Psych 285: Computational Statistics
and Statistical Visualization

Matrix Examples from Chapter 4, Section 4.4.7

;Arrays - multidimensional arrays (vectors are unidimensional arrays)
;note the #2A( ...  ) syntax for two-dimensional arrays (matrices)
;and the #3A( ... ) syntax for three-dimensional arrays, etc...

(setf mat (make-array '(2 3)))
(setf mat (make-array '(2 3) :initial-element 1))
(setf mat (make-array '(3 2) :initial-contents '((1 2) (3 4) (5 6))))

(make-array '(30 1) :initial-element 1)

(print-matrix mat)
(pm mat) ;ViSta only

(setf mat (matrix '(2 3) '(1 2 3 4 5 6)))

(aref mat 1 1)
(setf (aref mat 1 0) "A")

(select mat 1 1)
(select mat '(1 2) '(2 3))
(setf (select mat 1 0) 'B)

(array-rank mat)

(array-dimensions mat)
(array-dimension mat 0)
(array-total-size mat)

(setf abrasion (matrix (list 3 (length hardness))
                         (combine hardness tensile-strength abrasion-loss)))

Matrix Examples from Chapter 5, Section 4

(setf abrasion (transpose abrasion))
(print-matrix abrasion)
(pm abrasion) ;ViSta only

(print-matrix (matmult (transpose abrasion) abrasion ))

;bind-rows and bind-columns create matrices from lists, vectors, or matrices
(setf abrasion (bind-columns hardness tensile-strength abrasion-loss))
(pm abrasion)

;column-list and row-list break up a matrix into a list of rows or columns
(column-list abrasion)
(row-list abrasion

(defun column-means (mat)
  (mapcar #'mean (column-list mat)))
(column-means abrasion)

;transpose, identity-matrix

(pm (identity-matrix 4))
(pm (transpose abrasion))

;matmult and %* (undocumented)
(pm (%* (transpose abrasion) abrasion))
(setf one (make-array '(3) :initial-element 1) )
(%* abrasion one) ; sums up the values in each row

;inner-product, outer-product, cross-product
(%* '(1 2 3) '(4 5 6))
(inner-product '(1 2 3) '(4 5 6))
(pm (outer-product '(1 2 3) '(4 5 6)))
(pm (cross-product abrasion)) ; same as (%* (transpose abrasion) abrasion))

, diagonal (used in two ways)
(pm (diagonal (matmult(transpose abrasion) abrasion )))
(pm (diagonal (diagonal (matmult(transpose abrasion) abrasion ))))

;inverse
(setf cp (cross-product abrasion))
(pm (%* (inverse cp) cp))

;eigen, eigenvalues, eigenvectors, sv-decomp
(eigen cp)
(eigenvalues cp)
(eigenvectors cp)
(sv-decomp abrasion)

;chol-decomp, lu-decomp, qr-decomp