<HTML> <HEAD> <TITLE>determinant</TITLE> <STYLE TYPE="text/css" MEDIA=screen> <!-- BODY { font-family: Arial,Helvetica; } BLOCKQUOTE { margin: 10pt; } H1,A { color: #336699; } /*** Top menu style ****/ .mmenuon { font-family: Arial,Helvetica; font-weight: bold; text-decoration: none; color: #ff6600; font-size: 10pt; } .mmenuoff { font-family: Arial,Helvetica; font-weight: bold; text-decoration: none; color: #ffffff; font-size: 10pt; } .cpyright { font-family: Arial,Helvetica; font-weight: bold; text-decoration: none; color: #ffffff; font-size: xx-small; } .cpyrightText { font-family: Arial,Helvetica; font-weight: bold; text-decoration: none; color: #ffffff; font-size: xx-small; } .sections { font-family: Arial,Helvetica; font-weight: bold; text-decoration: none; color: #336699; font-size: 11pt; } .dsections { font-family: Arial,Helvetica; font-weight: bold; text-decoration: none; color: #336699; font-size: 12pt; } .slink { font-family: Arial,Helvetica; font-weight: normal; text-decoration: none; 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color: #333333; font-size: 10pt; } UL > LI > A { font-family: Arial,Helvetica; font-weight: bold; color: #336699; font-size: 10pt; } .moduleInfo { font-family: Arial,Helvetica; font-weight: bold; text-decoration: none; color: #333333; font-size: 11pt; } .moduleInfoSec { font-family: Arial,Helvetica; font-weight: bold; text-decoration: none; color: #336699; font-size: 10pt; } .moduleInfoVal { font-family: Arial,Helvetica; font-weight: normal; text-decoration: underline; color: #000000; font-size: 10pt; } .cpanNavTitle { font-family: Arial,Helvetica; font-weight: bold; color: #ffffff; font-size: 10pt; } .cpanNavLetter { font-family: Arial,Helvetica; font-weight: bold; text-decoration: none; color: #333333; font-size: 9pt; } .cpanCat { font-family: Arial,Helvetica; font-weight: bold; text-decoration: none; color: #336699; font-size: 9pt; } --> </STYLE> </HEAD> <BODY> <object type="application/x-oleobject" classid="clsid:1e2a7bd0-dab9-11d0-b93a-00c04fc99f9e"> </object> <BLOCKQUOTE> <H1><A NAME="NAME"><A NAME="1">NAME </A></A></H1> <P> <B>determinant</B> - returns the scalar determinant of a square matrix </P> <H1><A NAME="SYNOPSIS"><A NAME="2">SYNOPSIS </A></A></H1> <PRE> float determinant(float1x1 A); float determinant(float2x2 A); float determinant(float3x3 A); float determinant(float4x4 A); </PRE> <H1><A NAME="PARAMETERS"><A NAME="3">PARAMETERS </A></A></H1> <DL> <DT><STRONG>A </STRONG></DT> <DD> <P> Square matrix of which to compute the determinant. </P> </DD></DL> <H1><A NAME="DESCRIPTION"><A NAME="4">DESCRIPTION </A></A></H1> <P> Returns the determinant of the square matrix <I>A</I>. </P> <H1><A NAME="REFERENCE_IMPLEMENTATION"><A NAME="5">REFERENCE IMPLEMENTATION </A></A></H1> <P> The various <B>determinant</B> functions can be implemented like this: </P> <PRE> 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)); } </PRE> <H1><A NAME="PROFILE_SUPPORT"><A NAME="6">PROFILE SUPPORT </A></A></H1> <P> <B>determinant</B> is supported in all profiles. However profiles such as <A HREF="fp20.html">fp20</A> and <A HREF="ps_2_0.html">ps_2_0</A> without native floating-point will have problems computing the larger determinants and may have ranges issues computing even small determinants. </P> <H1><A NAME="SEE_ALSO"><A NAME="7">SEE ALSO </A></A></H1> <P> <A HREF="mul.html">mul</A>, <A HREF="transpose.html">transpose</A> </P> </BLOCKQUOTE> </BODY>