Merge pull request #1 from johanneslatzel/main

Rework of repository

Author: PBrdng

.gitignore

@@ -0,0 +1 @@
+.vscode

Julia Exercises/01_Ex4b.ipynb

@@ -3,6 +3,18 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "cdc2b6fb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "using Pkg\n",
+    "Pkg.activate(joinpath(dirname(pwd()), \"conf\", \"01_Ex4b\"))\n",
+    "Pkg.instantiate();"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
    "id": "42be4586",
    "metadata": {},
    "outputs": [],
@@ -12,12 +24,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 4,
    "id": "cc1ff067",
    "metadata": {
     "scrolled": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "3×2 Matrix{Float64}:\n",
+       "  1.0  -0.5\n",
+       "  0.0   0.0\n",
+       " -2.0   1.0"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "A = [1 -1/2; 0 0; -2 1]"
    ]
@@ -32,17 +57,40 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 5,
    "id": "938a0cfb",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "SVD{Float64, Float64, Matrix{Float64}, Vector{Float64}}\n",
+       "U factor:\n",
+       "3×2 Matrix{Float64}:\n",
+       " -0.447214  -0.894427\n",
+       "  0.0        0.0\n",
+       "  0.894427  -0.447214\n",
+       "singular values:\n",
+       "2-element Vector{Float64}:\n",
+       " 2.5000000000000004\n",
+       " 9.930136612989092e-17\n",
+       "Vt factor:\n",
+       "2×2 Matrix{Float64}:\n",
+       " -0.894427   0.447214\n",
+       " -0.447214  -0.894427"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "(U,S,Vt) = svd(A)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 6,
    "id": "6ecb1c61",
    "metadata": {},
    "outputs": [],
@@ -54,20 +102,44 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 7,
    "id": "da17abd5",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2×3 Matrix{Float64}:\n",
+       "  0.16  0.0  -0.32\n",
+       " -0.08  0.0   0.16"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "pinvA = pinv(A)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 8,
    "id": "f5df81eb",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2×3 Matrix{Float64}:\n",
+       " -4.02814e15  0.0  -2.01407e15\n",
+       "  8.05628e15  0.0   4.02814e15"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "bad_pinvA = V * Σ^(-1) * Ut"
    ]
@@ -82,36 +154,60 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 9,
    "id": "b6a999b1",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2×3 Matrix{Float64}:\n",
+       "  0.16  0.0  -0.32\n",
+       " -0.08  0.0   0.16"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "pinv(A, rtol=1e-16)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 10,
    "id": "811e8e05",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2×3 Matrix{Float64}:\n",
+       " 4.02814e15  0.0  2.01407e15\n",
+       " 8.05628e15  0.0  4.02814e15"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "pinv(A, rtol=1e-17)"
    ]
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Julia 1.7.2",
+   "display_name": "Julia 1.11.4",
    "language": "julia",
-   "name": "julia-1.7"
+   "name": "julia-1.11"
   },
   "language_info": {
    "file_extension": ".jl",
    "mimetype": "application/julia",
    "name": "julia",
-   "version": "1.7.2"
+   "version": "1.11.4"
   }
  },
  "nbformat": 4,