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