Add convenience functions for inverse and solve

mat64/la/la_util.go

@@ -5,6 +5,10 @@
 
 package la
 
+import (
+	"github.com/gonum/matrix/mat64"
+)
+
 func min(a, b int) int {
 	if a < b {
 		return a
@@ -18,3 +22,31 @@ func max(a, b int) int {
 	}
 	return b
 }
+
+// Det returns the determinant of the matrix a.
+func Det(a mat64.Matrix) float64 {
+	lu, _, sign := LUD(mat64.DenseCopyOf(a))
+	return LUDet(lu, sign)
+}
+
+// Inverse returns the inverse or pseudoinverse of the matrix a.
+func Inverse(a mat64.Matrix) *mat64.Dense {
+	m, _ := a.Dims()
+	d := make([]float64, m*m)
+	for i := 0; i < m*m; i += m + 1 {
+		d[i] = 1
+	}
+	eye, _ := mat64.NewDense(m, m, d)
+	return Solve(a, eye)
+}
+
+// Solve returns a matrix x that satisfies ax = b.
+func Solve(a, b mat64.Matrix) (x *mat64.Dense) {
+	m, n := a.Dims()
+	if m == n {
+		lu, piv, _ := LUD(mat64.DenseCopyOf(a))
+		return LUSolve(lu, mat64.DenseCopyOf(b), piv)
+	}
+	qr, rDiag := QRD(mat64.DenseCopyOf(a))
+	return QRSolve(qr, mat64.DenseCopyOf(b), rDiag)
+}