rpc debug
This commit is contained in:
nuknal
@@ -3,7 +3,6 @@ package producer
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import (
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"encoding/json"
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"fmt"
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"math"
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"os"
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"strings"
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@@ -15,14 +14,16 @@ import (
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"starwiz.cn/sjy01/image-proc/pkg/dem"
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)
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const FLT_EPSILON = 1.192092896e-07
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type RPC struct {
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lineOffset, lineScale float64
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sampOffset, sampScale float64
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latOffset, longOffset, heightOffset float64
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latScale, longScale, heightScale float64
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LineCoef RPCModel
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SampleCoef RPCModel
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LineCoef RPCModel
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SampCoef RPCModel
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minH, maxH float64
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GCPs []*GroundPoint
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@@ -55,8 +56,8 @@ type RPCModel struct {
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// rational polynomial coeffients
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func NewRPC(r *Registrator, scene *Scene, rpb string) *RPC {
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rpc := RPC{
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elevationLayer: 4,
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gridsize: 19,
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elevationLayer: 5,
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gridsize: 5,
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registrator: r,
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scene: scene,
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rpb: rpb,
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@@ -92,8 +93,6 @@ func (rpc *RPC) init() {
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// 虚拟控制点
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func (rpc *RPC) generateVirtualGCP() {
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log.Infof("Generating virtual GCPs, %d x %d x %d",
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rpc.gridsize+1, rpc.gridsize+1, rpc.elevationLayer+1)
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points := gridImage2(rpc.gridsize, rpc.gridsize,
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rpc.scene.Height, rpc.scene.Width,
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rpc.elevationLayer, int(rpc.minH), int(rpc.maxH))
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@@ -137,10 +136,10 @@ func (rpc *RPC) RPC() error {
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rpc.saveVec(strings.Replace(rpc.scene.Tiff, ".tiff", ".vec.txt", -1),
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rowVec, colVec, latVec, lonVec, heightVec)
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rpc.lineOffset = float64(rpc.scene.Height / 2)
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rpc.lineScale = float64(rpc.scene.Height)
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rpc.sampOffset = float64(rpc.scene.Width / 2)
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rpc.sampScale = float64(rpc.scene.Width)
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rpc.lineOffset = float64(rpc.scene.Height) / 2.0
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rpc.lineScale = float64(rpc.scene.Height) / 2.0
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rpc.sampOffset = float64(rpc.scene.Width) / 2.0
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rpc.sampScale = float64(rpc.scene.Width) / 2.0
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rowVec = normalize2(rowVec, rpc.lineOffset, rpc.lineScale)
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colVec = normalize2(colVec, rpc.sampOffset, rpc.sampScale)
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@@ -155,73 +154,42 @@ func (rpc *RPC) RPC() error {
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// x = (B^T * B)^-1 * B^T * l, 其中 x = [a1..a20 b2..b20]^T
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// 行参数
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B := buildDesignMatrix(rowVec, latVec, lonVec, heightVec)
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J, err := SolveNormalEquation(B, rowVec)
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// B := setupSystemOfEquations(rowVec, latVec, lonVec, heightVec)
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// J, err := SolveNormalEquation(B, rowVec)
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log.Println("solving row coefficients")
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J, err := solveCoefficients(rowVec, latVec, lonVec, heightVec)
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if err != nil {
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return err
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}
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// 列参数
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D := buildDesignMatrix(colVec, latVec, lonVec, heightVec)
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K, err := SolveNormalEquation(D, colVec)
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// D := setupSystemOfEquations(colVec, latVec, lonVec, heightVec)
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// K, err := SolveNormalEquation(D, colVec)
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log.Println("solving col coefficients")
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K, err := solveCoefficients(colVec, latVec, lonVec, heightVec)
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if err != nil {
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return err
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}
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for i := 0; i < 20; i++ {
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rpc.LineCoef.NumCoefficients[0] = J[0]
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rpc.LineCoef.DenCoefficients[0] = 1.0
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rpc.SampCoef.NumCoefficients[0] = K[0]
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rpc.SampCoef.DenCoefficients[0] = 1.0
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for i := 1; i < 20; i++ {
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rpc.LineCoef.NumCoefficients[i] = J[i]
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}
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rpc.LineCoef.DenCoefficients[0] = 1.0
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for i := 20; i < 39; i++ {
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rpc.LineCoef.DenCoefficients[i-19] = J[i]
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rpc.LineCoef.DenCoefficients[i] = J[i+19]
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rpc.SampCoef.NumCoefficients[i] = K[i]
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rpc.SampCoef.DenCoefficients[i] = K[i+19]
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}
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for i := 0; i < 20; i++ {
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rpc.SampleCoef.NumCoefficients[i] = K[i]
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}
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rpc.SampleCoef.DenCoefficients[0] = 1.0
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for i := 20; i < 39; i++ {
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rpc.SampleCoef.DenCoefficients[i-19] = K[i]
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}
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nameRPB := strings.Replace(rpc.scene.Tiff, ".tiff", ".sep.rpb", -1)
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rpc.saveRPB(nameRPB)
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r, c := B.Dims()
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M0 := mat.NewDense(r, c, nil)
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var BM0, M0D, M mat.Dense
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BM0.Augment(B, M0)
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M0D.Augment(M0, D)
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M.Stack(&BM0, &M0D)
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var L mat.Dense
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L.Stack(rowVec, colVec)
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coeffs, err := SolveNormalEquation(&M, mat.NewVecDense(rowVec.Len()+colVec.Len(), mat.Col(nil, 0, &L)))
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if err != nil {
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return err
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}
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for i := 0; i < 20; i++ {
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rpc.LineCoef.NumCoefficients[i] = coeffs[i]
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}
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rpc.LineCoef.DenCoefficients[0] = 1.0
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for i := 20; i < 39; i++ {
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rpc.LineCoef.DenCoefficients[i-19] = coeffs[i]
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}
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for i := 39; i < 59; i++ {
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rpc.SampleCoef.NumCoefficients[i-39] = coeffs[i]
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}
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rpc.SampleCoef.DenCoefficients[0] = 1.0
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for i := 59; i < 78; i++ {
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rpc.SampleCoef.DenCoefficients[i-58] = coeffs[i]
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}
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nameRPB0 := strings.Replace(rpc.scene.Tiff, ".tiff", ".rpb", -1)
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rpc.saveRPB(nameRPB0)
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projectedPoints := rpc.applyRFM(
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mat.NewVecDense(20, rpc.LineCoef.NumCoefficients[:]),
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mat.NewVecDense(20, rpc.LineCoef.DenCoefficients[:]),
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mat.NewVecDense(20, rpc.SampleCoef.NumCoefficients[:]),
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mat.NewVecDense(20, rpc.SampleCoef.DenCoefficients[:]),
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mat.NewVecDense(20, rpc.SampCoef.NumCoefficients[:]),
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mat.NewVecDense(20, rpc.SampCoef.DenCoefficients[:]),
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rpc.GCPs,
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)
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name := strings.Replace(rpc.scene.Tiff, ".tiff", ".gcp_proj.txt", -1)
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@@ -230,156 +198,19 @@ func (rpc *RPC) RPC() error {
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return nil
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}
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func normalize(v *mat.VecDense) (*mat.VecDense, float64, float64) {
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var vOff, vScale float64
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vOff = mat.Sum(v) / float64(v.Len())
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vScale = math.Max(math.Abs(mat.Max(v)-vOff), math.Abs(mat.Min(v)-vOff))
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for i := 0; i < v.Len(); i++ {
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v.SetVec(i, (v.AtVec(i)-vOff)/vScale)
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}
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return v, vOff, vScale
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}
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func normalize2(v *mat.VecDense, vOff, vScale float64) *mat.VecDense {
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for i := 0; i < v.Len(); i++ {
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v.SetVec(i, (v.AtVec(i)-vOff)/vScale)
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}
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return v
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}
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func buildDesignMatrix(vec, latVec, lonVec, heightVec *mat.VecDense) *mat.Dense {
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n := latVec.Len()
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// 设计矩阵 B = [ 20个分子系数 19个分母系数 ]
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B := mat.NewDense(n, 39, nil)
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for i := 0; i < n; i++ {
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P := latVec.AtVec(i)
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L := lonVec.AtVec(i)
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H := heightVec.AtVec(i)
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r_c := vec.AtVec(i)
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B.Set(i, 0, 1)
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B.Set(i, 1, L)
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B.Set(i, 2, P)
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B.Set(i, 3, H)
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B.Set(i, 4, L*P)
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B.Set(i, 5, L*H)
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B.Set(i, 6, P*H)
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B.Set(i, 7, L*L)
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B.Set(i, 8, P*P)
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B.Set(i, 9, H*H)
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B.Set(i, 10, P*L*H)
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B.Set(i, 11, L*L*L)
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B.Set(i, 12, L*P*P)
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B.Set(i, 13, L*H*H)
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B.Set(i, 14, L*L*P)
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B.Set(i, 15, P*P*P)
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B.Set(i, 16, P*H*H)
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B.Set(i, 17, L*L*H)
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B.Set(i, 18, P*P*H)
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B.Set(i, 19, H*H*H)
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B.Set(i, 20, -L*r_c)
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B.Set(i, 21, -P*r_c)
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B.Set(i, 22, -H*r_c)
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B.Set(i, 23, -L*P*r_c)
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B.Set(i, 24, -L*H*r_c)
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B.Set(i, 25, -P*H*r_c)
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B.Set(i, 26, -L*L*r_c)
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B.Set(i, 27, -P*P*r_c)
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B.Set(i, 28, -H*H*r_c)
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B.Set(i, 29, -P*L*H*r_c)
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B.Set(i, 30, -L*L*L*r_c)
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B.Set(i, 31, -L*P*P*r_c)
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B.Set(i, 32, -L*H*H*r_c)
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B.Set(i, 33, -L*L*P*r_c)
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B.Set(i, 34, -P*P*P*r_c)
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B.Set(i, 35, -P*H*H*r_c)
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B.Set(i, 36, -L*L*H*r_c)
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B.Set(i, 37, -P*P*H*r_c)
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B.Set(i, 38, -H*H*H*r_c)
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}
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return B
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}
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// SolveNormalEquation 使用正规方程法求解最小二乘问题
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func SolveNormalEquation(A *mat.Dense, b *mat.VecDense) ([]float64, error) {
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var At mat.Dense
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At.Mul(A.T(), A) // At = A^T * A
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// 求解 (A^T * A)^-1 * (A^T * b)
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var AtInv mat.Dense
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err := AtInv.Inverse(&At)
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if err != nil {
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// 岭估计方法调整法方程状态，使得矩阵非奇异，最小二乘平差可以收敛
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r, c := At.Dims()
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log.Infof("cannot inverse design matrix(%d*%d): %v", r, c, err)
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log.Info("try to adjust design matrix with +kI, k=0.0000001")
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k := 0.0000001 // [0.00000005, 0.000005]
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I := mat.NewDiagDense(r, nil)
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for i := 0; i < r; i++ {
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I.SetDiag(i, k)
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}
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At.Add(&At, I)
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err = AtInv.Inverse(&At)
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}
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if err != nil {
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log.Infof("cannot inverse design matrix: %v, try SVD method", err)
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// 计算矩阵的 SVD 分解
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var svd mat.SVD
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ok := svd.Factorize(&At, mat.SVDThin)
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if !ok {
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fmt.Println("SVD 分解失败")
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return nil, fmt.Errorf("设计矩阵不可逆, SVD 分解失败: %v", err)
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}
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// 获取 U、Σ 和 V^T
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var u, v mat.Dense
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svd.UTo(&u)
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svd.VTo(&v)
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sigma := svd.Values(nil)
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// 计算 Σ^+ (Sigma pseudo-inverse)
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m, n := u.Dims()
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sigmaInv := mat.NewDense(n, m, nil)
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for i := 0; i < len(sigma); i++ {
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if sigma[i] > 1e-10 { // 避免除以零
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sigmaInv.Set(i, i, 1/sigma[i])
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}
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}
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// 计算 V * Σ^+ * U^T
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var temp mat.Dense
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temp.Mul(&v, sigmaInv)
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AtInv.Mul(&temp, u.T())
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}
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var Atb mat.VecDense
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Atb.MulVec(A.T(), b) // Atb = A^T * b
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var x mat.VecDense
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x.MulVec(&AtInv, &Atb) // x = (A^T * A)^-1 * (A^T * b)
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return mat.Col(nil, 0, &x), nil
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}
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func (rpc *RPC) Output() string {
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var lineNumCoef, lineDenCoef, sampNumCoef, sampDenCoef string
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for i := 0; i < 20; i++ {
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if i < 19 {
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lineNumCoef += fmt.Sprintf("\t\t%.15e,\n", rpc.LineCoef.NumCoefficients[i])
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lineDenCoef += fmt.Sprintf("\t\t%.15e,\n", rpc.LineCoef.DenCoefficients[i])
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sampNumCoef += fmt.Sprintf("\t\t%.15e,\n", rpc.SampleCoef.NumCoefficients[i])
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sampDenCoef += fmt.Sprintf("\t\t%.15e,\n", rpc.SampleCoef.DenCoefficients[i])
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sampNumCoef += fmt.Sprintf("\t\t%.15e,\n", rpc.SampCoef.NumCoefficients[i])
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sampDenCoef += fmt.Sprintf("\t\t%.15e,\n", rpc.SampCoef.DenCoefficients[i])
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} else {
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lineNumCoef += fmt.Sprintf("\t\t%.15e", rpc.LineCoef.NumCoefficients[i])
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lineDenCoef += fmt.Sprintf("\t\t%.15e", rpc.LineCoef.DenCoefficients[i])
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sampNumCoef += fmt.Sprintf("\t\t%.15e", rpc.SampleCoef.NumCoefficients[i])
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sampDenCoef += fmt.Sprintf("\t\t%.15e", rpc.SampleCoef.DenCoefficients[i])
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sampNumCoef += fmt.Sprintf("\t\t%.15e", rpc.SampCoef.NumCoefficients[i])
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sampDenCoef += fmt.Sprintf("\t\t%.15e", rpc.SampCoef.DenCoefficients[i])
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}
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}
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@@ -497,57 +328,20 @@ func (rpc *RPC) saveVec(name string, rowVec, colVec, latVec, lonVec, heightVec *
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func (rpc *RPC) applyRFM(num_line, den_line, num_samp, den_samp *mat.VecDense, points []*GroundPoint) []*GroundPoint {
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var res []*GroundPoint
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for _, p := range points {
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var r GroundPoint
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r.Y = rpc.project(num_line, den_line, p.P, p.L, p.H)
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r.Y = r.Y*rpc.lineScale + rpc.lineOffset
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r.X = rpc.project(num_samp, den_samp, p.P, p.L, p.H)
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r.X = r.X*rpc.sampScale + rpc.sampOffset
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P := (p.P - rpc.latOffset) / rpc.latScale
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L := (p.L - rpc.longOffset) / rpc.longScale
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H := (p.H - rpc.heightOffset) / rpc.heightScale
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r.Y = project(num_line, den_line, P, L, H)
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r.X = project(num_samp, den_samp, P, L, H)
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r.P = p.P
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r.L = p.L
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r.H = p.H
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r.Y = (r.Y*rpc.lineScale + rpc.lineOffset)
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r.X = (r.X*rpc.sampScale + rpc.sampOffset)
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res = append(res, &r)
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}
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return res
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}
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func (rpc *RPC) localize(num, den *mat.VecDense, row, col float64) (P, L, H float64) {
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return
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}
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func (rpc *RPC) project(num, den *mat.VecDense, P, L, H float64) (v float64) {
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v = rpc.applyPoly(num, P, L, H) / rpc.applyPoly(den, P, L, H)
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return v
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}
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func (rpc *RPC) applyPoly(poly *mat.VecDense, P, L, H float64) (v float64) {
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P = (P - rpc.latOffset) / rpc.latScale
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L = (L - rpc.longOffset) / rpc.longScale
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H = (H - rpc.heightOffset) / rpc.heightScale
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v = 0.0
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v += poly.AtVec(0)
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v += poly.AtVec(1) * L
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v += poly.AtVec(2) * P
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v += poly.AtVec(3) * H
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v += poly.AtVec(4) * L * P
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v += poly.AtVec(5) * L * H
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v += poly.AtVec(6) * P * H
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v += poly.AtVec(7) * L * L
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v += poly.AtVec(8) * P * P
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v += poly.AtVec(9) * H * H
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v += poly.AtVec(10) * P * L * H
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v += poly.AtVec(11) * L * L * L
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v += poly.AtVec(12) * L * P * P
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v += poly.AtVec(13) * L * H * H
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v += poly.AtVec(14) * L * L * P
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v += poly.AtVec(15) * P * P * P
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v += poly.AtVec(16) * P * H * H
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v += poly.AtVec(17) * L * L * H
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v += poly.AtVec(18) * P * P * H
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v += poly.AtVec(19) * H * H * H
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return v
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}
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382
pkg/producer/rpc_helper.go
Normal file
382
pkg/producer/rpc_helper.go
Normal file
@@ -0,0 +1,382 @@
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package producer
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import (
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"fmt"
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"math"
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log "github.com/sirupsen/logrus"
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"gonum.org/v1/gonum/mat"
|
||||
)
|
||||
|
||||
func normalize(v *mat.VecDense) (*mat.VecDense, float64, float64) {
|
||||
var vOff, vScale float64
|
||||
vOff = mat.Sum(v) / float64(v.Len())
|
||||
vScale = math.Max(math.Abs(mat.Max(v)-vOff), math.Abs(mat.Min(v)-vOff))
|
||||
for i := 0; i < v.Len(); i++ {
|
||||
v.SetVec(i, (v.AtVec(i)-vOff)/vScale)
|
||||
}
|
||||
|
||||
return v, vOff, vScale
|
||||
}
|
||||
|
||||
func normalize2(v *mat.VecDense, vOff, vScale float64) *mat.VecDense {
|
||||
for i := 0; i < v.Len(); i++ {
|
||||
v.SetVec(i, (v.AtVec(i)-vOff)/vScale)
|
||||
}
|
||||
|
||||
return v
|
||||
}
|
||||
|
||||
func solveCoefficients(f, latVec, lonVec, heightVec *mat.VecDense) ([]float64, error) {
|
||||
M := setupSystemOfEquations(f, latVec, lonVec, heightVec)
|
||||
n := f.Len()
|
||||
weights := mat.NewDiagDense(n, nil)
|
||||
for i := 0; i < n; i++ {
|
||||
weights.SetDiag(i, 1.0)
|
||||
}
|
||||
w2 := mat.NewDiagDense(n, nil)
|
||||
|
||||
iterations := 0
|
||||
var x mat.VecDense
|
||||
// var e0 float64
|
||||
|
||||
for iterations < 20 {
|
||||
iterations++
|
||||
|
||||
// w2 = weights^2
|
||||
for i := 0; i < n; i++ {
|
||||
w2.SetDiag(i, weights.At(i, i)*weights.At(i, i))
|
||||
}
|
||||
|
||||
// x = (M^T * w2 * M)^-1 * M^T * w2 * R
|
||||
var MtW2 mat.Dense
|
||||
MtW2.Mul(M.T(), w2)
|
||||
var MtW2M mat.Dense
|
||||
MtW2M.Mul(&MtW2, M)
|
||||
|
||||
invMtW2M, err := invertRPCMatrix(&MtW2M)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
var MtW2F mat.VecDense
|
||||
MtW2F.MulVec(&MtW2, f)
|
||||
|
||||
x.MulVec(invMtW2M, &MtW2F)
|
||||
|
||||
numerator := mat.NewVecDense(20, nil)
|
||||
denominator := mat.NewVecDense(20, nil)
|
||||
numerator.SetVec(0, x.AtVec(0))
|
||||
denominator.SetVec(0, 1.0)
|
||||
for idx := 1; idx < 20; idx++ {
|
||||
numerator.SetVec(idx, x.AtVec(idx))
|
||||
denominator.SetVec(idx, x.AtVec(idx+19))
|
||||
}
|
||||
|
||||
weights = setupWeightMatrix(denominator, latVec, lonVec, heightVec)
|
||||
|
||||
// residual = m.t()*w2*(m*tempCoeff-r);
|
||||
// var temp0, temp1, residual mat.VecDense
|
||||
// temp0.MulVec(M, &x)
|
||||
// temp1.SubVec(&temp0, f)
|
||||
// residual.MulVec(&MtW2, &temp1)
|
||||
// var square mat.Dense
|
||||
// square.Mul(residual.T(), &residual)
|
||||
// residualValue := math.Sqrt(square.At(0, 0))
|
||||
// if residualValue < 0.0001 {
|
||||
// break
|
||||
// }
|
||||
|
||||
// fmt.Printf("residual value: %.16f\n", residualValue)
|
||||
// fmt.Printf("iterations: %d\n", iterations)
|
||||
|
||||
e := 0.0
|
||||
for i := 0; i < n; i++ {
|
||||
Rcal := project(numerator, denominator, latVec.AtVec(i), lonVec.AtVec(i), heightVec.AtVec(i))
|
||||
e += math.Pow(Rcal-f.AtVec(i), 2)
|
||||
}
|
||||
e = math.Sqrt(e / float64(n))
|
||||
fmt.Println("iterations:", iterations, "r error:", e)
|
||||
|
||||
if e < 1e-5 {
|
||||
break
|
||||
}
|
||||
|
||||
// dnum := mat.NewVecDense(20, nil)
|
||||
// b0, b1 := true, true
|
||||
// dden := mat.NewVecDense(19, nil)
|
||||
// for i := 0; i < n; i++ {
|
||||
// dnum.SetVec(i, math.Abs(numerator.AtVec(i)-numerator0.AtVec(i)))
|
||||
// numerator0.SetVec(i, numerator.AtVec(i))
|
||||
// fmt.Println("dnum:", i, dnum.AtVec(i))
|
||||
// if dnum.AtVec(i) > 0.000001 {
|
||||
// b0 = false
|
||||
// break
|
||||
// }
|
||||
// }
|
||||
// for i := 1; i < n; i++ {
|
||||
// dden.SetVec(i, math.Abs(denominator.AtVec(i)-denominator0.AtVec(i)))
|
||||
// denominator0.SetVec(i, denominator.AtVec(i))
|
||||
// if dden.AtVec(i) > 0.000001 {
|
||||
// b1 = false
|
||||
// break
|
||||
// }
|
||||
// }
|
||||
|
||||
// if b0 && b1 {
|
||||
// break
|
||||
// }
|
||||
}
|
||||
|
||||
log.Println("iterations:", iterations)
|
||||
|
||||
return mat.Col(nil, 0, &x), nil
|
||||
}
|
||||
|
||||
func setupSystemOfEquations(Rn, latVec, lonVec, heightVec *mat.VecDense) *mat.Dense {
|
||||
n := latVec.Len()
|
||||
// 设计矩阵 B = [ 20个分子系数 19个分母系数 ]
|
||||
B := mat.NewDense(n, 39, nil)
|
||||
for i := 0; i < n; i++ {
|
||||
P := latVec.AtVec(i)
|
||||
L := lonVec.AtVec(i)
|
||||
H := heightVec.AtVec(i)
|
||||
r := Rn.AtVec(i)
|
||||
|
||||
B.Set(i, 0, 1)
|
||||
B.Set(i, 1, L)
|
||||
B.Set(i, 2, P)
|
||||
B.Set(i, 3, H)
|
||||
B.Set(i, 4, L*P)
|
||||
B.Set(i, 5, L*H)
|
||||
B.Set(i, 6, P*H)
|
||||
B.Set(i, 7, L*L)
|
||||
B.Set(i, 8, P*P)
|
||||
B.Set(i, 9, H*H)
|
||||
B.Set(i, 10, P*L*H)
|
||||
B.Set(i, 11, L*L*L)
|
||||
B.Set(i, 12, L*P*P)
|
||||
B.Set(i, 13, L*H*H)
|
||||
B.Set(i, 14, L*L*P)
|
||||
B.Set(i, 15, P*P*P)
|
||||
B.Set(i, 16, P*H*H)
|
||||
B.Set(i, 17, L*L*H)
|
||||
B.Set(i, 18, P*P*H)
|
||||
B.Set(i, 19, H*H*H)
|
||||
B.Set(i, 20, -L*r)
|
||||
B.Set(i, 21, -P*r)
|
||||
B.Set(i, 22, -H*r)
|
||||
B.Set(i, 23, -L*P*r)
|
||||
B.Set(i, 24, -L*H*r)
|
||||
B.Set(i, 25, -P*H*r)
|
||||
B.Set(i, 26, -L*L*r)
|
||||
B.Set(i, 27, -P*P*r)
|
||||
B.Set(i, 28, -H*H*r)
|
||||
B.Set(i, 29, -P*L*H*r)
|
||||
B.Set(i, 30, -L*L*L*r)
|
||||
B.Set(i, 31, -L*P*P*r)
|
||||
B.Set(i, 32, -L*H*H*r)
|
||||
B.Set(i, 33, -L*L*P*r)
|
||||
B.Set(i, 34, -P*P*P*r)
|
||||
B.Set(i, 35, -P*H*H*r)
|
||||
B.Set(i, 36, -L*L*H*r)
|
||||
B.Set(i, 37, -P*P*H*r)
|
||||
B.Set(i, 38, -H*H*H*r)
|
||||
}
|
||||
|
||||
return B
|
||||
}
|
||||
|
||||
// 构建权矩阵 [ 1/B ]
|
||||
func setupWeightMatrix(coeffs, latVec, lonVec, heightVec *mat.VecDense) *mat.DiagDense {
|
||||
n := latVec.Len()
|
||||
row := mat.NewDense(n, 20, nil)
|
||||
result := mat.NewDiagDense(n, nil)
|
||||
for i := 0; i < n; i++ {
|
||||
P := latVec.AtVec(i)
|
||||
L := lonVec.AtVec(i)
|
||||
H := heightVec.AtVec(i)
|
||||
|
||||
row.Set(i, 0, 1)
|
||||
row.Set(i, 1, L)
|
||||
row.Set(i, 2, P)
|
||||
row.Set(i, 3, H)
|
||||
row.Set(i, 4, L*P)
|
||||
row.Set(i, 5, L*H)
|
||||
row.Set(i, 6, P*H)
|
||||
row.Set(i, 7, L*L)
|
||||
row.Set(i, 8, P*P)
|
||||
row.Set(i, 9, H*H)
|
||||
row.Set(i, 10, P*L*H)
|
||||
row.Set(i, 11, L*L*L)
|
||||
row.Set(i, 12, L*P*P)
|
||||
row.Set(i, 13, L*H*H)
|
||||
row.Set(i, 14, L*L*P)
|
||||
row.Set(i, 15, P*P*P)
|
||||
row.Set(i, 16, P*H*H)
|
||||
row.Set(i, 17, L*L*H)
|
||||
row.Set(i, 18, P*P*H)
|
||||
row.Set(i, 19, H*H*H)
|
||||
|
||||
var B float64
|
||||
for idx2 := 0; idx2 < 20; idx2++ {
|
||||
B += coeffs.AtVec(idx2) * row.At(i, idx2)
|
||||
}
|
||||
|
||||
result.SetDiag(i, 1/B)
|
||||
}
|
||||
|
||||
return result
|
||||
}
|
||||
|
||||
func invertRPCMatrix(At *mat.Dense) (*mat.Dense, error) {
|
||||
var AtInv mat.Dense
|
||||
err := AtInv.Inverse(At)
|
||||
|
||||
if err != nil {
|
||||
// 岭估计方法调整法方程状态，使得矩阵非奇异，最小二乘平差可以收敛
|
||||
r, c := At.Dims()
|
||||
log.Infof("cannot inverse matrix(%d*%d): %v", r, c, err)
|
||||
k := 0.0000001 // [0.00000005, 0.000005]
|
||||
log.Infof("try to adjust matrix with +kI, k=%.8f", k)
|
||||
I := mat.NewDiagDense(r, nil)
|
||||
for i := 0; i < r; i++ {
|
||||
I.SetDiag(i, k)
|
||||
}
|
||||
At.Add(At, I)
|
||||
|
||||
err = AtInv.Inverse(At)
|
||||
}
|
||||
|
||||
if err != nil {
|
||||
log.Infof("cannot inverse matrix: %v, try SVD method", err)
|
||||
// 计算矩阵的 SVD 分解
|
||||
var svd mat.SVD
|
||||
ok := svd.Factorize(At, mat.SVDThin)
|
||||
if !ok {
|
||||
fmt.Println("SVD 分解失败")
|
||||
return nil, fmt.Errorf("设计矩阵不可逆, SVD 分解失败: %v", err)
|
||||
}
|
||||
|
||||
// 获取 U、Σ 和 V^T
|
||||
var u, v mat.Dense
|
||||
svd.UTo(&u)
|
||||
svd.VTo(&v)
|
||||
sigma := svd.Values(nil)
|
||||
|
||||
// 计算 Σ^+ (Sigma pseudo-inverse)
|
||||
m, n := u.Dims()
|
||||
sigmaInv := mat.NewDense(n, m, nil)
|
||||
for i := 0; i < len(sigma); i++ {
|
||||
if sigma[i] > 1e-10 { // 避免除以零
|
||||
sigmaInv.Set(i, i, 1/sigma[i])
|
||||
}
|
||||
}
|
||||
|
||||
// 计算 V * Σ^+ * U^T
|
||||
var temp mat.Dense
|
||||
temp.Mul(&v, sigmaInv)
|
||||
AtInv.Mul(&temp, u.T())
|
||||
}
|
||||
|
||||
return &AtInv, nil
|
||||
}
|
||||
|
||||
// SolveNormalEquation 使用正规方程法求解最小二乘问题
|
||||
func SolveNormalEquation(A *mat.Dense, b *mat.VecDense) ([]float64, error) {
|
||||
var At mat.Dense
|
||||
At.Mul(A.T(), A) // At = A^T * A
|
||||
|
||||
// 求解 (A^T * A)^-1 * (A^T * b)
|
||||
var AtInv mat.Dense
|
||||
err := AtInv.Inverse(&At)
|
||||
|
||||
if err != nil {
|
||||
// 岭估计方法调整法方程状态，使得矩阵非奇异，最小二乘平差可以收敛
|
||||
r, c := At.Dims()
|
||||
log.Infof("cannot inverse design matrix(%d*%d): %v", r, c, err)
|
||||
log.Info("try to adjust design matrix with +kI, k=0.0000001")
|
||||
k := 0.0000001 // [0.00000005, 0.000005]
|
||||
I := mat.NewDiagDense(r, nil)
|
||||
for i := 0; i < r; i++ {
|
||||
I.SetDiag(i, k)
|
||||
}
|
||||
At.Add(&At, I)
|
||||
|
||||
err = AtInv.Inverse(&At)
|
||||
}
|
||||
|
||||
if err != nil {
|
||||
log.Infof("cannot inverse design matrix: %v, try SVD method", err)
|
||||
// 计算矩阵的 SVD 分解
|
||||
var svd mat.SVD
|
||||
ok := svd.Factorize(&At, mat.SVDThin)
|
||||
if !ok {
|
||||
fmt.Println("SVD 分解失败")
|
||||
return nil, fmt.Errorf("设计矩阵不可逆, SVD 分解失败: %v", err)
|
||||
}
|
||||
|
||||
// 获取 U、Σ 和 V^T
|
||||
var u, v mat.Dense
|
||||
svd.UTo(&u)
|
||||
svd.VTo(&v)
|
||||
sigma := svd.Values(nil)
|
||||
|
||||
// 计算 Σ^+ (Sigma pseudo-inverse)
|
||||
m, n := u.Dims()
|
||||
sigmaInv := mat.NewDense(n, m, nil)
|
||||
for i := 0; i < len(sigma); i++ {
|
||||
if sigma[i] > 1e-10 { // 避免除以零
|
||||
sigmaInv.Set(i, i, 1/sigma[i])
|
||||
}
|
||||
}
|
||||
|
||||
// 计算 V * Σ^+ * U^T
|
||||
var temp mat.Dense
|
||||
temp.Mul(&v, sigmaInv)
|
||||
AtInv.Mul(&temp, u.T())
|
||||
}
|
||||
|
||||
var Atb mat.VecDense
|
||||
Atb.MulVec(A.T(), b) // Atb = A^T * b
|
||||
|
||||
var x mat.VecDense
|
||||
x.MulVec(&AtInv, &Atb) // x = (A^T * A)^-1 * (A^T * b)
|
||||
|
||||
return mat.Col(nil, 0, &x), nil
|
||||
}
|
||||
|
||||
func localize(num, den *mat.VecDense, row, col float64) (P, L, H float64) {
|
||||
|
||||
return
|
||||
}
|
||||
|
||||
func project(num, den *mat.VecDense, P, L, H float64) (v float64) {
|
||||
v = applyPoly(num, P, L, H) / applyPoly(den, P, L, H)
|
||||
return v
|
||||
}
|
||||
|
||||
func applyPoly(poly *mat.VecDense,
|
||||
P, L, H float64) (v float64) {
|
||||
v = 0.0
|
||||
v += poly.AtVec(0)
|
||||
v += poly.AtVec(1) * L
|
||||
v += poly.AtVec(2) * P
|
||||
v += poly.AtVec(3) * H
|
||||
v += poly.AtVec(4) * L * P
|
||||
v += poly.AtVec(5) * L * H
|
||||
v += poly.AtVec(6) * P * H
|
||||
v += poly.AtVec(7) * L * L
|
||||
v += poly.AtVec(8) * P * P
|
||||
v += poly.AtVec(9) * H * H
|
||||
v += poly.AtVec(10) * P * L * H
|
||||
v += poly.AtVec(11) * L * L * L
|
||||
v += poly.AtVec(12) * L * P * P
|
||||
v += poly.AtVec(13) * L * H * H
|
||||
v += poly.AtVec(14) * L * L * P
|
||||
v += poly.AtVec(15) * P * P * P
|
||||
v += poly.AtVec(16) * P * H * H
|
||||
v += poly.AtVec(17) * L * L * H
|
||||
v += poly.AtVec(18) * P * P * H
|
||||
v += poly.AtVec(19) * H * H * H
|
||||
return v
|
||||
}
|
||||
Reference in New Issue
Block a user