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https://gitlab.com/freepascal.org/fpc/source.git
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904 lines
26 KiB
PHP
904 lines
26 KiB
PHP
{*****************************************************************************
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Methods of the matrix object
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*****************************************************************************}
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constructor objectname.init_zero;
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begin
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fillchar(data,sizeof(data),0);
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end;
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constructor objectname.init_identity;
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begin
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fillchar(data,sizeof(data),0);
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data[0,0]:=1;
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data[1,1]:=1;
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{$if matsize>=3}
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data[2,2]:=1;
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{$endif}
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{$if matsize>=4}
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data[3,3]:=1;
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{$endif}
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end;
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constructor objectname.init(aa
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,ab
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{$if matsize>=3},ac{$endif}
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{$if matsize>=4},ad{$endif}
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,ba
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,bb
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{$if matsize>=3},bc{$endif}
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{$if matsize>=4},bd{$endif}
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{$if matsize>=3}
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,ca
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,cb
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,cc
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{$if matsize>=4},cd{$endif}
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{$endif}
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{$if matsize>=4}
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,da
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,db
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,dc
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,dd
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{$endif}:datatype);
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begin
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data[0,0]:=aa;
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data[0,1]:=ab;
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{$if matsize>=3}data[0,2]:=ac;{$endif}
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{$if matsize>=4}data[0,3]:=ad;{$endif}
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data[1,0]:=ba;
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data[1,1]:=bb;
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{$if matsize>=3}data[1,2]:=bc;{$endif}
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{$if matsize>=4}data[1,3]:=bd;{$endif}
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{$if matsize>=3}
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data[2,0]:=ca;
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data[2,1]:=cb;
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data[2,2]:=cc;
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{$if matsize>=4}data[2,3]:=cd;{$endif}
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{$endif}
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{$if matsize>=4}
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data[3,0]:=da;
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data[3,1]:=db;
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data[3,2]:=dc;
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data[3,3]:=dd;
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{$endif}
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end;
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function objectname.get_column(c:byte):vectorcompanion;
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begin
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get_column.data[0]:=data[0,c];
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get_column.data[1]:=data[1,c];
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{$if matsize>=3}
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get_column.data[2]:=data[2,c];
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{$endif}
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{$if matsize>=4}
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get_column.data[3]:=data[3,c];
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{$endif}
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end;
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function objectname.get_row(r:byte):vectorcompanion;
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begin
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get_row.data:=data[r];
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end;
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procedure objectname.set_column(c:byte;const v:vectorcompanion);
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begin
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data[0,c]:=v.data[0];
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data[1,c]:=v.data[1];
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{$if matsize>=3}
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data[2,c]:=v.data[2];
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{$endif}
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{$if matsize>=4}
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data[3,c]:=v.data[3];
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{$endif}
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end;
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procedure objectname.set_row(r:byte;const v:vectorcompanion);
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begin
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data[r]:=v.data;
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end;
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function objectname.transpose:objectname;
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begin
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transpose.data[0,0]:=data[0,0];
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transpose.data[0,1]:=data[1,0];
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{$if matsize>=3}
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transpose.data[0,2]:=data[2,0];
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{$endif}
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{$if matsize>=4}
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transpose.data[0,3]:=data[3,0];
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{$endif}
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transpose.data[1,0]:=data[0,1];
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transpose.data[1,1]:=data[1,1];
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{$if matsize>=3}
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transpose.data[1,2]:=data[2,1];
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{$endif}
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{$if matsize>=4}
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transpose.data[1,3]:=data[3,1];
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{$endif}
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{$if matsize>=3}
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transpose.data[2,0]:=data[0,2];
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transpose.data[2,1]:=data[1,2];
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transpose.data[2,2]:=data[2,2];
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{$endif}
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{$if matsize>=4}
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transpose.data[2,3]:=data[3,2];
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transpose.data[3,0]:=data[0,3];
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transpose.data[3,1]:=data[1,3];
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transpose.data[3,2]:=data[2,3];
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transpose.data[3,3]:=data[3,3];
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{$endif}
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end;
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{$if matsize=2}
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function objectname.determinant:datatype;
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begin
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determinant:=data[0,0]*data[1,1]-data[0,1]*data[1,0];
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end;
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{$endif}
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{$if matsize=3}
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function objectname.determinant:datatype;
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begin
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determinant:=data[0,0]*(data[1,1]*data[2,2]-data[1,2]*data[2,1])-
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data[0,1]*(data[1,0]*data[2,2]-data[1,2]*data[2,0])+
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data[0,2]*(data[1,0]*data[2,1]-data[1,1]*data[2,0]);
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end;
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{$endif}
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{$if matsize=4}
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function objectname.determinant:datatype;
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begin
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determinant:=(data[0,0]*data[1,1]-data[0,1]*data[1,0])*(data[2,2]*data[3,3]-data[2,3]*data[3,2])-
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(data[0,0]*data[1,2]-data[0,2]*data[1,0])*(data[2,1]*data[3,3]-data[2,3]*data[3,1])+
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(data[0,0]*data[1,3]-data[0,3]*data[1,0])*(data[2,1]*data[3,2]-data[2,2]*data[3,1])+
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(data[0,1]*data[1,2]-data[0,2]*data[1,1])*(data[2,0]*data[3,3]-data[2,3]*data[3,0])-
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(data[0,1]*data[1,3]-data[0,3]*data[1,1])*(data[2,0]*data[3,2]-data[2,2]*data[3,0])+
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(data[0,2]*data[1,3]-data[0,3]*data[1,2])*(data[2,0]*data[3,1]-data[2,1]*data[3,0]);
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end;
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{$endif}
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{$if matsize=2}
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function objectname.inverse(Adeterminant:datatype):objectname;
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begin
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Adeterminant:=1/Adeterminant;
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inverse.data[0,0]:=data[1,1]*Adeterminant;
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inverse.data[0,1]:=-data[0,1]*Adeterminant;
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inverse.data[1,0]:=-data[1,0]*Adeterminant;
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inverse.data[1,1]:=data[0,0]*Adeterminant;
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end;
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{$endif}
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{$if matsize=3}
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function objectname.inverse(Adeterminant:datatype):objectname;
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begin
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Adeterminant:=1/Adeterminant;
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inverse.data[0,0]:=(data[1,1]*data[2,2]-data[2,1]*data[1,2])*Adeterminant;
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inverse.data[0,1]:=-(data[1,0]*data[2,2]-data[2,0]*data[1,2])*Adeterminant;
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inverse.data[0,2]:=(data[1,0]*data[2,1]-data[2,0]*data[1,1])*Adeterminant;
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inverse.data[1,0]:=-(data[0,1]*data[2,2]-data[2,1]*data[0,2])*Adeterminant;
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inverse.data[1,1]:=(data[0,0]*data[2,2]-data[2,0]*data[0,2])*Adeterminant;
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inverse.data[1,2]:=-(data[0,0]*data[2,1]-data[2,0]*data[0,1])*Adeterminant;
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inverse.data[2,0]:=(data[0,1]*data[1,2]-data[1,1]*data[0,2])*Adeterminant;
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inverse.data[2,1]:=-(data[0,0]*data[1,2]-data[1,0]*data[0,2])*Adeterminant;
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inverse.data[2,2]:=(data[0,0]*data[1,1]-data[1,0]*data[0,1])*Adeterminant;
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end;
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{$endif}
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{$if matsize=4}
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function objectname.inverse(Adeterminant:datatype):objectname;
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begin
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Adeterminant:=1/Adeterminant;
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inverse.data[0,0]:=Adeterminant*(data[1,1]*(data[2,2]*data[3,3]-data[2,3]*data[3,2])+
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data[1,2]*(data[2,3]*data[3,1]-data[2,1]*data[3,3])+
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data[1,3]*(data[2,1]*data[3,2]-data[2,2]*data[3,1]));
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inverse.data[0,1]:=Adeterminant*(data[2,1]*(data[0,2]*data[3,3]-data[0,3]*data[3,2])+
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data[2,2]*(data[0,3]*data[3,1]-data[0,1]*data[3,3])+
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data[2,3]*(data[0,1]*data[3,2]-data[0,2]*data[3,1]));
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inverse.data[0,2]:=Adeterminant*(data[3,1]*(data[0,2]*data[1,3]-data[0,3]*data[1,2])+
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data[3,2]*(data[0,3]*data[1,1]-data[0,1]*data[1,3])+
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data[3,3]*(data[0,1]*data[1,2]-data[0,2]*data[1,1]));
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inverse.data[0,3]:=Adeterminant*(data[0,1]*(data[1,3]*data[2,2]-data[1,2]*data[2,3])+
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data[0,2]*(data[1,1]*data[2,3]-data[1,3]*data[2,1])+
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data[0,3]*(data[1,2]*data[2,1]-data[1,1]*data[2,2]));
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inverse.data[1,0]:=Adeterminant*(data[1,2]*(data[2,0]*data[3,3]-data[2,3]*data[3,0])+
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data[1,3]*(data[2,2]*data[3,0]-data[2,0]*data[3,2])+
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data[1,0]*(data[2,3]*data[3,2]-data[2,2]*data[3,3]));
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inverse.data[1,1]:=Adeterminant*(data[2,2]*(data[0,0]*data[3,3]-data[0,3]*data[3,0])+
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data[2,3]*(data[0,2]*data[3,0]-data[0,0]*data[3,2])+
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data[2,0]*(data[0,3]*data[3,2]-data[0,2]*data[3,3]));
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inverse.data[1,2]:=Adeterminant*(data[3,2]*(data[0,0]*data[1,3]-data[0,3]*data[1,0])+
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data[3,3]*(data[0,2]*data[1,0]-data[0,0]*data[1,2])+
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data[3,0]*(data[0,3]*data[1,2]-data[0,2]*data[1,3]));
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inverse.data[1,3]:=Adeterminant*(data[0,2]*(data[1,3]*data[2,0]-data[1,0]*data[2,3])+
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data[0,3]*(data[1,0]*data[2,2]-data[1,2]*data[2,0])+
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data[0,0]*(data[1,2]*data[2,3]-data[1,3]*data[2,2]));
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inverse.data[2,0]:=Adeterminant*(data[1,3]*(data[2,0]*data[3,1]-data[2,1]*data[3,0])+
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data[1,0]*(data[2,1]*data[3,3]-data[2,3]*data[3,1])+
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data[1,1]*(data[2,3]*data[3,0]-data[2,0]*data[3,3]));
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inverse.data[2,1]:=Adeterminant*(data[2,3]*(data[0,0]*data[3,1]-data[0,1]*data[3,0])+
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data[2,0]*(data[0,1]*data[3,3]-data[0,3]*data[3,1])+
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data[2,1]*(data[0,3]*data[3,0]-data[0,0]*data[3,3]));
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inverse.data[2,2]:=Adeterminant*(data[3,3]*(data[0,0]*data[1,1]-data[0,1]*data[1,0])+
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data[3,0]*(data[0,1]*data[1,3]-data[0,3]*data[1,1])+
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data[3,1]*(data[0,3]*data[1,0]-data[0,0]*data[1,3]));
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inverse.data[2,3]:=Adeterminant*(data[0,3]*(data[1,1]*data[2,0]-data[1,0]*data[2,1])+
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data[0,0]*(data[1,3]*data[2,1]-data[1,1]*data[2,3])+
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data[0,1]*(data[1,0]*data[2,3]-data[1,3]*data[2,0]));
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inverse.data[3,0]:=Adeterminant*(data[1,0]*(data[2,2]*data[3,1]-data[2,1]*data[3,2])+
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data[1,1]*(data[2,0]*data[3,2]-data[2,2]*data[3,0])+
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data[1,2]*(data[2,1]*data[3,0]-data[2,0]*data[3,1]));
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inverse.data[3,1]:=Adeterminant*(data[2,0]*(data[0,2]*data[3,1]-data[0,1]*data[3,2])+
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data[2,1]*(data[0,0]*data[3,2]-data[0,2]*data[3,0])+
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data[2,2]*(data[0,1]*data[3,0]-data[0,0]*data[3,1]));
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inverse.data[3,2]:=Adeterminant*(data[3,0]*(data[0,2]*data[1,1]-data[0,1]*data[1,2])+
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data[3,1]*(data[0,0]*data[1,2]-data[0,2]*data[1,0])+
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data[3,2]*(data[0,1]*data[1,0]-data[0,0]*data[1,1]));
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inverse.data[3,3]:=Adeterminant*(data[0,0]*(data[1,1]*data[2,2]-data[1,2]*data[2,1])+
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data[0,1]*(data[1,2]*data[2,0]-data[1,0]*data[2,2])+
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data[0,2]*(data[1,0]*data[2,1]-data[1,1]*data[2,0]));
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end;
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{$endif}
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{*****************************************************************************
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Conversion from matrix2
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*****************************************************************************}
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{$if (matsize<>2) or (datatype<>single)}
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operator := (const v:Tmatrix2_single) result:objectname;
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begin
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result.data[0,0]:=v.data[0,0];
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result.data[0,1]:=v.data[0,1];
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{$if matsize>=3}
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result.data[0,2]:=0;
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{$endif}
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{$if matsize>=4}
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result.data[0,3]:=0;
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{$endif}
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result.data[1,0]:=v.data[1,0];
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result.data[1,1]:=v.data[1,1];
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{$if matsize>=3}
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result.data[1,2]:=0;
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{$endif}
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{$if matsize>=4}
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result.data[1,3]:=0;
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{$endif}
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{$if matsize>=3}
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result.data[2,0]:=0;
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result.data[2,1]:=0;
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result.data[2,2]:=0;
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{$endif}
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{$if matsize>=4}
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result.data[2,3]:=0;
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result.data[3,0]:=0;
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result.data[3,1]:=0;
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result.data[3,2]:=0;
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result.data[3,3]:=0;
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{$endif}
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end;
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{$endif}
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{$if (matsize<>2) or (datatype<>double)}
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operator := (const v:Tmatrix2_double) result:objectname;
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begin
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result.data[0,0]:=v.data[0,0];
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result.data[0,1]:=v.data[0,1];
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{$if matsize>=3}
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result.data[0,2]:=0;
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{$endif}
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{$if matsize>=4}
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result.data[0,3]:=0;
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{$endif}
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result.data[1,0]:=v.data[1,0];
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result.data[1,1]:=v.data[1,1];
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{$if matsize>=3}
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result.data[1,2]:=0;
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{$endif}
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{$if matsize>=4}
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result.data[1,3]:=0;
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{$endif}
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{$if matsize>=3}
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result.data[2,0]:=0;
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result.data[2,1]:=0;
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result.data[2,2]:=0;
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{$endif}
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{$if matsize>=4}
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result.data[2,3]:=0;
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result.data[3,0]:=0;
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result.data[3,1]:=0;
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result.data[3,2]:=0;
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result.data[3,3]:=0;
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{$endif}
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end;
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{$endif}
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{$if (matsize<>2) or (datatype<>extended)}
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operator := (const v:Tmatrix2_extended) result:objectname;
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begin
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result.data[0,0]:=v.data[0,0];
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result.data[0,1]:=v.data[0,1];
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{$if matsize>=3}
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result.data[0,2]:=0;
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{$endif}
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{$if matsize>=4}
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result.data[0,3]:=0;
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{$endif}
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result.data[1,0]:=v.data[1,0];
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result.data[1,1]:=v.data[1,1];
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{$if matsize>=3}
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result.data[1,2]:=0;
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{$endif}
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{$if matsize>=4}
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result.data[1,3]:=0;
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{$endif}
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{$if matsize>=3}
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result.data[2,0]:=0;
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result.data[2,1]:=0;
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result.data[2,2]:=0;
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{$endif}
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{$if matsize>=4}
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result.data[2,3]:=0;
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result.data[3,0]:=0;
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result.data[3,1]:=0;
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result.data[3,2]:=0;
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result.data[3,3]:=0;
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{$endif}
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end;
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{$endif}
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{*****************************************************************************
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Conversion from matrix3
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*****************************************************************************}
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{$if (matsize<>3) or (datatype<>single)}
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operator := (const v:Tmatrix3_single) result:objectname;
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begin
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result.data[0,0]:=v.data[0,0];
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result.data[0,1]:=v.data[0,1];
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{$if matsize>=3}
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result.data[0,2]:=v.data[0,2];
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{$endif}
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{$if matsize>=4}
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result.data[0,3]:=0;
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{$endif}
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result.data[1,0]:=v.data[1,0];
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result.data[1,1]:=v.data[1,1];
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{$if matsize>=3}
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result.data[1,2]:=v.data[1,2];
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{$endif}
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{$if matsize>=4}
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result.data[1,3]:=0;
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{$endif}
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{$if matsize>=3}
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result.data[2,0]:=v.data[2,0];
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result.data[2,1]:=v.data[2,1];
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result.data[2,2]:=v.data[2,2];
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{$endif}
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{$if matsize>=4}
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result.data[2,3]:=0;
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|
result.data[3,0]:=0;
|
|
result.data[3,1]:=0;
|
|
result.data[3,2]:=0;
|
|
result.data[3,3]:=0;
|
|
{$endif}
|
|
end;
|
|
{$endif}
|
|
|
|
{$if (matsize<>3) or (datatype<>double)}
|
|
operator := (const v:Tmatrix3_double) result:objectname;
|
|
|
|
begin
|
|
result.data[0,0]:=v.data[0,0];
|
|
result.data[0,1]:=v.data[0,1];
|
|
{$if matsize>=3}
|
|
result.data[0,2]:=v.data[0,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[0,3]:=0;
|
|
{$endif}
|
|
result.data[1,0]:=v.data[1,0];
|
|
result.data[1,1]:=v.data[1,1];
|
|
{$if matsize>=3}
|
|
result.data[1,2]:=v.data[1,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[1,3]:=0;
|
|
{$endif}
|
|
{$if matsize>=3}
|
|
result.data[2,0]:=v.data[2,0];
|
|
result.data[2,1]:=v.data[2,1];
|
|
result.data[2,2]:=v.data[2,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[2,3]:=0;
|
|
result.data[3,0]:=0;
|
|
result.data[3,1]:=0;
|
|
result.data[3,2]:=0;
|
|
result.data[3,3]:=0;
|
|
{$endif}
|
|
end;
|
|
{$endif}
|
|
|
|
{$if (matsize<>3) or (datatype<>extended)}
|
|
operator := (const v:Tmatrix3_extended) result:objectname;
|
|
|
|
begin
|
|
result.data[0,0]:=v.data[0,0];
|
|
result.data[0,1]:=v.data[0,1];
|
|
{$if matsize>=3}
|
|
result.data[0,2]:=v.data[0,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[0,3]:=0;
|
|
{$endif}
|
|
result.data[1,0]:=v.data[1,0];
|
|
result.data[1,1]:=v.data[1,1];
|
|
{$if matsize>=3}
|
|
result.data[1,2]:=v.data[1,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[1,3]:=0;
|
|
{$endif}
|
|
{$if matsize>=3}
|
|
result.data[2,0]:=v.data[2,0];
|
|
result.data[2,1]:=v.data[2,1];
|
|
result.data[2,2]:=v.data[2,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[2,3]:=0;
|
|
result.data[3,0]:=0;
|
|
result.data[3,1]:=0;
|
|
result.data[3,2]:=0;
|
|
result.data[3,3]:=0;
|
|
{$endif}
|
|
end;
|
|
{$endif}
|
|
|
|
{*****************************************************************************
|
|
Conversion from matrix4
|
|
*****************************************************************************}
|
|
|
|
{$if (matsize<>4) or (datatype<>single)}
|
|
operator := (const v:Tmatrix4_single) result:objectname;
|
|
|
|
begin
|
|
result.data[0,0]:=v.data[0,0];
|
|
result.data[0,1]:=v.data[0,1];
|
|
{$if matsize>=3}
|
|
result.data[0,2]:=v.data[0,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[0,3]:=v.data[0,3];
|
|
{$endif}
|
|
result.data[1,0]:=v.data[1,0];
|
|
result.data[1,1]:=v.data[1,1];
|
|
{$if matsize>=3}
|
|
result.data[1,2]:=v.data[1,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[1,3]:=v.data[1,3];
|
|
{$endif}
|
|
{$if matsize>=3}
|
|
result.data[2,0]:=v.data[2,0];
|
|
result.data[2,1]:=v.data[2,1];
|
|
result.data[2,2]:=v.data[2,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[2,3]:=v.data[2,3];
|
|
result.data[3,0]:=v.data[3,0];
|
|
result.data[3,1]:=v.data[3,1];
|
|
result.data[3,2]:=v.data[3,2];
|
|
result.data[3,3]:=v.data[3,3];
|
|
{$endif}
|
|
end;
|
|
{$endif}
|
|
|
|
{$if (matsize<>4) or (datatype<>double)}
|
|
operator := (const v:Tmatrix4_double) result:objectname;
|
|
|
|
begin
|
|
result.data[0,0]:=v.data[0,0];
|
|
result.data[0,1]:=v.data[0,1];
|
|
{$if matsize>=3}
|
|
result.data[0,2]:=v.data[0,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[0,3]:=v.data[0,3];
|
|
{$endif}
|
|
result.data[1,0]:=v.data[1,0];
|
|
result.data[1,1]:=v.data[1,1];
|
|
{$if matsize>=3}
|
|
result.data[1,2]:=v.data[1,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[1,3]:=v.data[1,3];
|
|
{$endif}
|
|
{$if matsize>=3}
|
|
result.data[2,0]:=v.data[2,0];
|
|
result.data[2,1]:=v.data[2,1];
|
|
result.data[2,2]:=v.data[2,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[2,3]:=v.data[2,3];
|
|
result.data[3,0]:=v.data[3,0];
|
|
result.data[3,1]:=v.data[3,1];
|
|
result.data[3,2]:=v.data[3,2];
|
|
result.data[3,3]:=v.data[3,3];
|
|
{$endif}
|
|
end;
|
|
{$endif}
|
|
|
|
{$if (matsize<>4) or (datatype<>extended)}
|
|
operator := (const v:Tmatrix4_extended) result:objectname;
|
|
|
|
begin
|
|
result.data[0,0]:=v.data[0,0];
|
|
result.data[0,1]:=v.data[0,1];
|
|
{$if matsize>=3}
|
|
result.data[0,2]:=v.data[0,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[0,3]:=v.data[0,3];
|
|
{$endif}
|
|
result.data[1,0]:=v.data[1,0];
|
|
result.data[1,1]:=v.data[1,1];
|
|
{$if matsize>=3}
|
|
result.data[1,2]:=v.data[1,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[1,3]:=v.data[1,3];
|
|
{$endif}
|
|
{$if matsize>=3}
|
|
result.data[2,0]:=v.data[2,0];
|
|
result.data[2,1]:=v.data[2,1];
|
|
result.data[2,2]:=v.data[2,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[2,3]:=v.data[2,3];
|
|
result.data[3,0]:=v.data[3,0];
|
|
result.data[3,1]:=v.data[3,1];
|
|
result.data[3,2]:=v.data[3,2];
|
|
result.data[3,3]:=v.data[3,3];
|
|
{$endif}
|
|
end;
|
|
{$endif}
|
|
|
|
{*****************************************************************************
|
|
Matrix to matrix operations
|
|
*****************************************************************************}
|
|
|
|
operator + (const m1,m2:objectname) result:objectname;
|
|
|
|
{Add the elements of a matrix to each other.}
|
|
|
|
begin
|
|
result.data[0,0]:=m1.data[0,0]+m2.data[0,0];
|
|
result.data[0,1]:=m1.data[0,1]+m2.data[0,1];
|
|
{$if matsize>=3}
|
|
result.data[0,2]:=m1.data[0,2]+m2.data[0,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[0,3]:=m1.data[0,3]+m2.data[0,3];
|
|
{$endif}
|
|
result.data[1,0]:=m1.data[1,0]+m2.data[1,0];
|
|
result.data[1,1]:=m1.data[1,1]+m2.data[1,1];
|
|
{$if matsize>=3}
|
|
result.data[1,2]:=m1.data[1,2]+m2.data[1,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[1,3]:=m1.data[1,3]+m2.data[1,3];
|
|
{$endif}
|
|
{$if matsize>=3}
|
|
result.data[2,0]:=m1.data[2,0]+m2.data[2,0];
|
|
result.data[2,1]:=m1.data[2,1]+m2.data[2,1];
|
|
result.data[2,2]:=m1.data[2,2]+m2.data[2,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[2,3]:=m1.data[2,3]+m2.data[2,3];
|
|
result.data[3,0]:=m1.data[3,0]+m2.data[3,0];
|
|
result.data[3,1]:=m1.data[3,1]+m2.data[3,1];
|
|
result.data[3,2]:=m1.data[3,2]+m2.data[3,2];
|
|
result.data[3,3]:=m1.data[3,3]+m2.data[3,3];
|
|
{$endif}
|
|
end;
|
|
|
|
operator - (const m1,m2:objectname) result:objectname;
|
|
|
|
{Subtract the elements of two matrixes from each other.}
|
|
|
|
begin
|
|
result.data[0,0]:=m1.data[0,0]-m2.data[0,0];
|
|
result.data[0,1]:=m1.data[0,1]-m2.data[0,1];
|
|
{$if matsize>=3}
|
|
result.data[0,2]:=m1.data[0,2]-m2.data[0,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[0,3]:=m1.data[0,3]-m2.data[0,3];
|
|
{$endif}
|
|
result.data[1,0]:=m1.data[1,0]-m2.data[1,0];
|
|
result.data[1,1]:=m1.data[1,1]-m2.data[1,1];
|
|
{$if matsize>=3}
|
|
result.data[1,2]:=m1.data[1,2]-m2.data[1,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[1,3]:=m1.data[1,3]-m2.data[1,3];
|
|
{$endif}
|
|
{$if matsize>=3}
|
|
result.data[2,0]:=m1.data[2,0]-m2.data[2,0];
|
|
result.data[2,1]:=m1.data[2,1]-m2.data[2,1];
|
|
result.data[2,2]:=m1.data[2,2]-m2.data[2,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[2,3]:=m1.data[2,3]-m2.data[2,3];
|
|
result.data[3,0]:=m1.data[3,0]-m2.data[3,0];
|
|
result.data[3,1]:=m1.data[3,1]-m2.data[3,1];
|
|
result.data[3,2]:=m1.data[3,2]-m2.data[3,2];
|
|
result.data[3,3]:=m1.data[3,3]-m2.data[3,3];
|
|
{$endif}
|
|
end;
|
|
|
|
operator - (const m1:objectname) result:objectname;
|
|
|
|
{Negate the elements of a matrix.}
|
|
|
|
begin
|
|
result.data[0,0]:=-m1.data[0,0];
|
|
result.data[0,1]:=-m1.data[0,1];
|
|
{$if matsize>=3}
|
|
result.data[0,2]:=-m1.data[0,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[0,3]:=-m1.data[0,3];
|
|
{$endif}
|
|
result.data[1,0]:=-m1.data[1,0];
|
|
result.data[1,1]:=-m1.data[1,1];
|
|
{$if matsize>=3}
|
|
result.data[1,2]:=-m1.data[1,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[1,3]:=-m1.data[1,3];
|
|
{$endif}
|
|
{$if matsize>=3}
|
|
result.data[2,0]:=-m1.data[2,0];
|
|
result.data[2,1]:=-m1.data[2,1];
|
|
result.data[2,2]:=-m1.data[2,2];
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[2,3]:=-m1.data[2,3];
|
|
result.data[3,0]:=-m1.data[3,0];
|
|
result.data[3,1]:=-m1.data[3,1];
|
|
result.data[3,2]:=-m1.data[3,2];
|
|
result.data[3,3]:=-m1.data[3,3];
|
|
{$endif}
|
|
end;
|
|
|
|
operator * (const m1,m2:objectname) result:objectname;
|
|
|
|
{Multiply two matrixes.}
|
|
|
|
var r:array[0..matsize-1] of datatype;
|
|
i:byte;
|
|
|
|
begin
|
|
for i:=0 to matsize-1 do
|
|
begin
|
|
r:=m1.data[i];
|
|
result.data[i,0]:=r[0]*m2.data[0,0]
|
|
+r[1]*m2.data[1,0]
|
|
{$if matsize>=3}+r[2]*m2.data[2,0]{$endif}
|
|
{$if matsize>=4}+r[3]*m2.data[3,0]{$endif};
|
|
result.data[i,1]:=r[0]*m2.data[0,1]
|
|
+r[1]*m2.data[1,1]
|
|
{$if matsize>=3}+r[2]*m2.data[2,1]{$endif}
|
|
{$if matsize>=4}+r[3]*m2.data[3,1]{$endif};
|
|
{$if matsize>=3}
|
|
result.data[i,2]:=r[0]*m2.data[0,2]
|
|
+r[1]*m2.data[1,2]
|
|
+r[2]*m2.data[2,2]
|
|
{$if matsize>=4}+r[3]*m2.data[3,2]{$endif};
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[i,3]:=r[0]*m2.data[0,3]
|
|
+r[1]*m2.data[1,3]
|
|
+r[2]*m2.data[2,3]
|
|
+r[3]*m2.data[3,3];
|
|
{$endif}
|
|
end;
|
|
end;
|
|
|
|
{*****************************************************************************
|
|
Vector/matrix operations
|
|
*****************************************************************************}
|
|
|
|
operator * (const m:objectname;const v:vectorcompanion) result:vectorcompanion;
|
|
|
|
{Multiplies a matrix with a vector.}
|
|
|
|
begin
|
|
result.data[0]:=m.data[0,0]*v.data[0]
|
|
+m.data[1,0]*v.data[1]
|
|
{$if matsize>=3}+m.data[2,0]*v.data[2]{$endif}
|
|
{$if matsize>=4}+m.data[3,0]*v.data[3]{$endif};
|
|
result.data[1]:=m.data[0,1]*v.data[0]
|
|
+m.data[1,1]*v.data[1]
|
|
{$if matsize>=3}+m.data[2,1]*v.data[2]{$endif}
|
|
{$if matsize>=4}+m.data[3,1]*v.data[3]{$endif};
|
|
{$if matsize>=3}
|
|
result.data[2]:=m.data[0,2]*v.data[0]
|
|
+m.data[1,2]*v.data[1]
|
|
+m.data[2,2]*v.data[2]
|
|
{$if matsize>=4}+m.data[3,2]*v.data[3]{$endif};
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[3]:=m.data[0,3]*v.data[0]
|
|
+m.data[1,3]*v.data[1]
|
|
+m.data[2,3]*v.data[2]
|
|
+m.data[3,3]*v.data[3];
|
|
{$endif}
|
|
end;
|
|
|
|
{*****************************************************************************
|
|
Matrix/scalar operations
|
|
*****************************************************************************}
|
|
|
|
operator + (const m:objectname;const x:datatype) result:objectname;
|
|
|
|
{Adds to the elements of a matrix.}
|
|
|
|
begin
|
|
result.data[0,0]:=m.data[0,0]+x;
|
|
result.data[0,1]:=m.data[0,1]+x;
|
|
{$if matsize>=3}
|
|
result.data[0,2]:=m.data[0,2]+x;
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[0,3]:=m.data[0,3]+x;
|
|
{$endif}
|
|
result.data[1,0]:=m.data[1,0]+x;
|
|
result.data[1,1]:=m.data[1,1]+x;
|
|
{$if matsize>=3}
|
|
result.data[1,2]:=m.data[1,2]+x;
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[1,3]:=m.data[1,3]+x;
|
|
{$endif}
|
|
{$if matsize>=3}
|
|
result.data[2,0]:=m.data[2,0]+x;
|
|
result.data[2,1]:=m.data[2,1]+x;
|
|
result.data[2,2]:=m.data[2,2]+x;
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[2,3]:=m.data[2,3]+x;
|
|
result.data[3,0]:=m.data[3,0]+x;
|
|
result.data[3,1]:=m.data[3,1]+x;
|
|
result.data[3,2]:=m.data[3,2]+x;
|
|
result.data[3,3]:=m.data[3,3]+x;
|
|
{$endif}
|
|
end;
|
|
|
|
operator - (const m:objectname;const x:datatype) result:objectname;
|
|
|
|
{Subtracts from the elements of a matrix.}
|
|
|
|
begin
|
|
result.data[0,0]:=m.data[0,0]-x;
|
|
result.data[0,1]:=m.data[0,1]-x;
|
|
{$if matsize>=3}
|
|
result.data[0,2]:=m.data[0,2]-x;
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[0,3]:=m.data[0,3]-x;
|
|
{$endif}
|
|
result.data[1,0]:=m.data[1,0]-x;
|
|
result.data[1,1]:=m.data[1,1]-x;
|
|
{$if matsize>=3}
|
|
result.data[1,2]:=m.data[1,2]-x;
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[1,3]:=m.data[1,3]-x;
|
|
{$endif}
|
|
{$if matsize>=3}
|
|
result.data[2,0]:=m.data[2,0]-x;
|
|
result.data[2,1]:=m.data[2,1]-x;
|
|
result.data[2,2]:=m.data[2,2]-x;
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[2,3]:=m.data[2,3]-x;
|
|
result.data[3,0]:=m.data[3,0]-x;
|
|
result.data[3,1]:=m.data[3,1]-x;
|
|
result.data[3,2]:=m.data[3,2]-x;
|
|
result.data[3,3]:=m.data[3,3]-x;
|
|
{$endif}
|
|
end;
|
|
|
|
operator * (const m:objectname;const x:datatype) result:objectname;
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|
|
|
{Multiplies the elements of a matrix.}
|
|
|
|
begin
|
|
result.data[0,0]:=m.data[0,0]*x;
|
|
result.data[0,1]:=m.data[0,1]*x;
|
|
{$if matsize>=3}
|
|
result.data[0,2]:=m.data[0,2]*x;
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[0,3]:=m.data[0,3]*x;
|
|
{$endif}
|
|
result.data[1,0]:=m.data[1,0]*x;
|
|
result.data[1,1]:=m.data[1,1]*x;
|
|
{$if matsize>=3}
|
|
result.data[1,2]:=m.data[1,2]*x;
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[1,3]:=m.data[1,3]*x;
|
|
{$endif}
|
|
{$if matsize>=3}
|
|
result.data[2,0]:=m.data[2,0]*x;
|
|
result.data[2,1]:=m.data[2,1]*x;
|
|
result.data[2,2]:=m.data[2,2]*x;
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[2,3]:=m.data[2,3]*x;
|
|
result.data[3,0]:=m.data[3,0]*x;
|
|
result.data[3,1]:=m.data[3,1]*x;
|
|
result.data[3,2]:=m.data[3,2]*x;
|
|
result.data[3,3]:=m.data[3,3]*x;
|
|
{$endif}
|
|
end;
|
|
|
|
operator / (const m:objectname;const x:datatype) result:objectname;
|
|
|
|
{Divides the elements of a matrix.
|
|
|
|
In most cases, you will want to avoid this and multiply by the inverse.
|
|
In case you need to preserve accuracy, dividing might be better though.}
|
|
|
|
begin
|
|
result.data[0,0]:=m.data[0,0]/x;
|
|
result.data[0,1]:=m.data[0,1]/x;
|
|
{$if matsize>=3}
|
|
result.data[0,2]:=m.data[0,2]/x;
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[0,3]:=m.data[0,3]/x;
|
|
{$endif}
|
|
result.data[1,0]:=m.data[1,0]/x;
|
|
result.data[1,1]:=m.data[1,1]/x;
|
|
{$if matsize>=3}
|
|
result.data[1,2]:=m.data[1,2]/x;
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[1,3]:=m.data[1,3]/x;
|
|
{$endif}
|
|
{$if matsize>=3}
|
|
result.data[2,0]:=m.data[2,0]/x;
|
|
result.data[2,1]:=m.data[2,1]/x;
|
|
result.data[2,2]:=m.data[2,2]/x;
|
|
{$endif}
|
|
{$if matsize>=4}
|
|
result.data[2,3]:=m.data[2,3]/x;
|
|
result.data[3,0]:=m.data[3,0]/x;
|
|
result.data[3,1]:=m.data[3,1]/x;
|
|
result.data[3,2]:=m.data[3,2]/x;
|
|
result.data[3,3]:=m.data[3,3]/x;
|
|
{$endif}
|
|
end;
|
|
|