];
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
public MatrixOperations Add(MatrixOperations other)
|
||||
{
|
||||
if (RowCount != other.RowCount || ColumnCount != other.ColumnCount)
|
||||
{
|
||||
throw new ArgumentException("矩阵维度不匹配，无法相加。");
|
||||
}
|
||||
MatrixOperations result = new MatrixOperations(RowCount, ColumnCount);
|
||||
for (int i = 0; i < RowCount; i++)
|
||||
{
|
||||
for (int j = 0; j < ColumnCount; j++)
|
||||
{
|
||||
result[i, j] = this[i, j] + other[i, j];
|
||||
}
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
public MatrixOperations Sub (MatrixOperations other)
|
||||
{
|
||||
if (RowCount != other.RowCount || ColumnCount != other.ColumnCount)
|
||||
{
|
||||
throw new ArgumentException("矩阵维度不匹配，无法相减。");
|
||||
}
|
||||
MatrixOperations result = new MatrixOperations(RowCount, ColumnCount);
|
||||
for (int i = 0; i < RowCount; i++)
|
||||
{
|
||||
for (int j = 0; j < ColumnCount; j++)
|
||||
{
|
||||
result[i, j] = this[i, j] - other[i, j];
|
||||
}
|
||||
}
|
||||
return result;
|
||||
|
||||
}
|
||||
|
||||
public MatrixOperations Multiply(MatrixOperations other)
|
||||
{
|
||||
if (ColumnCount != other.RowCount)
|
||||
{
|
||||
throw new ArgumentException("矩阵维度不匹配，无法相乘。");
|
||||
}
|
||||
MatrixOperations result = new MatrixOperations(RowCount, other.ColumnCount);
|
||||
for (int i = 0; i < RowCount; i++)
|
||||
{
|
||||
for (int j = 0; j < other.ColumnCount; j++)
|
||||
{
|
||||
double sum = 0;
|
||||
for (int k = 0; k < ColumnCount; k++)
|
||||
{
|
||||
sum += this[i, k] * other[k, j];
|
||||
}
|
||||
result[i, j] = sum;
|
||||
}
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
public MatrixOperations Transpose()
|
||||
{
|
||||
MatrixOperations result = new MatrixOperations(ColumnCount, RowCount);
|
||||
for (int i = 0; i < RowCount; i++)
|
||||
{
|
||||
for (int j = 0; j < ColumnCount; j++)
|
||||
{
|
||||
result[j, i] = this[i, j];
|
||||
}
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
public MatrixOperations Inverse()
|
||||
{
|
||||
if (RowCount != ColumnCount)
|
||||
{
|
||||
throw new ArgumentException("只有方阵才有逆矩阵。");
|
||||
}
|
||||
int n = RowCount;
|
||||
MatrixOperations augmented = new MatrixOperations(n, 2 * n);
|
||||
// 构造增广矩阵 [A | I]
|
||||
for (int i = 0; i < n; i++)
|
||||
{
|
||||
for (int j = 0; j < n; j++)
|
||||
{
|
||||
augmented[i, j] = this[i, j];
|
||||
}
|
||||
augmented[i, n + i] = 1; // 添加单位矩阵部分
|
||||
}
|
||||
// 使用高斯消元法将左侧变为单位矩阵
|
||||
for (int i = 0; i < n; i++)
|
||||
{
|
||||
// 寻找主元素
|
||||
int pivotRow = i;
|
||||
for (int row = i + 1; row < n; row++)
|
||||
{
|
||||
if (Math.Abs(augmented[row, i]) > Math.Abs(augmented[pivotRow, i]))
|
||||
{
|
||||
pivotRow = row;
|
||||
}
|
||||
}
|
||||
if (Math.Abs(augmented[pivotRow, i]) < eps)
|
||||
{
|
||||
throw new InvalidOperationException("矩阵不可逆。");
|
||||
}
|
||||
// 交换行
|
||||
if (pivotRow != i)
|
||||
{
|
||||
for (int col = 0; col < 2 * n; col++)
|
||||
{
|
||||
double temp = augmented[i, col];
|
||||
augmented[i, col] = augmented[pivotRow, col];
|
||||
augmented[pivotRow, col] = temp;
|
||||
}
|
||||
}
|
||||
// 将主元素归一化
|
||||
double pivotValue = augmented[i, i];
|
||||
for (int col = 0; col < 2 * n; col++)
|
||||
{
|
||||
augmented[i, col] /= pivotValue;
|
||||
}
|
||||
// 消去其他行的当前列
|
||||
for (int row = 0; row < n; row++)
|
||||
{
|
||||
if (row != i)
|
||||
{
|
||||
double factor = augmented[row, i];
|
||||
for (int col = 0; col < 2 * n; col++)
|
||||
{
|
||||
augmented[row, col] -= factor * augmented[i, col];
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
// 提取右侧的逆矩阵
|
||||
MatrixOperations inverse = new MatrixOperations(n, n);
|
||||
for (int i = 0; i < n; i++)
|
||||
{
|
||||
for (int j = 0; j < n; j++)
|
||||
{
|
||||
inverse[i, j] = augmented[i, n + j];
|
||||
}
|
||||
}
|
||||
return inverse;
|
||||
}
|
||||
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user