determinant

> # NAME

> determinant - returns the scalar determinant of a square matrix

> # SYNOPSIS

>       float determinant(float1x1 A);
>       float determinant(float2x2 A);
>       float determinant(float3x3 A);
>       float determinant(float4x4 A);

> # PARAMETERS

> A

>   Square matrix of which to compute the determinant.

> # DESCRIPTION

> Returns the determinant of the square matrix A.

> # REFERENCE IMPLEMENTATION

> The various determinant functions can be implemented like this:

>       float determinant(float1x1 A)
>       {
>         return A._m00;
>       }

>       float determinant(float2x2 A)
>       {
>         return A._m00*A._m11 - A._m01*A._m10;
>       }

>       float determinant(float3x3 A)
>       {
>         return dot(A._m00_m01_m02,
>                    A._m11_m12_m10 * A._m22_m20_m21
>                  - A._m12_m10_m11 * A._m21_m22_m20);
>       }

>       float determinant(float4x4 A) {
>         return dot(float4(1,-1,1,-1) * A._m00_m01_m02_m03,
>                      A._m11_m12_m13_m10*(  A._m22_m23_m20_m21*A._m33_m30_m31_m32
>                                          - A._m23_m20_m21_m22*A._m32_m33_m30_m31)
>                    + A._m12_m13_m10_m11*(  A._m23_m20_m21_m22*A._m31_m32_m33_m30
>                                          - A._m21_m22_m23_m20*A._m33_m30_m31_m32)
>                    + A._m13_m10_m11_m12*(  A._m21_m22_m23_m20*A._m32_m33_m30_m31
>                                          - A._m22_m23_m20_m21*A._m31_m32_m33_m30));
>       }

> # PROFILE SUPPORT

> determinant is supported in all profiles. However profiles such as fp20 and ps_2 without native floating-point will have problems computing the larger determinants and may have ranges issues computing even small determinants.

> # SEE ALSO

> mul, transpose