Question

How can be an array of double (1D) stored using protocol buffer?
What about multi-dimensional (2D or 3D) dense arrays?

Answer 1

An array of double would be best stored via

repeated double foo = 5 [packed=true];

repeated makes it act as a list, allowing multiple items; packed avoids a header per item.

There is no direct support for rectangular (or higher) arrays in protobuf. The closest is to store something like:

repeated innerType foo = 5; // note, can't be "packed"

message innerType {
    repeated double foo = 1 [packed=true];
}

this is broadly akin to a jagged array, but with an element between each tier.