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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.214922Z",
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}
},
"outputs": [],
"source": [
"import numpy as np\n",
"from numpy.linalg import eig\n",
"from numpy import matrix\n",
"import sympy as sy\n",
"import mpmath\n",
"from sympy import *\n",
"from mpmath import *\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.221870Z",
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"shell.execute_reply.started": "2021-10-07T06:52:24.221812Z"
}
},
"outputs": [],
"source": [
"x=sy.Symbol('x')\n",
"y=sy.Symbol('y')\n",
"z=sy.Symbol('z')"
]
},
{
"cell_type": "markdown",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-05T07:32:12.720671Z",
"iopub.status.busy": "2021-10-05T07:32:12.720204Z",
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"shell.execute_reply.started": "2021-10-05T07:32:12.720628Z"
}
},
"source": [
"**Lets define a Matrix** "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.236323Z",
"iopub.status.busy": "2021-10-07T06:52:24.235736Z",
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}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}1 & 2\\\\9 & 4\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[1, 2],\n",
"[9, 4]])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a= sy.Matrix(2,2,[1,2,9,4])\n",
"a"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.250628Z",
"iopub.status.busy": "2021-10-07T06:52:24.250254Z",
"iopub.status.idle": "2021-10-07T06:52:24.263720Z",
"shell.execute_reply": "2021-10-07T06:52:24.262482Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.250560Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}1 & 2\\\\1 & 1\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[1, 2],\n",
"[1, 1]])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"b = sy.Matrix( [ [1,2] , [1,1] ] )\n",
"b"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.265779Z",
"iopub.status.busy": "2021-10-07T06:52:24.265417Z",
"iopub.status.idle": "2021-10-07T06:52:24.280015Z",
"shell.execute_reply": "2021-10-07T06:52:24.279161Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.265711Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}3 & 1 & -1\\\\2 & 2 & -1\\\\2 & 2 & 0\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[3, 1, -1],\n",
"[2, 2, -1],\n",
"[2, 2, 0]])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m = sy.Matrix(3,3,[3,1,-1,2,2,-1,2,2,0])\n",
"m"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Lets do some basic Matrix operations**\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.283417Z",
"iopub.status.busy": "2021-10-07T06:52:24.282643Z",
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"shell.execute_reply.started": "2021-10-07T06:52:24.283357Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}2 & 4\\\\10 & 5\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[ 2, 4],\n",
"[10, 5]])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a + b"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.294375Z",
"iopub.status.busy": "2021-10-07T06:52:24.294092Z",
"iopub.status.idle": "2021-10-07T06:52:24.306825Z",
"shell.execute_reply": "2021-10-07T06:52:24.306082Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.294298Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}3 & 4\\\\13 & 22\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[ 3, 4],\n",
"[13, 22]])"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a*b # this ai * bj"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**inverse**"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.308526Z",
"iopub.status.busy": "2021-10-07T06:52:24.308095Z",
"iopub.status.idle": "2021-10-07T06:52:24.323283Z",
"shell.execute_reply": "2021-10-07T06:52:24.322431Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.308465Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}- \\frac{2}{7} & \\frac{1}{7}\\\\\\frac{9}{14} & - \\frac{1}{14}\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[-2/7, 1/7],\n",
"[9/14, -1/14]])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a**-1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**transpose**"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.325020Z",
"iopub.status.busy": "2021-10-07T06:52:24.324567Z",
"iopub.status.idle": "2021-10-07T06:52:24.335774Z",
"shell.execute_reply": "2021-10-07T06:52:24.334920Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.324980Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}1 & 9\\\\2 & 4\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[1, 9],\n",
"[2, 4]])"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a.T"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**identity matrix**"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.337431Z",
"iopub.status.busy": "2021-10-07T06:52:24.337016Z",
"iopub.status.idle": "2021-10-07T06:52:24.351792Z",
"shell.execute_reply": "2021-10-07T06:52:24.350998Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.337281Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0\\\\0 & 1 & 0\\\\0 & 0 & 1\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[1, 0, 0],\n",
"[0, 1, 0],\n",
"[0, 0, 1]])"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sy.eye(3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**diagonal matrix**"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.354994Z",
"iopub.status.busy": "2021-10-07T06:52:24.354432Z",
"iopub.status.idle": "2021-10-07T06:52:24.365365Z",
"shell.execute_reply": "2021-10-07T06:52:24.363954Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.354938Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0\\\\0 & 2 & 0\\\\0 & 0 & 3\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[1, 0, 0],\n",
"[0, 2, 0],\n",
"[0, 0, 3]])"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sy.diag(1,2,3)\n",
"#sy.diag(x+1,x+2,x+3) # diagonal matrix"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**determinant of matrix**"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.368737Z",
"iopub.status.busy": "2021-10-07T06:52:24.368319Z",
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"shell.execute_reply": "2021-10-07T06:52:24.377358Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.368679Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle -14$"
],
"text/plain": [
"-14"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sy.det(a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Find dot/inner product of a vector**"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.379824Z",
"iopub.status.busy": "2021-10-07T06:52:24.379373Z",
"iopub.status.idle": "2021-10-07T06:52:24.391822Z",
"shell.execute_reply": "2021-10-07T06:52:24.390586Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.379782Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle 1$"
],
"text/plain": [
"1"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a = sy.Matrix([3,4,-1])\n",
"b = sy.Matrix([2,-1,1])\n",
"\n",
"a.dot(b)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**find unit length of vectoer**"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.393956Z",
"iopub.status.busy": "2021-10-07T06:52:24.393524Z",
"iopub.status.idle": "2021-10-07T06:52:24.402002Z",
"shell.execute_reply": "2021-10-07T06:52:24.401301Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.393898Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle 2.44948974278318$"
],
"text/plain": [
"2.44948974278318"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def magnitude(vector) :\n",
" return sy.sqrt(vector.dot(vector))\n",
"magnitude(b).evalf()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Find angle bet 2 vectors**"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.403918Z",
"iopub.status.busy": "2021-10-07T06:52:24.403501Z",
"iopub.status.idle": "2021-10-07T06:52:24.412512Z",
"shell.execute_reply": "2021-10-07T06:52:24.411844Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.403864Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle 85.407751113661$"
],
"text/plain": [
"85.4077511136610"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"angle = sy.acos(a.dot(b) /(magnitude(a)*magnitude(b)) ).evalf()\n",
"angle*180/pi"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Orthogonality**"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.414273Z",
"iopub.status.busy": "2021-10-07T06:52:24.414023Z",
"iopub.status.idle": "2021-10-07T06:52:24.423988Z",
"shell.execute_reply": "2021-10-07T06:52:24.422686Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.414230Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a & b are not orthogonal sets in R\n"
]
}
],
"source": [
"if a.dot(b) == 0 :\n",
" if a.dot(a) == b.dot(b) == 1 :\n",
" print('a & b are orthonormal sets in R')\n",
" else :\n",
" print('a & b are not orthonormal sets in R')\n",
" print('But a & b are orthogonal sets in R')\n",
"else : \n",
" print('a & b are not orthogonal sets in R')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Linear Dependence / Independence**"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.426596Z",
"iopub.status.busy": "2021-10-07T06:52:24.425967Z",
"iopub.status.idle": "2021-10-07T06:52:24.434998Z",
"shell.execute_reply": "2021-10-07T06:52:24.434043Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.426268Z"
}
},
"outputs": [],
"source": [
"a = sy.Matrix([1,3,0])\n",
"b = sy.Matrix([2,0,1])\n",
"c = sy.Matrix([3,3,1])\n",
"\n",
"solve1 = x*a + y*b + z*c\n",
"\n",
"#L = sy.Matrix(sy.solve_poly_system ( [solve1[0] , solve1[1],solve1[2]], x, y,z))\n",
"#r,c = L.shape\n",
"\n",
"#if L == sy.zeros(r,c) :\n",
"# print('a,b,c are linearly independent')\n",
"#else :\n",
"# print('a,b,c are linearly dependent')\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.437110Z",
"iopub.status.busy": "2021-10-07T06:52:24.436581Z",
"iopub.status.idle": "2021-10-07T06:52:24.451973Z",
"shell.execute_reply": "2021-10-07T06:52:24.450766Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.437051Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}x + 2 y + 3 z\\\\3 x + 3 z\\\\y + z\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[x + 2*y + 3*z],\n",
"[ 3*x + 3*z],\n",
"[ y + z]])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"solve1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**find eigenvalue/vector**"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:04:26.813233Z",
"iopub.status.busy": "2021-10-07T07:04:26.812906Z",
"iopub.status.idle": "2021-10-07T07:04:26.823731Z",
"shell.execute_reply": "2021-10-07T07:04:26.822166Z",
"shell.execute_reply.started": "2021-10-07T07:04:26.813169Z"
}
},
"outputs": [],
"source": [
"M = sy.Matrix(4,3,[1,-1,2,2,3,4,-3,2,3,3,4,5])\n",
"m = M*M.T"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"execution": {
"iopub.status.busy": "2021-10-07T07:54:14.636935Z",
"iopub.status.idle": "2021-10-07T07:54:14.637626Z"
}
},
"outputs": [],
"source": [
"#q = m.eigenvects()\n",
"#for i in range(len(q)):\n",
"# print('Eigenvalue ', q[i][0].evalf() , ' has multiciplity ',q[i][1],' & eigenvector ',q[i][-1])"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:13:04.579873Z",
"iopub.status.busy": "2021-10-07T07:13:04.579502Z",
"iopub.status.idle": "2021-10-07T07:13:04.604246Z",
"shell.execute_reply": "2021-10-07T07:13:04.602748Z",
"shell.execute_reply.started": "2021-10-07T07:13:04.579817Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Eigenvalue 85.934903833959 - 0.e-20*I has multiciplity 1\n",
"Eigenvalue 4.03935299870572 + 0.e-21*I has multiciplity 1\n",
"Eigenvalue 17.0257431673353 - 0.e-21*I has multiciplity 1\n",
"Eigenvalue 0 has multiciplity 1\n"
]
}
],
"source": [
"p = m.eigenvals()\n",
"for key,value in p.items():\n",
" print('Eigenvalue ',key.evalf() ,' has multiciplity ' , value)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**OR**"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:46:43.166960Z",
"iopub.status.busy": "2021-10-07T07:46:43.166656Z",
"iopub.status.idle": "2021-10-07T07:46:43.177211Z",
"shell.execute_reply": "2021-10-07T07:46:43.175854Z",
"shell.execute_reply.started": "2021-10-07T07:46:43.166918Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"(array([ 8.59349038e+01, 1.70257432e+01, 4.03935300e+00, -2.10376436e-15]),\n",
" array([[-0.13910258, -0.17261518, -0.9737285 , 0.05203149],\n",
" [-0.5788883 , -0.10522179, 0.05825542, -0.80648807],\n",
" [-0.27605195, 0.95067628, -0.12561769, 0.06503936],\n",
" [-0.75454233, -0.23525938, 0.18077418, 0.58535425]]))"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A = np.array([[1,-1,2],[2,3,4],[-3,2,3],[3,4,5]])\n",
"a = np.matmul(A,A.T)\n",
"np.linalg.eig(a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**find characterploynomial**"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.496532Z",
"iopub.status.busy": "2021-10-07T06:52:24.495835Z",
"iopub.status.idle": "2021-10-07T06:52:24.512774Z",
"shell.execute_reply": "2021-10-07T06:52:24.511739Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.496270Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the character ploynomial is PurePoly(x**4 - 107*x**3 + 1879*x**2 - 5910*x, x, domain='ZZ')\n",
"the factors are \n"
]
},
{
"data": {
"text/latex": [
"$\\displaystyle x \\left(x^{3} - 107 x^{2} + 1879 x - 5910\\right)$"
],
"text/plain": [
"x*(x**3 - 107*x**2 + 1879*x - 5910)"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c = m.charpoly(x)\n",
"print('the character ploynomial is ',c)\n",
"\n",
"print('the factors are ')\n",
"sy.factor(c)"
]
},
{
"cell_type": "markdown",
"metadata": {
"execution": {
"iopub.execute_input": "2021-09-27T15:42:17.303606Z",
"iopub.status.busy": "2021-09-27T15:42:17.303325Z",
"iopub.status.idle": "2021-09-27T15:42:17.313166Z",
"shell.execute_reply": "2021-09-27T15:42:17.312216Z",
"shell.execute_reply.started": "2021-09-27T15:42:17.303555Z"
}
},
"source": [
"**Diagonalize a matrix**"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.514556Z",
"iopub.status.busy": "2021-10-07T06:52:24.514283Z",
"iopub.status.idle": "2021-10-07T06:52:24.578454Z",
"shell.execute_reply": "2021-10-07T06:52:24.577360Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.514510Z"
}
},
"outputs": [],
"source": [
"b = sy.Matrix( [ [1,2] , [1,1] ] )\n",
"(P,D) = b.diagonalize()"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.580516Z",
"iopub.status.busy": "2021-10-07T06:52:24.580139Z",
"iopub.status.idle": "2021-10-07T06:52:24.589141Z",
"shell.execute_reply": "2021-10-07T06:52:24.588022Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.580445Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}1 - \\sqrt{2} & 0\\\\0 & 1 + \\sqrt{2}\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[1 - sqrt(2), 0],\n",
"[ 0, 1 + sqrt(2)]])"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"D"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.591687Z",
"iopub.status.busy": "2021-10-07T06:52:24.591358Z",
"iopub.status.idle": "2021-10-07T06:52:24.600987Z",
"shell.execute_reply": "2021-10-07T06:52:24.599754Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.591646Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}- \\sqrt{2} & \\sqrt{2}\\\\1 & 1\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[-sqrt(2), sqrt(2)],\n",
"[ 1, 1]])"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"P"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.602661Z",
"iopub.status.busy": "2021-10-07T06:52:24.602320Z",
"iopub.status.idle": "2021-10-07T06:52:24.615890Z",
"shell.execute_reply": "2021-10-07T06:52:24.614571Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.602610Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"False"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"P**-1 * b * P == D"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Check if a matrix is diagonalizable**"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:44:57.922240Z",
"iopub.status.busy": "2021-10-07T07:44:57.921906Z",
"iopub.status.idle": "2021-10-07T07:44:57.929470Z",
"shell.execute_reply": "2021-10-07T07:44:57.928359Z",
"shell.execute_reply.started": "2021-10-07T07:44:57.922187Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m.is_diagonalizable()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**find singular value decomposition**"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:51:20.931238Z",
"iopub.status.busy": "2021-10-07T07:51:20.930834Z",
"iopub.status.idle": "2021-10-07T07:51:20.937585Z",
"shell.execute_reply": "2021-10-07T07:51:20.935870Z",
"shell.execute_reply.started": "2021-10-07T07:51:20.931175Z"
}
},
"outputs": [],
"source": [
"#A = np.array([[1,2],[3,4],[5,6],[7,8]])\n",
"U, S, V = np.linalg.svd(A)\n"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:51:25.353534Z",
"iopub.status.busy": "2021-10-07T07:51:25.353144Z",
"iopub.status.idle": "2021-10-07T07:51:25.358348Z",
"shell.execute_reply": "2021-10-07T07:51:25.357474Z",
"shell.execute_reply.started": "2021-10-07T07:51:25.353469Z"
}
},
"outputs": [],
"source": [
"r,c = A.shape"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:51:27.045817Z",
"iopub.status.busy": "2021-10-07T07:51:27.045243Z",
"iopub.status.idle": "2021-10-07T07:51:27.054849Z",
"shell.execute_reply": "2021-10-07T07:51:27.053519Z",
"shell.execute_reply.started": "2021-10-07T07:51:27.045749Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([[-0.13910258, 0.17261518, -0.9737285 , 0.05203149],\n",
" [-0.5788883 , 0.10522179, 0.05825542, -0.80648807],\n",
" [-0.27605195, -0.95067628, -0.12561769, 0.06503936],\n",
" [-0.75454233, 0.23525938, 0.18077418, 0.58535425]])"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"U"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:51:28.685691Z",
"iopub.status.busy": "2021-10-07T07:51:28.685300Z",
"iopub.status.idle": "2021-10-07T07:51:28.692505Z",
"shell.execute_reply": "2021-10-07T07:51:28.691822Z",
"shell.execute_reply.started": "2021-10-07T07:51:28.685636Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([[9.27010808, 0. , 0. ],\n",
" [0. , 4.12622626, 0. ],\n",
" [0. , 0. , 2.00981417],\n",
" [0. , 0. , 0. ]])"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"S \n",
"s = np.zeros((r, c))\n",
"np.fill_diagonal(s, S) #s = np.array([[14.2690955,0],[0,0.62682823],[0,0],[0,0]])\n",
"s"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:51:39.306340Z",
"iopub.status.busy": "2021-10-07T07:51:39.305840Z",
"iopub.status.idle": "2021-10-07T07:51:39.312474Z",
"shell.execute_reply": "2021-10-07T07:51:39.311594Z",
"shell.execute_reply.started": "2021-10-07T07:51:39.306284Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([[-0.29474849, -0.55747306, -0.77611025],\n",
" [ 0.95507747, -0.19806593, -0.22044705],\n",
" [ 0.03082771, 0.80622185, -0.5908096 ]])"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"V"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:51:40.677665Z",
"iopub.status.busy": "2021-10-07T07:51:40.677197Z",
"iopub.status.idle": "2021-10-07T07:51:40.684755Z",
"shell.execute_reply": "2021-10-07T07:51:40.683968Z",
"shell.execute_reply.started": "2021-10-07T07:51:40.677600Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1., -1., 2.],\n",
" [ 2., 3., 4.],\n",
" [-3., 2., 3.],\n",
" [ 3., 4., 5.]])"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.matmul(np.matmul(U,s),V)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**hence proved U*S*V is A**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Find hessian of matrix**"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.746445Z",
"iopub.status.busy": "2021-10-07T06:52:24.746124Z",
"iopub.status.idle": "2021-10-07T06:52:24.753620Z",
"shell.execute_reply": "2021-10-07T06:52:24.752574Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.746392Z"
}
},
"outputs": [],
"source": [
"from sympy import hessian , Function , pprint"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.756625Z",
"iopub.status.busy": "2021-10-07T06:52:24.755997Z",
"iopub.status.idle": "2021-10-07T06:52:24.765530Z",
"shell.execute_reply": "2021-10-07T06:52:24.764452Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.756527Z"
}
},
"outputs": [],
"source": [
"f = Function('f')(x,y,z)\n",
"g1 = Function('g')(x,y,z)\n",
"g2 = sy.sin(x*y*z)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T06:52:24.767695Z",
"iopub.status.busy": "2021-10-07T06:52:24.767344Z",
"iopub.status.idle": "2021-10-07T06:52:24.808346Z",
"shell.execute_reply": "2021-10-07T06:52:24.807203Z",
"shell.execute_reply.started": "2021-10-07T06:52:24.767627Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}0 & 0 & \\frac{\\partial}{\\partial x} g{\\left(x,y,z \\right)} & \\frac{\\partial}{\\partial y} g{\\left(x,y,z \\right)} & \\frac{\\partial}{\\partial z} g{\\left(x,y,z \\right)}\\\\0 & 0 & y z \\cos{\\left(x y z \\right)} & x z \\cos{\\left(x y z \\right)} & x y \\cos{\\left(x y z \\right)}\\\\\\frac{\\partial}{\\partial x} g{\\left(x,y,z \\right)} & y z \\cos{\\left(x y z \\right)} & \\frac{\\partial^{2}}{\\partial x^{2}} f{\\left(x,y,z \\right)} & \\frac{\\partial^{2}}{\\partial y\\partial x} f{\\left(x,y,z \\right)} & \\frac{\\partial^{2}}{\\partial z\\partial x} f{\\left(x,y,z \\right)}\\\\\\frac{\\partial}{\\partial y} g{\\left(x,y,z \\right)} & x z \\cos{\\left(x y z \\right)} & \\frac{\\partial^{2}}{\\partial y\\partial x} f{\\left(x,y,z \\right)} & \\frac{\\partial^{2}}{\\partial y^{2}} f{\\left(x,y,z \\right)} & \\frac{\\partial^{2}}{\\partial z\\partial y} f{\\left(x,y,z \\right)}\\\\\\frac{\\partial}{\\partial z} g{\\left(x,y,z \\right)} & x y \\cos{\\left(x y z \\right)} & \\frac{\\partial^{2}}{\\partial z\\partial x} f{\\left(x,y,z \\right)} & \\frac{\\partial^{2}}{\\partial z\\partial y} f{\\left(x,y,z \\right)} & \\frac{\\partial^{2}}{\\partial z^{2}} f{\\left(x,y,z \\right)}\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[ 0, 0, Derivative(g(x, y, z), x), Derivative(g(x, y, z), y), Derivative(g(x, y, z), z)],\n",
"[ 0, 0, y*z*cos(x*y*z), x*z*cos(x*y*z), x*y*cos(x*y*z)],\n",
"[Derivative(g(x, y, z), x), y*z*cos(x*y*z), Derivative(f(x, y, z), (x, 2)), Derivative(f(x, y, z), x, y), Derivative(f(x, y, z), x, z)],\n",
"[Derivative(g(x, y, z), y), x*z*cos(x*y*z), Derivative(f(x, y, z), x, y), Derivative(f(x, y, z), (y, 2)), Derivative(f(x, y, z), y, z)],\n",
"[Derivative(g(x, y, z), z), x*y*cos(x*y*z), Derivative(f(x, y, z), x, z), Derivative(f(x, y, z), y, z), Derivative(f(x, y, z), (z, 2))]])"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"hessian(f,(x,y,z),[g1,g2])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.6"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
|
0076/528/76528856.ipynb
|
s3://data-agents/kaggle-outputs/sharded/018_00076.jsonl.gz
|
{
"cells": [
{
"cell_type": "markdown",
"id": "f8cd47c7",
"metadata": {
"_cell_guid": "af4252ad-f822-45d3-b9c2-f26af7608ef4",
"_uuid": "de34d146-4c69-4b7c-82f6-11d6287f6094",
"execution": {
"iopub.execute_input": "2021-10-07T06:47:44.152391Z",
"iopub.status.busy": "2021-10-07T06:47:44.152048Z",
"iopub.status.idle": "2021-10-07T06:47:44.18282Z",
"shell.execute_reply": "2021-10-07T06:47:44.182194Z",
"shell.execute_reply.started": "2021-10-07T06:47:44.152311Z"
},
"jupyter": {
"outputs_hidden": false
},
"papermill": {
"duration": 0.007756,
"end_time": "2021-10-07T07:58:11.138368",
"exception": false,
"start_time": "2021-10-07T07:58:11.130612",
"status": "completed"
},
"tags": []
},
"source": [
"## 문제1\n",
"- 데이터셋(basic1.csv)의 'f5' 컬럼을 기준으로 상위 10개의 데이터를 구하고,\n",
"- 'f5'컬럼 10개 중 최소값으로 데이터를 대체한 후, \n",
"- 'age'컬럼에서 80 이상인 데이터의'f5 컬럼 평균값 구하기"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "eb7b7db1",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:11.164660Z",
"iopub.status.busy": "2021-10-07T07:58:11.163756Z",
"iopub.status.idle": "2021-10-07T07:58:11.167623Z",
"shell.execute_reply": "2021-10-07T07:58:11.167021Z",
"shell.execute_reply.started": "2021-10-07T07:48:20.293391Z"
},
"papermill": {
"duration": 0.020766,
"end_time": "2021-10-07T07:58:11.167790",
"exception": false,
"start_time": "2021-10-07T07:58:11.147024",
"status": "completed"
},
"tags": []
},
"outputs": [],
"source": [
"# 라이브러리\n",
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "060280e8",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:11.185256Z",
"iopub.status.busy": "2021-10-07T07:58:11.184650Z",
"iopub.status.idle": "2021-10-07T07:58:11.240426Z",
"shell.execute_reply": "2021-10-07T07:58:11.240960Z",
"shell.execute_reply.started": "2021-10-07T07:48:20.578043Z"
},
"papermill": {
"duration": 0.066847,
"end_time": "2021-10-07T07:58:11.241133",
"exception": false,
"start_time": "2021-10-07T07:58:11.174286",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>id</th>\n",
" <th>age</th>\n",
" <th>city</th>\n",
" <th>f1</th>\n",
" <th>f2</th>\n",
" <th>f3</th>\n",
" <th>f4</th>\n",
" <th>f5</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>id01</td>\n",
" <td>2.0</td>\n",
" <td>서울</td>\n",
" <td>NaN</td>\n",
" <td>0</td>\n",
" <td>NaN</td>\n",
" <td>ENFJ</td>\n",
" <td>91.297791</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>id02</td>\n",
" <td>9.0</td>\n",
" <td>서울</td>\n",
" <td>70.0</td>\n",
" <td>1</td>\n",
" <td>NaN</td>\n",
" <td>ENFJ</td>\n",
" <td>60.339826</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>id03</td>\n",
" <td>27.0</td>\n",
" <td>서울</td>\n",
" <td>61.0</td>\n",
" <td>1</td>\n",
" <td>NaN</td>\n",
" <td>ISTJ</td>\n",
" <td>17.252986</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>id04</td>\n",
" <td>75.0</td>\n",
" <td>서울</td>\n",
" <td>NaN</td>\n",
" <td>2</td>\n",
" <td>NaN</td>\n",
" <td>INFP</td>\n",
" <td>52.667078</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>id05</td>\n",
" <td>24.0</td>\n",
" <td>서울</td>\n",
" <td>85.0</td>\n",
" <td>2</td>\n",
" <td>NaN</td>\n",
" <td>ISFJ</td>\n",
" <td>29.269869</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" id age city f1 f2 f3 f4 f5\n",
"0 id01 2.0 서울 NaN 0 NaN ENFJ 91.297791\n",
"1 id02 9.0 서울 70.0 1 NaN ENFJ 60.339826\n",
"2 id03 27.0 서울 61.0 1 NaN ISTJ 17.252986\n",
"3 id04 75.0 서울 NaN 2 NaN INFP 52.667078\n",
"4 id05 24.0 서울 85.0 2 NaN ISFJ 29.269869"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 데이터 불러오기\n",
"df = pd.read_csv('../input/bigdatacertificationkr/basic1.csv')\n",
"df.head()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "07da7f32",
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"start_time": "2021-10-07T07:58:11.248518",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"data": {
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" <td>NaN</td>\n",
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" <td>77.0</td>\n",
" <td>경기</td>\n",
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" <td>NaN</td>\n",
" <td>INFP</td>\n",
" <td>98.429899</td>\n",
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" <tr>\n",
" <th>98</th>\n",
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" <td>1.0</td>\n",
" <td>경기</td>\n",
" <td>47.0</td>\n",
" <td>0</td>\n",
" <td>NaN</td>\n",
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" <td>97.381034</td>\n",
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" <tr>\n",
" <th>91</th>\n",
" <td>id92</td>\n",
" <td>97.0</td>\n",
" <td>경기</td>\n",
" <td>78.0</td>\n",
" <td>1</td>\n",
" <td>NaN</td>\n",
" <td>INFP</td>\n",
" <td>97.381034</td>\n",
" </tr>\n",
" <tr>\n",
" <th>86</th>\n",
" <td>id87</td>\n",
" <td>19.0</td>\n",
" <td>경기</td>\n",
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" <td>NaN</td>\n",
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" <td>8.0</td>\n",
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" <tr>\n",
" <th>11</th>\n",
" <td>id12</td>\n",
" <td>20.0</td>\n",
" <td>서울</td>\n",
" <td>NaN</td>\n",
" <td>0</td>\n",
" <td>NaN</td>\n",
" <td>ESTP</td>\n",
" <td>91.297791</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>id20</td>\n",
" <td>11.0</td>\n",
" <td>서울</td>\n",
" <td>51.0</td>\n",
" <td>1</td>\n",
" <td>NaN</td>\n",
" <td>INTJ</td>\n",
" <td>91.297791</td>\n",
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],
"text/plain": [
" id age city f1 f2 f3 f4 f5\n",
"10 id11 40.0 서울 68.0 0 NaN ENFP 98.429899\n",
"97 id98 39.0 경기 58.0 2 NaN INFP 98.429899\n",
"9 id10 95.0 서울 74.0 1 NaN ISFP 98.429899\n",
"76 id77 77.0 경기 31.0 0 NaN INFP 98.429899\n",
"98 id99 1.0 경기 47.0 0 NaN ESFJ 97.381034\n",
"91 id92 97.0 경기 78.0 1 NaN INFP 97.381034\n",
"86 id87 19.0 경기 NaN 1 NaN ISFP 97.381034\n",
"71 id72 8.0 경기 97.0 0 NaN ESTJ 97.381034\n",
"11 id12 20.0 서울 NaN 0 NaN ESTP 91.297791\n",
"19 id20 11.0 서울 51.0 1 NaN INTJ 91.297791"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# f5컬럼을 기준으로 내림차순 정렬\n",
"df = df.sort_values('f5', ascending=False)\n",
"df.head(10)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "6eb3e173",
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"status": "completed"
},
"tags": []
},
"outputs": [
{
"data": {
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" <th>city</th>\n",
" <th>f1</th>\n",
" <th>f2</th>\n",
" <th>f3</th>\n",
" <th>f4</th>\n",
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" </tr>\n",
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" <tr>\n",
" <th>0</th>\n",
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" <th>3</th>\n",
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" <td>77.0</td>\n",
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" <td>31.0</td>\n",
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" <td>NaN</td>\n",
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" <td>98.429899</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>id99</td>\n",
" <td>1.0</td>\n",
" <td>경기</td>\n",
" <td>47.0</td>\n",
" <td>0</td>\n",
" <td>NaN</td>\n",
" <td>ESFJ</td>\n",
" <td>97.381034</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>id92</td>\n",
" <td>97.0</td>\n",
" <td>경기</td>\n",
" <td>78.0</td>\n",
" <td>1</td>\n",
" <td>NaN</td>\n",
" <td>INFP</td>\n",
" <td>97.381034</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>id87</td>\n",
" <td>19.0</td>\n",
" <td>경기</td>\n",
" <td>NaN</td>\n",
" <td>1</td>\n",
" <td>NaN</td>\n",
" <td>ISFP</td>\n",
" <td>97.381034</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>id72</td>\n",
" <td>8.0</td>\n",
" <td>경기</td>\n",
" <td>97.0</td>\n",
" <td>0</td>\n",
" <td>NaN</td>\n",
" <td>ESTJ</td>\n",
" <td>97.381034</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>id12</td>\n",
" <td>20.0</td>\n",
" <td>서울</td>\n",
" <td>NaN</td>\n",
" <td>0</td>\n",
" <td>NaN</td>\n",
" <td>ESTP</td>\n",
" <td>91.297791</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>id20</td>\n",
" <td>11.0</td>\n",
" <td>서울</td>\n",
" <td>51.0</td>\n",
" <td>1</td>\n",
" <td>NaN</td>\n",
" <td>INTJ</td>\n",
" <td>91.297791</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" id age city f1 f2 f3 f4 f5\n",
"0 id11 40.0 서울 68.0 0 NaN ENFP 98.429899\n",
"1 id98 39.0 경기 58.0 2 NaN INFP 98.429899\n",
"2 id10 95.0 서울 74.0 1 NaN ISFP 98.429899\n",
"3 id77 77.0 경기 31.0 0 NaN INFP 98.429899\n",
"4 id99 1.0 경기 47.0 0 NaN ESFJ 97.381034\n",
"5 id92 97.0 경기 78.0 1 NaN INFP 97.381034\n",
"6 id87 19.0 경기 NaN 1 NaN ISFP 97.381034\n",
"7 id72 8.0 경기 97.0 0 NaN ESTJ 97.381034\n",
"8 id12 20.0 서울 NaN 0 NaN ESTP 91.297791\n",
"9 id20 11.0 서울 51.0 1 NaN INTJ 91.297791"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 참고 - 인덱스 초기화\n",
"df = df.reset_index(drop=True)\n",
"df.head(10)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "7b024069",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:11.370039Z",
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"status": "completed"
},
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"91.29779092"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 최소값 찾기\n",
"min = df['f5'][:10].min()\n",
"# min = 91.297791\n",
"min"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "0970494a",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:11.399396Z",
"iopub.status.busy": "2021-10-07T07:58:11.398601Z",
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},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"63.07232761739131\n"
]
}
],
"source": [
"# 80세 이상의 f5컬럼 평균\n",
"print(df[df['age']>=80]['f5'].mean())"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
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}
|
0076/528/76528885.ipynb
|
s3://data-agents/kaggle-outputs/sharded/018_00076.jsonl.gz
|
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "992d5174",
"metadata": {
"_cell_guid": "b1076dfc-b9ad-4769-8c92-a6c4dae69d19",
"_uuid": "8f2839f25d086af736a60e9eeb907d3b93b6e0e5",
"execution": {
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"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"/kaggle/input/titanic/train.csv\n",
"/kaggle/input/titanic/test.csv\n",
"/kaggle/input/titanic/gender_submission.csv\n"
]
}
],
"source": [
"# This Python 3 environment comes with many helpful analytics libraries installed\n",
"# It is defined by the kaggle/python Docker image: https://github.com/kaggle/docker-python\n",
"# For example, here's several helpful packages to load\n",
"\n",
"import numpy as np # linear algebra\n",
"import pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)\n",
"\n",
"# Input data files are available in the read-only \"../input/\" directory\n",
"# For example, running this (by clicking run or pressing Shift+Enter) will list all files under the input directory\n",
"\n",
"import os\n",
"for dirname, _, filenames in os.walk('/kaggle/input'):\n",
" for filename in filenames:\n",
" print(os.path.join(dirname, filename))\n",
"\n",
"# You can write up to 20GB to the current directory (/kaggle/working/) that gets preserved as output when you create a version using \"Save & Run All\" \n",
"# You can also write temporary files to /kaggle/temp/, but they won't be saved outside of the current session"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "a013691a",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:48.184093Z",
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},
"tags": []
},
"outputs": [],
"source": [
"df_train = pd.read_csv(\"/kaggle/input/titanic/train.csv\")\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "ce94a037",
"metadata": {
"execution": {
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{
"data": {
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" <th>PassengerId</th>\n",
" <th>Survived</th>\n",
" <th>Pclass</th>\n",
" <th>Name</th>\n",
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" <td>35.0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
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" <td>C123</td>\n",
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" <td>Montvila, Rev. Juozas</td>\n",
" <td>male</td>\n",
" <td>27.0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>211536</td>\n",
" <td>13.0000</td>\n",
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" <th>887</th>\n",
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" <td>19.0</td>\n",
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" <td>0</td>\n",
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" <td>Behr, Mr. Karl Howell</td>\n",
" <td>male</td>\n",
" <td>26.0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
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"text/plain": [
" PassengerId Survived Pclass \\\n",
"0 1 0 3 \n",
"1 2 1 1 \n",
"2 3 1 3 \n",
"3 4 1 1 \n",
"4 5 0 3 \n",
".. ... ... ... \n",
"886 887 0 2 \n",
"887 888 1 1 \n",
"888 889 0 3 \n",
"889 890 1 1 \n",
"890 891 0 3 \n",
"\n",
" Name Sex Age SibSp \\\n",
"0 Braund, Mr. Owen Harris male 22.0 1 \n",
"1 Cumings, Mrs. John Bradley (Florence Briggs Th... female 38.0 1 \n",
"2 Heikkinen, Miss. Laina female 26.0 0 \n",
"3 Futrelle, Mrs. Jacques Heath (Lily May Peel) female 35.0 1 \n",
"4 Allen, Mr. William Henry male 35.0 0 \n",
".. ... ... ... ... \n",
"886 Montvila, Rev. Juozas male 27.0 0 \n",
"887 Graham, Miss. Margaret Edith female 19.0 0 \n",
"888 Johnston, Miss. Catherine Helen \"Carrie\" female NaN 1 \n",
"889 Behr, Mr. Karl Howell male 26.0 0 \n",
"890 Dooley, Mr. Patrick male 32.0 0 \n",
"\n",
" Parch Ticket Fare Cabin Embarked \n",
"0 0 A/5 21171 7.2500 NaN S \n",
"1 0 PC 17599 71.2833 C85 C \n",
"2 0 STON/O2. 3101282 7.9250 NaN S \n",
"3 0 113803 53.1000 C123 S \n",
"4 0 373450 8.0500 NaN S \n",
".. ... ... ... ... ... \n",
"886 0 211536 13.0000 NaN S \n",
"887 0 112053 30.0000 B42 S \n",
"888 2 W./C. 6607 23.4500 NaN S \n",
"889 0 111369 30.0000 C148 C \n",
"890 0 370376 7.7500 NaN Q \n",
"\n",
"[891 rows x 12 columns]"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df_train"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "a3bc3dd3",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:48.300309Z",
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"status": "completed"
},
"tags": []
},
"outputs": [],
"source": [
"df = df_train.copy()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "aec94879",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:48.333294Z",
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},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"30.62617924528302\n"
]
}
],
"source": [
"## 1.\tKazada ölenlerin yaş ortalamasını bulunuz\n",
"average_age = df.loc[df[\"Survived\"] == 0][\"Age\"].mean()\n",
"print(average_age)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "1996097e",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:48.373829Z",
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"shell.execute_reply.started": "2021-10-07T06:39:18.856226Z"
},
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"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"34.94558161648169 13.5\n"
]
}
],
"source": [
"## 2.\tKazada ölenlerin bilet fiyatlarının ortalamasını ve medyanını bulunuz\n",
"average_fare = df.loc[df[\"Age\"] > 15][\"Fare\"].mean()\n",
"median_fare = df.loc[df[\"Age\"] > 15][\"Fare\"].median() \n",
"print(average_fare, median_fare)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "bd9e29ad",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:48.416892Z",
"iopub.status.busy": "2021-10-07T07:58:48.416170Z",
"iopub.status.idle": "2021-10-07T07:58:48.420651Z",
"shell.execute_reply": "2021-10-07T07:58:48.421162Z",
"shell.execute_reply.started": "2021-10-07T06:43:08.820288Z"
},
"papermill": {
"duration": 0.024792,
"end_time": "2021-10-07T07:58:48.421346",
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"start_time": "2021-10-07T07:58:48.396554",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"31.618055555555557\n"
]
}
],
"source": [
"## 3.\tKazada ölen erkeklerin yaş ortalamasını bulunuz\n",
"average_male_age = df.loc[(df[\"Sex\"] == \"male\") & (df[\"Survived\"] == 0)][\"Age\"].mean()\n",
"print(average_male_age)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "c6c6796c",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:48.455733Z",
"iopub.status.busy": "2021-10-07T07:58:48.451560Z",
"iopub.status.idle": "2021-10-07T07:58:48.458366Z",
"shell.execute_reply": "2021-10-07T07:58:48.459001Z",
"shell.execute_reply.started": "2021-10-07T06:43:33.760068Z"
},
"papermill": {
"duration": 0.02398,
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"start_time": "2021-10-07T07:58:48.435193",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"25.046875\n"
]
}
],
"source": [
"## 4.\tKazada ölen Kadınların yaş ortalamasını bulunuz\n",
"average_female_age = df.loc[(df[\"Sex\"] == \"female\") & (df[\"Survived\"] == 0)][\"Age\"].mean()\n",
"print(average_female_age)\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "db1e517f",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:48.492218Z",
"iopub.status.busy": "2021-10-07T07:58:48.491578Z",
"iopub.status.idle": "2021-10-07T07:58:48.498319Z",
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"shell.execute_reply.started": "2021-10-07T06:44:27.494586Z"
},
"papermill": {
"duration": 0.02491,
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"start_time": "2021-10-07T07:58:48.474084",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"28.343689655172415\n"
]
}
],
"source": [
"## 5.\tKazadan kurtulanların yaş ortalamasını bulunuz\n",
"average_age = df.loc[df[\"Survived\"] == 1][\"Age\"].mean()\n",
"print(average_age)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "2081a228",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:48.536232Z",
"iopub.status.busy": "2021-10-07T07:58:48.535299Z",
"iopub.status.idle": "2021-10-07T07:58:48.539378Z",
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"shell.execute_reply.started": "2021-10-07T06:45:42.479088Z"
},
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"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"48.39540760233917\n"
]
}
],
"source": [
"## 6.\tKazadan kurtulanların bilet fiyatlarının ortalamasını bulunuz\n",
"average_fare_srv = df.loc[df[\"Survived\"]==1][\"Fare\"].mean()\n",
"print(average_fare_srv)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "a4e66451",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:48.573240Z",
"iopub.status.busy": "2021-10-07T07:58:48.572598Z",
"iopub.status.idle": "2021-10-07T07:58:48.579967Z",
"shell.execute_reply": "2021-10-07T07:58:48.579454Z",
"shell.execute_reply.started": "2021-10-07T06:48:36.828598Z"
},
"papermill": {
"duration": 0.024846,
"end_time": "2021-10-07T07:58:48.580107",
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"start_time": "2021-10-07T07:58:48.555261",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"342\n"
]
}
],
"source": [
"## 7.\tKazadan kurtulan toplam kişi sayısını bulunuz… \n",
"survived = len(df.loc[df[\"Survived\"]==1])\n",
"print(survived)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "dcca28d6",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:48.617812Z",
"iopub.status.busy": "2021-10-07T07:58:48.616278Z",
"iopub.status.idle": "2021-10-07T07:58:48.621082Z",
"shell.execute_reply": "2021-10-07T07:58:48.621493Z",
"shell.execute_reply.started": "2021-10-07T06:49:41.264858Z"
},
"papermill": {
"duration": 0.026527,
"end_time": "2021-10-07T07:58:48.621662",
"exception": false,
"start_time": "2021-10-07T07:58:48.595135",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"13.92915\n"
]
}
],
"source": [
"## 8.\t10 yaşından küçüklerin bilet fiyatlarının medyan değerini bulunuz\n",
"\n",
"blw_ten = df.loc[df[\"Age\"] > 10][\"Fare\"].median()\n",
"print(blw_ten)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "7dd8bace",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:48.663355Z",
"iopub.status.busy": "2021-10-07T07:58:48.662132Z",
"iopub.status.idle": "2021-10-07T07:58:48.672707Z",
"shell.execute_reply": "2021-10-07T07:58:48.671961Z",
"shell.execute_reply.started": "2021-10-07T06:54:52.961382Z"
},
"papermill": {
"duration": 0.035896,
"end_time": "2021-10-07T07:58:48.672924",
"exception": false,
"start_time": "2021-10-07T07:58:48.637028",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Pclass\n",
"1 84.154687\n",
"2 20.662183\n",
"3 13.675550\n",
"Name: Fare, dtype: float64 Pclass\n",
"1 60.2875\n",
"2 14.2500\n",
"3 8.0500\n",
"Name: Fare, dtype: float64\n"
]
}
],
"source": [
"## 9.\t1.sınıf, 2.sınıf ve 3.sınıf bilet fiyatlarının ortalama ve medyanlarını karşılaştırınız.\n",
"\n",
"price_comp_mean = df.groupby(\"Pclass\")[\"Fare\"].mean()\n",
"price_comp_median = df.groupby(\"Pclass\")[\"Fare\"].median()\n",
"\n",
"print(price_comp_mean, price_comp_median)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "ae45bb6d",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:48.717774Z",
"iopub.status.busy": "2021-10-07T07:58:48.716844Z",
"iopub.status.idle": "2021-10-07T07:58:48.720813Z",
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"shell.execute_reply.started": "2021-10-07T07:56:11.857142Z"
},
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"duration": 0.031719,
"end_time": "2021-10-07T07:58:48.721751",
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"start_time": "2021-10-07T07:58:48.690032",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sex\n",
"female 0.257962\n",
"male 0.811092\n",
"Name: Survived, dtype: float64\n"
]
}
],
"source": [
"## 10.\tKazada ölen kadınların oranı ile erkeklerin oranını karşılaştırınız. \n",
"## (Örnek: erkekler için; ölen erkeklerin, erkek sayısına bölümü bu oranı vermektetedir.\n",
"\n",
"death_by_sex = 1- df.groupby(\"Sex\")[\"Survived\"].mean()\n",
"print(death_by_sex)"
]
},
{
"cell_type": "code",
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"id": "5d5b0ef0",
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"status": "completed"
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"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
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" vertical-align: middle;\n",
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" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>PassengerId</th>\n",
" <th>Survived</th>\n",
" <th>Pclass</th>\n",
" <th>Age</th>\n",
" <th>SibSp</th>\n",
" <th>Parch</th>\n",
" <th>Fare</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Sex</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>female</th>\n",
" <td>429.699571</td>\n",
" <td>1.0</td>\n",
" <td>1.918455</td>\n",
" <td>28.847716</td>\n",
" <td>0.515021</td>\n",
" <td>0.515021</td>\n",
" <td>51.938573</td>\n",
" </tr>\n",
" <tr>\n",
" <th>male</th>\n",
" <td>475.724771</td>\n",
" <td>1.0</td>\n",
" <td>2.018349</td>\n",
" <td>27.276022</td>\n",
" <td>0.385321</td>\n",
" <td>0.357798</td>\n",
" <td>40.821484</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" PassengerId Survived Pclass Age SibSp Parch \\\n",
"Sex \n",
"female 429.699571 1.0 1.918455 28.847716 0.515021 0.515021 \n",
"male 475.724771 1.0 2.018349 27.276022 0.385321 0.357798 \n",
"\n",
" Fare \n",
"Sex \n",
"female 51.938573 \n",
"male 40.821484 "
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.loc[df[\"Survived\"] == 1].groupby(\"Sex\").mean()"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "842053dd",
"metadata": {
"execution": {
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},
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Sex Survived\n",
"female 1 233\n",
" 0 81\n",
"male 0 468\n",
" 1 109\n",
"Name: Survived, dtype: int64"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.groupby(\"Sex\")[\"Survived\"].value_counts()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "248a2f4f",
"metadata": {
"execution": {
"iopub.execute_input": "2021-10-07T07:58:48.882217Z",
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"outputs": [
{
"data": {
"text/plain": [
"0.18890814558058924"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"109 / (109+468)"
]
},
{
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"execution_count": null,
"id": "8917fd2b",
"metadata": {
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}
},
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}
|
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