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3
Task/Polynomial-regression/00-META.yaml
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3
Task/Polynomial-regression/00-META.yaml
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@ -0,0 +1,3 @@
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---
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from: http://rosettacode.org/wiki/Polynomial_regression
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note: Mathematical operations|Matrices
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12
Task/Polynomial-regression/00-TASK.txt
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12
Task/Polynomial-regression/00-TASK.txt
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Find an approximating polynomial of known degree for a given data.
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Example:
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For input data:
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x = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
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y = {1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321};
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The approximating polynomial is:
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3 x<sup>2</sup> + 2 x + 1
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Here, the polynomial's coefficients are (3, 2, 1).
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This task is intended as a subtask for [[Measure relative performance of sorting algorithms implementations]].
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33
Task/Polynomial-regression/11l/polynomial-regression.11l
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33
Task/Polynomial-regression/11l/polynomial-regression.11l
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@ -0,0 +1,33 @@
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F average(arr)
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R sum(arr) / Float(arr.len)
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F poly_regression(x, y)
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V xm = average(x)
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V ym = average(y)
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V x2m = average(x.map(i -> i * i))
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V x3m = average(x.map(i -> i ^ 3))
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V x4m = average(x.map(i -> i ^ 4))
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V xym = average(zip(x, y).map((i, j) -> i * j))
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V x2ym = average(zip(x, y).map((i, j) -> i * i * j))
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V sxx = x2m - xm * xm
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V sxy = xym - xm * ym
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V sxx2 = x3m - xm * x2m
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V sx2x2 = x4m - x2m * x2m
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V sx2y = x2ym - x2m * ym
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V b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
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V c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
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V a = ym - b * xm - c * x2m
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F abc(xx)
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R (@a + @b * xx) + (@c * xx * xx)
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print("y = #. + #.x + #.x^2\n".format(a, b, c))
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print(‘ Input Approximation’)
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print(‘ x y y1’)
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L(i) 0 .< x.len
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print(‘#2 #3 #3.1’.format(x[i], y[i], abc(i)))
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V x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
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V y = [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321]
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poly_regression(x, y)
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114
Task/Polynomial-regression/ALGOL-68/polynomial-regression.alg
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114
Task/Polynomial-regression/ALGOL-68/polynomial-regression.alg
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MODE FIELD = REAL;
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MODE
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VEC = [0]FIELD,
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MAT = [0,0]FIELD;
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PROC VOID raise index error := VOID: (
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print(("stop", new line));
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stop
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);
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COMMENT from http://rosettacode.org/wiki/Matrix_Transpose#ALGOL_68 END COMMENT
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OP ZIP = ([,]FIELD in)[,]FIELD:(
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[2 LWB in:2 UPB in,1 LWB in:1UPB in]FIELD out;
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FOR i FROM LWB in TO UPB in DO
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out[,i]:=in[i,]
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OD;
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out
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);
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COMMENT from http://rosettacode.org/wiki/Matrix_multiplication#ALGOL_68 END COMMENT
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OP * = (VEC a,b)FIELD: ( # basically the dot product #
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FIELD result:=0;
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IF LWB a/=LWB b OR UPB a/=UPB b THEN raise index error FI;
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FOR i FROM LWB a TO UPB a DO result+:= a[i]*b[i] OD;
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result
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);
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OP * = (VEC a, MAT b)VEC: ( # overload vector times matrix #
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[2 LWB b:2 UPB b]FIELD result;
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IF LWB a/=LWB b OR UPB a/=UPB b THEN raise index error FI;
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FOR j FROM 2 LWB b TO 2 UPB b DO result[j]:=a*b[,j] OD;
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result
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);
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OP * = (MAT a, b)MAT: ( # overload matrix times matrix #
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[LWB a:UPB a, 2 LWB b:2 UPB b]FIELD result;
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IF 2 LWB a/=LWB b OR 2 UPB a/=UPB b THEN raise index error FI;
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FOR k FROM LWB result TO UPB result DO result[k,]:=a[k,]*b OD;
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result
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);
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COMMENT from http://rosettacode.org/wiki/Pyramid_of_numbers#ALGOL_68 END COMMENT
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OP / = (VEC a, MAT b)VEC: ( # vector division #
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[LWB a:UPB a,1]FIELD transpose a;
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transpose a[,1]:=a;
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(transpose a/b)[,1]
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);
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OP / = (MAT a, MAT b)MAT:( # matrix division #
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[LWB b:UPB b]INT p ;
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INT sign;
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[,]FIELD lu = lu decomp(b, p, sign);
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[LWB a:UPB a, 2 LWB a:2 UPB a]FIELD out;
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FOR col FROM 2 LWB a TO 2 UPB a DO
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out[,col] := lu solve(b, lu, p, a[,col]) [@LWB out[,col]]
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OD;
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out
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);
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FORMAT int repr = $g(0)$,
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real repr = $g(-7,4)$;
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PROC fit = (VEC x, y, INT order)VEC:
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BEGIN
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[0:order, LWB x:UPB x]FIELD a; # the plane #
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FOR i FROM 2 LWB a TO 2 UPB a DO
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FOR j FROM LWB a TO UPB a DO
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a [j, i] := x [i]**j
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OD
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OD;
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( y * ZIP a ) / ( a * ZIP a )
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END # fit #;
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PROC print polynomial = (VEC x)VOID: (
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BOOL empty := TRUE;
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FOR i FROM UPB x BY -1 TO LWB x DO
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IF x[i] NE 0 THEN
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IF x[i] > 0 AND NOT empty THEN print ("+") FI;
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empty := FALSE;
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IF x[i] NE 1 OR i=0 THEN
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IF ENTIER x[i] = x[i] THEN
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printf((int repr, x[i]))
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ELSE
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printf((real repr, x[i]))
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FI
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FI;
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CASE i+1 IN
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SKIP,print(("x"))
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OUT
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printf(($"x**"g(0)$,i))
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ESAC
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FI
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OD;
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IF empty THEN print("0") FI;
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print(new line)
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);
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fitting: BEGIN
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VEC c =
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fit
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( (0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0),
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(1.0, 6.0, 17.0, 34.0, 57.0, 86.0, 121.0, 162.0, 209.0, 262.0, 321.0),
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2
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);
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print polynomial(c);
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VEC d =
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fit
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( (0, 1, 2, 3, 4, 5, 6, 7, 8, 9),
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(2.7, 2.8, 31.4, 38.1, 58.0, 76.2, 100.5, 130.0, 149.3, 180.0),
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2
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);
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print polynomial(d)
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END # fitting #
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84
Task/Polynomial-regression/AWK/polynomial-regression.awk
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84
Task/Polynomial-regression/AWK/polynomial-regression.awk
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@ -0,0 +1,84 @@
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BEGIN{
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i = 0;
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xa[i] = 0; i++;
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xa[i] = 1; i++;
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xa[i] = 2; i++;
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xa[i] = 3; i++;
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xa[i] = 4; i++;
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xa[i] = 5; i++;
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xa[i] = 6; i++;
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xa[i] = 7; i++;
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xa[i] = 8; i++;
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xa[i] = 9; i++;
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xa[i] = 10; i++;
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i = 0;
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ya[i] = 1; i++;
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ya[i] = 6; i++;
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ya[i] = 17; i++;
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ya[i] = 34; i++;
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ya[i] = 57; i++;
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ya[i] = 86; i++;
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ya[i] =121; i++;
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ya[i] =162; i++;
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ya[i] =209; i++;
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ya[i] =262; i++;
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ya[i] =321; i++;
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exit;
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}
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{
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# (nothing to do)
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}
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END{
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a = 0; b = 0; c = 0; # globals - will change by regression()
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regression(xa,ya);
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printf("y = %6.2f x^2 + %6.2f x + %6.2f\n",c,b,a);
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printf("%-13s %-8s\n","Input","Approximation");
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printf("%-6s %-6s %-8s\n","x","y","y^")
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for (i=0;i<length(xa);i++) {
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printf("%6.1f %6.1f %8.3f\n",xa[i],ya[i],eval(a,b,c,xa[i]));
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}
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}
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function eval(a,b,c,x) {
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return a+b*x+c*x*x;
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}
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# locals
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function regression(x,y, n,xm,ym,x2m,x3m,x4m,xym,x2ym,sxx,sxy,sxx2,sx2x2,sx2y) {
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n = 0
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xm = 0.0;
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ym = 0.0;
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x2m = 0.0;
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x3m = 0.0;
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x4m = 0.0;
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xym = 0.0;
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x2ym = 0.0;
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for (i in x) {
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xm += x[i];
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ym += y[i];
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x2m += x[i] * x[i];
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x3m += x[i] * x[i] * x[i];
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x4m += x[i] * x[i] * x[i] * x[i];
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xym += x[i] * y[i];
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x2ym += x[i] * x[i] * y[i];
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n++;
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}
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xm = xm / n;
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ym = ym / n;
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x2m = x2m / n;
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x3m = x3m / n;
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x4m = x4m / n;
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xym = xym / n;
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x2ym = x2ym / n;
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sxx = x2m - xm * xm;
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sxy = xym - xm * ym;
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sxx2 = x3m - xm * x2m;
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sx2x2 = x4m - x2m * x2m;
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sx2y = x2ym - x2m * ym;
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b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
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c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
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a = ym - b * xm - c * x2m;
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}
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12
Task/Polynomial-regression/Ada/polynomial-regression-1.ada
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12
Task/Polynomial-regression/Ada/polynomial-regression-1.ada
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with Ada.Numerics.Real_Arrays; use Ada.Numerics.Real_Arrays;
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function Fit (X, Y : Real_Vector; N : Positive) return Real_Vector is
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A : Real_Matrix (0..N, X'Range); -- The plane
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begin
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for I in A'Range (2) loop
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for J in A'Range (1) loop
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A (J, I) := X (I)**J;
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end loop;
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end loop;
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return Solve (A * Transpose (A), A * Y);
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end Fit;
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15
Task/Polynomial-regression/Ada/polynomial-regression-2.ada
Normal file
15
Task/Polynomial-regression/Ada/polynomial-regression-2.ada
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with Fit;
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with Ada.Float_Text_IO; use Ada.Float_Text_IO;
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procedure Fitting is
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C : constant Real_Vector :=
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Fit
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( (0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0),
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(1.0, 6.0, 17.0, 34.0, 57.0, 86.0, 121.0, 162.0, 209.0, 262.0, 321.0),
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2
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);
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begin
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Put (C (0), Aft => 3, Exp => 0);
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Put (C (1), Aft => 3, Exp => 0);
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Put (C (2), Aft => 3, Exp => 0);
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end Fitting;
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regression(xa,ya){
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n := xa.Count()
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xm := ym := x2m := x3m := x4m := xym := x2ym := 0
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loop % n {
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i := A_Index
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xm := xm + xa[i]
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ym := ym + ya[i]
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x2m := x2m + xa[i] * xa[i]
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x3m := x3m + xa[i] * xa[i] * xa[i]
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x4m := x4m + xa[i] * xa[i] * xa[i] * xa[i]
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xym := xym + xa[i] * ya[i]
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x2ym := x2ym + xa[i] * xa[i] * ya[i]
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}
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xm := xm / n
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ym := ym / n
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x2m := x2m / n
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x3m := x3m / n
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x4m := x4m / n
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xym := xym / n
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x2ym := x2ym / n
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sxx := x2m - xm * xm
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sxy := xym - xm * ym
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sxx2 := x3m - xm * x2m
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sx2x2 := x4m - x2m * x2m
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sx2y := x2ym - x2m * ym
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b := (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
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c := (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
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a := ym - b * xm - c * x2m
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result := "Input`tApproximation`nx y`ty1`n"
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loop % n
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i := A_Index, result .= xa[i] ", " ya[i] "`t" eval(a, b, c, xa[i]) "`n"
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return "y = " c "x^2" " + " b "x + " a "`n`n" result
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}
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eval(a,b,c,x){
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return a + (b + c*x) * x
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}
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@ -0,0 +1,4 @@
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xa := [0, 1, 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10]
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ya := [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321]
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MsgBox % result := regression(xa, ya)
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return
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@ -0,0 +1,49 @@
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INSTALL @lib$+"ARRAYLIB"
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Max% = 10000
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DIM vector(5), matrix(5,5)
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DIM x(Max%), x2(Max%), x3(Max%), x4(Max%), x5(Max%)
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DIM x6(Max%), x7(Max%), x8(Max%), x9(Max%), x10(Max%)
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DIM y(Max%), xy(Max%), x2y(Max%), x3y(Max%), x4y(Max%), x5y(Max%)
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npts% = 11
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x() = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
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y() = 1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321
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sum_x = SUM(x())
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x2() = x() * x() : sum_x2 = SUM(x2())
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x3() = x() * x2() : sum_x3 = SUM(x3())
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x4() = x2() * x2() : sum_x4 = SUM(x4())
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x5() = x2() * x3() : sum_x5 = SUM(x5())
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x6() = x3() * x3() : sum_x6 = SUM(x6())
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x7() = x3() * x4() : sum_x7 = SUM(x7())
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x8() = x4() * x4() : sum_x8 = SUM(x8())
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x9() = x4() * x5() : sum_x9 = SUM(x9())
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x10() = x5() * x5() : sum_x10 = SUM(x10())
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sum_y = SUM(y())
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xy() = x() * y() : sum_xy = SUM(xy())
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x2y() = x2() * y() : sum_x2y = SUM(x2y())
|
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x3y() = x3() * y() : sum_x3y = SUM(x3y())
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x4y() = x4() * y() : sum_x4y = SUM(x4y())
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x5y() = x5() * y() : sum_x5y = SUM(x5y())
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|
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matrix() = \
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\ npts%, sum_x, sum_x2, sum_x3, sum_x4, sum_x5, \
|
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\ sum_x, sum_x2, sum_x3, sum_x4, sum_x5, sum_x6, \
|
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\ sum_x2, sum_x3, sum_x4, sum_x5, sum_x6, sum_x7, \
|
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\ sum_x3, sum_x4, sum_x5, sum_x6, sum_x7, sum_x8, \
|
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\ sum_x4, sum_x5, sum_x6, sum_x7, sum_x8, sum_x9, \
|
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\ sum_x5, sum_x6, sum_x7, sum_x8, sum_x9, sum_x10
|
||||
|
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vector() = \
|
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\ sum_y, sum_xy, sum_x2y, sum_x3y, sum_x4y, sum_x5y
|
||||
|
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PROC_invert(matrix())
|
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vector() = matrix().vector()
|
||||
|
||||
@% = &2040A
|
||||
PRINT "Polynomial coefficients = "
|
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FOR term% = 5 TO 0 STEP -1
|
||||
PRINT ;vector(term%) " * x^" STR$(term%)
|
||||
NEXT
|
||||
62
Task/Polynomial-regression/C++/polynomial-regression.cpp
Normal file
62
Task/Polynomial-regression/C++/polynomial-regression.cpp
Normal file
|
|
@ -0,0 +1,62 @@
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|||
#include <algorithm>
|
||||
#include <iostream>
|
||||
#include <numeric>
|
||||
#include <vector>
|
||||
|
||||
void polyRegression(const std::vector<int>& x, const std::vector<int>& y) {
|
||||
int n = x.size();
|
||||
std::vector<int> r(n);
|
||||
std::iota(r.begin(), r.end(), 0);
|
||||
double xm = std::accumulate(x.begin(), x.end(), 0.0) / x.size();
|
||||
double ym = std::accumulate(y.begin(), y.end(), 0.0) / y.size();
|
||||
double x2m = std::transform_reduce(r.begin(), r.end(), 0.0, std::plus<double>{}, [](double a) {return a * a; }) / r.size();
|
||||
double x3m = std::transform_reduce(r.begin(), r.end(), 0.0, std::plus<double>{}, [](double a) {return a * a * a; }) / r.size();
|
||||
double x4m = std::transform_reduce(r.begin(), r.end(), 0.0, std::plus<double>{}, [](double a) {return a * a * a * a; }) / r.size();
|
||||
|
||||
double xym = std::transform_reduce(x.begin(), x.end(), y.begin(), 0.0, std::plus<double>{}, std::multiplies<double>{});
|
||||
xym /= fmin(x.size(), y.size());
|
||||
|
||||
double x2ym = std::transform_reduce(x.begin(), x.end(), y.begin(), 0.0, std::plus<double>{}, [](double a, double b) { return a * a * b; });
|
||||
x2ym /= fmin(x.size(), y.size());
|
||||
|
||||
double sxx = x2m - xm * xm;
|
||||
double sxy = xym - xm * ym;
|
||||
double sxx2 = x3m - xm * x2m;
|
||||
double sx2x2 = x4m - x2m * x2m;
|
||||
double sx2y = x2ym - x2m * ym;
|
||||
|
||||
double b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
|
||||
double c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
|
||||
double a = ym - b * xm - c * x2m;
|
||||
|
||||
auto abc = [a, b, c](int xx) {
|
||||
return a + b * xx + c * xx*xx;
|
||||
};
|
||||
|
||||
std::cout << "y = " << a << " + " << b << "x + " << c << "x^2" << std::endl;
|
||||
std::cout << " Input Approximation" << std::endl;
|
||||
std::cout << " x y y1" << std::endl;
|
||||
|
||||
auto xit = x.cbegin();
|
||||
auto xend = x.cend();
|
||||
auto yit = y.cbegin();
|
||||
auto yend = y.cend();
|
||||
while (xit != xend && yit != yend) {
|
||||
printf("%2d %3d %5.1f\n", *xit, *yit, abc(*xit));
|
||||
xit = std::next(xit);
|
||||
yit = std::next(yit);
|
||||
}
|
||||
}
|
||||
|
||||
int main() {
|
||||
using namespace std;
|
||||
|
||||
vector<int> x(11);
|
||||
iota(x.begin(), x.end(), 0);
|
||||
|
||||
vector<int> y{ 1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321 };
|
||||
|
||||
polyRegression(x, y);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
public static double[] Polyfit(double[] x, double[] y, int degree)
|
||||
{
|
||||
// Vandermonde matrix
|
||||
var v = new DenseMatrix(x.Length, degree + 1);
|
||||
for (int i = 0; i < v.RowCount; i++)
|
||||
for (int j = 0; j <= degree; j++) v[i, j] = Math.Pow(x[i], j);
|
||||
var yv = new DenseVector(y).ToColumnMatrix();
|
||||
QR<double> qr = v.QR();
|
||||
// Math.Net doesn't have an "economy" QR, so:
|
||||
// cut R short to square upper triangle, then recompute Q
|
||||
var r = qr.R.SubMatrix(0, degree + 1, 0, degree + 1);
|
||||
var q = v.Multiply(r.Inverse());
|
||||
var p = r.Inverse().Multiply(q.TransposeThisAndMultiply(yv));
|
||||
return p.Column(0).ToArray();
|
||||
}
|
||||
|
|
@ -0,0 +1,12 @@
|
|||
static void Main(string[] args)
|
||||
{
|
||||
const int degree = 2;
|
||||
var x = new[] {0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0};
|
||||
var y = new[] {1.0, 6.0, 17.0, 34.0, 57.0, 86.0, 121.0, 162.0, 209.0, 262.0, 321.0};
|
||||
var p = Polyfit(x, y, degree);
|
||||
foreach (var d in p) Console.Write("{0} ",d);
|
||||
Console.WriteLine();
|
||||
for (int i = 0; i < x.Length; i++ )
|
||||
Console.WriteLine("{0} => {1} diff {2}", x[i], Polynomial.Evaluate(x[i], p), y[i] - Polynomial.Evaluate(x[i], p));
|
||||
Console.ReadKey(true);
|
||||
}
|
||||
8
Task/Polynomial-regression/C/polynomial-regression-1.c
Normal file
8
Task/Polynomial-regression/C/polynomial-regression-1.c
Normal file
|
|
@ -0,0 +1,8 @@
|
|||
#ifndef _POLIFITGSL_H
|
||||
#define _POLIFITGSL_H
|
||||
#include <gsl/gsl_multifit.h>
|
||||
#include <stdbool.h>
|
||||
#include <math.h>
|
||||
bool polynomialfit(int obs, int degree,
|
||||
double *dx, double *dy, double *store); /* n, p */
|
||||
#endif
|
||||
41
Task/Polynomial-regression/C/polynomial-regression-2.c
Normal file
41
Task/Polynomial-regression/C/polynomial-regression-2.c
Normal file
|
|
@ -0,0 +1,41 @@
|
|||
#include "polifitgsl.h"
|
||||
|
||||
bool polynomialfit(int obs, int degree,
|
||||
double *dx, double *dy, double *store) /* n, p */
|
||||
{
|
||||
gsl_multifit_linear_workspace *ws;
|
||||
gsl_matrix *cov, *X;
|
||||
gsl_vector *y, *c;
|
||||
double chisq;
|
||||
|
||||
int i, j;
|
||||
|
||||
X = gsl_matrix_alloc(obs, degree);
|
||||
y = gsl_vector_alloc(obs);
|
||||
c = gsl_vector_alloc(degree);
|
||||
cov = gsl_matrix_alloc(degree, degree);
|
||||
|
||||
for(i=0; i < obs; i++) {
|
||||
for(j=0; j < degree; j++) {
|
||||
gsl_matrix_set(X, i, j, pow(dx[i], j));
|
||||
}
|
||||
gsl_vector_set(y, i, dy[i]);
|
||||
}
|
||||
|
||||
ws = gsl_multifit_linear_alloc(obs, degree);
|
||||
gsl_multifit_linear(X, y, c, cov, &chisq, ws);
|
||||
|
||||
/* store result ... */
|
||||
for(i=0; i < degree; i++)
|
||||
{
|
||||
store[i] = gsl_vector_get(c, i);
|
||||
}
|
||||
|
||||
gsl_multifit_linear_free(ws);
|
||||
gsl_matrix_free(X);
|
||||
gsl_matrix_free(cov);
|
||||
gsl_vector_free(y);
|
||||
gsl_vector_free(c);
|
||||
return true; /* we do not "analyse" the result (cov matrix mainly)
|
||||
to know if the fit is "good" */
|
||||
}
|
||||
21
Task/Polynomial-regression/C/polynomial-regression-3.c
Normal file
21
Task/Polynomial-regression/C/polynomial-regression-3.c
Normal file
|
|
@ -0,0 +1,21 @@
|
|||
#include <stdio.h>
|
||||
|
||||
#include "polifitgsl.h"
|
||||
|
||||
#define NP 11
|
||||
double x[] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
|
||||
double y[] = {1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321};
|
||||
|
||||
#define DEGREE 3
|
||||
double coeff[DEGREE];
|
||||
|
||||
int main()
|
||||
{
|
||||
int i;
|
||||
|
||||
polynomialfit(NP, DEGREE, x, y, coeff);
|
||||
for(i=0; i < DEGREE; i++) {
|
||||
printf("%lf\n", coeff[i]);
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -0,0 +1,9 @@
|
|||
;; Least square fit of a polynomial of order n the x-y-curve.
|
||||
(defun polyfit (x y n)
|
||||
(let* ((m (cadr (array-dimensions x)))
|
||||
(A (make-array `(,m ,(+ n 1)) :initial-element 0)))
|
||||
(loop for i from 0 to (- m 1) do
|
||||
(loop for j from 0 to n do
|
||||
(setf (aref A i j)
|
||||
(expt (aref x 0 i) j))))
|
||||
(lsqr A (mtp y))))
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
(let ((x (make-array '(1 11) :initial-contents '((0 1 2 3 4 5 6 7 8 9 10))))
|
||||
(y (make-array '(1 11) :initial-contents '((1 6 17 34 57 86 121 162 209 262 321)))))
|
||||
(polyfit x y 2))
|
||||
|
||||
#2A((0.9999999999999759d0) (2.000000000000005d0) (3.0d0))
|
||||
47
Task/Polynomial-regression/D/polynomial-regression.d
Normal file
47
Task/Polynomial-regression/D/polynomial-regression.d
Normal file
|
|
@ -0,0 +1,47 @@
|
|||
import std.algorithm;
|
||||
import std.range;
|
||||
import std.stdio;
|
||||
|
||||
auto average(R)(R r) {
|
||||
auto t = r.fold!("a+b", "a+1")(0, 0);
|
||||
return cast(double) t[0] / t[1];
|
||||
}
|
||||
|
||||
void polyRegression(int[] x, int[] y) {
|
||||
auto n = x.length;
|
||||
auto r = iota(0, n).array;
|
||||
auto xm = x.average();
|
||||
auto ym = y.average();
|
||||
auto x2m = r.map!"a*a".average();
|
||||
auto x3m = r.map!"a*a*a".average();
|
||||
auto x4m = r.map!"a*a*a*a".average();
|
||||
auto xym = x.zip(y).map!"a[0]*a[1]".average();
|
||||
auto x2ym = x.zip(y).map!"a[0]*a[0]*a[1]".average();
|
||||
|
||||
auto sxx = x2m - xm * xm;
|
||||
auto sxy = xym - xm * ym;
|
||||
auto sxx2 = x3m - xm * x2m;
|
||||
auto sx2x2 = x4m - x2m * x2m;
|
||||
auto sx2y = x2ym - x2m * ym;
|
||||
|
||||
auto b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
|
||||
auto c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
|
||||
auto a = ym - b * xm - c * x2m;
|
||||
|
||||
real abc(int xx) {
|
||||
return a + b * xx + c * xx * xx;
|
||||
}
|
||||
|
||||
writeln("y = ", a, " + ", b, "x + ", c, "x^2");
|
||||
writeln(" Input Approximation");
|
||||
writeln(" x y y1");
|
||||
foreach (i; 0..n) {
|
||||
writefln("%2d %3d %5.1f", x[i], y[i], abc(x[i]));
|
||||
}
|
||||
}
|
||||
|
||||
void main() {
|
||||
auto x = iota(0, 11).array;
|
||||
auto y = [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321];
|
||||
polyRegression(x, y);
|
||||
}
|
||||
|
|
@ -0,0 +1,3 @@
|
|||
(let ((x '(0 1 2 3 4 5 6 7 8 9 10))
|
||||
(y '(1 6 17 34 57 86 121 162 209 262 321)))
|
||||
(calc-eval "fit(a*x^2+b*x+c,[x],[a,b,c],[$1 $2])" nil (cons 'vec x) (cons 'vec y)))
|
||||
64
Task/Polynomial-regression/Fortran/polynomial-regression-1.f
Normal file
64
Task/Polynomial-regression/Fortran/polynomial-regression-1.f
Normal file
|
|
@ -0,0 +1,64 @@
|
|||
module fitting
|
||||
contains
|
||||
|
||||
function polyfit(vx, vy, d)
|
||||
implicit none
|
||||
integer, intent(in) :: d
|
||||
integer, parameter :: dp = selected_real_kind(15, 307)
|
||||
real(dp), dimension(d+1) :: polyfit
|
||||
real(dp), dimension(:), intent(in) :: vx, vy
|
||||
|
||||
real(dp), dimension(:,:), allocatable :: X
|
||||
real(dp), dimension(:,:), allocatable :: XT
|
||||
real(dp), dimension(:,:), allocatable :: XTX
|
||||
|
||||
integer :: i, j
|
||||
|
||||
integer :: n, lda, lwork
|
||||
integer :: info
|
||||
integer, dimension(:), allocatable :: ipiv
|
||||
real(dp), dimension(:), allocatable :: work
|
||||
|
||||
n = d+1
|
||||
lda = n
|
||||
lwork = n
|
||||
|
||||
allocate(ipiv(n))
|
||||
allocate(work(lwork))
|
||||
allocate(XT(n, size(vx)))
|
||||
allocate(X(size(vx), n))
|
||||
allocate(XTX(n, n))
|
||||
|
||||
! prepare the matrix
|
||||
do i = 0, d
|
||||
do j = 1, size(vx)
|
||||
X(j, i+1) = vx(j)**i
|
||||
end do
|
||||
end do
|
||||
|
||||
XT = transpose(X)
|
||||
XTX = matmul(XT, X)
|
||||
|
||||
! calls to LAPACK subs DGETRF and DGETRI
|
||||
call DGETRF(n, n, XTX, lda, ipiv, info)
|
||||
if ( info /= 0 ) then
|
||||
print *, "problem"
|
||||
return
|
||||
end if
|
||||
call DGETRI(n, XTX, lda, ipiv, work, lwork, info)
|
||||
if ( info /= 0 ) then
|
||||
print *, "problem"
|
||||
return
|
||||
end if
|
||||
|
||||
polyfit = matmul( matmul(XTX, XT), vy)
|
||||
|
||||
deallocate(ipiv)
|
||||
deallocate(work)
|
||||
deallocate(X)
|
||||
deallocate(XT)
|
||||
deallocate(XTX)
|
||||
|
||||
end function
|
||||
|
||||
end module
|
||||
19
Task/Polynomial-regression/Fortran/polynomial-regression-2.f
Normal file
19
Task/Polynomial-regression/Fortran/polynomial-regression-2.f
Normal file
|
|
@ -0,0 +1,19 @@
|
|||
program PolynomalFitting
|
||||
use fitting
|
||||
implicit none
|
||||
|
||||
! let us test it
|
||||
integer, parameter :: degree = 2
|
||||
integer, parameter :: dp = selected_real_kind(15, 307)
|
||||
integer :: i
|
||||
real(dp), dimension(11) :: x = (/ (i,i=0,10) /)
|
||||
real(dp), dimension(11) :: y = (/ 1, 6, 17, 34, &
|
||||
57, 86, 121, 162, &
|
||||
209, 262, 321 /)
|
||||
real(dp), dimension(degree+1) :: a
|
||||
|
||||
a = polyfit(x, y, degree)
|
||||
|
||||
write (*, '(F9.4)') a
|
||||
|
||||
end program
|
||||
188
Task/Polynomial-regression/FreeBASIC/polynomial-regression.basic
Normal file
188
Task/Polynomial-regression/FreeBASIC/polynomial-regression.basic
Normal file
|
|
@ -0,0 +1,188 @@
|
|||
#Include "crt.bi" 'for rounding only
|
||||
|
||||
Type vector
|
||||
Dim As Double element(Any)
|
||||
End Type
|
||||
|
||||
Type matrix
|
||||
Dim As Double element(Any,Any)
|
||||
Declare Function inverse() As matrix
|
||||
Declare Function transpose() As matrix
|
||||
private:
|
||||
Declare Function GaussJordan(As vector) As vector
|
||||
End Type
|
||||
|
||||
'mult operators
|
||||
Operator *(m1 As matrix,m2 As matrix) As matrix
|
||||
Dim rows As Integer=Ubound(m1.element,1)
|
||||
Dim columns As Integer=Ubound(m2.element,2)
|
||||
If Ubound(m1.element,2)<>Ubound(m2.element,1) Then
|
||||
Print "Can't do"
|
||||
Exit Operator
|
||||
End If
|
||||
Dim As matrix ans
|
||||
Redim ans.element(rows,columns)
|
||||
Dim rxc As Double
|
||||
For r As Integer=1 To rows
|
||||
For c As Integer=1 To columns
|
||||
rxc=0
|
||||
For k As Integer = 1 To Ubound(m1.element,2)
|
||||
rxc=rxc+m1.element(r,k)*m2.element(k,c)
|
||||
Next k
|
||||
ans.element(r,c)=rxc
|
||||
Next c
|
||||
Next r
|
||||
Operator= ans
|
||||
End Operator
|
||||
|
||||
Operator *(m1 As matrix,m2 As vector) As vector
|
||||
Dim rows As Integer=Ubound(m1.element,1)
|
||||
Dim columns As Integer=Ubound(m2.element,2)
|
||||
If Ubound(m1.element,2)<>Ubound(m2.element) Then
|
||||
Print "Can't do"
|
||||
Exit Operator
|
||||
End If
|
||||
Dim As vector ans
|
||||
Redim ans.element(rows)
|
||||
Dim rxc As Double
|
||||
For r As Integer=1 To rows
|
||||
rxc=0
|
||||
For k As Integer = 1 To Ubound(m1.element,2)
|
||||
rxc=rxc+m1.element(r,k)*m2.element(k)
|
||||
Next k
|
||||
ans.element(r)=rxc
|
||||
Next r
|
||||
Operator= ans
|
||||
End Operator
|
||||
|
||||
Function matrix.transpose() As matrix
|
||||
Dim As matrix b
|
||||
Redim b.element(1 To Ubound(this.element,2),1 To Ubound(this.element,1))
|
||||
For i As Long=1 To Ubound(this.element,1)
|
||||
For j As Long=1 To Ubound(this.element,2)
|
||||
b.element(j,i)=this.element(i,j)
|
||||
Next
|
||||
Next
|
||||
Return b
|
||||
End Function
|
||||
|
||||
Function matrix.GaussJordan(rhs As vector) As vector
|
||||
Dim As Integer n=Ubound(rhs.element)
|
||||
Dim As vector ans=rhs,r=rhs
|
||||
Dim As matrix b=This
|
||||
#macro pivot(num)
|
||||
For p1 As Integer = num To n - 1
|
||||
For p2 As Integer = p1 + 1 To n
|
||||
If Abs(b.element(p1,num))<Abs(b.element(p2,num)) Then
|
||||
Swap r.element(p1),r.element(p2)
|
||||
For g As Integer=1 To n
|
||||
Swap b.element(p1,g),b.element(p2,g)
|
||||
Next g
|
||||
End If
|
||||
Next p2
|
||||
Next p1
|
||||
#endmacro
|
||||
For k As Integer=1 To n-1
|
||||
pivot(k)
|
||||
For row As Integer =k To n-1
|
||||
If b.element(row+1,k)=0 Then Exit For
|
||||
Var f=b.element(k,k)/b.element(row+1,k)
|
||||
r.element(row+1)=r.element(row+1)*f-r.element(k)
|
||||
For g As Integer=1 To n
|
||||
b.element((row+1),g)=b.element((row+1),g)*f-b.element(k,g)
|
||||
Next g
|
||||
Next row
|
||||
Next k
|
||||
'back substitute
|
||||
For z As Integer=n To 1 Step -1
|
||||
ans.element(z)=r.element(z)/b.element(z,z)
|
||||
For j As Integer = n To z+1 Step -1
|
||||
ans.element(z)=ans.element(z)-(b.element(z,j)*ans.element(j)/b.element(z,z))
|
||||
Next j
|
||||
Next z
|
||||
Function = ans
|
||||
End Function
|
||||
|
||||
Function matrix.inverse() As matrix
|
||||
Var ub1=Ubound(this.element,1),ub2=Ubound(this.element,2)
|
||||
Dim As matrix ans
|
||||
Dim As vector temp,null_
|
||||
Redim temp.element(1 To ub1):Redim null_.element(1 To ub1)
|
||||
Redim ans.element(1 To ub1,1 To ub2)
|
||||
For a As Integer=1 To ub1
|
||||
temp=null_
|
||||
temp.element(a)=1
|
||||
temp=GaussJordan(temp)
|
||||
For b As Integer=1 To ub1
|
||||
ans.element(b,a)=temp.element(b)
|
||||
Next b
|
||||
Next a
|
||||
Return ans
|
||||
End Function
|
||||
|
||||
'vandermode of x
|
||||
Function vandermonde(x_values() As Double,w As Long) As matrix
|
||||
Dim As matrix mat
|
||||
Var n=Ubound(x_values)
|
||||
Redim mat.element(1 To n,1 To w)
|
||||
For a As Integer=1 To n
|
||||
For b As Integer=1 To w
|
||||
mat.element(a,b)=x_values(a)^(b-1)
|
||||
Next b
|
||||
Next a
|
||||
Return mat
|
||||
End Function
|
||||
|
||||
'main preocedure
|
||||
Sub regress(x_values() As Double,y_values() As Double,ans() As Double,n As Long)
|
||||
Redim ans(1 To Ubound(x_values))
|
||||
Dim As matrix m1= vandermonde(x_values(),n)
|
||||
Dim As matrix T=m1.transpose
|
||||
Dim As vector y
|
||||
Redim y.element(1 To Ubound(ans))
|
||||
For n As Long=1 To Ubound(y_values)
|
||||
y.element(n)=y_values(n)
|
||||
Next n
|
||||
Dim As vector result=(((T*m1).inverse)*T)*y
|
||||
Redim Preserve ans(1 To n)
|
||||
For n As Long=1 To Ubound(ans)
|
||||
ans(n)=result.element(n)
|
||||
Next n
|
||||
End Sub
|
||||
|
||||
'Evaluate a polynomial at x
|
||||
Function polyeval(Coefficients() As Double,Byval x As Double) As Double
|
||||
Dim As Double acc
|
||||
For i As Long=Ubound(Coefficients) To Lbound(Coefficients) Step -1
|
||||
acc=acc*x+Coefficients(i)
|
||||
Next i
|
||||
Return acc
|
||||
End Function
|
||||
|
||||
Function CRound(Byval x As Double,Byval precision As Integer=30) As String
|
||||
If precision>30 Then precision=30
|
||||
Dim As zstring * 40 z:Var s="%." &str(Abs(precision)) &"f"
|
||||
sprintf(z,s,x)
|
||||
If Val(z) Then Return Rtrim(Rtrim(z,"0"),".")Else Return "0"
|
||||
End Function
|
||||
|
||||
Function show(a() As Double,places as long=10) As String
|
||||
Dim As String s,g
|
||||
For n As Long=Lbound(a) To Ubound(a)
|
||||
If n<3 Then g="" Else g="^"+Str(n-1)
|
||||
if val(cround(a(n),places))<>0 then
|
||||
s+= Iif(Sgn(a(n))>=0,"+","")+cround(a(n),places)+ Iif(n=Lbound(a),"","*x"+g)+" "
|
||||
end if
|
||||
Next n
|
||||
Return s
|
||||
End Function
|
||||
|
||||
|
||||
dim as double x(1 to ...)={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
|
||||
dim as double y(1 to ...)={1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321}
|
||||
|
||||
Redim As Double ans()
|
||||
regress(x(),y(),ans(),3)
|
||||
|
||||
print show(ans())
|
||||
sleep
|
||||
12
Task/Polynomial-regression/GAP/polynomial-regression.gap
Normal file
12
Task/Polynomial-regression/GAP/polynomial-regression.gap
Normal file
|
|
@ -0,0 +1,12 @@
|
|||
PolynomialRegression := function(x, y, n)
|
||||
local a;
|
||||
a := List([0 .. n], i -> List(x, s -> s^i));
|
||||
return TransposedMat((a * TransposedMat(a))^-1 * a * TransposedMat([y]))[1];
|
||||
end;
|
||||
|
||||
x := [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
|
||||
y := [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321];
|
||||
|
||||
# Return coefficients in ascending degree order
|
||||
PolynomialRegression(x, y, 2);
|
||||
# [ 1, 2, 3 ]
|
||||
|
|
@ -0,0 +1,24 @@
|
|||
# The polynomial approximation
|
||||
f(x) = a*x**2 + b*x + c
|
||||
|
||||
# Initial values for parameters
|
||||
a = 0.1
|
||||
b = 0.1
|
||||
c = 0.1
|
||||
|
||||
# Fit f to the following data by modifying the variables a, b, c
|
||||
fit f(x) '-' via a, b, c
|
||||
0 1
|
||||
1 6
|
||||
2 17
|
||||
3 34
|
||||
4 57
|
||||
5 86
|
||||
6 121
|
||||
7 162
|
||||
8 209
|
||||
9 262
|
||||
10 321
|
||||
e
|
||||
|
||||
print sprintf("\n --- \n Polynomial fit: %.4f x^2 + %.4f x + %.4f\n", a, b, c)
|
||||
41
Task/Polynomial-regression/Go/polynomial-regression-1.go
Normal file
41
Task/Polynomial-regression/Go/polynomial-regression-1.go
Normal file
|
|
@ -0,0 +1,41 @@
|
|||
package main
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"log"
|
||||
|
||||
"gonum.org/v1/gonum/mat"
|
||||
)
|
||||
|
||||
func main() {
|
||||
var (
|
||||
x = []float64{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
|
||||
y = []float64{1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321}
|
||||
|
||||
degree = 2
|
||||
|
||||
a = Vandermonde(x, degree+1)
|
||||
b = mat.NewDense(len(y), 1, y)
|
||||
c = mat.NewDense(degree+1, 1, nil)
|
||||
)
|
||||
|
||||
var qr mat.QR
|
||||
qr.Factorize(a)
|
||||
|
||||
const trans = false
|
||||
err := qr.SolveTo(c, trans, b)
|
||||
if err != nil {
|
||||
log.Fatalf("could not solve QR: %+v", err)
|
||||
}
|
||||
fmt.Printf("%.3f\n", mat.Formatted(c))
|
||||
}
|
||||
|
||||
func Vandermonde(a []float64, d int) *mat.Dense {
|
||||
x := mat.NewDense(len(a), d, nil)
|
||||
for i := range a {
|
||||
for j, p := 0, 1.0; j < d; j, p = j+1, p*a[i] {
|
||||
x.Set(i, j, p)
|
||||
}
|
||||
}
|
||||
return x
|
||||
}
|
||||
41
Task/Polynomial-regression/Go/polynomial-regression-2.go
Normal file
41
Task/Polynomial-regression/Go/polynomial-regression-2.go
Normal file
|
|
@ -0,0 +1,41 @@
|
|||
package main
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
|
||||
"github.com/skelterjohn/go.matrix"
|
||||
)
|
||||
|
||||
var xGiven = []float64{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
|
||||
var yGiven = []float64{1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321}
|
||||
var degree = 2
|
||||
|
||||
func main() {
|
||||
m := len(yGiven)
|
||||
n := degree + 1
|
||||
y := matrix.MakeDenseMatrix(yGiven, m, 1)
|
||||
x := matrix.Zeros(m, n)
|
||||
for i := 0; i < m; i++ {
|
||||
ip := float64(1)
|
||||
for j := 0; j < n; j++ {
|
||||
x.Set(i, j, ip)
|
||||
ip *= xGiven[i]
|
||||
}
|
||||
}
|
||||
|
||||
q, r := x.QR()
|
||||
qty, err := q.Transpose().Times(y)
|
||||
if err != nil {
|
||||
fmt.Println(err)
|
||||
return
|
||||
}
|
||||
c := make([]float64, n)
|
||||
for i := n - 1; i >= 0; i-- {
|
||||
c[i] = qty.Get(i, 0)
|
||||
for j := i + 1; j < n; j++ {
|
||||
c[i] -= c[j] * r.Get(i, j)
|
||||
}
|
||||
c[i] /= r.Get(i, i)
|
||||
}
|
||||
fmt.Println(c)
|
||||
}
|
||||
|
|
@ -0,0 +1,11 @@
|
|||
import Data.List
|
||||
import Data.Array
|
||||
import Control.Monad
|
||||
import Control.Arrow
|
||||
import Matrix.LU
|
||||
|
||||
ppoly p x = map (x**) p
|
||||
|
||||
polyfit d ry = elems $ solve mat vec where
|
||||
mat = listArray ((1,1), (d,d)) $ liftM2 concatMap ppoly id [0..fromIntegral $ pred d]
|
||||
vec = listArray (1,d) $ take d ry
|
||||
|
|
@ -0,0 +1,2 @@
|
|||
*Main> polyfit 3 [1,6,17,34,57,86,121,162,209,262,321]
|
||||
[1.0,2.0,3.0]
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
REAL :: n=10, x(n), y(n), m=3, p(m)
|
||||
|
||||
x = (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
|
||||
y = (1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321)
|
||||
|
||||
p = 2 ! initial guess for the polynom's coefficients
|
||||
|
||||
SOLVE(NUL=Theory()-y(nr), Unknown=p, DataIdx=nr, Iters=iterations)
|
||||
|
||||
WRITE(ClipBoard, Name) p, iterations
|
||||
|
||||
FUNCTION Theory()
|
||||
! called by the solver of the SOLVE function. All variables are global
|
||||
Theory = p(1)*x(nr)^2 + p(2)*x(nr) + p(3)
|
||||
END
|
||||
6
Task/Polynomial-regression/Hy/polynomial-regression.hy
Normal file
6
Task/Polynomial-regression/Hy/polynomial-regression.hy
Normal file
|
|
@ -0,0 +1,6 @@
|
|||
(import [numpy [polyfit]])
|
||||
|
||||
(setv x (range 11))
|
||||
(setv y [1 6 17 34 57 86 121 162 209 262 321])
|
||||
|
||||
(print (polyfit x y 2))
|
||||
3
Task/Polynomial-regression/J/polynomial-regression-1.j
Normal file
3
Task/Polynomial-regression/J/polynomial-regression-1.j
Normal file
|
|
@ -0,0 +1,3 @@
|
|||
Y=:1 6 17 34 57 86 121 162 209 262 321
|
||||
(%. ^/~@x:@i.@#) Y
|
||||
1 2 3 0 0 0 0 0 0 0 0
|
||||
2
Task/Polynomial-regression/J/polynomial-regression-2.j
Normal file
2
Task/Polynomial-regression/J/polynomial-regression-2.j
Normal file
|
|
@ -0,0 +1,2 @@
|
|||
Y %. (i.3) ^/~ i.#Y
|
||||
1 2 3
|
||||
49
Task/Polynomial-regression/Java/polynomial-regression.java
Normal file
49
Task/Polynomial-regression/Java/polynomial-regression.java
Normal file
|
|
@ -0,0 +1,49 @@
|
|||
import java.util.Arrays;
|
||||
import java.util.function.IntToDoubleFunction;
|
||||
import java.util.stream.IntStream;
|
||||
|
||||
public class PolynomialRegression {
|
||||
private static void polyRegression(int[] x, int[] y) {
|
||||
int n = x.length;
|
||||
double xm = Arrays.stream(x).average().orElse(Double.NaN);
|
||||
double ym = Arrays.stream(y).average().orElse(Double.NaN);
|
||||
double x2m = Arrays.stream(x).map(a -> a * a).average().orElse(Double.NaN);
|
||||
double x3m = Arrays.stream(x).map(a -> a * a * a).average().orElse(Double.NaN);
|
||||
double x4m = Arrays.stream(x).map(a -> a * a * a * a).average().orElse(Double.NaN);
|
||||
double xym = 0.0;
|
||||
for (int i = 0; i < x.length && i < y.length; ++i) {
|
||||
xym += x[i] * y[i];
|
||||
}
|
||||
xym /= Math.min(x.length, y.length);
|
||||
double x2ym = 0.0;
|
||||
for (int i = 0; i < x.length && i < y.length; ++i) {
|
||||
x2ym += x[i] * x[i] * y[i];
|
||||
}
|
||||
x2ym /= Math.min(x.length, y.length);
|
||||
|
||||
double sxx = x2m - xm * xm;
|
||||
double sxy = xym - xm * ym;
|
||||
double sxx2 = x3m - xm * x2m;
|
||||
double sx2x2 = x4m - x2m * x2m;
|
||||
double sx2y = x2ym - x2m * ym;
|
||||
|
||||
double b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
|
||||
double c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
|
||||
double a = ym - b * xm - c * x2m;
|
||||
|
||||
IntToDoubleFunction abc = (int xx) -> a + b * xx + c * xx * xx;
|
||||
|
||||
System.out.println("y = " + a + " + " + b + "x + " + c + "x^2");
|
||||
System.out.println(" Input Approximation");
|
||||
System.out.println(" x y y1");
|
||||
for (int i = 0; i < n; ++i) {
|
||||
System.out.printf("%2d %3d %5.1f\n", x[i], y[i], abc.applyAsDouble(x[i]));
|
||||
}
|
||||
}
|
||||
|
||||
public static void main(String[] args) {
|
||||
int[] x = IntStream.range(0, 11).toArray();
|
||||
int[] y = new int[]{1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321};
|
||||
polyRegression(x, y);
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
polyfit(x::Vector, y::Vector, deg::Int) = collect(v ^ p for v in x, p in 0:deg) \ y
|
||||
|
||||
x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
|
||||
y = [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321]
|
||||
@show polyfit(x, y, 2)
|
||||
|
|
@ -0,0 +1,36 @@
|
|||
// version 1.1.51
|
||||
|
||||
fun polyRegression(x: IntArray, y: IntArray) {
|
||||
val xm = x.average()
|
||||
val ym = y.average()
|
||||
val x2m = x.map { it * it }.average()
|
||||
val x3m = x.map { it * it * it }.average()
|
||||
val x4m = x.map { it * it * it * it }.average()
|
||||
val xym = x.zip(y).map { it.first * it.second }.average()
|
||||
val x2ym = x.zip(y).map { it.first * it.first * it.second }.average()
|
||||
|
||||
val sxx = x2m - xm * xm
|
||||
val sxy = xym - xm * ym
|
||||
val sxx2 = x3m - xm * x2m
|
||||
val sx2x2 = x4m - x2m * x2m
|
||||
val sx2y = x2ym - x2m * ym
|
||||
|
||||
val b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
|
||||
val c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
|
||||
val a = ym - b * xm - c * x2m
|
||||
|
||||
fun abc(xx: Int) = a + b * xx + c * xx * xx
|
||||
|
||||
println("y = $a + ${b}x + ${c}x^2\n")
|
||||
println(" Input Approximation")
|
||||
println(" x y y1")
|
||||
for ((xi, yi) in x zip y) {
|
||||
System.out.printf("%2d %3d %5.1f\n", xi, yi, abc(xi))
|
||||
}
|
||||
}
|
||||
|
||||
fun main() {
|
||||
val x = IntArray(11) { it }
|
||||
val y = intArrayOf(1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321)
|
||||
polyRegression(x, y)
|
||||
}
|
||||
52
Task/Polynomial-regression/Lua/polynomial-regression.lua
Normal file
52
Task/Polynomial-regression/Lua/polynomial-regression.lua
Normal file
|
|
@ -0,0 +1,52 @@
|
|||
function eval(a,b,c,x)
|
||||
return a + (b + c * x) * x
|
||||
end
|
||||
|
||||
function regression(xa,ya)
|
||||
local n = #xa
|
||||
|
||||
local xm = 0.0
|
||||
local ym = 0.0
|
||||
local x2m = 0.0
|
||||
local x3m = 0.0
|
||||
local x4m = 0.0
|
||||
local xym = 0.0
|
||||
local x2ym = 0.0
|
||||
|
||||
for i=1,n do
|
||||
xm = xm + xa[i]
|
||||
ym = ym + ya[i]
|
||||
x2m = x2m + xa[i] * xa[i]
|
||||
x3m = x3m + xa[i] * xa[i] * xa[i]
|
||||
x4m = x4m + xa[i] * xa[i] * xa[i] * xa[i]
|
||||
xym = xym + xa[i] * ya[i]
|
||||
x2ym = x2ym + xa[i] * xa[i] * ya[i]
|
||||
end
|
||||
xm = xm / n
|
||||
ym = ym / n
|
||||
x2m = x2m / n
|
||||
x3m = x3m / n
|
||||
x4m = x4m / n
|
||||
xym = xym / n
|
||||
x2ym = x2ym / n
|
||||
|
||||
local sxx = x2m - xm * xm
|
||||
local sxy = xym - xm * ym
|
||||
local sxx2 = x3m - xm * x2m
|
||||
local sx2x2 = x4m - x2m * x2m
|
||||
local sx2y = x2ym - x2m * ym
|
||||
|
||||
local b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
|
||||
local c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
|
||||
local a = ym - b * xm - c * x2m
|
||||
|
||||
print("y = "..a.." + "..b.."x + "..c.."x^2")
|
||||
|
||||
for i=1,n do
|
||||
print(string.format("%2d %3d %3d", xa[i], ya[i], eval(a, b, c, xa[i])))
|
||||
end
|
||||
end
|
||||
|
||||
local xa = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
|
||||
local ya = {1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321}
|
||||
regression(xa, ya)
|
||||
|
|
@ -0,0 +1,7 @@
|
|||
>> x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
|
||||
>> y = [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321];
|
||||
>> polyfit(x,y,2)
|
||||
|
||||
ans =
|
||||
|
||||
2.999999999999998 2.000000000000019 0.999999999999956
|
||||
|
|
@ -0,0 +1,2 @@
|
|||
with(CurveFitting);
|
||||
PolynomialInterpolation([[0, 1], [1, 6], [2, 17], [3, 34], [4, 57], [5, 86], [6, 121], [7, 162], [8, 209], [9, 262], [10, 321]], 'x');
|
||||
|
|
@ -0,0 +1,2 @@
|
|||
data = Transpose@{Range[0, 10], {1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321}};
|
||||
Fit[data, {1, x, x^2}, x]
|
||||
|
|
@ -0,0 +1 @@
|
|||
Simplify@InterpolatingPolynomial[{{0, 1}, {1, 6}, {2, 17}, {3, 34}, {4, 57}, {5, 86}, {6, 121}, {7, 162}, {8, 209}, {9, 262}, {10, 321}}, x]
|
||||
|
|
@ -0,0 +1 @@
|
|||
curve fit (0,1), (1,6), (2,17), (3,34), (4,57), (5,86), (6,121), (7,162), (8,209), (9,262), (10,321)
|
||||
|
|
@ -0,0 +1,87 @@
|
|||
MODULE PolynomialRegression;
|
||||
FROM FormatString IMPORT FormatString;
|
||||
FROM RealStr IMPORT RealToStr;
|
||||
FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
|
||||
|
||||
PROCEDURE Eval(a,b,c,x : REAL) : REAL;
|
||||
BEGIN
|
||||
RETURN a + b*x + c*x*x;
|
||||
END Eval;
|
||||
|
||||
PROCEDURE Regression(x,y : ARRAY OF INTEGER);
|
||||
VAR
|
||||
n,i : INTEGER;
|
||||
xm,x2m,x3m,x4m : REAL;
|
||||
ym : REAL;
|
||||
xym,x2ym : REAL;
|
||||
sxx,sxy,sxx2,sx2x2,sx2y : REAL;
|
||||
a,b,c : REAL;
|
||||
buf : ARRAY[0..63] OF CHAR;
|
||||
BEGIN
|
||||
n := SIZE(x)/SIZE(INTEGER);
|
||||
|
||||
xm := 0.0;
|
||||
ym := 0.0;
|
||||
x2m := 0.0;
|
||||
x3m := 0.0;
|
||||
x4m := 0.0;
|
||||
xym := 0.0;
|
||||
x2ym := 0.0;
|
||||
FOR i:=0 TO n-1 DO
|
||||
xm := xm + FLOAT(x[i]);
|
||||
ym := ym + FLOAT(y[i]);
|
||||
x2m := x2m + FLOAT(x[i]) * FLOAT(x[i]);
|
||||
x3m := x3m + FLOAT(x[i]) * FLOAT(x[i]) * FLOAT(x[i]);
|
||||
x4m := x4m + FLOAT(x[i]) * FLOAT(x[i]) * FLOAT(x[i]) * FLOAT(x[i]);
|
||||
xym := xym + FLOAT(x[i]) * FLOAT(y[i]);
|
||||
x2ym := x2ym + FLOAT(x[i]) * FLOAT(x[i]) * FLOAT(y[i]);
|
||||
END;
|
||||
xm := xm / FLOAT(n);
|
||||
ym := ym / FLOAT(n);
|
||||
x2m := x2m / FLOAT(n);
|
||||
x3m := x3m / FLOAT(n);
|
||||
x4m := x4m / FLOAT(n);
|
||||
xym := xym / FLOAT(n);
|
||||
x2ym := x2ym / FLOAT(n);
|
||||
|
||||
sxx := x2m - xm * xm;
|
||||
sxy := xym - xm * ym;
|
||||
sxx2 := x3m - xm * x2m;
|
||||
sx2x2 := x4m - x2m * x2m;
|
||||
sx2y := x2ym - x2m * ym;
|
||||
|
||||
b := (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
|
||||
c := (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
|
||||
a := ym - b * xm - c * x2m;
|
||||
|
||||
WriteString("y = ");
|
||||
RealToStr(a, buf);
|
||||
WriteString(buf);
|
||||
WriteString(" + ");
|
||||
RealToStr(b, buf);
|
||||
WriteString(buf);
|
||||
WriteString("x + ");
|
||||
RealToStr(c, buf);
|
||||
WriteString(buf);
|
||||
WriteString("x^2");
|
||||
WriteLn;
|
||||
|
||||
FOR i:=0 TO n-1 DO
|
||||
FormatString("%2i %3i ", buf, x[i], y[i]);
|
||||
WriteString(buf);
|
||||
RealToStr(Eval(a,b,c,FLOAT(x[i])), buf);
|
||||
WriteString(buf);
|
||||
WriteLn;
|
||||
END;
|
||||
END Regression;
|
||||
|
||||
TYPE R = ARRAY[0..10] OF INTEGER;
|
||||
VAR
|
||||
x,y : R;
|
||||
BEGIN
|
||||
x := R{0,1,2,3,4,5,6,7,8,9,10};
|
||||
y := R{1,6,17,34,57,86,121,162,209,262,321};
|
||||
Regression(x,y);
|
||||
|
||||
ReadChar;
|
||||
END PolynomialRegression.
|
||||
34
Task/Polynomial-regression/Nim/polynomial-regression.nim
Normal file
34
Task/Polynomial-regression/Nim/polynomial-regression.nim
Normal file
|
|
@ -0,0 +1,34 @@
|
|||
import lenientops, sequtils, stats, strformat
|
||||
|
||||
proc polyRegression(x, y: openArray[int]) =
|
||||
|
||||
let xm = mean(x)
|
||||
let ym = mean(y)
|
||||
let x2m = mean(x.mapIt(it * it))
|
||||
let x3m = mean(x.mapIt(it * it * it))
|
||||
let x4m = mean(x.mapIt(it * it * it * it))
|
||||
let xym = mean(zip(x, y).mapIt(it[0] * it[1]))
|
||||
let x2ym = mean(zip(x, y).mapIt(it[0] * it[0] * it[1]))
|
||||
|
||||
let sxx = x2m - xm * xm
|
||||
let sxy = xym - xm * ym
|
||||
let sxx2 = x3m - xm * x2m
|
||||
let sx2x2 = x4m - x2m * x2m
|
||||
let sx2y = x2ym - x2m * ym
|
||||
|
||||
let b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
|
||||
let c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
|
||||
let a = ym - b * xm - c * x2m
|
||||
|
||||
func abc(x: int): float = a + b * x + c * x * x
|
||||
|
||||
echo &"y = {a} + {b}x + {c}x²\n"
|
||||
echo " Input Approximation"
|
||||
echo " x y y1"
|
||||
for (xi, yi) in zip(x, y):
|
||||
echo &"{xi:2} {yi:3} {abc(xi):5}"
|
||||
|
||||
|
||||
let x = toSeq(0..10)
|
||||
let y = [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321]
|
||||
polyRegression(x, y)
|
||||
41
Task/Polynomial-regression/OCaml/polynomial-regression.ocaml
Normal file
41
Task/Polynomial-regression/OCaml/polynomial-regression.ocaml
Normal file
|
|
@ -0,0 +1,41 @@
|
|||
open Base
|
||||
open Stdio
|
||||
|
||||
let mean fa =
|
||||
let open Float in
|
||||
(Array.reduce_exn fa ~f:(+)) / (of_int (Array.length fa))
|
||||
|
||||
let regression xs ys =
|
||||
let open Float in
|
||||
let xm = mean xs in
|
||||
let ym = mean ys in
|
||||
let x2m = Array.map xs ~f:(fun x -> x * x) |> mean in
|
||||
let x3m = Array.map xs ~f:(fun x -> x * x * x) |> mean in
|
||||
let x4m = Array.map xs ~f:(fun x -> let x2 = x * x in x2 * x2) |> mean in
|
||||
let xzipy = Array.zip_exn xs ys in
|
||||
let xym = Array.map xzipy ~f:(fun (x, y) -> x * y) |> mean in
|
||||
let x2ym = Array.map xzipy ~f:(fun (x, y) -> x * x * y) |> mean in
|
||||
|
||||
let sxx = x2m - xm * xm in
|
||||
let sxy = xym - xm * ym in
|
||||
let sxx2 = x3m - xm * x2m in
|
||||
let sx2x2 = x4m - x2m * x2m in
|
||||
let sx2y = x2ym - x2m * ym in
|
||||
|
||||
let b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2) in
|
||||
let c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2) in
|
||||
let a = ym - b * xm - c * x2m in
|
||||
|
||||
let abc xx = a + b * xx + c * xx * xx in
|
||||
|
||||
printf "y = %.1f + %.1fx + %.1fx^2\n\n" a b c;
|
||||
printf " Input Approximation\n";
|
||||
printf " x y y1\n";
|
||||
Array.iter xzipy ~f:(fun (xi, yi) ->
|
||||
printf "%2g %3g %5.1f\n" xi yi (abc xi)
|
||||
)
|
||||
|
||||
let () =
|
||||
let x = Array.init 11 ~f:Float.of_int in
|
||||
let y = [| 1.; 6.; 17.; 34.; 57.; 86.; 121.; 162.; 209.; 262.; 321. |] in
|
||||
regression x y
|
||||
|
|
@ -0,0 +1,3 @@
|
|||
x = [0:10];
|
||||
y = [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321];
|
||||
coeffs = polyfit(x, y, 2)
|
||||
|
|
@ -0,0 +1 @@
|
|||
polinterpolate([0,1,2,3,4,5,6,7,8,9,10],[1,6,17,34,57,86,121,162,209,262,321])
|
||||
|
|
@ -0,0 +1 @@
|
|||
polinterpolate([0..10],[1,6,17,34,57,86,121,162,209,262,321])
|
||||
|
|
@ -0,0 +1,2 @@
|
|||
V=[1,6,17,34,57,86,121,162,209,262,321]~;
|
||||
M=matrix(#V,3,i,j,(i-1)^(j-1));Polrev(matsolve(M~*M,M~*V))
|
||||
|
|
@ -0,0 +1,2 @@
|
|||
lsf(X,Y,n)=my(M=matrix(#X,n+1,i,j,X[i]^(j-1))); Polrev(matsolve(M~*M,M~*Y~))
|
||||
lsf([0..10], [1,6,17,34,57,86,121,162,209,262,321], 2)
|
||||
14
Task/Polynomial-regression/Perl/polynomial-regression-1.pl
Normal file
14
Task/Polynomial-regression/Perl/polynomial-regression-1.pl
Normal file
|
|
@ -0,0 +1,14 @@
|
|||
use strict;
|
||||
use warnings;
|
||||
use Statistics::Regression;
|
||||
|
||||
my @x = <0 1 2 3 4 5 6 7 8 9 10>;
|
||||
my @y = <1 6 17 34 57 86 121 162 209 262 321>;
|
||||
|
||||
my @model = ('const', 'X', 'X**2');
|
||||
|
||||
my $reg = Statistics::Regression->new( '', [@model] );
|
||||
$reg->include( $y[$_], [ 1.0, $x[$_], $x[$_]**2 ]) for 0..@y-1;
|
||||
my @coeff = $reg->theta();
|
||||
|
||||
printf "%-6s %8.3f\n", $model[$_], $coeff[$_] for 0..@model-1;
|
||||
25
Task/Polynomial-regression/Perl/polynomial-regression-2.pl
Normal file
25
Task/Polynomial-regression/Perl/polynomial-regression-2.pl
Normal file
|
|
@ -0,0 +1,25 @@
|
|||
#!/usr/bin/perl -w
|
||||
use strict;
|
||||
|
||||
use PDL;
|
||||
use PDL::Math;
|
||||
use PDL::Fit::Polynomial;
|
||||
|
||||
my $x = float [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
|
||||
my $y = float [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321];
|
||||
# above will output: 3.00000037788248 * $x**2 + 1.99999750988868 * $x + 1.00000180493936
|
||||
|
||||
# $x = float [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9];
|
||||
# $y = float [ 2.7, 2.8, 31.4, 38.1, 58.0, 76.2, 100.5, 130.0, 149.3, 180.0];
|
||||
# above correctly returns: " 1.08484845125187 * $x**2 + 10.3551513321297 * $x-0.616363852007752 "
|
||||
|
||||
my ($yfit, $coeffs) = fitpoly1d $x, $y, 3; # 3rd degree
|
||||
|
||||
foreach (reverse(0..$coeffs->dim(0)-1)) {
|
||||
print " +" unless(($coeffs->at($_) <0) || $_==$coeffs->dim(0)-1); # let the unary minus replace the + operator
|
||||
print " ";
|
||||
print $coeffs->at($_);
|
||||
print " * \$x" if($_);
|
||||
print "**$_" if($_>1);
|
||||
print "\n" unless($_)
|
||||
}
|
||||
73
Task/Polynomial-regression/Phix/polynomial-regression.phix
Normal file
73
Task/Polynomial-regression/Phix/polynomial-regression.phix
Normal file
|
|
@ -0,0 +1,73 @@
|
|||
(phixonline)-->
|
||||
<span style="color: #000080;font-style:italic;">-- demo\rosetta\Polynomial_regression.exw</span>
|
||||
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
|
||||
<span style="color: #008080;">constant</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">},</span>
|
||||
<span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">17</span><span style="color: #0000FF;">,</span><span style="color: #000000;">34</span><span style="color: #0000FF;">,</span><span style="color: #000000;">57</span><span style="color: #0000FF;">,</span><span style="color: #000000;">86</span><span style="color: #0000FF;">,</span><span style="color: #000000;">121</span><span style="color: #0000FF;">,</span><span style="color: #000000;">162</span><span style="color: #0000FF;">,</span><span style="color: #000000;">209</span><span style="color: #0000FF;">,</span><span style="color: #000000;">262</span><span style="color: #0000FF;">,</span><span style="color: #000000;">321</span><span style="color: #0000FF;">},</span>
|
||||
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">regression</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">xm</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ym</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x2m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x3m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x4m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">xym</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x2ym</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">xi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span>
|
||||
<span style="color: #000000;">yi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000000;">xm</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">xi</span>
|
||||
<span style="color: #000000;">ym</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">yi</span>
|
||||
<span style="color: #000000;">x2m</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">x3m</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">x4m</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">xym</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">xi</span><span style="color: #0000FF;">*</span><span style="color: #000000;">yi</span>
|
||||
<span style="color: #000000;">x2ym</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">yi</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #000000;">xm</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">n</span>
|
||||
<span style="color: #000000;">ym</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">n</span>
|
||||
<span style="color: #000000;">x2m</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">n</span>
|
||||
<span style="color: #000000;">x3m</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">n</span>
|
||||
<span style="color: #000000;">x4m</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">n</span>
|
||||
<span style="color: #000000;">xym</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">n</span>
|
||||
<span style="color: #000000;">x2ym</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">n</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">Sxx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x2m</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">Sxy</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">xym</span><span style="color: #0000FF;">-</span><span style="color: #000000;">xm</span><span style="color: #0000FF;">*</span><span style="color: #000000;">ym</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">Sxx2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x3m</span><span style="color: #0000FF;">-</span><span style="color: #000000;">xm</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x2m</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">Sx2x2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x4m</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x2m</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">Sx2y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x2ym</span><span style="color: #0000FF;">-</span><span style="color: #000000;">x2m</span><span style="color: #0000FF;">*</span><span style="color: #000000;">ym</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">B</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">Sxy</span><span style="color: #0000FF;">*</span><span style="color: #000000;">Sx2x2</span><span style="color: #0000FF;">-</span><span style="color: #000000;">Sx2y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">Sxx2</span><span style="color: #0000FF;">)/(</span><span style="color: #000000;">Sxx</span><span style="color: #0000FF;">*</span><span style="color: #000000;">Sx2x2</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">Sxx2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)),</span>
|
||||
<span style="color: #000000;">C</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">Sx2y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">Sxx</span><span style="color: #0000FF;">-</span><span style="color: #000000;">Sxy</span><span style="color: #0000FF;">*</span><span style="color: #000000;">Sxx2</span><span style="color: #0000FF;">)/(</span><span style="color: #000000;">Sxx</span><span style="color: #0000FF;">*</span><span style="color: #000000;">Sx2x2</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">Sxx2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)),</span>
|
||||
<span style="color: #000000;">A</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ym</span><span style="color: #0000FF;">-</span><span style="color: #000000;">B</span><span style="color: #0000FF;">*</span><span style="color: #000000;">xm</span><span style="color: #0000FF;">-</span><span style="color: #000000;">C</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x2m</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">C</span><span style="color: #0000FF;">,</span><span style="color: #000000;">B</span><span style="color: #0000FF;">,</span><span style="color: #000000;">A</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">regression</span><span style="color: #0000FF;">()</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">b</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">c</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"y=%gx^2+%gx+%g\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n x y f(x)\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" %2d %3d %3g\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">y</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])})</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
|
||||
<span style="color: #000080;font-style:italic;">-- And a simple plot (re-using x,y from above)</span>
|
||||
|
||||
<span style="color: #008080;">include</span> <span style="color: #000000;">pGUI</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
|
||||
<span style="color: #008080;">include</span> <span style="color: #000000;">IupGraph</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">get_data</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000000;">graph</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">w</span><span style="color: #0000FF;">,</span><span style="color: #000000;">h</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupGetIntInt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"DRAWSIZE"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">IupSetInt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"YTICK"</span><span style="color: #0000FF;">,</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;"><</span><span style="color: #000000;">240</span><span style="color: #0000FF;">?</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;"><</span><span style="color: #000000;">150</span><span style="color: #0000FF;">?</span><span style="color: #000000;">80</span><span style="color: #0000FF;">:</span><span style="color: #000000;">40</span><span style="color: #0000FF;">):</span><span style="color: #000000;">20</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #004600;">CD_RED</span><span style="color: #0000FF;">}}</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #7060A8;">IupOpen</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">graph</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">IupGraph</span><span style="color: #0000FF;">(</span><span style="color: #000000;">get_data</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"RASTERSIZE=640x440"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">IupSetAttributes</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"XTICK=1,XMIN=0,XMAX=10"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">IupSetAttributes</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"YTICK=20,YMIN=0,YMAX=320"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">dlg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupDialog</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">`TITLE="simple plot"`</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">IupSetAttributes</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"MINSIZE=245x150"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">IupShow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #7060A8;">IupMainLoop</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #7060A8;">IupClose</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<!--
|
||||
|
|
@ -0,0 +1,80 @@
|
|||
function qr([double[][]]$A) {
|
||||
$m,$n = $A.count, $A[0].count
|
||||
$pm,$pn = ($m-1), ($n-1)
|
||||
[double[][]]$Q = 0..($m-1) | foreach{$row = @(0) * $m; $row[$_] = 1; ,$row}
|
||||
[double[][]]$R = $A | foreach{$row = $_; ,@(0..$pn | foreach{$row[$_]})}
|
||||
foreach ($h in 0..$pn) {
|
||||
[double[]]$u = $R[$h..$pm] | foreach{$_[$h]}
|
||||
[double]$nu = $u | foreach {[double]$sq = 0} {$sq += $_*$_} {[Math]::Sqrt($sq)}
|
||||
$u[0] -= if ($u[0] -lt 1) {$nu} else {-$nu}
|
||||
[double]$nu = $u | foreach {$sq = 0} {$sq += $_*$_} {[Math]::Sqrt($sq)}
|
||||
[double[]]$u = $u | foreach { $_/$nu}
|
||||
[double[][]]$v = 0..($u.Count - 1) | foreach{$i = $_; ,($u | foreach{2*$u[$i]*$_})}
|
||||
[double[][]]$CR = $R | foreach{$row = $_; ,@(0..$pn | foreach{$row[$_]})}
|
||||
[double[][]]$CQ = $Q | foreach{$row = $_; ,@(0..$pm | foreach{$row[$_]})}
|
||||
foreach ($i in $h..$pm) {
|
||||
foreach ($j in $h..$pn) {
|
||||
$R[$i][$j] -= $h..$pm | foreach {[double]$sum = 0} {$sum += $v[$i-$h][$_-$h]*$CR[$_][$j]} {$sum}
|
||||
}
|
||||
}
|
||||
if (0 -eq $h) {
|
||||
foreach ($i in $h..$pm) {
|
||||
foreach ($j in $h..$pm) {
|
||||
$Q[$i][$j] -= $h..$pm | foreach {$sum = 0} {$sum += $v[$i][$_]*$CQ[$_][$j]} {$sum}
|
||||
}
|
||||
}
|
||||
} else {
|
||||
$p = $h-1
|
||||
foreach ($i in $h..$pm) {
|
||||
foreach ($j in 0..$p) {
|
||||
$Q[$i][$j] -= $h..$pm | foreach {$sum = 0} {$sum += $v[$i-$h][$_-$h]*$CQ[$_][$j]} {$sum}
|
||||
}
|
||||
foreach ($j in $h..$pm) {
|
||||
$Q[$i][$j] -= $h..$pm | foreach {$sum = 0} {$sum += $v[$i-$h][$_-$h]*$CQ[$_][$j]} {$sum}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
foreach ($i in 0..$pm) {
|
||||
foreach ($j in $i..$pm) {$Q[$i][$j],$Q[$j][$i] = $Q[$j][$i],$Q[$i][$j]}
|
||||
}
|
||||
[PSCustomObject]@{"Q" = $Q; "R" = $R}
|
||||
}
|
||||
|
||||
function leastsquares([Double[][]]$A,[Double[]]$y) {
|
||||
$QR = qr $A
|
||||
[Double[][]]$Q = $QR.Q
|
||||
[Double[][]]$R = $QR.R
|
||||
$m,$n = $A.count, $A[0].count
|
||||
[Double[]]$z = foreach ($j in 0..($m-1)) {
|
||||
0..($m-1) | foreach {$sum = 0} {$sum += $Q[$_][$j]*$y[$_]} {$sum}
|
||||
}
|
||||
[Double[]]$x = @(0)*$n
|
||||
for ($i = $n-1; $i -ge 0; $i--) {
|
||||
for ($j = $i+1; $j -lt $n; $j++) {
|
||||
$z[$i] -= $x[$j]*$R[$i][$j]
|
||||
}
|
||||
$x[$i] = $z[$i]/$R[$i][$i]
|
||||
}
|
||||
$x
|
||||
}
|
||||
|
||||
function polyfit([Double[]]$x,[Double[]]$y,$n) {
|
||||
$m = $x.Count
|
||||
[Double[][]]$A = 0..($m-1) | foreach{$row = @(1) * ($n+1); ,$row}
|
||||
for ($i = 0; $i -lt $m; $i++) {
|
||||
for ($j = $n-1; 0 -le $j; $j--) {
|
||||
$A[$i][$j] = $A[$i][$j+1]*$x[$i]
|
||||
}
|
||||
}
|
||||
leastsquares $A $y
|
||||
}
|
||||
|
||||
function show($m) {$m | foreach {write-host "$_"}}
|
||||
|
||||
$A = @(@(12,-51,4), @(6,167,-68), @(-4,24,-41))
|
||||
$x = @(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
|
||||
$y = @(1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321)
|
||||
"polyfit "
|
||||
"X^2 X constant"
|
||||
"$(polyfit $x $y 2)"
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
>>> x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
|
||||
>>> y = [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321]
|
||||
>>> coeffs = numpy.polyfit(x,y,deg=2)
|
||||
>>> coeffs
|
||||
array([ 3., 2., 1.])
|
||||
|
|
@ -0,0 +1,3 @@
|
|||
>>> yf = numpy.polyval(numpy.poly1d(coeffs), x)
|
||||
>>> yf
|
||||
array([ 1., 6., 17., 34., 57., 86., 121., 162., 209., 262., 321.])
|
||||
|
|
@ -0,0 +1,2 @@
|
|||
>>> '%.1g' % max(y-yf)
|
||||
'1e-013'
|
||||
|
|
@ -0,0 +1,2 @@
|
|||
>>> x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
|
||||
>>> y = [2.7, 2.8, 31.4, 38.1, 58.0, 76.2, 100.5, 130.0, 149.3, 180.0]
|
||||
|
|
@ -0,0 +1,4 @@
|
|||
>>> p = numpy.poly1d(numpy.polyfit(x, y, deg=2), variable='N')
|
||||
>>> print p
|
||||
2
|
||||
1.085 N + 10.36 N - 0.6164
|
||||
3
Task/Polynomial-regression/R/polynomial-regression-1.r
Normal file
3
Task/Polynomial-regression/R/polynomial-regression-1.r
Normal file
|
|
@ -0,0 +1,3 @@
|
|||
x <- c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
|
||||
y <- c(1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321)
|
||||
coef(lm(y ~ x + I(x^2)))
|
||||
1
Task/Polynomial-regression/R/polynomial-regression-2.r
Normal file
1
Task/Polynomial-regression/R/polynomial-regression-2.r
Normal file
|
|
@ -0,0 +1 @@
|
|||
coef(lm(y ~ poly(x, 2, raw=T)))
|
||||
51
Task/Polynomial-regression/REXX/polynomial-regression.rexx
Normal file
51
Task/Polynomial-regression/REXX/polynomial-regression.rexx
Normal file
|
|
@ -0,0 +1,51 @@
|
|||
/* REXX ---------------------------------------------------------------
|
||||
* Implementation of http://keisan.casio.com/exec/system/14059932254941
|
||||
*--------------------------------------------------------------------*/
|
||||
xl='0 1 2 3 4 5 6 7 8 9 10'
|
||||
yl='1 6 17 34 57 86 121 162 209 262 321'
|
||||
n=11
|
||||
Do i=1 To n
|
||||
Parse Var xl x.i xl
|
||||
Parse Var yl y.i yl
|
||||
End
|
||||
xm=0
|
||||
ym=0
|
||||
x2m=0
|
||||
x3m=0
|
||||
x4m=0
|
||||
xym=0
|
||||
x2ym=0
|
||||
Do i=1 To n
|
||||
xm=xm+x.i
|
||||
ym=ym+y.i
|
||||
x2m=x2m+x.i**2
|
||||
x3m=x3m+x.i**3
|
||||
x4m=x4m+x.i**4
|
||||
xym=xym+x.i*y.i
|
||||
x2ym=x2ym+(x.i**2)*y.i
|
||||
End
|
||||
xm =xm /n
|
||||
ym =ym /n
|
||||
x2m=x2m/n
|
||||
x3m=x3m/n
|
||||
x4m=x4m/n
|
||||
xym=xym/n
|
||||
x2ym=x2ym/n
|
||||
Sxx=x2m-xm**2
|
||||
Sxy=xym-xm*ym
|
||||
Sxx2=x3m-xm*x2m
|
||||
Sx2x2=x4m-x2m**2
|
||||
Sx2y=x2ym-x2m*ym
|
||||
B=(Sxy*Sx2x2-Sx2y*Sxx2)/(Sxx*Sx2x2-Sxx2**2)
|
||||
C=(Sx2y*Sxx-Sxy*Sxx2)/(Sxx*Sx2x2-Sxx2**2)
|
||||
A=ym-B*xm-C*x2m
|
||||
Say 'y='a'+'||b'*x+'c'*x**2'
|
||||
Say ' Input "Approximation"'
|
||||
Say ' x y y1'
|
||||
Do i=1 To 11
|
||||
Say right(x.i,2) right(y.i,3) format(fun(x.i),5,3)
|
||||
End
|
||||
Exit
|
||||
fun:
|
||||
Parse Arg x
|
||||
Return a+b*x+c*x**2
|
||||
18
Task/Polynomial-regression/Racket/polynomial-regression.rkt
Normal file
18
Task/Polynomial-regression/Racket/polynomial-regression.rkt
Normal file
|
|
@ -0,0 +1,18 @@
|
|||
#lang racket
|
||||
(require math plot)
|
||||
|
||||
(define xs '(0 1 2 3 4 5 6 7 8 9 10))
|
||||
(define ys '(1 6 17 34 57 86 121 162 209 262 321))
|
||||
|
||||
(define (fit x y n)
|
||||
(define Y (->col-matrix y))
|
||||
(define V (vandermonde-matrix x (+ n 1)))
|
||||
(define VT (matrix-transpose V))
|
||||
(matrix->vector (matrix-solve (matrix* VT V) (matrix* VT Y))))
|
||||
|
||||
(define ((poly v) x)
|
||||
(for/sum ([c v] [i (in-naturals)])
|
||||
(* c (expt x i))))
|
||||
|
||||
(plot (list (points (map vector xs ys))
|
||||
(function (poly (fit xs ys 2)))))
|
||||
20
Task/Polynomial-regression/Raku/polynomial-regression.raku
Normal file
20
Task/Polynomial-regression/Raku/polynomial-regression.raku
Normal file
|
|
@ -0,0 +1,20 @@
|
|||
use Clifford;
|
||||
|
||||
constant @x1 = <0 1 2 3 4 5 6 7 8 9 10>;
|
||||
constant @y = <1 6 17 34 57 86 121 162 209 262 321>;
|
||||
|
||||
constant $x0 = [+] @e[^@x1];
|
||||
constant $x1 = [+] @x1 Z* @e;
|
||||
constant $x2 = [+] @x1 »**» 2 Z* @e;
|
||||
|
||||
constant $y = [+] @y Z* @e;
|
||||
|
||||
my $J = $x1 ∧ $x2;
|
||||
my $I = $x0 ∧ $J;
|
||||
|
||||
my $I2 = ($I·$I.reversion).Real;
|
||||
|
||||
.say for
|
||||
(($y ∧ $J)·$I.reversion)/$I2,
|
||||
(($y ∧ ($x2 ∧ $x0))·$I.reversion)/$I2,
|
||||
(($y ∧ ($x0 ∧ $x1))·$I.reversion)/$I2;
|
||||
10
Task/Polynomial-regression/Ruby/polynomial-regression-1.rb
Normal file
10
Task/Polynomial-regression/Ruby/polynomial-regression-1.rb
Normal file
|
|
@ -0,0 +1,10 @@
|
|||
require 'matrix'
|
||||
|
||||
def regress x, y, degree
|
||||
x_data = x.map { |xi| (0..degree).map { |pow| (xi**pow).to_r } }
|
||||
|
||||
mx = Matrix[*x_data]
|
||||
my = Matrix.column_vector(y)
|
||||
|
||||
((mx.t * mx).inv * mx.t * my).transpose.to_a[0].map(&:to_f)
|
||||
end
|
||||
|
|
@ -0,0 +1,3 @@
|
|||
p regress([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
|
||||
[1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321],
|
||||
2)
|
||||
34
Task/Polynomial-regression/Scala/polynomial-regression.scala
Normal file
34
Task/Polynomial-regression/Scala/polynomial-regression.scala
Normal file
|
|
@ -0,0 +1,34 @@
|
|||
object PolynomialRegression extends App {
|
||||
private def xy = Seq(1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321).zipWithIndex.map(_.swap)
|
||||
|
||||
private def polyRegression(xy: Seq[(Int, Int)]): Unit = {
|
||||
val r = xy.indices
|
||||
|
||||
def average[U](ts: Iterable[U])(implicit num: Numeric[U]) = num.toDouble(ts.sum) / ts.size
|
||||
|
||||
def x3m: Double = average(r.map(a => a * a * a))
|
||||
def x4m: Double = average(r.map(a => a * a * a * a))
|
||||
def x2ym = xy.reduce((a, x) => (a._1 + x._1 * x._1 * x._2, 0))._1.toDouble / xy.size
|
||||
def xym = xy.reduce((a, x) => (a._1 + x._1 * x._2, 0))._1.toDouble / xy.size
|
||||
|
||||
val x2m: Double = average(r.map(a => a * a))
|
||||
val (xm, ym) = (average(xy.map(_._1)), average(xy.map(_._2)))
|
||||
val (sxx, sxy) = (x2m - xm * xm, xym - xm * ym)
|
||||
val sxx2: Double = x3m - xm * x2m
|
||||
val sx2x2: Double = x4m - x2m * x2m
|
||||
val sx2y: Double = x2ym - x2m * ym
|
||||
val c: Double = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
|
||||
val b: Double = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
|
||||
val a: Double = ym - b * xm - c * x2m
|
||||
|
||||
def abc(xx: Int) = a + b * xx + c * xx * xx
|
||||
|
||||
println(s"y = $a + ${b}x + ${c}x^2")
|
||||
println(" Input Approximation")
|
||||
println(" x y y1")
|
||||
xy.foreach {el => println(f"${el._1}%2d ${el._2}%3d ${abc(el._1)}%5.1f")}
|
||||
}
|
||||
|
||||
polyRegression(xy)
|
||||
|
||||
}
|
||||
20
Task/Polynomial-regression/Sidef/polynomial-regression.sidef
Normal file
20
Task/Polynomial-regression/Sidef/polynomial-regression.sidef
Normal file
|
|
@ -0,0 +1,20 @@
|
|||
func regress(x, y, degree) {
|
||||
var A = Matrix.build(x.len, degree+1, {|i,j|
|
||||
x[i]**j
|
||||
})
|
||||
|
||||
var B = Matrix.column_vector(y...)
|
||||
((A.transpose * A)**(-1) * A.transpose * B).transpose[0]
|
||||
}
|
||||
|
||||
func poly(x) {
|
||||
3*x**2 + 2*x + 1
|
||||
}
|
||||
|
||||
var coeff = regress(
|
||||
10.of { _ },
|
||||
10.of { poly(_) },
|
||||
2
|
||||
)
|
||||
|
||||
say coeff
|
||||
33
Task/Polynomial-regression/Stata/polynomial-regression.stata
Normal file
33
Task/Polynomial-regression/Stata/polynomial-regression.stata
Normal file
|
|
@ -0,0 +1,33 @@
|
|||
. clear
|
||||
. input x y
|
||||
0 1
|
||||
1 6
|
||||
2 17
|
||||
3 34
|
||||
4 57
|
||||
5 86
|
||||
6 121
|
||||
7 162
|
||||
8 209
|
||||
9 262
|
||||
10 321
|
||||
end
|
||||
|
||||
. regress y c.x##c.x
|
||||
|
||||
Source | SS df MS Number of obs = 11
|
||||
-------------+---------------------------------- F(2, 8) = .
|
||||
Model | 120362 2 60181 Prob > F = .
|
||||
Residual | 0 8 0 R-squared = 1.0000
|
||||
-------------+---------------------------------- Adj R-squared = 1.0000
|
||||
Total | 120362 10 12036.2 Root MSE = 0
|
||||
|
||||
------------------------------------------------------------------------------
|
||||
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
|
||||
-------------+----------------------------------------------------------------
|
||||
x | 2 . . . . .
|
||||
|
|
||||
c.x#c.x | 3 . . . . .
|
||||
|
|
||||
_cons | 1 . . . . .
|
||||
------------------------------------------------------------------------------
|
||||
41
Task/Polynomial-regression/Swift/polynomial-regression.swift
Normal file
41
Task/Polynomial-regression/Swift/polynomial-regression.swift
Normal file
|
|
@ -0,0 +1,41 @@
|
|||
let x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
|
||||
let y = [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321]
|
||||
|
||||
func average(_ input: [Int]) -> Int {
|
||||
return input.reduce(0, +) / input.count
|
||||
}
|
||||
|
||||
func polyRegression(x: [Int], y: [Int]) {
|
||||
let xm = average(x)
|
||||
let ym = average(y)
|
||||
let x2m = average(x.map { $0 * $0 })
|
||||
let x3m = average(x.map { $0 * $0 * $0 })
|
||||
let x4m = average(x.map { $0 * $0 * $0 * $0 })
|
||||
let xym = average(zip(x,y).map { $0 * $1 })
|
||||
let x2ym = average(zip(x,y).map { $0 * $0 * $1 })
|
||||
|
||||
let sxx = x2m - xm * xm
|
||||
let sxy = xym - xm * ym
|
||||
let sxx2 = x3m - xm * x2m
|
||||
let sx2x2 = x4m - x2m * x2m
|
||||
let sx2y = x2ym - x2m * ym
|
||||
|
||||
let b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
|
||||
let c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
|
||||
let a = ym - b * xm - c * x2m
|
||||
|
||||
func abc(xx: Int) -> Int {
|
||||
return (a + b * xx) + (c * xx * xx)
|
||||
}
|
||||
|
||||
print("y = \(a) + \(b)x + \(c)x^2\n")
|
||||
print(" Input Approximation")
|
||||
print(" x y y1")
|
||||
|
||||
for i in 0 ..< x.count {
|
||||
let result = Double(abc(xx: i))
|
||||
print(String(format: "%2d %3d %5.1f", x[i], y[i], result))
|
||||
}
|
||||
}
|
||||
|
||||
polyRegression(x: x, y: y)
|
||||
|
|
@ -0,0 +1,4 @@
|
|||
DelVar X
|
||||
seq(X,X,0,10) → L1
|
||||
{1,6,17,34,57,86,121,162,209,262,321} → L2
|
||||
QuadReg L1,L2
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
DelVar x
|
||||
seq(x,x,0,10) → xs
|
||||
{1,6,17,34,57,86,121,162,209,262,321} → ys
|
||||
QuadReg xs,ys
|
||||
Disp regeq(x)
|
||||
49
Task/Polynomial-regression/Tcl/polynomial-regression.tcl
Normal file
49
Task/Polynomial-regression/Tcl/polynomial-regression.tcl
Normal file
|
|
@ -0,0 +1,49 @@
|
|||
package require math::linearalgebra
|
||||
|
||||
proc build.matrix {xvec degree} {
|
||||
set sums [llength $xvec]
|
||||
for {set i 1} {$i <= 2*$degree} {incr i} {
|
||||
set sum 0
|
||||
foreach x $xvec {
|
||||
set sum [expr {$sum + pow($x,$i)}]
|
||||
}
|
||||
lappend sums $sum
|
||||
}
|
||||
|
||||
set order [expr {$degree + 1}]
|
||||
set A [math::linearalgebra::mkMatrix $order $order 0]
|
||||
for {set i 0} {$i <= $degree} {incr i} {
|
||||
set A [math::linearalgebra::setrow A $i [lrange $sums $i $i+$degree]]
|
||||
}
|
||||
return $A
|
||||
}
|
||||
|
||||
proc build.vector {xvec yvec degree} {
|
||||
set sums [list]
|
||||
for {set i 0} {$i <= $degree} {incr i} {
|
||||
set sum 0
|
||||
foreach x $xvec y $yvec {
|
||||
set sum [expr {$sum + $y * pow($x,$i)}]
|
||||
}
|
||||
lappend sums $sum
|
||||
}
|
||||
|
||||
set x [math::linearalgebra::mkVector [expr {$degree + 1}] 0]
|
||||
for {set i 0} {$i <= $degree} {incr i} {
|
||||
set x [math::linearalgebra::setelem x $i [lindex $sums $i]]
|
||||
}
|
||||
return $x
|
||||
}
|
||||
|
||||
# Now, to solve the example from the top of this page
|
||||
set x {0 1 2 3 4 5 6 7 8 9 10}
|
||||
set y {1 6 17 34 57 86 121 162 209 262 321}
|
||||
|
||||
# build the system A.x=b
|
||||
set degree 2
|
||||
set A [build.matrix $x $degree]
|
||||
set b [build.vector $x $y $degree]
|
||||
# solve it
|
||||
set coeffs [math::linearalgebra::solveGauss $A $b]
|
||||
# show results
|
||||
puts $coeffs
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
#import std
|
||||
#import nat
|
||||
#import flo
|
||||
|
||||
(fit "n") ("x","y") = ..dgelsd\"y" (gang \/*pow float*x iota successor "n")* "x"
|
||||
|
|
@ -0,0 +1,6 @@
|
|||
x = <0.,1.,2.,3.,4.,5.,6.,7.,8.,9.,10.>
|
||||
y = <1.,6.,17.,34.,57.,86.,121.,162.,209.,262.,321.>
|
||||
|
||||
#cast %eL
|
||||
|
||||
example = fit2(x,y)
|
||||
30
Task/Polynomial-regression/VBA/polynomial-regression.vba
Normal file
30
Task/Polynomial-regression/VBA/polynomial-regression.vba
Normal file
|
|
@ -0,0 +1,30 @@
|
|||
Option Base 1
|
||||
Private Function polynomial_regression(y As Variant, x As Variant, degree As Integer) As Variant
|
||||
Dim a() As Double
|
||||
ReDim a(UBound(x), 2)
|
||||
For i = 1 To UBound(x)
|
||||
For j = 1 To degree
|
||||
a(i, j) = x(i) ^ j
|
||||
Next j
|
||||
Next i
|
||||
polynomial_regression = WorksheetFunction.LinEst(WorksheetFunction.Transpose(y), a, True, True)
|
||||
End Function
|
||||
Public Sub main()
|
||||
x = [{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}]
|
||||
y = [{1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321}]
|
||||
result = polynomial_regression(y, x, 2)
|
||||
Debug.Print "coefficients : ";
|
||||
For i = UBound(result, 2) To 1 Step -1
|
||||
Debug.Print Format(result(1, i), "0.#####"),
|
||||
Next i
|
||||
Debug.Print
|
||||
Debug.Print "standard errors: ";
|
||||
For i = UBound(result, 2) To 1 Step -1
|
||||
Debug.Print Format(result(2, i), "0.#####"),
|
||||
Next i
|
||||
Debug.Print vbCrLf
|
||||
Debug.Print "R^2 ="; result(3, 1)
|
||||
Debug.Print "F ="; result(4, 1)
|
||||
Debug.Print "Degrees of freedom:"; result(4, 2)
|
||||
Debug.Print "Standard error of y estimate:"; result(3, 2)
|
||||
End Sub
|
||||
36
Task/Polynomial-regression/Wren/polynomial-regression.wren
Normal file
36
Task/Polynomial-regression/Wren/polynomial-regression.wren
Normal file
|
|
@ -0,0 +1,36 @@
|
|||
import "/math" for Nums
|
||||
import "/seq" for Lst
|
||||
import "/fmt" for Fmt
|
||||
|
||||
var polynomialRegression = Fn.new { |x, y|
|
||||
var xm = Nums.mean(x)
|
||||
var ym = Nums.mean(y)
|
||||
var x2m = Nums.mean(x.map { |e| e * e })
|
||||
var x3m = Nums.mean(x.map { |e| e * e * e })
|
||||
var x4m = Nums.mean(x.map { |e| e * e * e * e })
|
||||
var z = Lst.zip(x, y)
|
||||
var xym = Nums.mean(z.map { |p| p[0] * p[1] })
|
||||
var x2ym = Nums.mean(z.map { |p| p[0] * p[0] * p[1] })
|
||||
|
||||
var sxx = x2m - xm * xm
|
||||
var sxy = xym - xm * ym
|
||||
var sxx2 = x3m - xm * x2m
|
||||
var sx2x2 = x4m - x2m * x2m
|
||||
var sx2y = x2ym - x2m * ym
|
||||
|
||||
var b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
|
||||
var c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
|
||||
var a = ym - b * xm - c * x2m
|
||||
|
||||
var abc = Fn.new { |xx| a + b * xx + c * xx * xx }
|
||||
|
||||
System.print("y = %(a) + %(b)x + %(c)x^2\n")
|
||||
System.print(" Input Approximation")
|
||||
System.print(" x y y1")
|
||||
for (p in z) Fmt.print("$2d $3d $5.1f", p[0], p[1], abc.call(p[0]))
|
||||
}
|
||||
|
||||
var x = List.filled(11, 0)
|
||||
for (i in 1..10) x[i] = i
|
||||
var y = [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321]
|
||||
polynomialRegression.call(x, y)
|
||||
|
|
@ -0,0 +1,7 @@
|
|||
var [const] GSL=Import("zklGSL"); // libGSL (GNU Scientific Library)
|
||||
xs:=GSL.VectorFromData(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10);
|
||||
ys:=GSL.VectorFromData(1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321);
|
||||
v :=GSL.polyFit(xs,ys,2);
|
||||
v.format().println();
|
||||
GSL.Helpers.polyString(v).println();
|
||||
GSL.Helpers.polyEval(v,xs).format().println();
|
||||
|
|
@ -0,0 +1,3 @@
|
|||
polyfit(T(T(0.0,1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0,10.0)),
|
||||
T(T(1.0,6.0,17.0,34.0,57.0,86.0,121.0,162.0,209.0,262.0,321.0)), 2)
|
||||
.flatten().println();
|
||||
Loading…
Add table
Add a link
Reference in a new issue