Decomposing a rotation matrix

I have a rotation matrix. How can I get the rotation around a specified axis contained within this matrix?

Edit:

It's a 3D matrix (4x4), and I want to know how far around a predetermined (not contained) axis the matrix rotates. I can already decompose the matrix but D3DX will only give the entire matrix as one rotation around one axis, whereas I need to split the matrix up into angle of rotation around an already-known axis, and the rest.

Sample code and brief problem description:

D3DXMATRIX CameraRotationMatrix;
D3DXVECTOR3 CameraPosition;
//D3DXVECTOR3 CameraRotation;

inline D3DXMATRIX GetRotationMatrix() {
    return CameraRotationMatrix;
}
inline void TranslateCamera(float x, float y, float z) {
    D3DXVECTOR3 rvec, vec(x, y, z);
#pragma warning(disable : 4238)
    D3DXVec3TransformNormal(&rvec, &vec, &GetRotationMatrix());
#pragma warning(default : 4238)
    CameraPosition += rvec;
    RecomputeVPMatrix();
}
inline void RotateCamera(float x, 开发者_Python百科float y, float z) {
    D3DXVECTOR3 RotationRequested(x, y, z);
    D3DXVECTOR3 XAxis, YAxis, ZAxis;
    D3DXMATRIX rotationx, rotationy, rotationz;
    XAxis = D3DXVECTOR3(1, 0, 0);
    YAxis = D3DXVECTOR3(0, 1, 0);
    ZAxis = D3DXVECTOR3(0, 0, 1);

#pragma warning(disable : 4238)
    D3DXVec3TransformNormal(&XAxis, &XAxis, &GetRotationMatrix());
    D3DXVec3TransformNormal(&YAxis, &YAxis, &GetRotationMatrix());
    D3DXVec3TransformNormal(&ZAxis, &ZAxis, &GetRotationMatrix());
#pragma warning(default : 4238)
    D3DXMatrixIdentity(&rotationx);
    D3DXMatrixIdentity(&rotationy);
    D3DXMatrixIdentity(&rotationz);
    D3DXMatrixRotationAxis(&rotationx, &XAxis, RotationRequested.x);
    D3DXMatrixRotationAxis(&rotationy, &YAxis, RotationRequested.y);
    D3DXMatrixRotationAxis(&rotationz, &ZAxis, RotationRequested.z);
    CameraRotationMatrix *= rotationz;
    CameraRotationMatrix *= rotationy;
    CameraRotationMatrix *= rotationx;
    RecomputeVPMatrix();
}
inline void RecomputeVPMatrix() {
    D3DXMATRIX ProjectionMatrix;
    D3DXMatrixPerspectiveFovLH(
        &ProjectionMatrix,
        FoV,
        (float)D3DDeviceParameters.BackBufferWidth / (float)D3DDeviceParameters.BackBufferHeight,
        FarPlane,
        NearPlane
    );

    D3DXVECTOR3 CamLookAt;
    D3DXVECTOR3 CamUpVec;

#pragma warning(disable : 4238)
    D3DXVec3TransformNormal(&CamLookAt, &D3DXVECTOR3(1, 0, 0), &GetRotationMatrix());
    D3DXVec3TransformNormal(&CamUpVec, &D3DXVECTOR3(0, 1, 0), &GetRotationMatrix());
#pragma warning(default : 4238)

    D3DXMATRIX ViewMatrix;
#pragma warning(disable : 4238)
    D3DXMatrixLookAtLH(&ViewMatrix, &CameraPosition, &(CamLookAt + CameraPosition), &CamUpVec);
#pragma warning(default : 4238)
    ViewProjectionMatrix = ViewMatrix * ProjectionMatrix;
    D3DVIEWPORT9 vp = {
        0,
        0,
        D3DDeviceParameters.BackBufferWidth,
        D3DDeviceParameters.BackBufferHeight,
        0,
        1
    };
    D3DDev->SetViewport(&vp);
}

Effectively, after a certain time, when RotateCamera is called, it begins to rotate in the relative X axis- even though constant zero is passed in for that request when responding to mouse input, so I know that when moving the mouse, the camera should not roll at all. I tried spamming 0,0,0 requests and saw no change (one per frame at 1500 frames per second), so I'm fairly sure that I'm not seeing FP error or matrix accumulation error. I tried writing a RotateCameraYZ function and stripping all X-axis from the function. I've spent several days trying to discover why this is the case, and eventually decided on just hacking around it.

So I want to get the rotation around the relative-x axis, transform the CameraRotation matrix, and then check it after to verify that it's the same, and if it isn't, add a correcting matrix.

Just for reference, I've seen some diagrams on Wikipedia, and I actually have a relatively strange axis layout, which is Y axis up, but X axis forwards and Z axis right, so Y axis yaw, Z axis pitch, X axis roll.

See Wikipedia.
Warning: Math ahead