determinant.3Cg

Langue: en

Version: 352785 (ubuntu - 24/10/10)

Section: 3 (Bibliothèques de fonctions)

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