Lookup Table nD — Control Systems/Lookup Tables

n-D Lookup Table

Control Systems / Lookup Tables

Maps three inputs through a rectangular volume: y = table(u1, u2, u3). The three axes are searched independently and the eight surrounding entries are blended – which for the Linear rule is ordinary trilinear interpolation.

Three dimensions is Simulink's own default for this block, and it is what this one is. For one or two axes use 1-D Lookup Table or 2-D Lookup Table, which are cheaper and read more clearly.

Ports

• Input u1 – the first axis' coordinate, a scalar.
• Input u2 – the second axis' coordinate, a scalar.
• Input u3 – the third axis' coordinate, a scalar.
• Output – the table's value y, a scalar.

All four ports are scalar: a triple of matrix inputs has no single sensible reading, so this block does not run elementwise.

Parameters

• Breakpoints 1, Breakpoints 2, Breakpoints 3 – the three axes, each a row or column vector of at least two strictly increasing values.
• Table Data – the volume, as a flat vector holding exactly n1×n2×n3 values in column-major order: entry (i, j, k) sits at index i + j·n1 + k·n1·n2, counting from zero. That is MATLAB's own reshape order, so reshape(TableData, [n1 n2 n3]) in MATLAB and this parameter are the same numbers in the same order. It is flat because an ICore configuration value is a matrix, and a matrix has no third dimension to write.
• Interpolation Method – what the table says between the points.
  • Linear point-slope – trilinear across the surrounding eight entries.
  • Flat – the entry at the breakpoint at or below each input, on all three axes independently.
  • Nearest – the entry at the nearer breakpoint on each axis; an exact tie takes the higher one.
• Extrapolation Method – what the table says outside its own range.
  • Linear – continue off the edge along the slopes of the edge cell. Off an edge, a face or a corner, one, two or all three axes extrapolate at once.
  • Clip – hold each input inside its own axis.
  Consulted only by Linear point-slope, as everywhere else in this family.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. The table and both rules are baked in at export time: the generated code is a three-level chain of comparisons with one expression per cell, so the table's shape decides its size. A large volume produces a large core – this is the block in the family where that matters most, since the cell count is the product of all three axes.

The three HDL targets are not simulation-only. Each cell's eight coefficients and each interval's reciprocal width are folded into constants, so a cell is a handful of multiplies and adds with no divider. The caveat is range – a signal is carried in Q16.16 there, so a breakpoint or table value outside ±32767 cannot be represented, and the trilinear cross term is where a large table value meets a large coordinate.

Simulink bridge

None, and the reason is structural rather than a gap in this block. Simulink's n-D Lookup Table requires its Table parameter to be a genuine 3-D array; a flat vector is rejected when the model is compiled. Crossing would therefore mean writing reshape([…],[n1 n2 n3]) rather than the config's own text – and the bridge passes parameter text through unchanged, while an ICore configuration value is a matrix and cannot hold that call either. Neither side can spell the other's shape, so the block reports itself as unsupported instead of carrying a mapping that would fail in front of a user.

Worth knowing if you go looking: Simulink's set_param accepts the flat vector without complaint. The failure appears only at compile time, so a bridge built on what set_param allows would look correct and break later.

1-D Lookup Table and 2-D Lookup Table have no such problem – a vector and a matrix are both directly expressible – and are mapped in full. This block is still covered by code export verification, which compares the ten generated languages against ICore's own solver and needs no Simulink counterpart.

Notes

• Algebraic, with no state.
• Not linear, and so deliberately carries no state space.
• See 2-D Lookup Table for two axes and Direct Lookup Table (n-D) for selection by index with no axis at all.