Matrix.Inv Method

Matrix Class

Overload List

#SignatureDescription
1function Inv: TMtx;Calculates matrix inverse (Mtx^-1).
└ indexed: function Inv(Index: Integer; Len: Integer): TMtxVec;
2function Inv(MtxType: TMtxType): TMtx;self = inverse of the matrix
3function Inv(const X: TMtxVec): TMtxVec;Calculate the inverse of all X object elements without the limiting operating.
└ indexed: function Inv(const X: TMtxVec; XIndex: Integer; Index: Integer; Len: Integer): TMtxVec;
4function Inv(const X: TMtxVec; Threshold: Double): TMtxVec;Calculate the inverse of all X object elements anmd store the results to calling object elements.
└ indexed: function Inv(const X: TMtxVec; Threshold: Double; XIndex: Integer; Index: Integer; Len: Integer): TMtxVec;
5function Inv(Threshold: Double): TMtxVec;Calculate the inverse of all calling object elements in-place.
└ indexed: function Inv(Threshold: Double; Index: Integer; Len: Integer): TMtxVec;

Overload 1: function Inv: TMtx;

Calculates matrix inverse (Mtx^-1).

Result: stored in self (calling object), returns self for chaining

Remarks:

Calculate the inverse (Mtx^-1) of the calling matrix. If the calling matrix is not Matrix.Quadratic, an exception is raised. Parameter TMtxType determines which optimized method will be used for calculating the inverse matrix. If MtxType is omitted, the default value mtGeneral (general quadratic matrix) is used.

Note
The MtxType parameter is not verified. To determine if the calling matrix type is actually MtxType, use the Matrix.DetectMtxType method.

Examples
var  A: Matrix;
begin
    A.SetIt(2,2,False,[1,2,
        2,4]);  // 2x2, real matrix
    A.Inv;
end;
See Also: Matrix.DetectMtxType, Matrix.MtxError

Indexed: function Inv(Index: Integer; Len: Integer): TMtxVec;

Calculate the inverse of calling object elements [Index]..[Index+Len-1] in-place.

#NameTypeDescription
1IndexIntegerstart index
2LenIntegerelement count

Result: stored in self (calling object), returns self for chaining

Remarks:

An exception is raised if array borders are overrun/underrun.

Examples
var a,b: Matrix;
begin
    a.SetIt(2,2,False,[1,2,3,4]);  // a = [1, 2, 3, 4]
    b.Inv(a,0.01); // b = [1.0, 0.5, 0.3333, 0.25]
    b := Inv(a,0.01);
end;

Overload 2: function Inv(MtxType: TMtxType): TMtx;

Compute inverse of the matrix.

#NameTypeDescription
1MtxTypeTMtxType

Result: stored in self (calling object), returns self for chaining

Remarks:

Specify the matrix type to select the most performance efficient algorithm.

Overload 3: function Inv(const X: TMtxVec): TMtxVec;

Calculate the inverse of all X object elements without the limiting operating.

#NameTypeDescription
1XTMtxVec

Result: stored in self (calling object), returns self for chaining

Remarks:

Store the results in calling object. Size and Matrix.Complex property of calling object are adjusted automatically. Does not compute matrix inverse. The limiting of the magnitude of each element by the lower bound of Threshold is left out.

Indexed: function Inv(const X: TMtxVec; XIndex: Integer; Index: Integer; Len: Integer): TMtxVec;

Calculate the inverse of X object elements [XIndex]..[XIndex+Len-1] without limiting operating.

#NameTypeDescription
1XTMtxVec
2XIndexIntegerX start index
3IndexIntegerstart index
4LenIntegerelement count

Result: stored in self (calling object), returns self for chaining

Remarks:

Store the results in calling object elements [Index]..[Index+Len-1]. An exception is raised if X and calling object Matrix.Complex property does not match or array borders are overrun/underrun.

Overload 4: function Inv(const X: TMtxVec; Threshold: Double): TMtxVec;

Calculate the inverse of all X object elements anmd store the results to calling object elements.

#NameTypeDescription
1XTMtxVec
2ThresholdDoublescalar

Result: stored in self (calling object), returns self for chaining

Remarks:

Size and Matrix.Complex property of calling obhect are adjusted automatically. The computation occurs after first limiting the magnitude of each element by the lower bound of Threshold. The limiting operation is performed to avoid division by zero. Since Threshold represents a magnitude, it is always real and must always be positive.

Note
For complex versions, the magnitude of the input is limited, but the phase remains unchanged. Zero-valued input is assumed to have zero phase.

Indexed: function Inv(const X: TMtxVec; Threshold: Double; XIndex: Integer; Index: Integer; Len: Integer): TMtxVec;

Calculate the inverse of X object elements [XIndex]..[XIndex+Len-1].

#NameTypeDescription
1XTMtxVec
2ThresholdDoublescalar
3XIndexIntegerX start index
4IndexIntegerstart index
5LenIntegerelement count

Result: stored in self (calling object), returns self for chaining

Remarks:

Limit the magnitude of each element by the lower bound of Threshold. Store the results in calling object elements [Index]..[Index+Len-1]. An exception is raised if X and calling object Matrix.Complex property do not match or array borders are overrun/underrun.

Overload 5: function Inv(Threshold: Double): TMtxVec;

Calculate the inverse of all calling object elements in-place.

#NameTypeDescription
1ThresholdDoublescalar

Result: stored in self (calling object), returns self for chaining

Remarks:

The computation occurs after first limiting the magnitude of each element by the lower bound of Threshold. The limiting operation is performed to avoid division by zero. Since Threshold represents a magnitude, it is always real and must always be positive. For complex versions, the magnitude of the input is limited, but the phase remains unchanged. Zero-valued input is assumed to have zero phase.

Indexed: function Inv(Threshold: Double; Index: Integer; Len: Integer): TMtxVec;

Calculate the inverse of calling object elements [Index]..[Index+Len-1] in-place.

#NameTypeDescription
1ThresholdDoublescalar
2IndexIntegerstart index
3LenIntegerelement count

Result: stored in self (calling object), returns self for chaining

Remarks:

Limit the magnitude of each element by the lower bound of Threshold. An exception is raised if array borders are overrun/underrun.