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matrix?
matrix-rows
matrix-cols
rectangle->matrix
matrix->rectangle
make-matrix
build-matrix
matrix-ref
matrix-set
matrix-where?
matrix-render
matrix-minor
matrix-set!
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1.16 Matrix Operations: "matrix.ss"

The experimental teachpack supports matrices and matrix operations. A matrix is just a rectangle of ’objects’. It is displayed as an image, just like the images from Manipulating Images: "image.ss". Matrices are images and, indeed, scenes in the sense of the Simulations and Animations: "world.ss".

No educational materials involving matrices exist.

The operations access a matrix in the usual (school-mathematics) manner: row first, column second.

The operations aren’t tuned for efficiency so don’t expect to build programs that process lots of data.

Rectangle A Rectangle (of X) is a non-empty list of lists containing X where all elements of the list are lists of equal (non-zero) length.

(matrix? o) → boolean?
  o : any/c
determines whether the given object is a matrix?

(matrix-rows m) → natural-number/c
  m : matrix?
determines how many rows this matrix m has

(matrix-cols m) → natural-number/c
  m : matrix?
determines ow many columns this matrix m has

(rectangle->matrix r) → matrix?
  r : Rectangle
creates a matrix from the given Rectangle

(matrix->rectangle m) → Rectangle
  m : matrix?
creates a rectangle from this matrix m

(make-matrix n m l) → matrix?
  n : natural-number/c
  m : natural-number/c
  l : (Listof X)
creates an n by m matrix from l

NOTE: make-matrix would consume an optional number of entries, if it were like make-vector

(build-matrix n m f) → matrix?
  n : natural-number/c
  m : natural-number/c
  f : 
(-> (and/c natural-number/c (</c m))
    (and/c natural-number/c (</c n))
    any/c)
creates an n by m matrix by applying f to (0 ,0), (0 ,1), ..., ((sub1 m) ,(sub1 n))

(matrix-ref m i j) → any/c
  m : matrix?
  i : (and/c natural-number/c (</c (matrix-rows m)))
  j : (and/c natural-number/c (</c (matrix-rows m)))
retrieve the item at (i,j) in matrix m

(matrix-set m i j x) → matrix?
  m : matrix?
  i : (and/c natural-number/c (</c (matrix-rows m)))
  j : (and/c natural-number/c (</c (matrix-rows m)))
  x : any/c
creates a new matrix with x at (i,j) and all other places the same as in m

(matrix-where? m pred?) → (listof posn?)
  m : matrix?
  pred? : (-> any/c boolean?)
(matrix-where? M P) produces a list of (make-posn i j) such that (P (matrix-ref M i j)) holds

(matrix-render m) → Rectangle
  m : matrix?
renders this matrix m as a rectangle of strings

(matrix-minor m i j) → matrix?
  m : matrix?
  i : (and/c natural-number/c (</c (matrix-rows m)))
  j : (and/c natural-number/c (</c (matrix-rows m)))
creates a matrix minor from m at (i,j)

(matrix-set! m i j x) → matrix?
  m : matrix?
  i : (and/c natural-number/c (</c (matrix-rows m)))
  j : (and/c natural-number/c (</c (matrix-rows m)))
  x : any/c
like matrix-set but uses a destructive update

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