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Pawel Sarkowicz
2026-03-31 16:05:58 -04:00
parent f81d01fe52
commit 290e8bc3e6
6 changed files with 134 additions and 1241 deletions
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238
notebooks/02_qr_svd.ipynb
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@@ -53,7 +53,7 @@
},
{
"cell_type": "code",
"execution_count": 2,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -78,34 +78,10 @@
},
{
"cell_type": "code",
"execution_count": 11,
"execution_count": null,
"id": "b48e6d97",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"QA = [[ 1. 0. 0.]\n",
" [-0. 1. 0.]\n",
" [-0. -0. 1.]\n",
" [-0. -0. -0.]]\n",
"\n",
"RA = [[1. 1. 1.]\n",
" [0. 1. 1.]\n",
" [0. 0. 1.]]\n",
"\n",
"QB = [[-0.5 0.8660254 0. ]\n",
" [-0.5 -0.28867513 0.81649658]\n",
" [-0.5 -0.28867513 -0.40824829]\n",
" [-0.5 -0.28867513 -0.40824829]]\n",
"\n",
"RB = [[-2. -1.5 -1. ]\n",
" [ 0. -0.8660254 -0.57735027]\n",
" [ 0. 0. -0.81649658]]\n"
]
}
],
"outputs": [],
"source": [
"print(f\"QA = {QA}\\n\")\n",
"print(f\"RA = {RA}\\n\")\n",
@@ -144,7 +120,7 @@
},
{
"cell_type": "code",
"execution_count": 12,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -171,23 +147,10 @@
},
{
"cell_type": "code",
"execution_count": 13,
"execution_count": null,
"id": "3f71de8a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1.00000000e+00],\n",
" [ 6.40987562e-17],\n",
" [-5.00000000e-01]])"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"outputs": [],
"source": [
"beta"
]
@@ -202,23 +165,10 @@
},
{
"cell_type": "code",
"execution_count": 14,
"execution_count": null,
"id": "dcda7f8d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1.00000000e+00],\n",
" [ 2.22044605e-16],\n",
" [-5.00000000e-01]])"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"outputs": [],
"source": [
"np.linalg.lstsq(A,b)[0]"
]
@@ -236,7 +186,7 @@
},
{
"cell_type": "code",
"execution_count": 15,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -278,30 +228,10 @@
},
{
"cell_type": "code",
"execution_count": 18,
"execution_count": null,
"id": "3d1e5bab",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Q = [[-0.4472136 0.32838365 0.40496317]\n",
" [-0.4472136 -0.63745061 -0.22042299]\n",
" [-0.4472136 0.42496708 -0.7689174 ]\n",
" [-0.4472136 0.32838365 0.40496317]\n",
" [-0.4472136 -0.44428376 0.17941406]] \n",
"\n",
"R = [[-2.23606798e+00 -3.95784032e+03 -7.15541753e+00]\n",
" [ 0.00000000e+00 -5.17687164e+02 -1.50670145e+00]\n",
" [ 0.00000000e+00 0.00000000e+00 7.27908474e-01]] \n",
"\n",
"beta = [[-3.05053797e-13]\n",
" [ 3.00000000e-01]\n",
" [ 5.00000000e+00]]\n"
]
}
],
"outputs": [],
"source": [
"print(f\"Q = {Q} \\n\\nR = {R} \\n\\nbeta = {beta}\")"
]
@@ -334,7 +264,7 @@
},
{
"cell_type": "code",
"execution_count": 19,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -352,24 +282,10 @@
},
{
"cell_type": "code",
"execution_count": 20,
"execution_count": null,
"id": "5bfd7362",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1.00000000e+00, 2.89687929e-17, 2.89687929e-17, 2.89687929e-17],\n",
" [2.89687929e-17, 1.00000000e+00, 7.07349921e-17, 7.07349921e-17],\n",
" [2.89687929e-17, 7.07349921e-17, 5.00000000e-01, 5.00000000e-01],\n",
" [2.89687929e-17, 7.07349921e-17, 5.00000000e-01, 5.00000000e-01]])"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"outputs": [],
"source": [
"P"
]
@@ -486,7 +402,7 @@
},
{
"cell_type": "code",
"execution_count": 22,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -509,25 +425,10 @@
},
{
"cell_type": "code",
"execution_count": 23,
"execution_count": null,
"id": "5336313f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"U = [[-0.70710678 -0.70710678]\n",
" [-0.70710678 0.70710678]]\n",
"\n",
"S = [5. 3.]\n",
"\n",
"Vh.T = [[-7.07106781e-01 -2.35702260e-01 -6.66666667e-01]\n",
" [-7.07106781e-01 2.35702260e-01 6.66666667e-01]\n",
" [-6.47932334e-17 -9.42809042e-01 3.33333333e-01]]\n"
]
}
],
"outputs": [],
"source": [
"print(f\"U = {U}\\n\\nS = {S}\\n\\nVh.T = {Vh.T}\")"
]
@@ -547,7 +448,7 @@
},
{
"cell_type": "code",
"execution_count": 24,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -572,38 +473,10 @@
},
{
"cell_type": "code",
"execution_count": 25,
"execution_count": null,
"id": "a13a3391",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"U_A = [[ 0.73697623 0.59100905 0.32798528 0. ]\n",
" [ 0.59100905 -0.32798528 -0.73697623 0. ]\n",
" [ 0.32798528 -0.73697623 0.59100905 0. ]\n",
" [ 0. 0. 0. 1. ]]\n",
"\n",
"S_A = [2.2469796 0.80193774 0.55495813]\n",
"\n",
"Vh_A.T = [[ 0.32798528 0.73697623 0.59100905]\n",
" [ 0.59100905 0.32798528 -0.73697623]\n",
" [ 0.73697623 -0.59100905 0.32798528]]\n",
"\n",
"U_B = [[-2.41816250e-01 7.12015746e-01 -6.59210496e-01 0.00000000e+00]\n",
" [-4.52990541e-01 5.17957311e-01 7.25616837e-01 6.71536163e-17]\n",
" [-6.06763739e-01 -3.35226641e-01 -1.39502200e-01 -7.07106781e-01]\n",
" [-6.06763739e-01 -3.35226641e-01 -1.39502200e-01 7.07106781e-01]]\n",
"\n",
"S_B = [2.8092118 0.88646771 0.56789441]\n",
"\n",
"Vh_B.T = [[-0.67931306 0.63117897 -0.37436195]\n",
" [-0.59323331 -0.17202654 0.7864357 ]\n",
" [-0.43198148 -0.75632002 -0.49129626]]\n"
]
}
],
"outputs": [],
"source": [
"print(f\"U_A = {U_A}\\n\\nS_A = {S_A}\\n\\nVh_A.T = {Vh_A.T}\\n\\nU_B = {U_B}\\n\\nS_B = {S_B}\\n\\nVh_B.T = {Vh_B.T}\")"
]
@@ -663,7 +536,7 @@
},
{
"cell_type": "code",
"execution_count": 26,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -700,23 +573,10 @@
},
{
"cell_type": "code",
"execution_count": 27,
"execution_count": null,
"id": "862ed810",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 2.74080345e+15],\n",
" [ 2.74080345e+15],\n",
" [-2.74080345e+15]])"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"outputs": [],
"source": [
"beta"
]
@@ -731,21 +591,10 @@
},
{
"cell_type": "code",
"execution_count": 28,
"execution_count": null,
"id": "2d3df55d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([3.00000000e+00, 1.00000000e+00, 1.21618839e-16])"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"outputs": [],
"source": [
"S"
]
@@ -761,7 +610,7 @@
},
{
"cell_type": "code",
"execution_count": 29,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -780,24 +629,10 @@
},
{
"cell_type": "code",
"execution_count": 31,
"execution_count": null,
"id": "2657ea4b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A_pinv=[[ 0.11111111 -0.44444444 0.55555556 0. ]\n",
" [ 0.11111111 0.55555556 -0.44444444 0. ]\n",
" [ 0.22222222 0.11111111 0.11111111 0. ]]\n",
"\n",
"beta=[[0.22222222]\n",
" [0.22222222]\n",
" [0.44444444]]\n"
]
}
],
"outputs": [],
"source": [
"print(f\"A_pinv={A_pinv}\\n\\nbeta={beta}\")"
]
@@ -827,7 +662,7 @@
},
{
"cell_type": "code",
"execution_count": 32,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -862,21 +697,10 @@
},
{
"cell_type": "code",
"execution_count": 33,
"execution_count": null,
"id": "8aa6bca9",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"np.float64(4329.082589067693)"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"outputs": [],
"source": [
"cond_X"
]