determinant
Keywords: determinant, NVIDIA, NVIDIA Cg Toolkit, Cg Toolkit, Shader, Shader Programming, GPU Shader Programming, GPU Program

> ## Name

> determinant - return 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 except fp20, vs_1_1, ps_1_1, ps_1_2 and ps_1_3. However profiles such as ps_2_0 without native floating-point will have problems computing the larger determinants and may have ranges issues computing even small determinants.

> ## See Also

> mul, transpose