I've got a simple (I think) question about OpenGL texture arrays. I create my texture array with something like the following:

glTexImage3D(GL_TEXTURE_2D_ARRAY,
             0,
             formatGL,
             width,
             height,
             slices,
             0,
             GL_RGBA,
             GL_UNSIGNED_BYTE,
             nullptr);

Note that I don't want to actually load any images into it yet. I'm just creating the structure that I'll be filling with data later on.

So my questions are:

1. How do I generate the mip chain for each "slice" of the texture array? I don't want to physically generate the mip, I just want to complete the texture by telling it about the mip. I can do this with 2D textures simply by calling the glTexImage2D function with the mip level, size and also passing in a nullptr. I can't see how to do this with the glTexImage3D function given there's no "slice" parameter. The OpenGL superbible example only loads a .bmp into the first mip level for each texture in the array. Is it correct to say that using glTexSubImage3D, passing in a nullptr, will create the mip level I want for a given texture in the array?

2. Documentation at khronos.org on glGenerateMipMap specifies GL_TEXTURE_2D or GL_TEXTURE_CUBE_MAP only. So is it correct to say I can't use this method for 2D texture arrays?

Here's what I do with 2D textures to create the mip chain:

size_t i = 0, mipSizeX = width, mipSizeY = height;

while(mipSizeX >= 1 || mipSizeY >= 1)
{
    // Generate image for this mip level
    glTexImage2D(GL_TEXTURE_2D,
                 i,
                 formatGL,
                 mipSizeX,
                 mipSizeY,
                 0,
                 GL_RGBA, 
                 GL_UNSIGNED_BYTE, 
                 nullptr);

    // Go to the next mip size.
    mipSizeX >>= 1;
    mipSizeY >>= 1;

    // and the next mipmap level.
    i++;
}