#### 1.20Matrix Functions: "matrix.ss"

 (require htdp/matrix)

The experimental teachpack supports matrices and matrix functions. 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 functions access a matrix in the usual (school-mathematics) manner: row first, column second.

The functions 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 (
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 (
retrieve the item at (i,j) in matrix m

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

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