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3
Task/Multiple-regression/00-META.yaml
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3
Task/Multiple-regression/00-META.yaml
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---
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from: http://rosettacode.org/wiki/Multiple_regression
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note: Probability and statistics
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14
Task/Multiple-regression/00-TASK.txt
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14
Task/Multiple-regression/00-TASK.txt
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;Task:
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Given a set of data vectors in the following format:
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<math>y = \{ y_1, y_2, ..., y_n \}\,</math>
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<math>X_i = \{ x_{i1}, x_{i2}, ..., x_{in} \}, i \in 1..k\,</math>
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Compute the vector <math>\beta = \{ \beta_1, \beta_2, ..., \beta_k \}</math> using [[wp:Ordinary least squares|ordinary least squares]] regression using the following equation:
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<math>y_j = \Sigma_i \beta_i \cdot x_{ij} , j \in 1..n</math>
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You can assume <i> y </i> is given to you as a vector (a one-dimensional array), and <i> X </i> is given to you as a two-dimensional array (i.e. matrix).
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<br><br>
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202
Task/Multiple-regression/ALGOL-68/multiple-regression.alg
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202
Task/Multiple-regression/ALGOL-68/multiple-regression.alg
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BEGIN # Multiple Regression - trnslation of the VB.NET sample but using the #
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# "to reduced row echelon form" routine from the Reduced row echelon Task #
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PROC require = ( BOOL condition, STRING message )VOID:
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IF NOT condition THEN
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print( ( message, newline ) );
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stop
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FI # requiree # ;
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MODE MATRIX = STRUCT( REF[,]REAL data
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, INT row count
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, INT col count
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);
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PRIO NEWMATRIX = 1;
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OP NEWMATRIX = ( INT rows, INT cols )MATRIX:
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BEGIN
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MATRIX result;
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require( rows > 0, "Need at least one row" );
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row count OF result := rows;
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require( cols > 0, "Need at least one column" );
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col count OF result := cols;
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data OF result := HEAP[ 1 : rows, 1 : cols ]REAL;
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FOR r TO rows DO FOR c TO cols DO ( data OF result )[ r, c ] := 0 OD OD;
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result
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END # NEWMATRIX # ;
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OP NEWMATRIX = ( [,]REAL source )MATRIX:
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BEGIN
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MATRIX result;
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INT rows = 1 + ( 1 UPB source - 1 LWB source );
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require( rows > 0, "Need at least one row" );
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row count OF result := rows;
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INT cols = 1 + ( 2 UPB source - 2 LWB source );
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require( cols > 0, "Need at least one column" );
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col count OF result := cols;
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data OF result := HEAP[ 1 : rows, 1 : cols ]REAL := source[ AT 1, AT 1 ];
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result
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END # NEWMATRIX # ;
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OP NEWMATRIX = ( []REAL source )MATRIX: # New Matrix(ConvertArray(source)) #
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BEGIN
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INT len = 1 + ( UPB source - LWB source );
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[ 1 : 1, 1 : len ]REAL dest;
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dest[ 1, : ] := source;
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NEWMATRIX dest
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END # NEWMATRIX # ;
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OP * = ( MATRIX m1, m2 )MATRIX:
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BEGIN
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INT rc1 = row count OF m1;
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INT cc1 = col count OF m1;
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INT rc2 = row count OF m2;
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INT cc2 = col count OF m2;
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require( cc1 = rc2, "Cannot multiply if the first columns does not equal the second rows" );
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MATRIX result := rc1 NEWMATRIX cc2;
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FOR i TO rc1 DO
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FOR j TO cc2 DO
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FOR k TO rc2 DO
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( data OF result ) [ i, j ] +:= ( data OF m1 )[ i, k ]
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* ( data OF m2 )[ k, j ]
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OD
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OD
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OD;
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result
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END # * # ;
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PROC transpose = ( MATRIX m )MATRIX:
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BEGIN
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INT rc = row count OF m;
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INT cc = col count OF m;
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MATRIX trans := cc NEWMATRIX rc;
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FOR i TO cc DO
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FOR j TO rc DO
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( data OF trans )[ i, j ] := ( data OF m )[ j, i ]
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OD
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OD;
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trans
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END # transpose # ;
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# BEGIN code from the Reduced row echelon form task #
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MODE FIELD = REAL; # FIELD can be REAL, LONG REAL etc, or COMPL, FRAC etc #
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MODE VEC = [0]FIELD;
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MODE MAT = [0,0]FIELD;
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PROC to reduced row echelon form = (REF MAT m)VOID: (
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INT lead col := 2 LWB m;
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FOR this row FROM LWB m TO UPB m DO
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IF lead col > 2 UPB m THEN return FI;
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INT other row := this row;
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WHILE m[other row,lead col] = 0 DO
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other row +:= 1;
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IF other row > UPB m THEN
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other row := this row;
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lead col +:= 1;
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IF lead col > 2 UPB m THEN return FI
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FI
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OD;
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IF this row /= other row THEN
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VEC swap = m[this row,lead col:];
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m[this row,lead col:] := m[other row,lead col:];
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m[other row,lead col:] := swap
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FI;
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FIELD scale = 1/m[this row,lead col];
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IF scale /= 1 THEN
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m[this row,lead col] := 1;
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FOR col FROM lead col+1 TO 2 UPB m DO m[this row,col] *:= scale OD
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FI;
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FOR other row FROM LWB m TO UPB m DO
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IF this row /= other row THEN
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REAL scale = m[other row,lead col];
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m[other row,lead col]:=0;
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FOR col FROM lead col+1 TO 2 UPB m DO m[other row,col] -:= scale*m[this row,col] OD
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FI
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OD;
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lead col +:= 1
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OD;
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return: EMPTY
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);
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# END code from the Reduced row echelon form task #
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PROC inverse = ( MATRIX m )MATRIX:
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BEGIN
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require( row count OF m = col count OF m, "Not a square matrix" );
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INT len = row count OF m;
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MATRIX aug := len NEWMATRIX ( 2 * len );
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FOR i TO len DO
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FOR j TO len DO
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( data OF aug )[ i, j ] := ( data OF m )[ i, j ];
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( data OF aug )[ i, j + len ] := 0
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OD;
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# augment identity matrix to right #
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( data OF aug )[ i, i + len ] := 1.0
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OD;
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to reduced row echelon form( data OF aug );
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MATRIX inv := len NEWMATRIX len;
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FOR i TO len DO
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FOR j FROM len + 1 TO 2 * len DO
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( data OF inv)[ i, j - len ] := ( data OF aug )[ i, j ]
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OD
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OD;
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inv
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END # inverse # ;
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PROC multiple regression = ( []REAL y, MATRIX x )[]REAL:
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BEGIN
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MATRIX tm := NEWMATRIX y;
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MATRIX cy := NEWMATRIX data OF transpose( tm );
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MATRIX cx := NEWMATRIX data OF transpose( x );
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( data OF transpose( inverse( x * cx ) * x * cy ) )[ 1, : ]
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END # multiple regression # ;
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OP PRINTARRAY = ( []REAL list )VOID:
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BEGIN
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print( ( "[" ) );
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FOR i FROM LWB list TO UPB list DO
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# convert list[ i ] to a string, remove trailing 0s and leading spaces #
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STRING v := fixed( list[ i ], -20, 15 )[ AT 1 ];
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WHILE v[ UPB v ] = "0" DO v := v[ : UPB v - 1 ] OD;
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IF v[ UPB v ] = "." THEN v := v[ : UPB v - 1 ] FI;
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WHILE v[ 1 ] = " " DO v := v[ 2 : ] OD;
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print( ( IF i > LWB list THEN ", " ELSE "" FI, v ) )
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OD;
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print( ( "]" ) )
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END # PRINTARRAY # ;
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BEGIN
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[]REAL y = ( 1.0, 2.0, 3.0, 4.0, 5.0 );
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MATRIX x := NEWMATRIX []REAL( 2.0, 1.0, 3.0, 4.0, 5.0 );
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[]REAL v = multiple regression( y, x );
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PRINTARRAY v;
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print( ( newline ) )
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END;
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BEGIN
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[]REAL y = ( 3.0, 4.0, 5.0 );
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MATRIX x := NEWMATRIX [,]REAL( ( 1.0, 2.0, 1.0 )
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, ( 1.0, 1.0, 2.0 )
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);
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[]REAL v = multiple regression( y, x );
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PRINTARRAY v;
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print( ( newline ) )
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END;
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BEGIN
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[]REAL y = ( 52.21, 53.12, 54.48, 55.84, 57.2, 58.57, 59.93
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, 61.29, 63.11, 64.47, 66.28, 68.1, 69.92, 72.19, 74.46
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);
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[]REAL a = ( 1.47, 1.5, 1.52, 1.55, 1.57, 1.6, 1.63, 1.65
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, 1.68, 1.7, 1.73, 1.75, 1.78, 1.8, 1.83
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);
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[ 1 : 3, 1 : 1 + ( UPB a - LWB a ) ]REAL xs;
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FOR i FROM LWB a TO UPB a DO
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xs[ 1, i ] := 1.0;
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xs[ 2, i ] := a[ i ];
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xs[ 3, i ] := a[ i ] * a[ i ]
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OD;
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MATRIX x := NEWMATRIX xs;
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[]REAL v = multiple regression( y, x );
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PRINTARRAY v;
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print( ( newline ) )
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END
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END
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38
Task/Multiple-regression/Ada/multiple-regression-1.ada
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38
Task/Multiple-regression/Ada/multiple-regression-1.ada
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generic
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type Element_Type is private;
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Zero : Element_Type;
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One : Element_Type;
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with function "+" (Left, Right : Element_Type) return Element_Type is <>;
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with function "-" (Left, Right : Element_Type) return Element_Type is <>;
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with function "*" (Left, Right : Element_Type) return Element_Type is <>;
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with function "/" (Left, Right : Element_Type) return Element_Type is <>;
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package Matrices is
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type Vector is array (Positive range <>) of Element_Type;
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type Matrix is
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array (Positive range <>, Positive range <>) of Element_Type;
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function "*" (Left, Right : Matrix) return Matrix;
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function Invert (Source : Matrix) return Matrix;
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function Reduced_Row_Echelon_Form (Source : Matrix) return Matrix;
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function Regression_Coefficients
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(Source : Vector;
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Regressors : Matrix)
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return Vector;
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function To_Column_Vector
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(Source : Matrix;
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Row : Positive := 1)
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return Vector;
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function To_Matrix
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(Source : Vector;
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Column_Vector : Boolean := True)
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return Matrix;
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function To_Row_Vector
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(Source : Matrix;
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Column : Positive := 1)
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return Vector;
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function Transpose (Source : Matrix) return Matrix;
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Size_Mismatch : exception;
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Not_Square_Matrix : exception;
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Not_Invertible : exception;
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end Matrices;
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189
Task/Multiple-regression/Ada/multiple-regression-2.ada
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189
Task/Multiple-regression/Ada/multiple-regression-2.ada
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package body Matrices is
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function "*" (Left, Right : Matrix) return Matrix is
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Result : Matrix (Left'Range (1), Right'Range (2)) :=
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(others => (others => Zero));
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begin
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if Left'Length (2) /= Right'Length (1) then
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raise Size_Mismatch;
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end if;
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for I in Result'Range (1) loop
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for K in Result'Range (2) loop
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for J in Left'Range (2) loop
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Result (I, K) := Result (I, K) + Left (I, J) * Right (J, K);
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end loop;
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end loop;
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end loop;
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return Result;
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end "*";
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function Invert (Source : Matrix) return Matrix is
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Expanded : Matrix (Source'Range (1),
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Source'First (2) .. Source'Last (2) * 2);
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Result : Matrix (Source'Range (1), Source'Range (2));
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begin
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-- Matrix has to be square.
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if Source'Length (1) /= Source'Length (2) then
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raise Not_Square_Matrix;
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end if;
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-- Copy Source into Expanded matrix and attach identity matrix to right
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for Row in Source'Range (1) loop
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for Col in Source'Range (2) loop
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Expanded (Row, Col) := Source (Row, Col);
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Expanded (Row, Source'Last (2) + Col) := Zero;
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end loop;
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Expanded (Row, Source'Last (2) + Row) := One;
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end loop;
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Expanded := Reduced_Row_Echelon_Form (Source => Expanded);
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-- Copy right side to Result (= inverted Source)
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for Row in Result'Range (1) loop
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for Col in Result'Range (2) loop
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Result (Row, Col) := Expanded (Row, Source'Last (2) + Col);
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end loop;
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end loop;
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return Result;
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end Invert;
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function Reduced_Row_Echelon_Form (Source : Matrix) return Matrix is
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procedure Divide_Row
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(From : in out Matrix;
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Row : Positive;
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Divisor : Element_Type)
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is
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begin
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for Col in From'Range (2) loop
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From (Row, Col) := From (Row, Col) / Divisor;
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end loop;
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end Divide_Row;
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procedure Subtract_Rows
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(From : in out Matrix;
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Subtrahend, Minuend : Positive;
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Factor : Element_Type)
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is
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begin
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for Col in From'Range (2) loop
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From (Minuend, Col) := From (Minuend, Col) -
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From (Subtrahend, Col) * Factor;
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end loop;
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end Subtract_Rows;
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procedure Swap_Rows (From : in out Matrix; First, Second : Positive) is
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Temporary : Element_Type;
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begin
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for Col in From'Range (2) loop
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Temporary := From (First, Col);
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From (First, Col) := From (Second, Col);
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From (Second, Col) := Temporary;
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end loop;
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end Swap_Rows;
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Result : Matrix := Source;
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Lead : Positive := Result'First (2);
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I : Positive;
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begin
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Rows : for Row in Result'Range (1) loop
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exit Rows when Lead > Result'Last (2);
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I := Row;
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while Result (I, Lead) = Zero loop
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I := I + 1;
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if I = Result'Last (1) then
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I := Row;
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Lead := Lead + 1;
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exit Rows when Lead = Result'Last (2);
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end if;
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end loop;
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if I /= Row then
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Swap_Rows (From => Result, First => I, Second => Row);
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end if;
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Divide_Row
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(From => Result,
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Row => Row,
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Divisor => Result (Row, Lead));
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for Other_Row in Result'Range (1) loop
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if Other_Row /= Row then
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Subtract_Rows
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(From => Result,
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Subtrahend => Row,
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Minuend => Other_Row,
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Factor => Result (Other_Row, Lead));
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end if;
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end loop;
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Lead := Lead + 1;
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end loop Rows;
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return Result;
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end Reduced_Row_Echelon_Form;
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function Regression_Coefficients
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(Source : Vector;
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Regressors : Matrix)
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return Vector
|
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is
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Result : Matrix (Regressors'Range (2), 1 .. 1);
|
||||
begin
|
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if Source'Length /= Regressors'Length (1) then
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raise Size_Mismatch;
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end if;
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declare
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Regressors_T : constant Matrix := Transpose (Regressors);
|
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begin
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Result := Invert (Regressors_T * Regressors) *
|
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Regressors_T *
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To_Matrix (Source);
|
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end;
|
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return To_Row_Vector (Source => Result);
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end Regression_Coefficients;
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function To_Column_Vector
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(Source : Matrix;
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Row : Positive := 1)
|
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return Vector
|
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is
|
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Result : Vector (Source'Range (2));
|
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begin
|
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for Column in Result'Range loop
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Result (Column) := Source (Row, Column);
|
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end loop;
|
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return Result;
|
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end To_Column_Vector;
|
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|
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function To_Matrix
|
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(Source : Vector;
|
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Column_Vector : Boolean := True)
|
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return Matrix
|
||||
is
|
||||
Result : Matrix (1 .. 1, Source'Range);
|
||||
begin
|
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for Column in Source'Range loop
|
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Result (1, Column) := Source (Column);
|
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end loop;
|
||||
if Column_Vector then
|
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return Transpose (Result);
|
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else
|
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return Result;
|
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end if;
|
||||
end To_Matrix;
|
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|
||||
function To_Row_Vector
|
||||
(Source : Matrix;
|
||||
Column : Positive := 1)
|
||||
return Vector
|
||||
is
|
||||
Result : Vector (Source'Range (1));
|
||||
begin
|
||||
for Row in Result'Range loop
|
||||
Result (Row) := Source (Row, Column);
|
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end loop;
|
||||
return Result;
|
||||
end To_Row_Vector;
|
||||
|
||||
function Transpose (Source : Matrix) return Matrix is
|
||||
Result : Matrix (Source'Range (2), Source'Range (1));
|
||||
begin
|
||||
for Row in Result'Range (1) loop
|
||||
for Column in Result'Range (2) loop
|
||||
Result (Row, Column) := Source (Column, Row);
|
||||
end loop;
|
||||
end loop;
|
||||
return Result;
|
||||
end Transpose;
|
||||
end Matrices;
|
||||
68
Task/Multiple-regression/Ada/multiple-regression-3.ada
Normal file
68
Task/Multiple-regression/Ada/multiple-regression-3.ada
Normal file
|
|
@ -0,0 +1,68 @@
|
|||
with Ada.Text_IO;
|
||||
with Matrices;
|
||||
procedure Multiple_Regression is
|
||||
package Float_Matrices is new Matrices (
|
||||
Element_Type => Float,
|
||||
Zero => 0.0,
|
||||
One => 1.0);
|
||||
subtype Vector is Float_Matrices.Vector;
|
||||
subtype Matrix is Float_Matrices.Matrix;
|
||||
use type Matrix;
|
||||
|
||||
procedure Output_Matrix (X : Matrix) is
|
||||
begin
|
||||
for Row in X'Range (1) loop
|
||||
for Col in X'Range (2) loop
|
||||
Ada.Text_IO.Put (Float'Image (X (Row, Col)) & ' ');
|
||||
end loop;
|
||||
Ada.Text_IO.New_Line;
|
||||
end loop;
|
||||
end Output_Matrix;
|
||||
|
||||
-- example from Ruby solution
|
||||
V : constant Vector := (1.0, 2.0, 3.0, 4.0, 5.0);
|
||||
M : constant Matrix :=
|
||||
((1 => 2.0),
|
||||
(1 => 1.0),
|
||||
(1 => 3.0),
|
||||
(1 => 4.0),
|
||||
(1 => 5.0));
|
||||
C : constant Vector :=
|
||||
Float_Matrices.Regression_Coefficients (Source => V, Regressors => M);
|
||||
-- Wikipedia example
|
||||
Weight : constant Vector (1 .. 15) :=
|
||||
(52.21, 53.12, 54.48, 55.84, 57.20,
|
||||
58.57, 59.93, 61.29, 63.11, 64.47,
|
||||
66.28, 68.10, 69.92, 72.19, 74.46);
|
||||
Height : Vector (1 .. 15) :=
|
||||
(1.47, 1.50, 1.52, 1.55, 1.57,
|
||||
1.60, 1.63, 1.65, 1.68, 1.70,
|
||||
1.73, 1.75, 1.78, 1.80, 1.83);
|
||||
Height_Matrix : Matrix (1 .. 15, 1 .. 3);
|
||||
begin
|
||||
Ada.Text_IO.Put_Line ("Example from Ruby solution:");
|
||||
Ada.Text_IO.Put_Line ("V:");
|
||||
Output_Matrix (Float_Matrices.To_Matrix (V));
|
||||
Ada.Text_IO.Put_Line ("M:");
|
||||
Output_Matrix (M);
|
||||
Ada.Text_IO.Put_Line ("C:");
|
||||
Output_Matrix (Float_Matrices.To_Matrix (C));
|
||||
Ada.Text_IO.New_Line;
|
||||
Ada.Text_IO.Put_Line ("Example from Wikipedia:");
|
||||
for I in Height'Range loop
|
||||
Height_Matrix (I, 1) := 1.0;
|
||||
Height_Matrix (I, 2) := Height (I);
|
||||
Height_Matrix (I, 3) := Height (I) ** 2;
|
||||
end loop;
|
||||
Ada.Text_IO.Put_Line ("Matrix:");
|
||||
Output_Matrix (Height_Matrix);
|
||||
declare
|
||||
Coefficients : constant Vector :=
|
||||
Float_Matrices.Regression_Coefficients
|
||||
(Source => Weight,
|
||||
Regressors => Height_Matrix);
|
||||
begin
|
||||
Ada.Text_IO.Put_Line ("Coefficients:");
|
||||
Output_Matrix (Float_Matrices.To_Matrix (Coefficients));
|
||||
end;
|
||||
end Multiple_Regression;
|
||||
29
Task/Multiple-regression/BBC-BASIC/multiple-regression.basic
Normal file
29
Task/Multiple-regression/BBC-BASIC/multiple-regression.basic
Normal file
|
|
@ -0,0 +1,29 @@
|
|||
*FLOAT 64
|
||||
INSTALL @lib$+"ARRAYLIB"
|
||||
|
||||
DIM y(14), x(2,14), c(2)
|
||||
y() = 52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29, \
|
||||
\ 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46
|
||||
x() = 1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, \
|
||||
\ 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83
|
||||
|
||||
FOR row% = DIM(x(),1) TO 0 STEP -1
|
||||
FOR col% = 0 TO DIM(x(),2)
|
||||
x(row%,col%) = x(0,col%) ^ row%
|
||||
NEXT
|
||||
NEXT row%
|
||||
|
||||
PROCmultipleregression(y(), x(), c())
|
||||
FOR i% = 0 TO DIM(c(),1) : PRINT c(i%) " "; : NEXT
|
||||
PRINT
|
||||
END
|
||||
|
||||
DEF PROCmultipleregression(y(), x(), c())
|
||||
LOCAL m(), t()
|
||||
DIM m(DIM(x(),1), DIM(x(),1)), t(DIM(x(),2),DIM(x(),1))
|
||||
PROC_transpose(x(), t())
|
||||
m() = x().t()
|
||||
PROC_invert(m())
|
||||
t() = t().m()
|
||||
c() = y().t()
|
||||
ENDPROC
|
||||
227
Task/Multiple-regression/C++/multiple-regression.cpp
Normal file
227
Task/Multiple-regression/C++/multiple-regression.cpp
Normal file
|
|
@ -0,0 +1,227 @@
|
|||
#include <array>
|
||||
#include <iostream>
|
||||
|
||||
void require(bool condition, const std::string &message) {
|
||||
if (condition) {
|
||||
return;
|
||||
}
|
||||
throw std::runtime_error(message);
|
||||
}
|
||||
|
||||
template<typename T, size_t N>
|
||||
std::ostream &operator<<(std::ostream &os, const std::array<T, N> &a) {
|
||||
auto it = a.cbegin();
|
||||
auto end = a.cend();
|
||||
|
||||
os << '[';
|
||||
if (it != end) {
|
||||
os << *it;
|
||||
it = std::next(it);
|
||||
}
|
||||
while (it != end) {
|
||||
os << ", " << *it;
|
||||
it = std::next(it);
|
||||
}
|
||||
return os << ']';
|
||||
}
|
||||
|
||||
template <size_t RC, size_t CC>
|
||||
class Matrix {
|
||||
std::array<std::array<double, CC>, RC> data;
|
||||
|
||||
public:
|
||||
Matrix() : data{} {
|
||||
// empty
|
||||
}
|
||||
|
||||
Matrix(std::initializer_list<std::initializer_list<double>> values) {
|
||||
size_t rp = 0;
|
||||
for (auto row : values) {
|
||||
size_t cp = 0;
|
||||
for (auto col : row) {
|
||||
data[rp][cp] = col;
|
||||
cp++;
|
||||
}
|
||||
rp++;
|
||||
}
|
||||
}
|
||||
|
||||
double get(size_t row, size_t col) const {
|
||||
return data[row][col];
|
||||
}
|
||||
|
||||
void set(size_t row, size_t col, double value) {
|
||||
data[row][col] = value;
|
||||
}
|
||||
|
||||
std::array<double, CC> get(size_t row) {
|
||||
return data[row];
|
||||
}
|
||||
|
||||
void set(size_t row, const std::array<double, CC> &values) {
|
||||
std::copy(values.begin(), values.end(), data[row].begin());
|
||||
}
|
||||
|
||||
template <size_t D>
|
||||
Matrix<RC, D> operator*(const Matrix<CC, D> &rhs) const {
|
||||
Matrix<RC, D> result;
|
||||
for (size_t i = 0; i < RC; i++) {
|
||||
for (size_t j = 0; j < D; j++) {
|
||||
for (size_t k = 0; k < CC; k++) {
|
||||
double prod = get(i, k) * rhs.get(k, j);
|
||||
result.set(i, j, result.get(i, j) + prod);
|
||||
}
|
||||
}
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
Matrix<CC, RC> transpose() const {
|
||||
Matrix<CC, RC> trans;
|
||||
for (size_t i = 0; i < RC; i++) {
|
||||
for (size_t j = 0; j < CC; j++) {
|
||||
trans.set(j, i, data[i][j]);
|
||||
}
|
||||
}
|
||||
return trans;
|
||||
}
|
||||
|
||||
void toReducedRowEchelonForm() {
|
||||
size_t lead = 0;
|
||||
for (size_t r = 0; r < RC; r++) {
|
||||
if (CC <= lead) {
|
||||
return;
|
||||
}
|
||||
auto i = r;
|
||||
|
||||
while (get(i, lead) == 0.0) {
|
||||
i++;
|
||||
if (RC == i) {
|
||||
i = r;
|
||||
lead++;
|
||||
if (CC == lead) {
|
||||
return;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
auto temp = get(i);
|
||||
set(i, get(r));
|
||||
set(r, temp);
|
||||
|
||||
if (get(r, lead) != 0.0) {
|
||||
auto div = get(r, lead);
|
||||
for (size_t j = 0; j < CC; j++) {
|
||||
set(r, j, get(r, j) / div);
|
||||
}
|
||||
}
|
||||
|
||||
for (size_t k = 0; k < RC; k++) {
|
||||
if (k != r) {
|
||||
auto mult = get(k, lead);
|
||||
for (size_t j = 0; j < CC; j++) {
|
||||
auto prod = get(r, j) * mult;
|
||||
set(k, j, get(k, j) - prod);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
lead++;
|
||||
}
|
||||
}
|
||||
|
||||
Matrix<RC, RC> inverse() {
|
||||
require(RC == CC, "Not a square matrix");
|
||||
|
||||
Matrix<RC, 2 * RC> aug;
|
||||
for (size_t i = 0; i < RC; i++) {
|
||||
for (size_t j = 0; j < RC; j++) {
|
||||
aug.set(i, j, get(i, j));
|
||||
}
|
||||
// augment identify matrix to right
|
||||
aug.set(i, i + RC, 1.0);
|
||||
}
|
||||
|
||||
aug.toReducedRowEchelonForm();
|
||||
|
||||
// remove identity matrix to left
|
||||
Matrix<RC, RC> inv;
|
||||
for (size_t i = 0; i < RC; i++) {
|
||||
for (size_t j = RC; j < 2 * RC; j++) {
|
||||
inv.set(i, j - RC, aug.get(i, j));
|
||||
}
|
||||
}
|
||||
return inv;
|
||||
}
|
||||
|
||||
template <size_t RC, size_t CC>
|
||||
friend std::ostream &operator<<(std::ostream &, const Matrix<RC, CC> &);
|
||||
};
|
||||
|
||||
template <size_t RC, size_t CC>
|
||||
std::ostream &operator<<(std::ostream &os, const Matrix<RC, CC> &m) {
|
||||
for (size_t i = 0; i < RC; i++) {
|
||||
os << '[';
|
||||
for (size_t j = 0; j < CC; j++) {
|
||||
if (j > 0) {
|
||||
os << ", ";
|
||||
}
|
||||
os << m.get(i, j);
|
||||
}
|
||||
os << "]\n";
|
||||
}
|
||||
|
||||
return os;
|
||||
}
|
||||
|
||||
template <size_t RC, size_t CC>
|
||||
std::array<double, RC> multiple_regression(const std::array<double, CC> &y, const Matrix<RC, CC> &x) {
|
||||
Matrix<1, CC> tm;
|
||||
tm.set(0, y);
|
||||
|
||||
auto cy = tm.transpose();
|
||||
auto cx = x.transpose();
|
||||
return ((x * cx).inverse() * x * cy).transpose().get(0);
|
||||
}
|
||||
|
||||
void case1() {
|
||||
std::array<double, 5> y{ 1.0, 2.0, 3.0, 4.0, 5.0 };
|
||||
Matrix<1, 5> x{ {2.0, 1.0, 3.0, 4.0, 5.0} };
|
||||
auto v = multiple_regression(y, x);
|
||||
std::cout << v << '\n';
|
||||
}
|
||||
|
||||
void case2() {
|
||||
std::array<double, 3> y{ 3.0, 4.0, 5.0 };
|
||||
Matrix<2, 3> x{
|
||||
{1.0, 2.0, 1.0},
|
||||
{1.0, 1.0, 2.0}
|
||||
};
|
||||
auto v = multiple_regression(y, x);
|
||||
std::cout << v << '\n';
|
||||
}
|
||||
|
||||
void case3() {
|
||||
std::array<double, 15> y{ 52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46 };
|
||||
std::array<double, 15> a{ 1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83 };
|
||||
|
||||
Matrix<3, 15> x;
|
||||
for (size_t i = 0; i < 15; i++) {
|
||||
x.set(0, i, 1.0);
|
||||
}
|
||||
x.set(1, a);
|
||||
for (size_t i = 0; i < 15; i++) {
|
||||
x.set(2, i, a[i] * a[i]);
|
||||
}
|
||||
|
||||
auto v = multiple_regression(y, x);
|
||||
std::cout << v << '\n';
|
||||
}
|
||||
|
||||
int main() {
|
||||
case1();
|
||||
case2();
|
||||
case3();
|
||||
|
||||
return 0;
|
||||
}
|
||||
18
Task/Multiple-regression/C-sharp/multiple-regression.cs
Normal file
18
Task/Multiple-regression/C-sharp/multiple-regression.cs
Normal file
|
|
@ -0,0 +1,18 @@
|
|||
using System;
|
||||
using MathNet.Numerics.LinearRegression;
|
||||
using MathNet.Numerics.LinearAlgebra;
|
||||
using MathNet.Numerics.LinearAlgebra.Double;
|
||||
|
||||
class Program
|
||||
{
|
||||
static void Main(string[] args)
|
||||
{
|
||||
var col = DenseVector.OfArray(new double[] { 1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65,
|
||||
1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83 });
|
||||
var X = DenseMatrix.OfColumns(new Vector<double>[] { col.PointwisePower(0), col, col.PointwisePower(2) });
|
||||
var y = DenseVector.OfArray(new double[] { 52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93,
|
||||
61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46 });
|
||||
var β = MultipleRegression.QR(X, y);
|
||||
Console.WriteLine(β);
|
||||
}
|
||||
}
|
||||
44
Task/Multiple-regression/C/multiple-regression.c
Normal file
44
Task/Multiple-regression/C/multiple-regression.c
Normal file
|
|
@ -0,0 +1,44 @@
|
|||
#include <stdio.h>
|
||||
#include <gsl/gsl_matrix.h>
|
||||
#include <gsl/gsl_math.h>
|
||||
#include <gsl/gsl_multifit.h>
|
||||
|
||||
double w[] = { 52.21, 53.12, 54.48, 55.84, 57.20,
|
||||
58.57, 59.93, 61.29, 63.11, 64.47,
|
||||
66.28, 68.10, 69.92, 72.19, 74.46 };
|
||||
double h[] = { 1.47, 1.50, 1.52, 1.55, 1.57,
|
||||
1.60, 1.63, 1.65, 1.68, 1.70,
|
||||
1.73, 1.75, 1.78, 1.80, 1.83 };
|
||||
|
||||
int main()
|
||||
{
|
||||
int n = sizeof(h)/sizeof(double);
|
||||
gsl_matrix *X = gsl_matrix_calloc(n, 3);
|
||||
gsl_vector *Y = gsl_vector_alloc(n);
|
||||
gsl_vector *beta = gsl_vector_alloc(3);
|
||||
|
||||
for (int i = 0; i < n; i++) {
|
||||
gsl_vector_set(Y, i, w[i]);
|
||||
|
||||
gsl_matrix_set(X, i, 0, 1);
|
||||
gsl_matrix_set(X, i, 1, h[i]);
|
||||
gsl_matrix_set(X, i, 2, h[i] * h[i]);
|
||||
}
|
||||
|
||||
double chisq;
|
||||
gsl_matrix *cov = gsl_matrix_alloc(3, 3);
|
||||
gsl_multifit_linear_workspace * wspc = gsl_multifit_linear_alloc(n, 3);
|
||||
gsl_multifit_linear(X, Y, beta, cov, &chisq, wspc);
|
||||
|
||||
printf("Beta:");
|
||||
for (int i = 0; i < 3; i++)
|
||||
printf(" %g", gsl_vector_get(beta, i));
|
||||
printf("\n");
|
||||
|
||||
gsl_matrix_free(X);
|
||||
gsl_matrix_free(cov);
|
||||
gsl_vector_free(Y);
|
||||
gsl_vector_free(beta);
|
||||
gsl_multifit_linear_free(wspc);
|
||||
|
||||
}
|
||||
|
|
@ -0,0 +1,33 @@
|
|||
;; Solve a linear system AX=B where A is symmetric and positive definite, so it can be Cholesky decomposed.
|
||||
(defun linsys (A B)
|
||||
(let* ((n (car (array-dimensions A)))
|
||||
(m (cadr (array-dimensions B)))
|
||||
(y (make-array n :element-type 'long-float :initial-element 0.0L0))
|
||||
(X (make-array `(,n ,m) :element-type 'long-float :initial-element 0.0L0))
|
||||
(L (chol A))) ; A=LL'
|
||||
|
||||
(loop for col from 0 to (- m 1) do
|
||||
;; Forward substitution: y = L\B
|
||||
(loop for k from 0 to (- n 1)
|
||||
do (setf (aref y k)
|
||||
(/ (- (aref B k col)
|
||||
(loop for j from 0 to (- k 1)
|
||||
sum (* (aref L k j)
|
||||
(aref y j))))
|
||||
(aref L k k))))
|
||||
|
||||
;; Back substitution. x=L'\y
|
||||
(loop for k from (- n 1) downto 0
|
||||
do (setf (aref X k col)
|
||||
(/ (- (aref y k)
|
||||
(loop for j from (+ k 1) to (- n 1)
|
||||
sum (* (aref L j k)
|
||||
(aref X j col))))
|
||||
(aref L k k)))))
|
||||
X))
|
||||
|
||||
;; Solve a linear least squares problem. Ax=b, with A being mxn, with m>n.
|
||||
;; Solves the linear system A'Ax=A'b.
|
||||
(defun lsqr (A b)
|
||||
(linsys (mmul (mtp A) A)
|
||||
(mmul (mtp A) b)))
|
||||
|
|
@ -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))
|
||||
224
Task/Multiple-regression/D/multiple-regression.d
Normal file
224
Task/Multiple-regression/D/multiple-regression.d
Normal file
|
|
@ -0,0 +1,224 @@
|
|||
import std.algorithm;
|
||||
import std.array;
|
||||
import std.exception;
|
||||
import std.range;
|
||||
import std.stdio;
|
||||
|
||||
public class Matrix {
|
||||
private double[][] data;
|
||||
private size_t rowCount;
|
||||
private size_t colCount;
|
||||
|
||||
public this(size_t size)
|
||||
in(size > 0, "Must have at least one element")
|
||||
{
|
||||
this(size, size);
|
||||
}
|
||||
|
||||
public this(size_t rows, size_t cols)
|
||||
in(rows > 0, "Must have at least one row")
|
||||
in(cols > 0, "Must have at least one column")
|
||||
{
|
||||
rowCount = rows;
|
||||
colCount = cols;
|
||||
|
||||
data = uninitializedArray!(double[][])(rows, cols);
|
||||
foreach (ref row; data) {
|
||||
row[] = 0.0;
|
||||
}
|
||||
}
|
||||
|
||||
public this(const double[][] source) {
|
||||
enforce(source.length > 0, "Must have at least one row");
|
||||
rowCount = source.length;
|
||||
|
||||
enforce(source[0].length > 0, "Must have at least one column");
|
||||
colCount = source[0].length;
|
||||
|
||||
data = uninitializedArray!(double[][])(rowCount, colCount);
|
||||
foreach (i; 0 .. rowCount) {
|
||||
enforce(source[i].length == colCount, "All rows must have equal columns");
|
||||
data[i] = source[i].dup;
|
||||
}
|
||||
}
|
||||
|
||||
public auto opIndex(size_t r, size_t c) const {
|
||||
return data[r][c];
|
||||
}
|
||||
|
||||
public auto opIndex(size_t r) const {
|
||||
return data[r];
|
||||
}
|
||||
|
||||
public auto opBinary(string op)(const Matrix rhs) const {
|
||||
static if (op == "*") {
|
||||
auto rc1 = rowCount;
|
||||
auto cc1 = colCount;
|
||||
auto rc2 = rhs.rowCount;
|
||||
auto cc2 = rhs.colCount;
|
||||
enforce(cc1 == rc2, "Cannot multiply if the first columns does not equal the second rows");
|
||||
auto result = new Matrix(rc1, cc2);
|
||||
foreach (i; 0 .. rc1) {
|
||||
foreach (j; 0 .. cc2) {
|
||||
foreach (k; 0 .. rc2) {
|
||||
result[i, j] += this[i, k] * rhs[k, j];
|
||||
}
|
||||
}
|
||||
}
|
||||
return result;
|
||||
} else {
|
||||
assert(false, "Not implemented");
|
||||
}
|
||||
}
|
||||
|
||||
public void opIndexAssign(double value, size_t r, size_t c) {
|
||||
data[r][c] = value;
|
||||
}
|
||||
|
||||
public void opIndexAssign(const double[] value, size_t r) {
|
||||
enforce(colCount == value.length, "Slice size must match column size");
|
||||
data[r] = value.dup;
|
||||
}
|
||||
|
||||
public void opIndexOpAssign(string op)(double value, size_t r, size_t c) {
|
||||
mixin("data[r][c] " ~ op ~ "= value;");
|
||||
}
|
||||
|
||||
public auto transpose() const {
|
||||
auto rc = rowCount;
|
||||
auto cc = colCount;
|
||||
auto t = new Matrix(cc, rc);
|
||||
foreach (i; 0 .. cc) {
|
||||
foreach (j; 0 .. rc) {
|
||||
t[i, j] = this[j, i];
|
||||
}
|
||||
}
|
||||
return t;
|
||||
}
|
||||
|
||||
public void toReducedRowEchelonForm() {
|
||||
auto lead = 0;
|
||||
auto rc = rowCount;
|
||||
auto cc = colCount;
|
||||
foreach (r; 0 .. rc) {
|
||||
if (cc <= lead) {
|
||||
return;
|
||||
}
|
||||
auto i = r;
|
||||
|
||||
while (this[i, lead] == 0.0) {
|
||||
i++;
|
||||
if (rc == i) {
|
||||
i = r;
|
||||
lead++;
|
||||
if (cc == lead) {
|
||||
return;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
auto temp = this[i];
|
||||
this[i] = this[r];
|
||||
this[r] = temp;
|
||||
|
||||
if (this[r, lead] != 0.0) {
|
||||
auto div = this[r, lead];
|
||||
foreach (j; 0 .. cc) {
|
||||
this[r, j] = this[r, j] / div;
|
||||
}
|
||||
}
|
||||
|
||||
foreach (k; 0 .. rc) {
|
||||
if (k != r) {
|
||||
auto mult = this[k, lead];
|
||||
foreach (j; 0 .. cc) {
|
||||
this[k, j] -= this[r, j] * mult;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
lead++;
|
||||
}
|
||||
}
|
||||
|
||||
public auto inverse() const {
|
||||
enforce(rowCount == colCount, "Not a square matrix");
|
||||
auto len = rowCount;
|
||||
auto aug = new Matrix(len, 2 * len);
|
||||
foreach (i; 0 .. len) {
|
||||
foreach (j; 0 .. len) {
|
||||
aug[i, j] = this[i, j];
|
||||
}
|
||||
// augment identity matrix to right
|
||||
aug[i, i + len] = 1.0;
|
||||
}
|
||||
aug.toReducedRowEchelonForm;
|
||||
auto inv = new Matrix(len);
|
||||
// remove identify matrix to left
|
||||
foreach (i; 0 .. len) {
|
||||
foreach (j; len .. 2 * len) {
|
||||
inv[i, j - len] = aug[i, j];
|
||||
}
|
||||
}
|
||||
return inv;
|
||||
}
|
||||
|
||||
void toString(scope void delegate(const(char)[]) sink) const {
|
||||
import std.format;
|
||||
auto fmt = FormatSpec!char("%s");
|
||||
|
||||
put(sink, "[");
|
||||
foreach (i; 0 .. rowCount) {
|
||||
if (i > 0) {
|
||||
put(sink, " [");
|
||||
} else {
|
||||
put(sink, "[");
|
||||
}
|
||||
|
||||
formatValue(sink, this[i, 0], fmt);
|
||||
foreach (j; 1 .. colCount) {
|
||||
put(sink, ", ");
|
||||
formatValue(sink, this[i, j], fmt);
|
||||
}
|
||||
|
||||
if (i + 1 < rowCount) {
|
||||
put(sink, "]\n");
|
||||
} else {
|
||||
put(sink, "]");
|
||||
}
|
||||
}
|
||||
put(sink, "]");
|
||||
}
|
||||
}
|
||||
|
||||
auto multipleRegression(double[] y, Matrix x) {
|
||||
auto tm = new Matrix([y]);
|
||||
auto cy = tm.transpose;
|
||||
auto cx = x.transpose;
|
||||
return ((x * cx).inverse * x * cy).transpose[0].dup;
|
||||
}
|
||||
|
||||
void main() {
|
||||
auto y = [1.0, 2.0, 3.0, 4.0, 5.0];
|
||||
auto x = new Matrix([[2.0, 1.0, 3.0, 4.0, 5.0]]);
|
||||
auto v = multipleRegression(y, x);
|
||||
v.writeln;
|
||||
|
||||
y = [3.0, 4.0, 5.0];
|
||||
x = new Matrix([
|
||||
[1.0, 2.0, 1.0],
|
||||
[1.0, 1.0, 2.0]
|
||||
]);
|
||||
v = multipleRegression(y, x);
|
||||
v.writeln;
|
||||
|
||||
y = [52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46];
|
||||
auto a = [1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83];
|
||||
x = new Matrix([
|
||||
repeat(1.0, a.length).array,
|
||||
a,
|
||||
a.map!"a * a".array
|
||||
]);
|
||||
v = multipleRegression(y, x);
|
||||
v.writeln;
|
||||
}
|
||||
82
Task/Multiple-regression/ERRE/multiple-regression.erre
Normal file
82
Task/Multiple-regression/ERRE/multiple-regression.erre
Normal file
|
|
@ -0,0 +1,82 @@
|
|||
PROGRAM MULTIPLE_REGRESSION
|
||||
|
||||
!$DOUBLE
|
||||
|
||||
CONST N=14,M=2,Q=3 ! number of points and M.R. polynom degree
|
||||
|
||||
DIM X[N],Y[N] ! data points
|
||||
DIM S[N],T[N] ! linear system coefficient
|
||||
DIM A[M,Q] ! sistem to be solved
|
||||
|
||||
BEGIN
|
||||
|
||||
DATA(1.47,1.50,1.52,1.55,1.57,1.60,1.63,1.65,1.68,1.70,1.73,1.75,1.78,1.80,1.83)
|
||||
DATA(52.21,53.12,54.48,55.84,57.20,58.57,59.93,61.29,63.11,64.47,66.28,68.10,69.92,72.19,74.46)
|
||||
|
||||
FOR I%=0 TO N DO
|
||||
READ(X[I%])
|
||||
END FOR
|
||||
|
||||
FOR I%=0 TO N DO
|
||||
READ(Y[I%])
|
||||
END FOR
|
||||
|
||||
FOR K%=0 TO 2*M DO
|
||||
S[K%]=0 T[K%]=0
|
||||
FOR I%=0 TO N DO
|
||||
S[K%]=S[K%]+X[I%]^K%
|
||||
IF K%<=M THEN T[K%]=T[K%]+Y[I%]*X[I%]^K% END IF
|
||||
END FOR
|
||||
END FOR
|
||||
|
||||
! build linear system
|
||||
|
||||
FOR ROW%=0 TO M DO
|
||||
FOR COL%=0 TO M DO
|
||||
A[ROW%,COL%]=S[ROW%+COL%]
|
||||
END FOR
|
||||
A[ROW%,COL%]=T[ROW%]
|
||||
END FOR
|
||||
|
||||
PRINT("LINEAR SYSTEM COEFFICENTS") PRINT
|
||||
FOR I%=0 TO M DO
|
||||
FOR J%=0 TO M+1 DO
|
||||
WRITE(" ######.#";A[I%,J%];)
|
||||
END FOR
|
||||
PRINT
|
||||
END FOR
|
||||
PRINT
|
||||
|
||||
FOR J%=0 TO M DO
|
||||
FOR I%=J% TO M DO
|
||||
EXIT IF A[I%,J%]<>0
|
||||
END FOR
|
||||
IF I%=M+1 THEN
|
||||
PRINT("SINGULAR MATRIX !")
|
||||
!$STOP
|
||||
END IF
|
||||
FOR K%=0 TO M+1 DO
|
||||
SWAP(A[J%,K%],A[I%,K%])
|
||||
END FOR
|
||||
Y=1/A[J%,J%]
|
||||
FOR K%=0 TO M+1 DO
|
||||
A[J%,K%]=Y*A[J%,K%]
|
||||
END FOR
|
||||
FOR I%=0 TO M DO
|
||||
IF I%<>J% THEN
|
||||
Y=-A[I%,J%]
|
||||
FOR K%=0 TO M+1 DO
|
||||
A[I%,K%]=A[I%,K%]+Y*A[J%,K%]
|
||||
END FOR
|
||||
END IF
|
||||
END FOR
|
||||
END FOR
|
||||
PRINT
|
||||
|
||||
PRINT("SOLUTIONS") PRINT
|
||||
FOR I%=0 TO M DO
|
||||
PRINT("c";I%;"=";)
|
||||
WRITE("#####.#######";A[I%,M+1])
|
||||
END FOR
|
||||
|
||||
END PROGRAM
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
(let ((x1 '(0 1 2 3 4 5 6 7 8 9 10))
|
||||
(x2 '(0 1 1 3 3 7 6 7 3 9 8))
|
||||
(y '(1 6 17 34 57 86 121 162 209 262 321)))
|
||||
(apply #'calc-eval "fit(a*X1+b*X2+c,[X1,X2],[a,b,c],[$1 $2 $3])" nil
|
||||
(mapcar (lambda (items) (cons 'vec items)) (list x1 x2 y))))
|
||||
85
Task/Multiple-regression/Fortran/multiple-regression.f
Normal file
85
Task/Multiple-regression/Fortran/multiple-regression.f
Normal file
|
|
@ -0,0 +1,85 @@
|
|||
*-----------------------------------------------------------------------
|
||||
* MR - multiple regression using the SLATEC library routine DHFTI
|
||||
*
|
||||
* Finds the nearest approximation to BETA in the system of linear equations:
|
||||
*
|
||||
* X(j,i) . BETA(i) = Y(j)
|
||||
* where
|
||||
* 1 ... j ... N
|
||||
* 1 ... i ... K
|
||||
* and
|
||||
* K .LE. N
|
||||
*
|
||||
* INPUT ARRAYS ARE DESTROYED!
|
||||
*
|
||||
*___Name___________Type_______________In/Out____Description_____________
|
||||
* X(N,K) Double precision In Predictors
|
||||
* Y(N) Double precision Both On input: N Observations
|
||||
* On output: K beta weights
|
||||
* N Integer In Number of observations
|
||||
* K Integer In Number of predictor variables
|
||||
* DWORK(N+2*K) Double precision Neither Workspace
|
||||
* IWORK(K) Integer Neither Workspace
|
||||
*-----------------------------------------------------------------------
|
||||
SUBROUTINE MR (X, Y, N, K, DWORK, IWORK)
|
||||
IMPLICIT NONE
|
||||
INTEGER K, N, IWORK
|
||||
DOUBLE PRECISION X, Y, DWORK
|
||||
DIMENSION X(N,K), Y(N), DWORK(N+2*K), IWORK(K)
|
||||
|
||||
* local variables
|
||||
INTEGER I, J
|
||||
DOUBLE PRECISION TAU, TOT
|
||||
|
||||
* maximum of all column sums of magnitudes
|
||||
TAU = 0.
|
||||
DO J = 1, K
|
||||
TOT = 0.
|
||||
DO I = 1, N
|
||||
TOT = TOT + ABS(X(I,J))
|
||||
END DO
|
||||
IF (TOT > TAU) TAU = TOT
|
||||
END DO
|
||||
TAU = TAU * EPSILON(TAU) ! tolerance argument
|
||||
|
||||
* call function
|
||||
CALL DHFTI (X, N, N, K, Y, N, 1, TAU,
|
||||
$ J, DWORK(1), DWORK(N+1), DWORK(N+K+1), IWORK)
|
||||
IF (J < K) PRINT *, 'mr: solution is rank deficient!'
|
||||
RETURN
|
||||
END ! of MR
|
||||
|
||||
*-----------------------------------------------------------------------
|
||||
PROGRAM t_mr ! polynomial regression example
|
||||
IMPLICIT NONE
|
||||
INTEGER N, K
|
||||
PARAMETER (N=15, K=3)
|
||||
INTEGER IWORK(K), I, J
|
||||
DOUBLE PRECISION XIN(N), X(N,K), Y(N), DWORK(N+2*K)
|
||||
|
||||
DATA XIN / 1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68,
|
||||
$ 1.70, 1.73, 1.75, 1.78, 1.80, 1.83 /
|
||||
DATA Y / 52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29,
|
||||
$ 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46 /
|
||||
|
||||
* make coefficient matrix
|
||||
DO J = 1, K
|
||||
DO I = 1, N
|
||||
X(I,J) = XIN(I) **(J-1)
|
||||
END DO
|
||||
END DO
|
||||
|
||||
* solve
|
||||
CALL MR (X, Y, N, K, DWORK, IWORK)
|
||||
|
||||
* print result
|
||||
10 FORMAT ('beta: ', $)
|
||||
20 FORMAT (F12.4, $)
|
||||
30 FORMAT ()
|
||||
PRINT 10
|
||||
DO J = 1, K
|
||||
PRINT 20, Y(J)
|
||||
END DO
|
||||
PRINT 30
|
||||
STOP 'program complete'
|
||||
END
|
||||
66
Task/Multiple-regression/FreeBASIC/multiple-regression.basic
Normal file
66
Task/Multiple-regression/FreeBASIC/multiple-regression.basic
Normal file
|
|
@ -0,0 +1,66 @@
|
|||
Const N = 14, M = 2, Q = 3 ' number of points and M.R. polynom degree
|
||||
|
||||
Dim As Double X(0 to N) = {1.47,1.50,1.52,1.55,1.57, _
|
||||
1.60,1.63,1.65,1.68,1.70,1.73,1.75,1.78,1.80,1.83} ' data points
|
||||
Dim As Double Y(0 to N) = {52.21,53.12,54.48,55.84,57.20, _
|
||||
58.57,59.93,61.29,63.11,64.47,66.28,68.10,69.92,72.19,74.46} ' data points
|
||||
Dim As Double S(N), T(N) ' linear system coefficient
|
||||
Dim As Double A(M, Q) ' sistem to be solved
|
||||
Dim As Integer i, k, j, fila, columna
|
||||
Dim as Double z
|
||||
|
||||
For k = 0 To 2*M
|
||||
S(k) = 0 : T(k) = 0
|
||||
For i = 0 To N
|
||||
S(k) += X(i) ^ k
|
||||
If k <= M Then T(k) += Y(i) * X(i) ^ k
|
||||
Next i
|
||||
Next k
|
||||
|
||||
' build linear system
|
||||
For fila = 0 To M
|
||||
For columna = 0 To M
|
||||
A(fila, columna) = S(fila+columna)
|
||||
Next columna
|
||||
A(fila, columna) = T(fila)
|
||||
Next fila
|
||||
|
||||
Print "Linear system coefficents:"
|
||||
For i = 0 To M
|
||||
For j = 0 To M+1
|
||||
Print Using "######.#"; A(i,j);
|
||||
Next j
|
||||
Print
|
||||
Next i
|
||||
|
||||
For j = 0 To M
|
||||
For i = j To M
|
||||
If A(i,j) <> 0 Then Exit For
|
||||
Next i
|
||||
If i = M+1 Then
|
||||
Print !"\nSINGULAR MATRIX '"
|
||||
Sleep: End
|
||||
End If
|
||||
For k = 0 To M+1
|
||||
Swap A(j,k), A(i,k)
|
||||
Next k
|
||||
z = 1 / A(j,j)
|
||||
For k = 0 To M+1
|
||||
A(j,k) = z * A(j,k)
|
||||
Next k
|
||||
For i = 0 To M
|
||||
If i <> j Then
|
||||
z = -A(i,j)
|
||||
For k = 0 To M+1
|
||||
A(i,k) += z * A(j,k)
|
||||
Next k
|
||||
End If
|
||||
Next i
|
||||
Next j
|
||||
|
||||
Print !"\nSolutions:"
|
||||
For i = 0 To M
|
||||
Print Using " #####.#######"; A(i,M+1);
|
||||
Next i
|
||||
|
||||
Sleep
|
||||
33
Task/Multiple-regression/Go/multiple-regression-1.go
Normal file
33
Task/Multiple-regression/Go/multiple-regression-1.go
Normal file
|
|
@ -0,0 +1,33 @@
|
|||
package main
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
|
||||
"github.com/gonum/matrix/mat64"
|
||||
)
|
||||
|
||||
func givens() (x, y *mat64.Dense) {
|
||||
height := []float64{1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63,
|
||||
1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83}
|
||||
weight := []float64{52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93,
|
||||
61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46}
|
||||
degree := 2
|
||||
x = Vandermonde(height, degree)
|
||||
y = mat64.NewDense(len(weight), 1, weight)
|
||||
return
|
||||
}
|
||||
|
||||
func Vandermonde(a []float64, degree int) *mat64.Dense {
|
||||
x := mat64.NewDense(len(a), degree+1, nil)
|
||||
for i := range a {
|
||||
for j, p := 0, 1.; j <= degree; j, p = j+1, p*a[i] {
|
||||
x.Set(i, j, p)
|
||||
}
|
||||
}
|
||||
return x
|
||||
}
|
||||
|
||||
func main() {
|
||||
x, y := givens()
|
||||
fmt.Printf("%.4f\n", mat64.Formatted(mat64.QR(x).Solve(y)))
|
||||
}
|
||||
46
Task/Multiple-regression/Go/multiple-regression-2.go
Normal file
46
Task/Multiple-regression/Go/multiple-regression-2.go
Normal file
|
|
@ -0,0 +1,46 @@
|
|||
package main
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
|
||||
"github.com/skelterjohn/go.matrix"
|
||||
)
|
||||
|
||||
func givens() (x, y *matrix.DenseMatrix) {
|
||||
height := []float64{1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63,
|
||||
1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83}
|
||||
weight := []float64{52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93,
|
||||
61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46}
|
||||
m := len(height)
|
||||
n := 3
|
||||
y = matrix.MakeDenseMatrix(weight, 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 *= height[i]
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
func main() {
|
||||
x, y := givens()
|
||||
n := x.Cols()
|
||||
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)
|
||||
}
|
||||
12
Task/Multiple-regression/Haskell/multiple-regression-1.hs
Normal file
12
Task/Multiple-regression/Haskell/multiple-regression-1.hs
Normal file
|
|
@ -0,0 +1,12 @@
|
|||
import Numeric.LinearAlgebra
|
||||
import Numeric.LinearAlgebra.LAPACK
|
||||
|
||||
m :: Matrix Double
|
||||
m = (3><3)
|
||||
[7.589183,1.703609,-4.477162,
|
||||
-4.597851,9.434889,-6.543450,
|
||||
0.4588202,-6.115153,1.331191]
|
||||
|
||||
v :: Matrix Double
|
||||
v = (3><1)
|
||||
[1.745005,-4.448092,-4.160842]
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
*Main> linearSolveLSR m v
|
||||
(3><1)
|
||||
[ 0.9335611922087276
|
||||
, 1.101323491272865
|
||||
, 1.6117769115824 ]
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
*Main> inv m `multiply` v
|
||||
(3><1)
|
||||
[ 0.9335611922087278
|
||||
, 1.101323491272865
|
||||
, 1.6117769115824006 ]
|
||||
13
Task/Multiple-regression/Hy/multiple-regression.hy
Normal file
13
Task/Multiple-regression/Hy/multiple-regression.hy
Normal file
|
|
@ -0,0 +1,13 @@
|
|||
(import
|
||||
[numpy [ones column-stack]]
|
||||
[numpy.random [randn]]
|
||||
[numpy.linalg [lstsq]])
|
||||
|
||||
(setv n 1000)
|
||||
(setv x1 (randn n))
|
||||
(setv x2 (randn n))
|
||||
(setv y (+ 3 (* 1 x1) (* -2 x2) (* .25 x1 x2) (randn n)))
|
||||
|
||||
(print (first (lstsq
|
||||
(column-stack (, (ones n) x1 x2 (* x1 x2)))
|
||||
y)))
|
||||
6
Task/Multiple-regression/J/multiple-regression-1.j
Normal file
6
Task/Multiple-regression/J/multiple-regression-1.j
Normal file
|
|
@ -0,0 +1,6 @@
|
|||
NB. Wikipedia data
|
||||
x=: 1.47 1.50 1.52 1.55 1.57 1.60 1.63 1.65 1.68 1.70 1.73 1.75 1.78 1.80 1.83
|
||||
y=: 52.21 53.12 54.48 55.84 57.20 58.57 59.93 61.29 63.11 64.47 66.28 68.10 69.92 72.19 74.46
|
||||
|
||||
y %. x ^/ i.3 NB. calculate coefficients b1, b2 and b3 for 2nd degree polynomial
|
||||
128.813 _143.162 61.9603
|
||||
12
Task/Multiple-regression/J/multiple-regression-2.j
Normal file
12
Task/Multiple-regression/J/multiple-regression-2.j
Normal file
|
|
@ -0,0 +1,12 @@
|
|||
X=: x ^/ i.3 NB. form Design matrix
|
||||
X=: (x^0) ,. (x^1) ,. (x^2) NB. equivalent of previous line
|
||||
4{.X NB. show first 4 rows of X
|
||||
1 1.47 2.1609
|
||||
1 1.5 2.25
|
||||
1 1.52 2.3104
|
||||
1 1.55 2.4025
|
||||
|
||||
NB. Where y is a set of observations and X is the design matrix
|
||||
NB. y %. X does matrix division and gives the regression coefficients
|
||||
y %. X
|
||||
128.813 _143.162 61.9603
|
||||
9
Task/Multiple-regression/J/multiple-regression-3.j
Normal file
9
Task/Multiple-regression/J/multiple-regression-3.j
Normal file
|
|
@ -0,0 +1,9 @@
|
|||
mp=: +/ .* NB. matrix product
|
||||
NB. %.X is matrix inverse of X
|
||||
NB. |:X is transpose of X
|
||||
|
||||
(%.(|:X) mp X) mp (|:X) mp y
|
||||
128.814 _143.163 61.9606
|
||||
xpy=: mp~ |: NB. Or factoring out "X prime y" (monadically "X prime X")
|
||||
X (%.@:xpy@[ mp xpy) y
|
||||
128.814 _143.163 61.9606
|
||||
4
Task/Multiple-regression/J/multiple-regression-4.j
Normal file
4
Task/Multiple-regression/J/multiple-regression-4.j
Normal file
|
|
@ -0,0 +1,4 @@
|
|||
load 'math/lapack'
|
||||
load 'math/lapack/gels'
|
||||
gels_jlapack_ X;y
|
||||
128.813 _143.162 61.9603
|
||||
209
Task/Multiple-regression/Java/multiple-regression.java
Normal file
209
Task/Multiple-regression/Java/multiple-regression.java
Normal file
|
|
@ -0,0 +1,209 @@
|
|||
import java.util.Arrays;
|
||||
import java.util.Objects;
|
||||
|
||||
public class MultipleRegression {
|
||||
public static void require(boolean condition, String message) {
|
||||
if (condition) {
|
||||
return;
|
||||
}
|
||||
throw new IllegalArgumentException(message);
|
||||
}
|
||||
|
||||
public static class Matrix {
|
||||
private final double[][] data;
|
||||
private final int rowCount;
|
||||
private final int colCount;
|
||||
|
||||
public Matrix(int rows, int cols) {
|
||||
require(rows > 0, "Need at least one row");
|
||||
this.rowCount = rows;
|
||||
|
||||
require(cols > 0, "Need at least one column");
|
||||
this.colCount = cols;
|
||||
|
||||
this.data = new double[rows][cols];
|
||||
for (double[] row : this.data) {
|
||||
Arrays.fill(row, 0.0);
|
||||
}
|
||||
}
|
||||
|
||||
public Matrix(double[][] source) {
|
||||
require(source.length > 0, "Need at least one row");
|
||||
this.rowCount = source.length;
|
||||
|
||||
require(source[0].length > 0, "Need at least one column");
|
||||
this.colCount = source[0].length;
|
||||
|
||||
this.data = new double[this.rowCount][this.colCount];
|
||||
for (int i = 0; i < this.rowCount; i++) {
|
||||
set(i, source[i]);
|
||||
}
|
||||
}
|
||||
|
||||
public double[] get(int row) {
|
||||
Objects.checkIndex(row, this.rowCount);
|
||||
return this.data[row];
|
||||
}
|
||||
|
||||
public void set(int row, double[] data) {
|
||||
Objects.checkIndex(row, this.rowCount);
|
||||
require(data.length == this.colCount, "The column in the row must match the number of columns in the matrix");
|
||||
System.arraycopy(data, 0, this.data[row], 0, this.colCount);
|
||||
}
|
||||
|
||||
public double get(int row, int col) {
|
||||
Objects.checkIndex(row, this.rowCount);
|
||||
Objects.checkIndex(col, this.colCount);
|
||||
return this.data[row][col];
|
||||
}
|
||||
|
||||
public void set(int row, int col, double value) {
|
||||
Objects.checkIndex(row, this.rowCount);
|
||||
Objects.checkIndex(col, this.colCount);
|
||||
this.data[row][col] = value;
|
||||
}
|
||||
|
||||
@SuppressWarnings("UnnecessaryLocalVariable")
|
||||
public Matrix times(Matrix that) {
|
||||
var rc1 = this.rowCount;
|
||||
var cc1 = this.colCount;
|
||||
var rc2 = that.rowCount;
|
||||
var cc2 = that.colCount;
|
||||
require(cc1 == rc2, "Cannot multiply if the first columns does not equal the second rows");
|
||||
var result = new Matrix(rc1, cc2);
|
||||
for (int i = 0; i < rc1; i++) {
|
||||
for (int j = 0; j < cc2; j++) {
|
||||
for (int k = 0; k < rc2; k++) {
|
||||
var prod = get(i, k) * that.get(k, j);
|
||||
result.set(i, j, result.get(i, j) + prod);
|
||||
}
|
||||
}
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
public Matrix transpose() {
|
||||
var rc = this.rowCount;
|
||||
var cc = this.colCount;
|
||||
var trans = new Matrix(cc, rc);
|
||||
for (int i = 0; i < cc; i++) {
|
||||
for (int j = 0; j < rc; j++) {
|
||||
trans.set(i, j, get(j, i));
|
||||
}
|
||||
}
|
||||
return trans;
|
||||
}
|
||||
|
||||
public void toReducedRowEchelonForm() {
|
||||
int lead = 0;
|
||||
var rc = this.rowCount;
|
||||
var cc = this.colCount;
|
||||
for (int r = 0; r < rc; r++) {
|
||||
if (cc <= lead) {
|
||||
return;
|
||||
}
|
||||
var i = r;
|
||||
|
||||
while (get(i, lead) == 0.0) {
|
||||
i++;
|
||||
if (rc == i) {
|
||||
i = r;
|
||||
lead++;
|
||||
if (cc == lead) {
|
||||
return;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
var temp = get(i);
|
||||
set(i, get(r));
|
||||
set(r, temp);
|
||||
|
||||
if (get(r, lead) != 0.0) {
|
||||
var div = get(r, lead);
|
||||
for (int j = 0; j < cc; j++) {
|
||||
set(r, j, get(r, j) / div);
|
||||
}
|
||||
}
|
||||
|
||||
for (int k = 0; k < rc; k++) {
|
||||
if (k != r) {
|
||||
var mult = get(k, lead);
|
||||
for (int j = 0; j < cc; j++) {
|
||||
var prod = get(r, j) * mult;
|
||||
set(k, j, get(k, j) - prod);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
lead++;
|
||||
}
|
||||
}
|
||||
|
||||
public Matrix inverse() {
|
||||
require(this.rowCount == this.colCount, "Not a square matrix");
|
||||
var len = this.rowCount;
|
||||
var aug = new Matrix(len, 2 * len);
|
||||
for (int i = 0; i < len; i++) {
|
||||
for (int j = 0; j < len; j++) {
|
||||
aug.set(i, j, get(i, j));
|
||||
}
|
||||
// augment identity matrix to right
|
||||
aug.set(i, i + len, 1.0);
|
||||
}
|
||||
aug.toReducedRowEchelonForm();
|
||||
var inv = new Matrix(len, len);
|
||||
// remove identity matrix to left
|
||||
for (int i = 0; i < len; i++) {
|
||||
for (int j = len; j < 2 * len; j++) {
|
||||
inv.set(i, j - len, aug.get(i, j));
|
||||
}
|
||||
}
|
||||
return inv;
|
||||
}
|
||||
}
|
||||
|
||||
public static double[] multipleRegression(double[] y, Matrix x) {
|
||||
var tm = new Matrix(new double[][]{y});
|
||||
var cy = tm.transpose();
|
||||
var cx = x.transpose();
|
||||
return x.times(cx).inverse().times(x).times(cy).transpose().get(0);
|
||||
}
|
||||
|
||||
public static void printVector(double[] v) {
|
||||
System.out.println(Arrays.toString(v));
|
||||
System.out.println();
|
||||
}
|
||||
|
||||
public static double[] repeat(int size, double value) {
|
||||
var a = new double[size];
|
||||
Arrays.fill(a, value);
|
||||
return a;
|
||||
}
|
||||
|
||||
public static void main(String[] args) {
|
||||
double[] y = new double[]{1.0, 2.0, 3.0, 4.0, 5.0};
|
||||
var x = new Matrix(new double[][]{{2.0, 1.0, 3.0, 4.0, 5.0}});
|
||||
var v = multipleRegression(y, x);
|
||||
printVector(v);
|
||||
|
||||
y = new double[]{3.0, 4.0, 5.0};
|
||||
x = new Matrix(new double[][]{
|
||||
{1.0, 2.0, 1.0},
|
||||
{1.0, 1.0, 2.0}
|
||||
});
|
||||
v = multipleRegression(y, x);
|
||||
printVector(v);
|
||||
|
||||
y = new double[]{52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46};
|
||||
var a = new double[]{1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83};
|
||||
x = new Matrix(new double[][]{
|
||||
repeat(a.length, 1.0),
|
||||
a,
|
||||
Arrays.stream(a).map(it -> it * it).toArray()
|
||||
});
|
||||
|
||||
v = multipleRegression(y, x);
|
||||
printVector(v);
|
||||
}
|
||||
}
|
||||
47
Task/Multiple-regression/JavaScript/multiple-regression.js
Normal file
47
Task/Multiple-regression/JavaScript/multiple-regression.js
Normal file
|
|
@ -0,0 +1,47 @@
|
|||
// modifies the matrix "in place"
|
||||
Matrix.prototype.inverse = function() {
|
||||
if (this.height != this.width) {
|
||||
throw "can't invert a non-square matrix";
|
||||
}
|
||||
|
||||
var I = new IdentityMatrix(this.height);
|
||||
for (var i = 0; i < this.height; i++)
|
||||
this.mtx[i] = this.mtx[i].concat(I.mtx[i])
|
||||
this.width *= 2;
|
||||
|
||||
this.toReducedRowEchelonForm();
|
||||
|
||||
for (var i = 0; i < this.height; i++)
|
||||
this.mtx[i].splice(0, this.height);
|
||||
this.width /= 2;
|
||||
|
||||
return this;
|
||||
}
|
||||
|
||||
function ColumnVector(ary) {
|
||||
return new Matrix(ary.map(function(v) {return [v]}))
|
||||
}
|
||||
ColumnVector.prototype = Matrix.prototype
|
||||
|
||||
Matrix.prototype.regression_coefficients = function(x) {
|
||||
var x_t = x.transpose();
|
||||
return x_t.mult(x).inverse().mult(x_t).mult(this);
|
||||
}
|
||||
|
||||
// the Ruby example
|
||||
var y = new ColumnVector([1,2,3,4,5]);
|
||||
var x = new ColumnVector([2,1,3,4,5]);
|
||||
print(y.regression_coefficients(x));
|
||||
print();
|
||||
|
||||
// the Tcl example
|
||||
y = new ColumnVector([
|
||||
52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29,
|
||||
63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46
|
||||
]);
|
||||
x = new Matrix(
|
||||
[1.47,1.50,1.52,1.55,1.57,1.60,1.63,1.65,1.68,1.70,1.73,1.75,1.78,1.80,1.83].map(
|
||||
function(v) {return [Math.pow(v,0), Math.pow(v,1), Math.pow(v,2)]}
|
||||
)
|
||||
);
|
||||
print(y.regression_coefficients(x));
|
||||
12
Task/Multiple-regression/Jq/multiple-regression-1.jq
Normal file
12
Task/Multiple-regression/Jq/multiple-regression-1.jq
Normal file
|
|
@ -0,0 +1,12 @@
|
|||
def dot_product(a; b):
|
||||
reduce range(0;a|length) as $i (0; . + (a[$i] * b[$i]) );
|
||||
|
||||
# A and B should both be numeric matrices, A being m by n, and B being n by p.
|
||||
def multiply(A; B):
|
||||
(B[0]|length) as $p
|
||||
| (B|transpose) as $BT
|
||||
| reduce range(0; A|length) as $i
|
||||
([];
|
||||
reduce range(0; $p) as $j
|
||||
(.;
|
||||
.[$i][$j] = dot_product( A[$i]; $BT[$j] ) ));
|
||||
24
Task/Multiple-regression/Jq/multiple-regression-2.jq
Normal file
24
Task/Multiple-regression/Jq/multiple-regression-2.jq
Normal file
|
|
@ -0,0 +1,24 @@
|
|||
def multipleRegression(y; x):
|
||||
(y|transpose) as $cy
|
||||
| (x|transpose) as $cx
|
||||
| multiply( multiply( multiply(x;$cx)|inverse; x); $cy)
|
||||
| transpose[0];
|
||||
|
||||
def ys: [
|
||||
[ [1, 2, 3, 4, 5] ],
|
||||
[ [3, 4, 5] ],
|
||||
[ [52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29,
|
||||
63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46] ]
|
||||
];
|
||||
|
||||
def a:
|
||||
[1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83];
|
||||
|
||||
def xs:[
|
||||
[ [2, 1, 3, 4, 5] ],
|
||||
[ [1, 2, 1], [1, 1, 2] ],
|
||||
[ [range(0;a|length) | 1], a, (a|map(.*.))]
|
||||
];
|
||||
|
||||
range(0; ys|length) as $i
|
||||
| multipleRegression(ys[$i]; xs[$i])
|
||||
4
Task/Multiple-regression/Julia/multiple-regression.julia
Normal file
4
Task/Multiple-regression/Julia/multiple-regression.julia
Normal file
|
|
@ -0,0 +1,4 @@
|
|||
x = [1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83]
|
||||
y = [52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46]
|
||||
X = [x.^0 x.^1 x.^2];
|
||||
b = X \ y
|
||||
121
Task/Multiple-regression/Kotlin/multiple-regression.kotlin
Normal file
121
Task/Multiple-regression/Kotlin/multiple-regression.kotlin
Normal file
|
|
@ -0,0 +1,121 @@
|
|||
// Version 1.2.31
|
||||
|
||||
typealias Vector = DoubleArray
|
||||
typealias Matrix = Array<Vector>
|
||||
|
||||
operator fun Matrix.times(other: Matrix): Matrix {
|
||||
val rows1 = this.size
|
||||
val cols1 = this[0].size
|
||||
val rows2 = other.size
|
||||
val cols2 = other[0].size
|
||||
require(cols1 == rows2)
|
||||
val result = Matrix(rows1) { Vector(cols2) }
|
||||
for (i in 0 until rows1) {
|
||||
for (j in 0 until cols2) {
|
||||
for (k in 0 until rows2) {
|
||||
result[i][j] += this[i][k] * other[k][j]
|
||||
}
|
||||
}
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
fun Matrix.transpose(): Matrix {
|
||||
val rows = this.size
|
||||
val cols = this[0].size
|
||||
val trans = Matrix(cols) { Vector(rows) }
|
||||
for (i in 0 until cols) {
|
||||
for (j in 0 until rows) trans[i][j] = this[j][i]
|
||||
}
|
||||
return trans
|
||||
}
|
||||
|
||||
fun Matrix.inverse(): Matrix {
|
||||
val len = this.size
|
||||
require(this.all { it.size == len }) { "Not a square matrix" }
|
||||
val aug = Array(len) { DoubleArray(2 * len) }
|
||||
for (i in 0 until len) {
|
||||
for (j in 0 until len) aug[i][j] = this[i][j]
|
||||
// augment by identity matrix to right
|
||||
aug[i][i + len] = 1.0
|
||||
}
|
||||
aug.toReducedRowEchelonForm()
|
||||
val inv = Array(len) { DoubleArray(len) }
|
||||
// remove identity matrix to left
|
||||
for (i in 0 until len) {
|
||||
for (j in len until 2 * len) inv[i][j - len] = aug[i][j]
|
||||
}
|
||||
return inv
|
||||
}
|
||||
|
||||
fun Matrix.toReducedRowEchelonForm() {
|
||||
var lead = 0
|
||||
val rowCount = this.size
|
||||
val colCount = this[0].size
|
||||
for (r in 0 until rowCount) {
|
||||
if (colCount <= lead) return
|
||||
var i = r
|
||||
|
||||
while (this[i][lead] == 0.0) {
|
||||
i++
|
||||
if (rowCount == i) {
|
||||
i = r
|
||||
lead++
|
||||
if (colCount == lead) return
|
||||
}
|
||||
}
|
||||
|
||||
val temp = this[i]
|
||||
this[i] = this[r]
|
||||
this[r] = temp
|
||||
|
||||
if (this[r][lead] != 0.0) {
|
||||
val div = this[r][lead]
|
||||
for (j in 0 until colCount) this[r][j] /= div
|
||||
}
|
||||
|
||||
for (k in 0 until rowCount) {
|
||||
if (k != r) {
|
||||
val mult = this[k][lead]
|
||||
for (j in 0 until colCount) this[k][j] -= this[r][j] * mult
|
||||
}
|
||||
}
|
||||
|
||||
lead++
|
||||
}
|
||||
}
|
||||
|
||||
fun printVector(v: Vector) {
|
||||
println(v.asList())
|
||||
println()
|
||||
}
|
||||
|
||||
fun multipleRegression(y: Vector, x: Matrix): Vector {
|
||||
val cy = (arrayOf(y)).transpose() // convert 'y' to column vector
|
||||
val cx = x.transpose() // convert 'x' to column vector array
|
||||
return ((x * cx).inverse() * x * cy).transpose()[0]
|
||||
}
|
||||
|
||||
fun main(args: Array<String>) {
|
||||
var y = doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0)
|
||||
var x = arrayOf(doubleArrayOf(2.0, 1.0, 3.0, 4.0, 5.0))
|
||||
var v = multipleRegression(y, x)
|
||||
printVector(v)
|
||||
|
||||
y = doubleArrayOf(3.0, 4.0, 5.0)
|
||||
x = arrayOf(
|
||||
doubleArrayOf(1.0, 2.0, 1.0),
|
||||
doubleArrayOf(1.0, 1.0, 2.0)
|
||||
)
|
||||
v = multipleRegression(y, x)
|
||||
printVector(v)
|
||||
|
||||
y = doubleArrayOf(52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29,
|
||||
63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46)
|
||||
|
||||
val a = doubleArrayOf(1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70,
|
||||
1.73, 1.75, 1.78, 1.80, 1.83)
|
||||
x = arrayOf(DoubleArray(a.size) { 1.0 }, a, a.map { it * it }.toDoubleArray())
|
||||
v = multipleRegression(y, x)
|
||||
printVector(v)
|
||||
}
|
||||
5
Task/Multiple-regression/MATLAB/multiple-regression-1.m
Normal file
5
Task/Multiple-regression/MATLAB/multiple-regression-1.m
Normal file
|
|
@ -0,0 +1,5 @@
|
|||
n=100; k=10;
|
||||
y = randn (1,n); % generate random vector y
|
||||
X = randn (k,n); % generate random matrix X
|
||||
b = y / X
|
||||
b = 0.1457109 -0.0777564 -0.0712427 -0.0166193 0.0292955 -0.0079111 0.2265894 -0.0561589 -0.1752146 -0.2577663
|
||||
13
Task/Multiple-regression/MATLAB/multiple-regression-2.m
Normal file
13
Task/Multiple-regression/MATLAB/multiple-regression-2.m
Normal file
|
|
@ -0,0 +1,13 @@
|
|||
yt = y'; Xt = X';
|
||||
bt = Xt \ yt
|
||||
bt =
|
||||
0.1457109
|
||||
-0.0777564
|
||||
-0.0712427
|
||||
-0.0166193
|
||||
0.0292955
|
||||
-0.0079111
|
||||
0.2265894
|
||||
-0.0561589
|
||||
-0.1752146
|
||||
-0.2577663
|
||||
6
Task/Multiple-regression/MATLAB/multiple-regression-3.m
Normal file
6
Task/Multiple-regression/MATLAB/multiple-regression-3.m
Normal file
|
|
@ -0,0 +1,6 @@
|
|||
x = [1.47 1.50 1.52 1.55 1.57 1.60 1.63 1.65 1.68 1.70 1.73 1.75 1.78 1.80 1.83]
|
||||
y = [52.21 53.12 54.48 55.84 57.20 58.57 59.93 61.29 63.11 64.47 66.28 68.10 69.92 72.19 74.46]
|
||||
X = [x.^0;x.^1;x.^2];
|
||||
b = y/X
|
||||
|
||||
128.813 -143.162 61.960
|
||||
1
Task/Multiple-regression/MATLAB/multiple-regression-4.m
Normal file
1
Task/Multiple-regression/MATLAB/multiple-regression-4.m
Normal file
|
|
@ -0,0 +1 @@
|
|||
b = y * X' * inv(X * X')
|
||||
1
Task/Multiple-regression/MATLAB/multiple-regression-5.m
Normal file
1
Task/Multiple-regression/MATLAB/multiple-regression-5.m
Normal file
|
|
@ -0,0 +1 @@
|
|||
b = y * pinv(X)
|
||||
|
|
@ -0,0 +1,3 @@
|
|||
n:=200:
|
||||
X:=<ArrayTools[RandomArray](n,4,distribution=normal)|Vector(n,1,datatype=float[8])>:
|
||||
Y:=X.<4.2,-2.8,-1.4,3.1,1.75>+convert(ArrayTools[RandomArray](n,1,distribution=normal),Vector):
|
||||
19
Task/Multiple-regression/Maple/multiple-regression-2.maple
Normal file
19
Task/Multiple-regression/Maple/multiple-regression-2.maple
Normal file
|
|
@ -0,0 +1,19 @@
|
|||
LinearAlgebra[LeastSquares](X,Y)^+;
|
||||
# [4.33701132468683, -2.78654498997457, -1.41840666085642, 2.92065133466547, 1.76076442997642]
|
||||
|
||||
Statistics[LinearFit]([x1,x2,x3,x4,c],X,Y,[x1,x2,x3,x4,c],summarize=true)
|
||||
# Summary:
|
||||
# ----------------
|
||||
# Model: 4.3370113*x1-2.7865450*x2-1.4184067*x3+2.9206513*x4+1.7607644*c
|
||||
# ----------------
|
||||
# Coefficients:
|
||||
# Estimate Std. Error t-value P(>|t|)
|
||||
# Parameter 1 4.3370 0.0691 62.7409 0.0000
|
||||
# Parameter 2 -2.7865 0.0661 -42.1637 0.0000
|
||||
# Parameter 3 -1.4184 0.0699 -20.2937 0.0000
|
||||
# Parameter 4 2.9207 0.0687 42.5380 0.0000
|
||||
# Parameter 5 1.7608 0.0701 25.1210 0.0000
|
||||
# ----------------
|
||||
# R-squared: 0.9767, Adjusted R-squared: 0.9761
|
||||
# 4.33701132468683 x1 - 2.78654498997457 x2 - 1.41840666085642 x3
|
||||
# + 2.92065133466547 x4 + 1.76076442997642 c
|
||||
|
|
@ -0,0 +1,4 @@
|
|||
x = {1.47, 1.50 , 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83};
|
||||
y = {52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46};
|
||||
X = {x^0, x^1, x^2};
|
||||
LeastSquares[Transpose@X, y]
|
||||
17
Task/Multiple-regression/Nim/multiple-regression.nim
Normal file
17
Task/Multiple-regression/Nim/multiple-regression.nim
Normal file
|
|
@ -0,0 +1,17 @@
|
|||
# Using Wikipedia data sample.
|
||||
|
||||
import math
|
||||
import arraymancer, sequtils
|
||||
|
||||
var
|
||||
|
||||
height = [1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65,
|
||||
1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83].toTensor()
|
||||
|
||||
weight = [52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29,
|
||||
63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46].toTensor()
|
||||
|
||||
# Create Vandermonde matrix.
|
||||
var a = stack(height.ones_like, height, height *. height, axis = 1)
|
||||
|
||||
echo toSeq(least_squares_solver(a, weight).solution.items)
|
||||
|
|
@ -0,0 +1,4 @@
|
|||
pseudoinv(M)=my(sz=matsize(M),T=conj(M))~;if(sz[1]<sz[2],T/(M*T),(T*M)^-1*T)
|
||||
addhelp(pseudoinv, "pseudoinv(M): Moore pseudoinverse of the matrix M.");
|
||||
|
||||
y*pseudoinv(X)
|
||||
13
Task/Multiple-regression/Perl/multiple-regression.pl
Normal file
13
Task/Multiple-regression/Perl/multiple-regression.pl
Normal file
|
|
@ -0,0 +1,13 @@
|
|||
use strict;
|
||||
use warnings;
|
||||
use Statistics::Regression;
|
||||
|
||||
my @y = (52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46);
|
||||
my @x = ( 1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83);
|
||||
|
||||
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;
|
||||
57
Task/Multiple-regression/Phix/multiple-regression.phix
Normal file
57
Task/Multiple-regression/Phix/multiple-regression.phix
Normal file
|
|
@ -0,0 +1,57 @@
|
|||
(phixonline)-->
|
||||
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
|
||||
<span style="color: #008080;">constant</span> <span style="color: #000000;">N</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">15</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">M</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1.47</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1.50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1.52</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1.55</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1.57</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">1.60</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1.63</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1.65</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1.68</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1.70</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">1.73</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1.75</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1.78</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1.80</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1.83</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;">52.21</span><span style="color: #0000FF;">,</span><span style="color: #000000;">53.12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">54.48</span><span style="color: #0000FF;">,</span><span style="color: #000000;">55.84</span><span style="color: #0000FF;">,</span><span style="color: #000000;">57.20</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">58.57</span><span style="color: #0000FF;">,</span><span style="color: #000000;">59.93</span><span style="color: #0000FF;">,</span><span style="color: #000000;">61.29</span><span style="color: #0000FF;">,</span><span style="color: #000000;">63.11</span><span style="color: #0000FF;">,</span><span style="color: #000000;">64.47</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">66.28</span><span style="color: #0000FF;">,</span><span style="color: #000000;">68.10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">69.92</span><span style="color: #0000FF;">,</span><span style="color: #000000;">72.19</span><span style="color: #0000FF;">,</span><span style="color: #000000;">74.46</span><span style="color: #0000FF;">},</span>
|
||||
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">N</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">N</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">M</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span><span style="color: #000000;">M</span><span style="color: #0000FF;">)</span>
|
||||
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">M</span> <span style="color: #008080;">do</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: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">power</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;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">M</span> <span style="color: #008080;">then</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</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: #7060A8;">power</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;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
|
||||
<span style="color: #000080;font-style:italic;">-- build linear system</span>
|
||||
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">M</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">M</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">row</span><span style="color: #0000FF;">,</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">row</span><span style="color: #0000FF;">+</span><span style="color: #000000;">col</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">row</span><span style="color: #0000FF;">,</span><span style="color: #000000;">M</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">row</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
|
||||
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Linear system coefficents:\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,{</span><span style="color: #004600;">pp_Nest</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_IntFmt</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%7.1f"</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_FltFmt</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%7.1f"</span><span style="color: #0000FF;">})</span>
|
||||
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">M</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">j</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">M</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #0000FF;">?</span><span style="color: #008000;">"SINGULAR MATRIX !"</span>
|
||||
<span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">M</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]}</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">Y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">M</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;"><></span><span style="color: #000000;">j</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">Y</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">M</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">Y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
|
||||
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Solutions:\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">columnize</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">M</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
|
||||
<!--
|
||||
43
Task/Multiple-regression/PicoLisp/multiple-regression-1.l
Normal file
43
Task/Multiple-regression/PicoLisp/multiple-regression-1.l
Normal file
|
|
@ -0,0 +1,43 @@
|
|||
(scl 20)
|
||||
|
||||
# Matrix transposition
|
||||
(de matTrans (Mat)
|
||||
(apply mapcar Mat list) )
|
||||
|
||||
# Matrix multiplication
|
||||
(de matMul (Mat1 Mat2)
|
||||
(mapcar
|
||||
'((Row)
|
||||
(apply mapcar Mat2
|
||||
'(@ (sum */ Row (rest) (1.0 .))) ) )
|
||||
Mat1 ) )
|
||||
|
||||
# Matrix identity
|
||||
(de matIdent (N)
|
||||
(let L (need N (1.0) 0)
|
||||
(mapcar '(() (copy (rot L))) L) ) )
|
||||
|
||||
# Reduced row echelon form
|
||||
(de reducedRowEchelonForm (Mat)
|
||||
(let (Lead 1 Cols (length (car Mat)))
|
||||
(for (X Mat X (cdr X))
|
||||
(NIL
|
||||
(loop
|
||||
(T (seek '((R) (n0 (get R 1 Lead))) X)
|
||||
@ )
|
||||
(T (> (inc 'Lead) Cols)) ) )
|
||||
(xchg @ X)
|
||||
(let D (get X 1 Lead)
|
||||
(map
|
||||
'((R) (set R (*/ (car R) 1.0 D)))
|
||||
(car X) ) )
|
||||
(for Y Mat
|
||||
(unless (== Y (car X))
|
||||
(let N (- (get Y Lead))
|
||||
(map
|
||||
'((Dst Src)
|
||||
(inc Dst (*/ N (car Src) 1.0)) )
|
||||
Y
|
||||
(car X) ) ) ) )
|
||||
(T (> (inc 'Lead) Cols)) ) )
|
||||
Mat )
|
||||
19
Task/Multiple-regression/PicoLisp/multiple-regression-2.l
Normal file
19
Task/Multiple-regression/PicoLisp/multiple-regression-2.l
Normal file
|
|
@ -0,0 +1,19 @@
|
|||
(de matInverse (Mat)
|
||||
(let N (length Mat)
|
||||
(unless (= N (length (car Mat)))
|
||||
(quit "can't invert a non-square matrix") )
|
||||
(mapc conc Mat (matIdent N))
|
||||
(mapcar '((L) (tail N L)) (reducedRowEchelonForm Mat)) ) )
|
||||
|
||||
(de columnVector (Ary)
|
||||
(mapcar cons Ary) )
|
||||
|
||||
(de regressionCoefficients (Mat X)
|
||||
(let Xt (matTrans X)
|
||||
(matMul (matMul (matInverse (matMul Xt X)) Xt) Mat) ) )
|
||||
|
||||
(setq
|
||||
Y (columnVector (1.0 2.0 3.0 4.0 5.0))
|
||||
X (columnVector (2.0 1.0 3.0 4.0 5.0)) )
|
||||
|
||||
(round (caar (regressionCoefficients Y X)) 17)
|
||||
11
Task/Multiple-regression/Python/multiple-regression-1.py
Normal file
11
Task/Multiple-regression/Python/multiple-regression-1.py
Normal file
|
|
@ -0,0 +1,11 @@
|
|||
import numpy as np
|
||||
|
||||
height = [1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63,
|
||||
1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83]
|
||||
weight = [52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93,
|
||||
61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46]
|
||||
|
||||
X = np.mat(height**np.arange(3)[:, None])
|
||||
y = np.mat(weight)
|
||||
|
||||
print(y * X.T * (X*X.T).I)
|
||||
11
Task/Multiple-regression/Python/multiple-regression-2.py
Normal file
11
Task/Multiple-regression/Python/multiple-regression-2.py
Normal file
|
|
@ -0,0 +1,11 @@
|
|||
import numpy as np
|
||||
|
||||
height = [1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63,
|
||||
1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83]
|
||||
weight = [52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93,
|
||||
61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46]
|
||||
|
||||
X = np.array(height)[:, None]**range(3)
|
||||
y = weight
|
||||
|
||||
print(np.linalg.lstsq(X, y)[0])
|
||||
4
Task/Multiple-regression/R/multiple-regression-1.r
Normal file
4
Task/Multiple-regression/R/multiple-regression-1.r
Normal file
|
|
@ -0,0 +1,4 @@
|
|||
x <- c(1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83)
|
||||
y <- c(52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46)
|
||||
|
||||
lm( y ~ x + I(x^2))
|
||||
16
Task/Multiple-regression/R/multiple-regression-2.r
Normal file
16
Task/Multiple-regression/R/multiple-regression-2.r
Normal file
|
|
@ -0,0 +1,16 @@
|
|||
simpleMultipleReg <- function(formula) {
|
||||
|
||||
## parse and evaluate the model formula
|
||||
mf <- model.frame(formula)
|
||||
|
||||
## create design matrix
|
||||
X <- model.matrix(mf)
|
||||
|
||||
## create dependent variable
|
||||
Y <- model.response(mf)
|
||||
|
||||
## solve
|
||||
solve(t(X) %*% X) %*% t(X) %*% Y
|
||||
}
|
||||
|
||||
simpleMultipleReg(y ~ x + I(x^2))
|
||||
1
Task/Multiple-regression/R/multiple-regression-3.r
Normal file
1
Task/Multiple-regression/R/multiple-regression-3.r
Normal file
|
|
@ -0,0 +1 @@
|
|||
solve(crossprod(X), crossprod(X, Y))
|
||||
21
Task/Multiple-regression/R/multiple-regression-4.r
Normal file
21
Task/Multiple-regression/R/multiple-regression-4.r
Normal file
|
|
@ -0,0 +1,21 @@
|
|||
lm.impl <- function(formula) {
|
||||
mf <- model.frame(formula)
|
||||
X <- model.matrix(mf)
|
||||
Y <- model.response(mf)
|
||||
qr.coef(qr(X), Y)
|
||||
}
|
||||
|
||||
|
||||
lm(y ~ x + I(x^2))
|
||||
|
||||
# Call:
|
||||
# lm(formula = y ~ x + I(x^2))
|
||||
#
|
||||
# Coefficients:
|
||||
# (Intercept) x I(x^2)
|
||||
# 128.81 -143.16 61.96
|
||||
|
||||
lm.impl(y ~ x + I(x^2))
|
||||
|
||||
# (Intercept) x I(x^2)
|
||||
# 128.81280 -143.16202 61.96033
|
||||
|
|
@ -0,0 +1,6 @@
|
|||
#lang racket
|
||||
(require math)
|
||||
(define T matrix-transpose)
|
||||
|
||||
(define (fit X y)
|
||||
(matrix-solve (matrix* (T X) X) (matrix* (T X) y)))
|
||||
10
Task/Multiple-regression/Racket/multiple-regression-2.rkt
Normal file
10
Task/Multiple-regression/Racket/multiple-regression-2.rkt
Normal file
|
|
@ -0,0 +1,10 @@
|
|||
(fit (matrix [[1 2]
|
||||
[2 5]
|
||||
[3 7]
|
||||
[4 9]])
|
||||
(matrix [[1]
|
||||
[2]
|
||||
[3]
|
||||
[9]]))
|
||||
{{out}}
|
||||
(array #[#[9 1/3] #[-3 1/3]])
|
||||
16
Task/Multiple-regression/Raku/multiple-regression.raku
Normal file
16
Task/Multiple-regression/Raku/multiple-regression.raku
Normal file
|
|
@ -0,0 +1,16 @@
|
|||
use Clifford;
|
||||
my @height = <1.47 1.50 1.52 1.55 1.57 1.60 1.63 1.65 1.68 1.70 1.73 1.75 1.78 1.80 1.83>;
|
||||
my @weight = <52.21 53.12 54.48 55.84 57.20 58.57 59.93 61.29 63.11 64.47 66.28 68.10 69.92 72.19 74.46>;
|
||||
|
||||
my $w = [+] @weight Z* @e;
|
||||
|
||||
my $h0 = [+] @e[^@weight];
|
||||
my $h1 = [+] @height Z* @e;
|
||||
my $h2 = [+] (@height X** 2) Z* @e;
|
||||
|
||||
my $I = $h0∧$h1∧$h2;
|
||||
my $I2 = ($I·$I.reversion).Real;
|
||||
|
||||
say "α = ", ($w∧$h1∧$h2)·$I.reversion/$I2;
|
||||
say "β = ", ($w∧$h2∧$h0)·$I.reversion/$I2;
|
||||
say "γ = ", ($w∧$h0∧$h1)·$I.reversion/$I2;
|
||||
8
Task/Multiple-regression/Ruby/multiple-regression-1.rb
Normal file
8
Task/Multiple-regression/Ruby/multiple-regression-1.rb
Normal file
|
|
@ -0,0 +1,8 @@
|
|||
require 'matrix'
|
||||
|
||||
def regression_coefficients y, x
|
||||
y = Matrix.column_vector y.map { |i| i.to_f }
|
||||
x = Matrix.columns x.map { |xi| xi.map { |i| i.to_f }}
|
||||
|
||||
(x.t * x).inverse * x.t * y
|
||||
end
|
||||
1
Task/Multiple-regression/Ruby/multiple-regression-2.rb
Normal file
1
Task/Multiple-regression/Ruby/multiple-regression-2.rb
Normal file
|
|
@ -0,0 +1 @@
|
|||
puts regression_coefficients([1, 2, 3, 4, 5], [ [2, 1, 3, 4, 5] ])
|
||||
1
Task/Multiple-regression/Ruby/multiple-regression-3.rb
Normal file
1
Task/Multiple-regression/Ruby/multiple-regression-3.rb
Normal file
|
|
@ -0,0 +1 @@
|
|||
puts regression_coefficients([3,4,5], [ [1,2,1], [1,1,2] ])
|
||||
14
Task/Multiple-regression/SPSS/multiple-regression-1.spss
Normal file
14
Task/Multiple-regression/SPSS/multiple-regression-1.spss
Normal file
|
|
@ -0,0 +1,14 @@
|
|||
set rng=mc seed=17760704.
|
||||
new file.
|
||||
input program.
|
||||
vector x(4).
|
||||
loop #i=1 to 200.
|
||||
loop #j=1 to 4.
|
||||
compute x(#j)=rv.normal(0,1).
|
||||
end loop.
|
||||
end case.
|
||||
end loop.
|
||||
end file.
|
||||
end input program.
|
||||
compute y=1.5+0.8*x1-0.7*x2+1.1*x3-1.7*x4+rv.normal(0,1).
|
||||
execute.
|
||||
2
Task/Multiple-regression/SPSS/multiple-regression-2.spss
Normal file
2
Task/Multiple-regression/SPSS/multiple-regression-2.spss
Normal file
|
|
@ -0,0 +1,2 @@
|
|||
regression /dependent=y
|
||||
/method=enter x1 x2 x3 x4.
|
||||
77
Task/Multiple-regression/SPSS/multiple-regression-3.spss
Normal file
77
Task/Multiple-regression/SPSS/multiple-regression-3.spss
Normal file
|
|
@ -0,0 +1,77 @@
|
|||
Regression
|
||||
Notes
|
||||
|--------------------------------------------------------------------|---------------------------------------------------------------------------|
|
||||
|Output Created |21-MAR-2020 23:17:33 |
|
||||
|--------------------------------------------------------------------|---------------------------------------------------------------------------|
|
||||
|Comments | |
|
||||
|----------------------|---------------------------------------------|---------------------------------------------------------------------------|
|
||||
|Input |Filter |<none> |
|
||||
| |---------------------------------------------|---------------------------------------------------------------------------|
|
||||
| |Weight |<none> |
|
||||
| |---------------------------------------------|---------------------------------------------------------------------------|
|
||||
| |Split File |<none> |
|
||||
| |---------------------------------------------|---------------------------------------------------------------------------|
|
||||
| |N of Rows in Working Data File |200 |
|
||||
|----------------------|---------------------------------------------|---------------------------------------------------------------------------|
|
||||
|Missing Value Handling|Definition of Missing |User-defined missing values are treated as missing. |
|
||||
| |---------------------------------------------|---------------------------------------------------------------------------|
|
||||
| |Cases Used |Statistics are based on cases with no missing values for any variable used.|
|
||||
|--------------------------------------------------------------------|---------------------------------------------------------------------------|
|
||||
|Syntax |regression /dependent=y /method=enter x1 x2 x3 x4. |
|
||||
|----------------------|---------------------------------------------|---------------------------------------------------------------------------|
|
||||
|Resources |Processor Time |00:00:00,00 |
|
||||
| |---------------------------------------------|---------------------------------------------------------------------------|
|
||||
| |Elapsed Time |00:00:00,00 |
|
||||
| |---------------------------------------------|---------------------------------------------------------------------------|
|
||||
| |Memory Required |4080 bytes |
|
||||
| |---------------------------------------------|---------------------------------------------------------------------------|
|
||||
| |Additional Memory Required for Residual Plots|0 bytes |
|
||||
|------------------------------------------------------------------------------------------------------------------------------------------------|
|
||||
|
||||
Variables Entered/Removeda
|
||||
|-----|-----------------|-----------------|------|
|
||||
|Model|Variables Entered|Variables Removed|Method|
|
||||
|-----|-----------------|-----------------|------|
|
||||
|1 |x4, x3, x2, x1b |. |Enter |
|
||||
|------------------------------------------------|
|
||||
a Dependent Variable: y
|
||||
b All requested variables entered.
|
||||
|
||||
Model Summary
|
||||
|-----|-----|--------|-----------------|--------------------------|
|
||||
|Model|R |R Square|Adjusted R Square|Std. Error of the Estimate|
|
||||
|-----|-----|--------|-----------------|--------------------------|
|
||||
|1 |,929a|,863 |,860 |,94928 |
|
||||
|-----------------------------------------------------------------|
|
||||
a Predictors: (Constant), x4, x3, x2, x1
|
||||
|
||||
ANOVAa
|
||||
|----------------|--------------|---|-----------|-------|-----|
|
||||
|Model |Sum of Squares|df |Mean Square|F |Sig. |
|
||||
|-----|----------|--------------|---|-----------|-------|-----|
|
||||
|1 |Regression|1106,659 |4 |276,665 |307,021|,000b|
|
||||
| |----------|--------------|---|-----------|-------|-----|
|
||||
| |Residual |175,720 |195|,901 | | |
|
||||
| |----------|--------------|---|-----------|-------|-----|
|
||||
| |Total |1282,379 |199| | | |
|
||||
|-------------------------------------------------------------|
|
||||
a Dependent Variable: y
|
||||
b Predictors: (Constant), x4, x3, x2, x1
|
||||
|
||||
Coefficientsa
|
||||
|----------------|--------------------------------------|-------------------------|-------|----|
|
||||
|Model |Unstandardized Coefficients |Standardized Coefficients|t |Sig.|
|
||||
| |---------------------------|----------|-------------------------| | |
|
||||
| |B |Std. Error|Beta | | |
|
||||
|-----|----------|---------------------------|----------|-------------------------|-------|----|
|
||||
|1 |(Constant)|1,550 |,067 | |23,003 |,000|
|
||||
| |----------|---------------------------|----------|-------------------------|-------|----|
|
||||
| |x1 |,831 |,062 |,360 |13,457 |,000|
|
||||
| |----------|---------------------------|----------|-------------------------|-------|----|
|
||||
| |x2 |-,604 |,075 |-,215 |-8,051 |,000|
|
||||
| |----------|---------------------------|----------|-------------------------|-------|----|
|
||||
| |x3 |1,098 |,065 |,451 |16,989 |,000|
|
||||
| |----------|---------------------------|----------|-------------------------|-------|----|
|
||||
| |x4 |-1,770 |,073 |-,656 |-24,306|,000|
|
||||
|----------------------------------------------------------------------------------------------|
|
||||
a Dependent Variable: y
|
||||
|
|
@ -0,0 +1,7 @@
|
|||
clear
|
||||
set seed 17760704
|
||||
set obs 200
|
||||
forv i=1/4 {
|
||||
gen x`i'=rnormal()
|
||||
}
|
||||
gen y=1.5+0.8*x1-0.7*x2+1.1*x3-1.7*x4+rnormal()
|
||||
|
|
@ -0,0 +1 @@
|
|||
reg y x*
|
||||
11
Task/Multiple-regression/Stata/multiple-regression-3.stata
Normal file
11
Task/Multiple-regression/Stata/multiple-regression-3.stata
Normal file
|
|
@ -0,0 +1,11 @@
|
|||
. di _b[x1]
|
||||
.75252466
|
||||
|
||||
. di _b[_cons]
|
||||
1.3991314
|
||||
|
||||
. di _se[x1]
|
||||
.06895593
|
||||
|
||||
. di _se[_cons]
|
||||
.06978623
|
||||
25
Task/Multiple-regression/Stata/multiple-regression-4.stata
Normal file
25
Task/Multiple-regression/Stata/multiple-regression-4.stata
Normal file
|
|
@ -0,0 +1,25 @@
|
|||
. estat ic
|
||||
|
||||
Akaike's information criterion and Bayesian information criterion
|
||||
|
||||
-----------------------------------------------------------------------------
|
||||
Model | Obs ll(null) ll(model) df AIC BIC
|
||||
-------------+---------------------------------------------------------------
|
||||
. | 200 -487.1455 -275.6985 5 561.397 577.8886
|
||||
-----------------------------------------------------------------------------
|
||||
Note: N=Obs used in calculating BIC; see [R] BIC note.
|
||||
|
||||
. estat vce
|
||||
|
||||
Covariance matrix of coefficients of regress model
|
||||
|
||||
e(V) | x1 x2 x3 x4 _cons
|
||||
-------------+------------------------------------------------------------
|
||||
x1 | .00475492
|
||||
x2 | -.00040258 .00486445
|
||||
x3 | -.00042516 .00017355 .00521125
|
||||
x4 | -.00011915 -.0002568 .00054646 .00386583
|
||||
_cons | .00030777 -.00031109 -.00023794 .00058926 .00487012
|
||||
|
||||
. predict yhat, xb
|
||||
. predict r, r
|
||||
|
|
@ -0,0 +1,3 @@
|
|||
{1.47,1.50,1.52,1.55,1.57,1.60,1.63,1.65,1.68,1.70,1.73,1.75,1.78,1.80,1.83}→L₁
|
||||
{52.21,53.12,54.48,55.84,57.20,58.57,59.93,61.29,63.11,64.47,66.28,68.10,69.92,72.19,74.46}→L₂
|
||||
QuadReg L₁,L₂
|
||||
16
Task/Multiple-regression/Tcl/multiple-regression-1.tcl
Normal file
16
Task/Multiple-regression/Tcl/multiple-regression-1.tcl
Normal file
|
|
@ -0,0 +1,16 @@
|
|||
package require math::linearalgebra
|
||||
namespace eval multipleRegression {
|
||||
namespace export regressionCoefficients
|
||||
namespace import ::math::linearalgebra::*
|
||||
|
||||
# Matrix inversion is defined in terms of Gaussian elimination
|
||||
# Note that we assume (correctly) that we have a square matrix
|
||||
proc invert {matrix} {
|
||||
solveGauss $matrix [mkIdentity [lindex [shape $matrix] 0]]
|
||||
}
|
||||
# Implement the Ordinary Least Squares method
|
||||
proc regressionCoefficients {y x} {
|
||||
matmul [matmul [invert [matmul $x [transpose $x]]] $x] $y
|
||||
}
|
||||
}
|
||||
namespace import multipleRegression::regressionCoefficients
|
||||
16
Task/Multiple-regression/Tcl/multiple-regression-2.tcl
Normal file
16
Task/Multiple-regression/Tcl/multiple-regression-2.tcl
Normal file
|
|
@ -0,0 +1,16 @@
|
|||
# Simple helper just for this example
|
||||
proc map {n exp list} {
|
||||
upvar 1 $n v
|
||||
set r {}; foreach v $list {lappend r [uplevel 1 $exp]}; return $r
|
||||
}
|
||||
|
||||
# Data from wikipedia
|
||||
set x {
|
||||
1.47 1.50 1.52 1.55 1.57 1.60 1.63 1.65 1.68 1.70 1.73 1.75 1.78 1.80 1.83
|
||||
}
|
||||
set y {
|
||||
52.21 53.12 54.48 55.84 57.20 58.57 59.93 61.29 63.11 64.47 66.28 68.10
|
||||
69.92 72.19 74.46
|
||||
}
|
||||
# Wikipedia states that fitting up to the square of x[i] is worth it
|
||||
puts [regressionCoefficients $y [map n {map v {expr {$v**$n}} $x} {0 1 2}]]
|
||||
|
|
@ -0,0 +1 @@
|
|||
regression_coefficients = lapack..dgelsd
|
||||
12
Task/Multiple-regression/Ursala/multiple-regression-2.ursala
Normal file
12
Task/Multiple-regression/Ursala/multiple-regression-2.ursala
Normal file
|
|
@ -0,0 +1,12 @@
|
|||
x =
|
||||
|
||||
<
|
||||
<7.589183e+00,1.703609e+00,-4.477162e+00>,
|
||||
<-4.597851e+00,9.434889e+00,-6.543450e+00>,
|
||||
<4.588202e-01,-6.115153e+00,1.331191e+00>>
|
||||
|
||||
y = <1.745005e+00,-4.448092e+00,-4.160842e+00>
|
||||
|
||||
#cast %eL
|
||||
|
||||
example = regression_coefficients(x,y)
|
||||
|
|
@ -0,0 +1,230 @@
|
|||
Module Module1
|
||||
|
||||
Sub Swap(Of T)(ByRef x As T, ByRef y As T)
|
||||
Dim temp = x
|
||||
x = y
|
||||
y = temp
|
||||
End Sub
|
||||
|
||||
Sub Require(condition As Boolean, message As String)
|
||||
If condition Then
|
||||
Return
|
||||
End If
|
||||
Throw New ArgumentException(message)
|
||||
End Sub
|
||||
|
||||
Class Matrix
|
||||
Private data As Double(,)
|
||||
Private rowCount As Integer
|
||||
Private colCount As Integer
|
||||
|
||||
Public Sub New(rows As Integer, cols As Integer)
|
||||
Require(rows > 0, "Need at least one row")
|
||||
rowCount = rows
|
||||
|
||||
Require(cols > 0, "Need at least one column")
|
||||
colCount = cols
|
||||
|
||||
data = New Double(rows - 1, cols - 1) {}
|
||||
End Sub
|
||||
|
||||
Public Sub New(source As Double(,))
|
||||
Dim rows = source.GetLength(0)
|
||||
Require(rows > 0, "Need at least one row")
|
||||
rowCount = rows
|
||||
|
||||
Dim cols = source.GetLength(1)
|
||||
Require(cols > 0, "Need at least one column")
|
||||
colCount = cols
|
||||
|
||||
data = New Double(rows - 1, cols - 1) {}
|
||||
For i = 1 To rows
|
||||
For j = 1 To cols
|
||||
data(i - 1, j - 1) = source(i - 1, j - 1)
|
||||
Next
|
||||
Next
|
||||
End Sub
|
||||
|
||||
Default Public Property Index(i As Integer, j As Integer) As Double
|
||||
Get
|
||||
Return data(i, j)
|
||||
End Get
|
||||
Set(value As Double)
|
||||
data(i, j) = value
|
||||
End Set
|
||||
End Property
|
||||
|
||||
Public Property Slice(i As Integer) As Double()
|
||||
Get
|
||||
Dim m(colCount - 1) As Double
|
||||
For j = 1 To colCount
|
||||
m(j - 1) = Index(i, j - 1)
|
||||
Next
|
||||
Return m
|
||||
End Get
|
||||
Set(value As Double())
|
||||
Require(colCount = value.Length, "Slice must match the number of columns")
|
||||
For j = 1 To colCount
|
||||
Index(i, j - 1) = value(j - 1)
|
||||
Next
|
||||
End Set
|
||||
End Property
|
||||
|
||||
Public Shared Operator *(m1 As Matrix, m2 As Matrix) As Matrix
|
||||
Dim rc1 = m1.rowCount
|
||||
Dim cc1 = m1.colCount
|
||||
Dim rc2 = m2.rowCount
|
||||
Dim cc2 = m2.colCount
|
||||
Require(cc1 = rc2, "Cannot multiply if the first columns does not equal the second rows")
|
||||
Dim result As New Matrix(rc1, cc2)
|
||||
For i = 1 To rc1
|
||||
For j = 1 To cc2
|
||||
For k = 1 To rc2
|
||||
result(i - 1, j - 1) += m1(i - 1, k - 1) * m2(k - 1, j - 1)
|
||||
Next
|
||||
Next
|
||||
Next
|
||||
Return result
|
||||
End Operator
|
||||
|
||||
Public Function Transpose() As Matrix
|
||||
Dim rc = rowCount
|
||||
Dim cc = colCount
|
||||
|
||||
Dim trans As New Matrix(cc, rc)
|
||||
For i = 1 To cc
|
||||
For j = 1 To rc
|
||||
trans(i - 1, j - 1) = Index(j - 1, i - 1)
|
||||
Next
|
||||
Next
|
||||
Return trans
|
||||
End Function
|
||||
|
||||
Public Sub ToReducedRowEchelonForm()
|
||||
Dim lead = 0
|
||||
Dim rc = rowCount
|
||||
Dim cc = colCount
|
||||
For r = 1 To rc
|
||||
If cc <= lead Then
|
||||
Return
|
||||
End If
|
||||
Dim i = r
|
||||
|
||||
While Index(i - 1, lead) = 0.0
|
||||
i += 1
|
||||
If rc = i Then
|
||||
i = r
|
||||
lead += 1
|
||||
If cc = lead Then
|
||||
Return
|
||||
End If
|
||||
End If
|
||||
End While
|
||||
|
||||
Dim temp = Slice(i - 1)
|
||||
Slice(i - 1) = Slice(r - 1)
|
||||
Slice(r - 1) = temp
|
||||
|
||||
If Index(r - 1, lead) <> 0.0 Then
|
||||
Dim div = Index(r - 1, lead)
|
||||
For j = 1 To cc
|
||||
Index(r - 1, j - 1) /= div
|
||||
Next
|
||||
End If
|
||||
|
||||
For k = 1 To rc
|
||||
If k <> r Then
|
||||
Dim mult = Index(k - 1, lead)
|
||||
For j = 1 To cc
|
||||
Index(k - 1, j - 1) -= Index(r - 1, j - 1) * mult
|
||||
Next
|
||||
End If
|
||||
Next
|
||||
|
||||
lead += 1
|
||||
Next
|
||||
End Sub
|
||||
|
||||
Public Function Inverse() As Matrix
|
||||
Require(rowCount = colCount, "Not a square matrix")
|
||||
Dim len = rowCount
|
||||
Dim aug As New Matrix(len, 2 * len)
|
||||
For i = 1 To len
|
||||
For j = 1 To len
|
||||
aug(i - 1, j - 1) = Index(i - 1, j - 1)
|
||||
Next
|
||||
REM augment identity matrix to right
|
||||
aug(i - 1, i + len - 1) = 1.0
|
||||
Next
|
||||
aug.ToReducedRowEchelonForm()
|
||||
Dim inv As New Matrix(len, len)
|
||||
For i = 1 To len
|
||||
For j = len + 1 To 2 * len
|
||||
inv(i - 1, j - len - 1) = aug(i - 1, j - 1)
|
||||
Next
|
||||
Next
|
||||
Return inv
|
||||
End Function
|
||||
End Class
|
||||
|
||||
Function ConvertArray(source As Double()) As Double(,)
|
||||
Dim dest(0, source.Length - 1) As Double
|
||||
For i = 1 To source.Length
|
||||
dest(0, i - 1) = source(i - 1)
|
||||
Next
|
||||
Return dest
|
||||
End Function
|
||||
|
||||
Function MultipleRegression(y As Double(), x As Matrix) As Double()
|
||||
Dim tm As New Matrix(ConvertArray(y))
|
||||
Dim cy = tm.Transpose
|
||||
Dim cx = x.Transpose
|
||||
Return ((x * cx).Inverse * x * cy).Transpose.Slice(0)
|
||||
End Function
|
||||
|
||||
Sub Print(v As Double())
|
||||
Dim it = v.GetEnumerator()
|
||||
|
||||
Console.Write("[")
|
||||
If it.MoveNext() Then
|
||||
Console.Write(it.Current)
|
||||
End If
|
||||
While it.MoveNext
|
||||
Console.Write(", ")
|
||||
Console.Write(it.Current)
|
||||
End While
|
||||
Console.Write("]")
|
||||
End Sub
|
||||
|
||||
Sub Main()
|
||||
Dim y() = {1.0, 2.0, 3.0, 4.0, 5.0}
|
||||
Dim x As New Matrix({{2.0, 1.0, 3.0, 4.0, 5.0}})
|
||||
Dim v = MultipleRegression(y, x)
|
||||
Print(v)
|
||||
Console.WriteLine()
|
||||
|
||||
y = {3.0, 4.0, 5.0}
|
||||
x = New Matrix({
|
||||
{1.0, 2.0, 1.0},
|
||||
{1.0, 1.0, 2.0}
|
||||
})
|
||||
v = MultipleRegression(y, x)
|
||||
Print(v)
|
||||
Console.WriteLine()
|
||||
|
||||
y = {52.21, 53.12, 54.48, 55.84, 57.2, 58.57, 59.93, 61.29, 63.11, 64.47, 66.28, 68.1, 69.92, 72.19, 74.46}
|
||||
Dim a = {1.47, 1.5, 1.52, 1.55, 1.57, 1.6, 1.63, 1.65, 1.68, 1.7, 1.73, 1.75, 1.78, 1.8, 1.83}
|
||||
|
||||
Dim xs(2, a.Length - 1) As Double
|
||||
For i = 1 To a.Length
|
||||
xs(0, i - 1) = 1.0
|
||||
xs(1, i - 1) = a(i - 1)
|
||||
xs(2, i - 1) = a(i - 1) * a(i - 1)
|
||||
Next
|
||||
x = New Matrix(xs)
|
||||
v = MultipleRegression(y, x)
|
||||
Print(v)
|
||||
Console.WriteLine()
|
||||
End Sub
|
||||
|
||||
End Module
|
||||
28
Task/Multiple-regression/Wren/multiple-regression.wren
Normal file
28
Task/Multiple-regression/Wren/multiple-regression.wren
Normal file
|
|
@ -0,0 +1,28 @@
|
|||
import "/matrix" for Matrix
|
||||
|
||||
var multipleRegression = Fn.new { |y, x|
|
||||
var cy = y.transpose
|
||||
var cx = x.transpose
|
||||
return ((x * cx).inverse * x * cy).transpose[0]
|
||||
}
|
||||
|
||||
var ys = [
|
||||
Matrix.new([ [1, 2, 3, 4, 5] ]),
|
||||
Matrix.new([ [3, 4, 5] ]),
|
||||
Matrix.new([ [52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29,
|
||||
63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46] ])
|
||||
]
|
||||
|
||||
var a = [1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83]
|
||||
|
||||
var xs = [
|
||||
Matrix.new([ [2, 1, 3, 4, 5] ]),
|
||||
Matrix.new([ [1, 2, 1], [1, 1, 2] ]),
|
||||
Matrix.new([ List.filled(a.count, 1), a, a.map { |e| e * e }.toList ])
|
||||
]
|
||||
|
||||
for (i in 0...ys.count) {
|
||||
var v = multipleRegression.call(ys[i], xs[i])
|
||||
System.print(v)
|
||||
System.print()
|
||||
}
|
||||
9
Task/Multiple-regression/Zkl/multiple-regression-1.zkl
Normal file
9
Task/Multiple-regression/Zkl/multiple-regression-1.zkl
Normal file
|
|
@ -0,0 +1,9 @@
|
|||
var [const] GSL=Import("zklGSL"); // libGSL (GNU Scientific Library)
|
||||
height:=GSL.VectorFromData(1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63,
|
||||
1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83);
|
||||
weight:=GSL.VectorFromData(52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93,
|
||||
61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46);
|
||||
v:=GSL.polyFit(height,weight,2);
|
||||
v.format().println();
|
||||
GSL.Helpers.polyString(v).println();
|
||||
GSL.Helpers.polyEval(v,height).format().println();
|
||||
56
Task/Multiple-regression/Zkl/multiple-regression-2.zkl
Normal file
56
Task/Multiple-regression/Zkl/multiple-regression-2.zkl
Normal file
|
|
@ -0,0 +1,56 @@
|
|||
// Solve a linear system AX=B where A is symmetric and positive definite, so it can be Cholesky decomposed.
|
||||
fcn linsys(A,B){
|
||||
n,m:=A.len(),B[1].len(); // A.rows,B.cols
|
||||
y:=n.pump(List.createLong(n).write,0.0); // writable vector of n zeros
|
||||
X:=make_array(n,m,0.0);
|
||||
L:=cholesky(A); // A=LL'
|
||||
|
||||
foreach col in (m){
|
||||
foreach k in (n){ // Forward substitution: y = L\B
|
||||
y[k]=( B[k][col] - k.reduce('wrap(s,j){ s + L[k][j]*y[j] },0.0) )
|
||||
/L[k][k];
|
||||
}
|
||||
foreach k in ([n-1..0,-1]){ // Back substitution. x=L'\y
|
||||
X[k][col]=
|
||||
( y[k] - (k+1).reduce(n-k-1,'wrap(s,j){ s + L[j][k]*X[j][col] },0.0) )
|
||||
/L[k][k];
|
||||
}
|
||||
}
|
||||
X
|
||||
}
|
||||
fcn cholesky(mat){ // Cholesky decomposition task
|
||||
rows:=mat.len();
|
||||
r:=(0).pump(rows,List().write, (0).pump(rows,List,0.0).copy); // matrix of zeros
|
||||
foreach i,j in (rows,i+1){
|
||||
s:=(0).reduce(j,'wrap(s,k){ s + r[i][k]*r[j][k] },0.0);
|
||||
r[i][j]=( if(i==j)(mat[i][i] - s).sqrt()
|
||||
else 1.0/r[j][j]*(mat[i][j] - s) );
|
||||
}
|
||||
r
|
||||
}
|
||||
|
||||
// Solve a linear least squares problem. Ax=b, with A being mxn, with m>n.
|
||||
// Solves the linear system A'Ax=A'b.
|
||||
fcn lsqr(A,b){
|
||||
at:=transpose(A);
|
||||
linsys(matMult(at,A), matMult(at,b));
|
||||
}
|
||||
// Least square fit of a polynomial of order n the x-y-curve.
|
||||
fcn polyfit(x,y,n){
|
||||
n+=1;
|
||||
m:=x[0].len(); // columns
|
||||
A:=make_array(m,n,0.0);
|
||||
foreach i,j in (m,n){ A[i][j]=x[0][i].pow(j); }
|
||||
lsqr(A, transpose(y));
|
||||
}
|
||||
fcn make_array(n,m,v){ (m).pump(List.createLong(m).write,v)*n }
|
||||
fcn matMult(a,b){
|
||||
n,m,p:=a[0].len(),a.len(),b[0].len();
|
||||
ans:=make_array(m,p,0.0);
|
||||
foreach i,j,k in (m,p,n){ ans[i][j]+=a[i][k]*b[k][j]; }
|
||||
ans
|
||||
}
|
||||
fcn transpose(M){
|
||||
if(M.len()==1) M[0].pump(List,List.create); // 1 row --> n columns
|
||||
else M[0].zip(M.xplode(1));
|
||||
}
|
||||
5
Task/Multiple-regression/Zkl/multiple-regression-3.zkl
Normal file
5
Task/Multiple-regression/Zkl/multiple-regression-3.zkl
Normal file
|
|
@ -0,0 +1,5 @@
|
|||
height:=T(T(1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63,
|
||||
1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83));
|
||||
weight:=T(T(52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93,
|
||||
61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46));
|
||||
polyfit(height,weight,2).flatten().println();
|
||||
Loading…
Add table
Add a link
Reference in a new issue