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以下是JohnsonGuo写的最小二乘法解线性方程组的源程序，有几 个地方不太明白主要是
调用的时候
procedure MinSqrMul(m, n: Integer; A: TMatrix; b: array of Double; var x: array of Double);
var
i, j, k: Integer;
ATA: array of array of Double;
ATb: array of Double;
Elem: Double;
begin
SetLength(ATA, n, n);
SetLength(ATb, n);
for i := 0 to n - 1 do
for j := 0 to n - 1 do begin
ATA[i, j] := 0;
for k := 0 to m - 1 do
ATA[i, j] := ATA[i, j] + A[k, i] * A[k, j];
end;
for i := 0 to n - 1 do begin
ATb := 0;
for j := 0 to m - 1 do
ATb := ATb + A[j, i] * b[j];
end;
for i := 0 to n - 1 do begin
Elem := ATA[i, i];
for j := i to n - 1 do
ATA[i, j] := ATA[i, j] / Elem;
ATb := ATb / Elem;
for k := i + 1 to n - 1 do begin
Elem := -ATA[k, i];
for j := [red]i + 1[/red] to n - 1 do
ATA[k, j] := ATA[k, j] + ATA[i, j] * Elem;
ATb[k] := ATb[k] + ATb * Elem;
end;
end;
x[n - 1] := ATb[n - 1];
for i := n - 2 downto 0 do begin
for j := i + 1 to n - 1 do
ATb := ATb - ATA[i, j] * x[j];
x := ATb;
end;
end;
以下是调用
procedure TForm1.FormClick(Sender: TObject);
var
A: TMatrix;
b: array [0..2] of Double;
x: array [0..1] of Double;
begin
SetLength(A, 3, 2);
A[0, 0] := 1; A[0, 1] := 2; b[0] := 3;
A[1, 0] := 1; A[1, 1] := 2; b[1] := 4;
A[2, 0] := 2; A[2, 1] := 1; b[2] := 3;
MinSqrMul(3, 2, A, b, x);
ShowMessage(Format('%f, %f', [x[0], x[1]]));
end;
我现在不明白调用的时候各个数据是什么。MinSqrMul(3, 2, A, b, x); 中
A应该是各点吧，那3，2，b,x是什么呢？
调用的时候
procedure MinSqrMul(m, n: Integer; A: TMatrix; b: array of Double; var x: array of Double);
var
i, j, k: Integer;
ATA: array of array of Double;
ATb: array of Double;
Elem: Double;
begin
SetLength(ATA, n, n);
SetLength(ATb, n);
for i := 0 to n - 1 do
for j := 0 to n - 1 do begin
ATA[i, j] := 0;
for k := 0 to m - 1 do
ATA[i, j] := ATA[i, j] + A[k, i] * A[k, j];
end;
for i := 0 to n - 1 do begin
ATb := 0;
for j := 0 to m - 1 do
ATb := ATb + A[j, i] * b[j];
end;
for i := 0 to n - 1 do begin
Elem := ATA[i, i];
for j := i to n - 1 do
ATA[i, j] := ATA[i, j] / Elem;
ATb := ATb / Elem;
for k := i + 1 to n - 1 do begin
Elem := -ATA[k, i];
for j := [red]i + 1[/red] to n - 1 do
ATA[k, j] := ATA[k, j] + ATA[i, j] * Elem;
ATb[k] := ATb[k] + ATb * Elem;
end;
end;
x[n - 1] := ATb[n - 1];
for i := n - 2 downto 0 do begin
for j := i + 1 to n - 1 do
ATb := ATb - ATA[i, j] * x[j];
x := ATb;
end;
end;
以下是调用
procedure TForm1.FormClick(Sender: TObject);
var
A: TMatrix;
b: array [0..2] of Double;
x: array [0..1] of Double;
begin
SetLength(A, 3, 2);
A[0, 0] := 1; A[0, 1] := 2; b[0] := 3;
A[1, 0] := 1; A[1, 1] := 2; b[1] := 4;
A[2, 0] := 2; A[2, 1] := 1; b[2] := 3;
MinSqrMul(3, 2, A, b, x);
ShowMessage(Format('%f, %f', [x[0], x[1]]));
end;
我现在不明白调用的时候各个数据是什么。MinSqrMul(3, 2, A, b, x); 中
A应该是各点吧，那3，2，b,x是什么呢？