From 3b998c060b31103df7e4e580c341b7bfb73c525f Mon Sep 17 00:00:00 2001
From: mehbark <terezi@pyrope.net>
Date: Sun, 15 Jan 2023 20:21:25 -0500
Subject: [PATCH] automation basically done

---
 src/matrix/auto.clj       | 38 +++++++++++++++++++++++++++++++++++---
 src/matrix/base.clj       | 10 +++++++++-
 src/matrix/core.clj       | 24 ++++++++++++++----------
 test/matrix/core_test.clj | 14 +++++++++++++-
 4 files changed, 71 insertions(+), 15 deletions(-)

diff --git a/src/matrix/auto.clj b/src/matrix/auto.clj
index 208b2c8..8aa96ac 100644
--- a/src/matrix/auto.clj
+++ b/src/matrix/auto.clj
@@ -35,18 +35,50 @@
           (for [y (range (inc col) (matrix-height m))]
             {:add-row col :times (- (at m col y)) :to-row y}))))
 
+; TODO: make-gaussian-eliminable, which swaps rows so that they can actually be gaussian-elim'd 
+
 (defn gaussian-elim
-  "Takes a matrix and returns the steps to put in the form
+  "Takes a matrix and returns the steps to put it in the form
    [[1 a ... | sum1]
     [0 1 ... | sum2]
     ...]
 
    Assumes a lot of things lol"
-  ([m]
-   (gaussian-elim m 0))
+  ([m] (gaussian-elim m 0))
   ([m col]
    (if (= col (matrix-height m))
      []
      (let [steps (gaussian-column m col)
            new   (apply-all-at-once m steps)]
        (concat steps (gaussian-elim new (inc col)))))))
+
+(defn back-sub-column
+  [m col]
+  (for [y (range 0 col)]
+    {:add-row col
+     :times   (- (at m col y))
+     :to-row  y}))
+
+; idea: clear backwards
+(defn back-sub
+  "Takes a gaussian-eliminated matrix and returns the steps to make the id matrix on the left side"
+  ([m] (back-sub m (dec (matrix-height m))))
+  ([m col]
+   (if (zero? col)
+     []
+     (let [steps (back-sub-column m col)
+           new   (apply-all-at-once m steps)]
+       (println new)
+       (concat steps (back-sub new (dec col)))))))
+
+(defn auto-steps-and-final
+  [m]
+  (let [g-elim-steps (gaussian-elim m)
+        after-g-elim (apply-all-at-once m g-elim-steps)
+        bsub-steps   (back-sub after-g-elim)
+        after-bsub   (apply-all-at-once after-g-elim bsub-steps)]
+    [(concat g-elim-steps bsub-steps)
+     after-bsub]))
+
+(def auto-steps (comp first auto-steps-and-final))
+(def auto-final (comp last  auto-steps-and-final))
diff --git a/src/matrix/base.clj b/src/matrix/base.clj
index ff3c7dc..b8aad46 100644
--- a/src/matrix/base.clj
+++ b/src/matrix/base.clj
@@ -3,7 +3,7 @@
 
 (defn to-vec
   [v]
-  (apply vector v))
+  (into [] v))
 
 (defn swap-rows
   "Swap rows n and m of the given matrix, 0-indexed"
@@ -105,3 +105,11 @@
   "Returns the number at x y in a matrix"
   [m x y]
   (get (get m y) x))
+
+(defn map-matrix
+  ([f] #(map-matrix f %))
+  ([f m]
+   (->> m
+        (map #(map f %))
+        (map to-vec)
+        to-vec)))
diff --git a/src/matrix/core.clj b/src/matrix/core.clj
index c7daa86..8bcb5ef 100644
--- a/src/matrix/core.clj
+++ b/src/matrix/core.clj
@@ -1,24 +1,28 @@
 (ns matrix.core
-  (:require [matrix.base        :refer :all])
+  (:require [clojure.string :as str]
+            [matrix.base        :refer :all])
   (:require [matrix.interactive :refer :all])
   (:require [matrix.auto        :refer :all])
+  (:require [matrix.render      :refer :all])
   (:gen-class))
 
 (defn -main
   "I don't do a whole lot ... yet."
   [& args]
-  (let [got (read)]
-    (-> (if (number? got)
-          (id-matrix got)
-          got)
-        matrix-repl
-        last)))
+  (let [[steps final] (auto-steps-and-final (read))]
+    (println "Steps:")
+    ;; (for [step steps]
+    ;;   (println (pretty-row-op step)))
+    (println (str/join "\n" (map pretty-row-op steps)))
+    (println "Final:")
+    (pprint-matrix final)))
 
 ; TODO: actual parsing of row operations
 ; TODO: parse equations (easy, but requires context (e.g. x = 1 could be any number of variables))
 ; TODO: undoing
   ; will have to have a higher level thing for storing state
   ; use a set for options on the higher-level thing #{:show-equations? :show-bar? :color?}
-; TODO: solving id-matrix
-; TODO: solving gaussian-eliminated matrix
-; TODO: automation 
+; DONE: solving id-matrix
+; DONE: solving gaussian-eliminated matrix
+; DONE: automation 
+; TODO: remove redundant row ops
diff --git a/test/matrix/core_test.clj b/test/matrix/core_test.clj
index bab7d97..7a468da 100644
--- a/test/matrix/core_test.clj
+++ b/test/matrix/core_test.clj
@@ -1,6 +1,7 @@
 (ns matrix.core-test
   (:require [clojure.test :refer :all]
-            [matrix.base :refer :all]))
+            [matrix.base :refer :all]
+            [matrix.auto :refer :all]))
 
 ; TODO: more tests
 
@@ -15,3 +16,14 @@
   (testing "Multiplying by two 1x1 ident matrix"
     (let [mat (id-matrix 1)]
       (is (= [[2]] (mul-row mat 2 0))))))
+
+(deftest test-auto
+  (testing "1 variable equation"
+    (is (= [[1 10]] (auto-final [[2 20]]))))
+  (testing "2 variable equation"
+    (is (= [[1 0 3]
+            [0 1 3]]
+           (map-matrix int
+                       (auto-final
+                        [[2  3 15]
+                         [1 -1  0]]))))))