restart: with(LinearAlgebra): with(VectorCalculus): with(CodeGeneration): with(ExcelTools): with(ArrayTools):

test_data:=Import("//ost.ch/dfs/iwk/work/6640_iwk/IWK-VT/1_Projekte/4_aFuE/ITBO_Smart_Factory_22-23_OST/01-A1-Laserschweissen/03_Experimentelle Untersuchungen/01_LSQ_SABE/Zurich_area_prices.xlsx","Area-Prices"); y:=test_data[2..,2]; p_2:=test_data[2..,1]; plot(p_2,y,style=point,symbol=asterisk, color="Blue"); m_:=Size(y); m:= m_[1]; alpha := 1: #learning rate;

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n := 2: theta_v := Vector[row](n, symbol = theta): L := [seq(theta[i], i = 1 .. n)]; parameter_v := Vector[column](n, symbol = p): p[1] := 1: #h := theta_v . parameter_v; h := p[2]*theta[2] + theta[1]; for j to n do h := subs(parse(String("p[", j, "]=p_", j, "[i];")), h); end do;

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cost := 1/(2*m)*add((h - y[i])^2, i = 1 .. 20);cost := simplify(%);plot(%,theta[1]): grad_cost := Gradient(cost, L); subs(theta[1] = 0,%);subs(theta[2] = 0,%);

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Warning, expecting only range variable theta[1] in expression .5000000000*theta[1]^2+(72.80000000*theta[2]-3832.450000)*theta[1]+3072.250000*theta[2]^2+8028187.775-303777.6500*theta[2] to be plotted but found name theta[2]

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new_theta := Vector[column](n); for i to n do new_theta[i] := theta[i] - (alpha . (grad_cost[i])); end do;

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new_theta := unapply(new_theta, L): cost := unapply(cost,L);simplify(%); temp_theta[1] := new_theta(0)[1]; #temp_theta[2] := new_theta(0,0)[2]; while cost(temp_theta[1],temp_theta[2])>1 do temp_theta[1] := new_theta(temp_theta[1],temp_theta[1])[1]; temp_theta[2] := new_theta(0,0)[2]; end whileLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lK2V4ZWN1dGFibGVHRjRGLw==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVjb3N0R0YoZio2JEkodGhldGFfMUdGKEkodGhldGFfMkdGKEYoNiRJKW9wZXJhdG9yR0YoSSZhcnJvd0dGKEYoLCwqJDkkIiIjJCIrKysrK10hIzUqJiwmOSUkIisrKyshRyghIikkISsrK1hLUSEiJyIiIkZFRjdGRUZFKiRGPkY4JCIrKytEc0lGRCQiK3Z4PUchKSEiJEZFRj4kISsrbHhQSSEiJUYoRihGKDcjRi4=

Zio2JEkodGhldGFfMUc2IkkodGhldGFfMkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCwqJDkkIiIjJCIrKysrK10hIzUqJiwmOSUkIisrKyshRyghIikkISsrK1hLUSEiJyIiIkY6RixGOkY6KiRGM0YtJCIrKytEc0lGOSQiK3Z4PUchKSEiJEY6RjMkISsrbHhQSSEiJUYlRiVGJQ==

Error, invalid input: new_theta uses a 2nd argument, theta_2, which is missing

Error, missing operator or `;`

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