Submatrix — Control Systems/Matrix Operations

Submatrix

Control Systems / Matrix Operations

Passes a rectangular window of the input through and drops the rest: y = u(r₁:r₂, c₁:c₂). The rows and the columns are selected independently, each by a span and, where the span needs them, a start and an end anchor. Nothing is scaled and no element is combined with another.

Ports

• Input – the matrix u, of any size [m,n]. The window is resolved against this size, so a range that reaches past it is reported when the model is built rather than clipped.
• Output – the selected window, [r₂−r₁+1, c₂−c₁+1]. Its size follows from the parameters and the input's size together; both ends are inclusive.

Parameters

Ten in all, five per dimension, and the two dimensions work identically.

• Row Span – which rows are considered at all:
  • All rows – every row; both row anchors are ignored.
  • One row – a single row, at the START anchor. The end anchor is ignored.
  • Range of rows – from the start anchor to the end anchor, inclusive. This is the default, as in Simulink.
• Row Start Mode – where the range begins, on a dimension of size n:
  • First – row 1. The default.
  • Index – the row named by Row Start Index, counting from 1.
  • Offset from last – n − the index, so an index of 0 is the last row itself.
  • Last – row n.
  • Middle – row floor(n/2)+1, which is the upper of the two middles when n is even.
  • Offset from middle – that middle plus the index.
• Row Start Index – the whole number the three indexed modes above read. Ignored by First, Last and Middle. Under Index it must be 1 or more; under the two offset modes 0 or more.
• Row End Mode – where the range ends. The same list without First, exactly as Simulink's dialog has it, and defaulting to Last.
• Row End Index – the whole number the end's indexed modes read.
• Column Span, Column Start Mode, Column Start Index, Column End Mode, Column End Index – the same five over the columns, with All columns / One column / Range of columns in place of the row spellings.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

A window that would start before the first element, end past the last, or end before it starts is reported when the model is built; the block does not clip silently.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. Because both ranges are config, the whole window is resolved at export time and the copy is unrolled: no span or anchor branch survives into the generated core, and nothing is tunable on it.

The three HDL targets are fully synthesizable. Selecting a window is pure data movement, so the values stay in the Q16.16 datapath and nothing is converted at the port boundary or approximated.

Simulink bridge

Import and export, mapped to simulink/Matrix Operations/Submatrix. All ten parameters cross, one for one, and every combo value is spelled here exactly as Simulink spells it, so the translation is lossless in both directions: "Row Span" → RowSpan, "Row Start Mode" → RowStartMode, "Row Start Index" → RowStartIndex, "Row End Mode" → RowEndMode, "Row End Index" → RowEndIndex, and the five column parameters onto ColSpan, ColStartMode, ColStartIndex, ColEndMode and ColEndIndex.

The Simulink block defines no SampleTime parameter, so the rate is not carried across: it stays on the ICore side, and a block configured with an explicit positive rate reports that the rate did not cross.

Notes

• Algebraic, with no state – pure signal reindexing.
• Deliberately carries no state space, even though selecting a window is linear: it reshapes, and a D matrix can rescale a signal but never re-index one.
• The Middle anchor takes the UPPER middle on an even dimension – floor(n/2)+1, so column 3 of 4 – which is what Simulink does and is worth knowing before relying on it.