Lookup Table 1D — Control Systems/Lookup Tables

1-D Lookup Table

Control Systems / Lookup Tables

Maps the input through a table of (breakpoint, value) pairs: y = table(u). Between two breakpoints the value comes from the chosen interpolation rule; outside the axis it comes from the chosen extrapolation rule. Applied entry by entry, so a matrix signal is looked up element for element.

This is Prelookup and Interpolation Using Prelookup done in one block, which is the right shape whenever one table owns its axis – and the wrong one when several tables share it, where doing the search once is the point.

Ports

• Input – the value u to look up, of any size [m,n].
• Output – the table's value y, of the SAME size [m,n]. The block never reshapes a signal.

Parameters

• Breakpoints – the axis, as a row or column vector; both spell the same list. At least two strictly increasing values: a repeated breakpoint is a zero-width interval whose slope is a division by zero, and a decreasing one describes no axis at all.
• Table Data – what the table is at each breakpoint, as a vector of the same length.
• Interpolation Method – what the table says between two breakpoints.
  • Linear point-slope – a straight line between the two neighbours.
  • Flat – the value at the breakpoint at or below the input, making the output a staircase that steps at each breakpoint.
  • Nearest – the value at the nearer breakpoint. An input exactly halfway between two takes the higher one.
• Extrapolation Method – what the table says outside its own range.
  • Linear – continue along the slope of the end interval.
  • Clip – hold the end value.
  Consulted only by Linear point-slope. Flat and Nearest never form a slope, so there is nothing for them to continue along and this parameter changes nothing – Simulink behaves the same way, verified against the R2026a block.
• 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 the two rules are baked into the arithmetic at export time rather than exposed as tunable parameters, and they have to be: the number of breakpoints decides how many branches the generated code has, so the table and the structure of the code cannot be separated. Each branch is emitted as its own comparison, which is the one shape all ten targets agree on.

The three HDL targets are not simulation-only. No divider is emitted: each interval's slope is folded into one constant at export time, so a branch is one multiply and one add. The HDL caveat is range rather than accuracy – a signal is carried in Q16.16 there, so a breakpoint or table value outside ±32767 cannot be represented.

Simulink bridge

Import and export, mapped to simulink/Lookup Tables/1-D Lookup Table. "Breakpoints" to BreakpointsForDimension1, "Table Data" to Table, "Interpolation Method" to InterpMethod and "Extrapolation Method" to ExtrapMethod – all four values are Simulink's own strings, so those mappings are 1:1 and lossless both ways. The block always writes NumberOfTableDimensions = 1, which is what having one input port means. "Sampling Time (s)" goes to SampleTime, as on every block.

Simulink offers three further interpolation methods on this block – Linear Lagrange, Cubic spline and Akima spline – which have no counterpart here. A model importing one of those is reported rather than silently mapped onto a straight line.

Notes

• Algebraic, with no state.
• Elementwise: the output carries the input's size, and each entry is looked up on its own.
• Not linear, and so deliberately carries no state space – model reduction reports it as unmergeable rather than absorbing the table. That holds even for a table whose points happen to lie on a line, because what the block does outside its range is still not that line unless the extrapolation says so.
• See 2-D Lookup Table and n-D Lookup Table for more axes, and Lookup Table Dynamic for a table that arrives on ports instead of from config.