added Gauss-Jordan

gallery/example2.pdf

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gallery/example3.typ

@@ -0,0 +1,27 @@
+#import "/src/lib.typ": *
+
+#let A = mat.mat(
+  (3, -3, -1, 2, -9),
+  (1, -1, 2, -1, -6),
+  (1, -1, 1, 1, -6),
+  (-1, 1, -1, -2, 7)
+)
+
+#let b = vec.vec(13, -6, 1, -3)
+
+#let A2 = mat.mul-row(A, 2, 3)
+#let A3 = mat.div-row(A, 1, 2)
+#let A4 = mat.add-row(A, 2, 3, f: 2)
+
+$
+  A = #mat.display(A) quad b = #vec.display(b)\
+  A_2 = #mat.display(A2)\
+  A_3 = #mat.display(A3)\
+  A_4 = #mat.display(A4)\
+$
+
+#let E = gauss.echelon(A)
+
+$
+  E = #mat.display(E)
+$

src/gauss.typ

@@ -0,0 +1,53 @@
+#import "mat.typ" as _mat
+
+#let find-next-non-null(mat, x: 0, start-y: 0) = {
+  for y in range(start-y, mat.h) {
+    if mat.rows.at(y).at(x) != 0 {
+      return y
+    }
+  }
+  return none
+}
+
+
+#let echelon(mat) = {
+  _mat._check(mat)
+  let dim = calc.min(mat.w, mat.h)
+  let mat = mat
+  
+  // Gauss
+  for i in range(dim) {
+    let pivot = mat.rows.at(i).at(i)
+
+    // Pivot != 0 -> divide to get 1
+    if pivot != 0 {
+      mat = _mat.div-row(mat, i, pivot)
+
+    } else {
+      let y = find-next-non-null(mat, x: i, start-y: i)
+      if y != none {
+        mat = _mat.add-row(mat, i, y, f: 1 / mat.rows.at(y).at(i))
+      }
+    }
+
+    // Make all rows below 0
+    for y in range(i + 1, mat.h) {
+      mat = _mat.add-row(mat, y, i, f: -mat.rows.at(y).at(i))
+    }
+  }
+
+  // Jordan
+  for y in range(dim) {
+    for x in range(y + 1, dim) {
+      mat = _mat.add-row(mat, y, x, f: -mat.rows.at(y).at(x))
+    }
+  }
+
+  return _mat.round(mat)
+}
+
+// solver = Solver(matrix, constants)
+// solver.solve()
+
+// gauss = Gaussificator(matrix, constants)
+// gauss.echelon()