Cg 3.1 Toolkit Documentation Cg / Standard Library / mul

## Name

mul - multiply a matrix by a column vector, row vector by a matrix, or matrix by a matrix

## Synopsis

```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);

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);

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);

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);

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);

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);

float1x1 mul(float1x1 A, float1x1 B);
float1x2 mul(float1x1 A, float1x2 B);
float1x3 mul(float1x1 A, float1x3 B);
float1x4 mul(float1x1 A, float1x4 B);

float1x1 mul(float1x2 A, float2x1 B);
float1x2 mul(float1x2 A, float2x2 B);
float1x3 mul(float1x2 A, float2x3 B);
float1x4 mul(float1x2 A, float2x4 B);

float1x1 mul(float1x3 A, float3x1 B);
float1x2 mul(float1x3 A, float3x2 B);
float1x3 mul(float1x3 A, float3x3 B);
float1x4 mul(float1x3 A, float3x4 B);

float1x1 mul(float1x4 A, float4x1 B);
float1x2 mul(float1x4 A, float4x2 B);
float1x3 mul(float1x4 A, float4x3 B);
float1x4 mul(float1x4 A, float4x4 B);

float2x1 mul(float2x1 A, float1x1 B);
float2x2 mul(float2x1 A, float1x2 B);
float2x3 mul(float2x1 A, float1x3 B);
float2x4 mul(float2x1 A, float1x4 B);

float2x1 mul(float2x2 A, float2x1 B);
float2x2 mul(float2x2 A, float2x2 B);
float2x3 mul(float2x2 A, float2x3 B);
float2x4 mul(float2x2 A, float2x4 B);

float2x1 mul(float2x3 A, float3x1 B);
float2x2 mul(float2x3 A, float3x2 B);
float2x3 mul(float2x3 A, float3x3 B);
float2x4 mul(float2x3 A, float3x4 B);

float2x1 mul(float2x4 A, float4x1 B);
float2x2 mul(float2x4 A, float4x2 B);
float2x3 mul(float2x4 A, float4x3 B);
float2x4 mul(float2x4 A, float4x4 B);

float3x1 mul(float3x1 A, float1x1 B);
float3x2 mul(float3x1 A, float1x2 B);
float3x3 mul(float3x1 A, float1x3 B);
float3x4 mul(float3x1 A, float1x4 B);

float3x1 mul(float3x2 A, float2x1 B);
float3x2 mul(float3x2 A, float2x2 B);
float3x3 mul(float3x2 A, float2x3 B);
float3x4 mul(float3x2 A, float2x4 B);

float3x1 mul(float3x3 A, float3x1 B);
float3x2 mul(float3x3 A, float3x2 B);
float3x3 mul(float3x3 A, float3x3 B);
float3x4 mul(float3x3 A, float3x4 B);

float3x1 mul(float3x4 A, float4x1 B);
float3x2 mul(float3x4 A, float4x2 B);
float3x3 mul(float3x4 A, float4x3 B);
float3x4 mul(float3x4 A, float4x4 B);

float4x1 mul(float4x1 A, float1x1 B);
float4x2 mul(float4x1 A, float1x2 B);
float4x3 mul(float4x1 A, float1x3 B);
float4x4 mul(float4x1 A, float1x4 B);

float4x1 mul(float4x2 A, float2x1 B);
float4x2 mul(float4x2 A, float2x2 B);
float4x3 mul(float4x2 A, float2x3 B);
float4x4 mul(float4x2 A, float2x4 B);

float4x1 mul(float4x3 A, float3x1 B);
float4x2 mul(float4x3 A, float3x2 B);
float4x3 mul(float4x3 A, float3x3 B);
float4x4 mul(float4x3 A, float3x4 B);

float4x1 mul(float4x4 A, float4x1 B);
float4x2 mul(float4x4 A, float4x2 B);
float4x3 mul(float4x4 A, float4x3 B);
float4x4 mul(float4x4 A, float4x4 B);
```

M
Matrix
v
Vector
A
Matrix
B
Matrix

## Description

Returns the vector result of multiplying a matrix M by a column vector v; a row vector v by a matrix M; or a matrix A by a second matrix B.

The following are algebrically equal (if not necessarily numerically equal):

```mul(M,v) == mul(v, tranpose(M))
mul(v,M) == mul(tranpose(M), v)
```

## Reference Implementation

mul for a float4x3 matrix by a float3 column vector could be implemented this way:

```float4 mul(float4x3 M, float3 v)
{
float4 r;

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 );

return r;
}
```

## Profile Support

mul is supported in all profiles except the fp20, ps_1_1, ps_1_2, and ps_1_3 fragment profiles.

The fixed3 matrix-by-vector and vector-by-matrix multiplies are very efficient in the fp30 profile.

## See Also

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