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.rm #[ #] #H #V #F C
.IX Title "mul Cg"
.TH mul Cg "" "Cg Toolkit 2.2" "Cg Standard Library"
.UC
.SH "NAME"
\&\fBmul\fR \- multiply a matrix by a column vector, row vector by a matrix, or matrix by a matrix
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 16
\&  float4 mul(float4x4 M, float4 v);
\&  float4 mul(float4x3 M, float3 v);
\&  float4 mul(float4x2 M, float2 v);
\&  float4 mul(float4x1 M, float1 v);
\&  float3 mul(float3x4 M, float4 v);
\&  float3 mul(float3x3 M, float3 v);
\&  float3 mul(float3x2 M, float2 v);
\&  float3 mul(float3x1 M, float1 v);
\&  float2 mul(float2x4 M, float4 v);
\&  float2 mul(float2x3 M, float3 v);
\&  float2 mul(float2x2 M, float2 v);
\&  float2 mul(float2x1 M, float1 v);
\&  float1 mul(float1x4 M, float4 v);
\&  float1 mul(float1x3 M, float3 v);
\&  float1 mul(float1x2 M, float2 v);
\&  float1 mul(float1x1 M, float1 v);
.Ve
.Vb 16
\&  float4 mul(float4 v, float4x4 M);
\&  float4 mul(float3 v, float3x4 M);
\&  float4 mul(float2 v, float2x4 M);
\&  float4 mul(float1 v, float1x4 M);
\&  float3 mul(float4 v, float4x3 M);
\&  float3 mul(float3 v, float3x3 M);
\&  float3 mul(float2 v, float2x3 M);
\&  float3 mul(float1 v, float1x3 M);
\&  float2 mul(float4 v, float4x2 M);
\&  float2 mul(float3 v, float3x2 M);
\&  float2 mul(float2 v, float2x2 M);
\&  float2 mul(float1 v, float1x2 M);
\&  float1 mul(float4 v, float4x1 M);
\&  float1 mul(float3 v, float3x1 M);
\&  float1 mul(float2 v, float2x1 M);
\&  float1 mul(float1 v, float1x1 M);
.Ve
.Vb 16
\&  half4 mul(half4x4 M, half4 v);
\&  half4 mul(half4x3 M, half3 v);
\&  half4 mul(half4x2 M, half2 v);
\&  half4 mul(half4x1 M, half1 v);
\&  half3 mul(half3x4 M, half4 v);
\&  half3 mul(half3x3 M, half3 v);
\&  half3 mul(half3x2 M, half2 v);
\&  half3 mul(half3x1 M, half1 v);
\&  half2 mul(half2x4 M, half4 v);
\&  half2 mul(half2x3 M, half3 v);
\&  half2 mul(half2x2 M, half2 v);
\&  half2 mul(half2x1 M, half1 v);
\&  half1 mul(half1x4 M, half4 v);
\&  half1 mul(half1x3 M, half3 v);
\&  half1 mul(half1x2 M, half2 v);
\&  half1 mul(half1x1 M, half1 v);
.Ve
.Vb 16
\&  half4 mul(half4 v, half4x4 M);
\&  half4 mul(half3 v, half3x4 M);
\&  half4 mul(half2 v, half2x4 M);
\&  half4 mul(half1 v, half1x4 M);
\&  half3 mul(half4 v, half4x3 M);
\&  half3 mul(half3 v, half3x3 M);
\&  half3 mul(half2 v, half2x3 M);
\&  half3 mul(half1 v, half1x3 M);
\&  half2 mul(half4 v, half4x2 M);
\&  half2 mul(half3 v, half3x2 M);
\&  half2 mul(half2 v, half2x2 M);
\&  half2 mul(half1 v, half1x2 M);
\&  half1 mul(half4 v, half4x1 M);
\&  half1 mul(half3 v, half3x1 M);
\&  half1 mul(half2 v, half2x1 M);
\&  half1 mul(half1 v, half1x1 M);
.Ve
.Vb 16
\&  fixed4 mul(fixed4x4 M, fixed4 v);
\&  fixed4 mul(fixed4x3 M, fixed3 v);
\&  fixed4 mul(fixed4x2 M, fixed2 v);
\&  fixed4 mul(fixed4x1 M, fixed1 v);
\&  fixed3 mul(fixed3x4 M, fixed4 v);
\&  fixed3 mul(fixed3x3 M, fixed3 v);
\&  fixed3 mul(fixed3x2 M, fixed2 v);
\&  fixed3 mul(fixed3x1 M, fixed1 v);
\&  fixed2 mul(fixed2x4 M, fixed4 v);
\&  fixed2 mul(fixed2x3 M, fixed3 v);
\&  fixed2 mul(fixed2x2 M, fixed2 v);
\&  fixed2 mul(fixed2x1 M, fixed1 v);
\&  fixed1 mul(fixed1x4 M, fixed4 v);
\&  fixed1 mul(fixed1x3 M, fixed3 v);
\&  fixed1 mul(fixed1x2 M, fixed2 v);
\&  fixed1 mul(fixed1x1 M, fixed1 v);
.Ve
.Vb 16
\&  fixed4 mul(fixed4 v, fixed4x4 M);
\&  fixed4 mul(fixed3 v, fixed3x4 M);
\&  fixed4 mul(fixed2 v, fixed2x4 M);
\&  fixed4 mul(fixed1 v, fixed1x4 M);
\&  fixed3 mul(fixed4 v, fixed4x3 M);
\&  fixed3 mul(fixed3 v, fixed3x3 M);
\&  fixed3 mul(fixed2 v, fixed2x3 M);
\&  fixed3 mul(fixed1 v, fixed1x3 M);
\&  fixed2 mul(fixed4 v, fixed4x2 M);
\&  fixed2 mul(fixed3 v, fixed3x2 M);
\&  fixed2 mul(fixed2 v, fixed2x2 M);
\&  fixed2 mul(fixed1 v, fixed1x2 M);
\&  fixed1 mul(fixed4 v, fixed4x1 M);
\&  fixed1 mul(fixed3 v, fixed3x1 M);
\&  fixed1 mul(fixed2 v, fixed2x1 M);
\&  fixed1 mul(fixed1 v, fixed1x1 M);
.Ve
.Vb 4
\&  float1x1 mul(float1x1 A, float1x1 B);
\&  float1x2 mul(float1x1 A, float1x2 B);
\&  float1x3 mul(float1x1 A, float1x3 B);
\&  float1x4 mul(float1x1 A, float1x4 B);
.Ve
.Vb 4
\&  float1x1 mul(float1x2 A, float2x1 B);
\&  float1x2 mul(float1x2 A, float2x2 B);
\&  float1x3 mul(float1x2 A, float2x3 B);
\&  float1x4 mul(float1x2 A, float2x4 B);
.Ve
.Vb 4
\&  float1x1 mul(float1x3 A, float3x1 B);
\&  float1x2 mul(float1x3 A, float3x2 B);
\&  float1x3 mul(float1x3 A, float3x3 B);
\&  float1x4 mul(float1x3 A, float3x4 B);
.Ve
.Vb 4
\&  float1x1 mul(float1x4 A, float4x1 B);
\&  float1x2 mul(float1x4 A, float4x2 B);
\&  float1x3 mul(float1x4 A, float4x3 B);
\&  float1x4 mul(float1x4 A, float4x4 B);
.Ve
.Vb 4
\&  float2x1 mul(float2x1 A, float1x1 B);
\&  float2x2 mul(float2x1 A, float1x2 B);
\&  float2x3 mul(float2x1 A, float1x3 B);
\&  float2x4 mul(float2x1 A, float1x4 B);
.Ve
.Vb 4
\&  float2x1 mul(float2x2 A, float2x1 B);
\&  float2x2 mul(float2x2 A, float2x2 B);
\&  float2x3 mul(float2x2 A, float2x3 B);
\&  float2x4 mul(float2x2 A, float2x4 B);
.Ve
.Vb 4
\&  float2x1 mul(float2x3 A, float3x1 B);
\&  float2x2 mul(float2x3 A, float3x2 B);
\&  float2x3 mul(float2x3 A, float3x3 B);
\&  float2x4 mul(float2x3 A, float3x4 B);
.Ve
.Vb 4
\&  float2x1 mul(float2x4 A, float4x1 B);
\&  float2x2 mul(float2x4 A, float4x2 B);
\&  float2x3 mul(float2x4 A, float4x3 B);
\&  float2x4 mul(float2x4 A, float4x4 B);
.Ve
.Vb 4
\&  float3x1 mul(float3x1 A, float1x1 B);
\&  float3x2 mul(float3x1 A, float1x2 B);
\&  float3x3 mul(float3x1 A, float1x3 B);
\&  float3x4 mul(float3x1 A, float1x4 B);
.Ve
.Vb 4
\&  float3x1 mul(float3x2 A, float2x1 B);
\&  float3x2 mul(float3x2 A, float2x2 B);
\&  float3x3 mul(float3x2 A, float2x3 B);
\&  float3x4 mul(float3x2 A, float2x4 B);
.Ve
.Vb 4
\&  float3x1 mul(float3x3 A, float3x1 B);
\&  float3x2 mul(float3x3 A, float3x2 B);
\&  float3x3 mul(float3x3 A, float3x3 B);
\&  float3x4 mul(float3x3 A, float3x4 B);
.Ve
.Vb 4
\&  float3x1 mul(float3x4 A, float4x1 B);
\&  float3x2 mul(float3x4 A, float4x2 B);
\&  float3x3 mul(float3x4 A, float4x3 B);
\&  float3x4 mul(float3x4 A, float4x4 B);
.Ve
.Vb 4
\&  float4x1 mul(float4x1 A, float1x1 B);
\&  float4x2 mul(float4x1 A, float1x2 B);
\&  float4x3 mul(float4x1 A, float1x3 B);
\&  float4x4 mul(float4x1 A, float1x4 B);
.Ve
.Vb 4
\&  float4x1 mul(float4x2 A, float2x1 B);
\&  float4x2 mul(float4x2 A, float2x2 B);
\&  float4x3 mul(float4x2 A, float2x3 B);
\&  float4x4 mul(float4x2 A, float2x4 B);
.Ve
.Vb 4
\&  float4x1 mul(float4x3 A, float3x1 B);
\&  float4x2 mul(float4x3 A, float3x2 B);
\&  float4x3 mul(float4x3 A, float3x3 B);
\&  float4x4 mul(float4x3 A, float3x4 B);
.Ve
.Vb 4
\&  float4x1 mul(float4x4 A, float4x1 B);
\&  float4x2 mul(float4x4 A, float4x2 B);
\&  float4x3 mul(float4x4 A, float4x3 B);
\&  float4x4 mul(float4x4 A, float4x4 B);
.Ve
.SH "PARAMETERS"
.IX Header "PARAMETERS"
.Ip "M" 8
.IX Item "M"
Matrix
.Ip "v" 8
.IX Item "v"
Vector
.Ip "A" 8
.IX Item "A"
Matrix
.Ip "B" 8
.IX Item "B"
Matrix
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
Returns the vector result of multiplying a matrix \fIM\fR by a column vector
\&\fIv\fR; a row vector \fIv\fR by a matrix \fIM\fR; or a matrix \fIA\fR by a second
matrix \fIB\fR.
.PP
The following are algebrically equal (if not necessarily numerically
equal):
.PP
.Vb 2
\&  mul(M,v) == mul(v, tranpose(M))
\&  mul(v,M) == mul(tranpose(M), v)
.Ve
.SH "REFERENCE IMPLEMENTATION"
.IX Header "REFERENCE IMPLEMENTATION"
\&\fBmul\fR for a \fBfloat4x3\fR matrix by a \fBfloat3\fR column vector could be
implemented this way:
.PP
.Vb 3
\&  float4 mul(float4x3 M, float3 v)
\&  {
\&    float4 r;
.Ve
.Vb 4
\&    r.x = dot( M._m00_m01_m02, v );
\&    r.y = dot( M._m10_m11_m12, v );
\&    r.z = dot( M._m20_m21_m22, v );
\&    r.w = dot( M._m30_m31_m32, v );
.Ve
.Vb 2
\&    return r;
\&  }
.Ve
.SH "PROFILE SUPPORT"
.IX Header "PROFILE SUPPORT"
\&\fBmul\fR is supported in all profiles.
.PP
The \fBfixed3\fR matrix-by-vector and vector-by-matrix multiplies are very
efficient in the fp20 and fp30 profiles.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
cross, dot, transpose
