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# Testing parents
test_parents <- matrix(c(1:8, c(2, 4, 6, 8, 7, 5, 3, 1)), nrow=2, byrow=T)
# Test 1
cxPoints_test1 <- c(1, 3, 5, 8)
# Test 2
cxPoints_test2 <- c(2, 3, 6)

##########
# gaperm_pbxCrossover_R has been *slightly* modified merely for pbx crossover testing purposes
##########

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# Load lpSolve
require(lpSolve)

## Set the coefficients of the decision variables -> C
C <- c(30, 40, 80)

# Create constraint martix B
A <- matrix(c(1, 1, -10,
              4, 3, -20,
              1, 0, -2,

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#-------------------------------------------------------------------------------
# Setup

require(dplyr)
require(e1071)

load(file="images_formatted.Rdata")
D <- out; rm(out)

# Scale the data. Note that scale returns a matrix

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#-------------------------------------------------------------------------------
# With built-in prcomp function:

# Compute PCA
pc <- prcomp(D, center = T, scale. = T)

# Eigenvalues
(pc$sdev^2)[1:20]

# Eigenvectors (loadings)

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#-------------------------------------------------------------------------------
# Projection of the average face onto the eigenvenctor space

# From a feature vector to a feature vector in the reduced feature space
proj_face_0 <- as.matrix(AverageFace[1, 2:4097]) %*% eigenvectors # for label 0
proj_face_1 <- as.matrix(AverageFace[2, 2:4097]) %*% eigenvectors # for label 1
proj_face_2 <- as.matrix(AverageFace[3, 2:4097]) %*% eigenvectors # for label 2

# Every face has different projection on eigenvector space.
# We can use these new fewer values for a classification task.

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#-------------------------------------------------------------------------------
# Plot of eigenfaces

# First 4 eigenfaces
plt_img(eigenvectors[, 1]) # Eigenface 1
plt_img(eigenvectors[, 2]) # Eigenface 2
plt_img(eigenvectors[, 3]) # Eigenface 3
plt_img(eigenvectors[, 4]) # Eigenface 4
plt_img(eigenvectors[, 20]) # Eigenface 20
# ...

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#-------------------------------------------------------------------------------
# Perform PCA on the data

# Step 1: scale data
# Scale as follows: mean equal to 0, stdv equal to 1
D <- scale(D)

# Step 2: calculate covariance matrix
A <- cov(D)
A_ <- t(D) %*% D / (nrow(D)-1)

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rm(list=ls())
require(dplyr)

load(file="images_formatted.Rdata")

D <- out; rm(out)
#-------------------------------------------------------------------------------
# Brief description of the data

# D is a 399x4096 matrix. It contains 399 images (rows) of 64x64 grayscale pixels (4096 columns)

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################################################################################
# This script converts the images in the following format:
#
# X -> converted to a 399x4096 matrix. Each row represents an image of 64x64
#      greyscale pixels
#
# y -> labels of the images
#
################################################################################

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# Imports
from sklearn.datasets import fetch_olivetti_faces
import numpy as np

# Download Olivetti faces dataset
olivetti = fetch_olivetti_faces()
x = olivetti.images
y = olivetti.target

# Print info on shapes and reshape where necessary