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.rm #[ #] #H #V #F C
.IX Title "determinant Cg"
.TH determinant Cg "" "Cg Toolkit 1.5" "Cg Standard Library"
.UC
.SH "NAME"
\&\fBdeterminant\fR \- returns the scalar determinant of a square matrix
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 4
\&  float determinant( float1x1 A );
\&  float determinant( float2x2 A );
\&  float determinant( float3x3 A );
\&  float determinant( float4x4 A );
.Ve
.SH "PARAMETERS"
.IX Header "PARAMETERS"
.Ip "A" 8
.IX Item "A"
Square matrix of which to compute the determinant.
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
Returns the determinant of the square matrix \fIA\fR.
.SH "REFERENCE IMPLEMENTATION"
.IX Header "REFERENCE IMPLEMENTATION"
The various \fBdeterminant\fR functions can be implemented like this:
.PP
.Vb 4
\&  float determinant(float1x1 A)
\&  {
\&    return A._m00;
\&  }
.Ve
.Vb 4
\&  float determinant(float2x2 A)
\&  {
\&    return A._m00*A._m11 - A._m01*A._m10;
\&  }
.Ve
.Vb 6
\&  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);
\&  }
.Ve
.Vb 9
\&  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));
\&  }
.Ve
.SH "PROFILE SUPPORT"
.IX Header "PROFILE SUPPORT"
\&\fBdeterminant\fR is supported in all profiles.  However profiles such as
fp20 and the ps_2 manpage without native floating-point will have problems
computing the larger determinants and may have ranges issues computing
even small determinants.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
the mul manpage,
the transpose manpage
