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#-------------------------------------------------------------

# Trains a 2-layer autoencoder with minibatch SGD, momentum and step-size decay.
# If invoked with H1 > H2 then it becomes a 'bowtie' structured autoencoder
# Weights are initialized using Glorot & Bengio (2010) AISTATS initialization.
# The script standardizes the input before training (can be turned off).
# Also, it randomly reshuffles rows before training.
# Currently, tanh is set to be the activation function. 
# By re-implementing 'func' DML-bodied function, one can change the activation.

# INPUT PARAMETERS:
# ---------------------------------------------------------------------------------------------
# NAME   	TYPE     DEFAULT  MEANING
# ---------------------------------------------------------------------------------------------
# X         String   ---      Filename where the input is stored
# H1        Int      ---      Number of neurons in the 1st hidden layer
# H2        Int      ---      Number of neurons in the 2nd hidden layer
# EPOCH     Int      ---      Number of epochs to train for
# fmt       String   'text'   Output format ("text", "csv", "binary" etc.)
# OBJ       Boolean  FALSE    If TRUE, Computes objective function value (squared-loss)
#                             at the end of each epoch. Note that, computing the full 
#                             objective can take a lot of time. 
# BATCH     Int      256      Mini-batch size (training parameter)
# STEP      Double   1e-5     Initial step size (training parameter)
# DECAY     Double   0.95     Decays step size after each epoch (training parameter)
# MOMENTUM  Double   0.9      Momentum parameter (training parameter)
# ---------------------------------------------------------------------------------------------
#
# OUTPUT PARAMETERS (all filenames):
# ---------------------------------------------------------------------------------------------
# NAME     TYPE   DEFAULT  MEANING
# ---------------------------------------------------------------------------------------------
# W1_out   String   ---   File to store weights between input layer and 1st hidden layer
# b1_out   String   ---   File to store bias between input layer and 1st hidden layer
# W2_out   String   ---   File to store weights between 1st hidden layer and 2nd hidden layer
# b2_out   String   ---   File to store bias between 1st hidden layer and 2nd hidden layer
# W3_out   String   ---   File to store weights between 2nd hidden layer and 3rd hidden layer
# b3_out   String   ---   File to store bias between 2nd hidden layer and 3rd hidden layer
# W4_out   String   ---   File to store weights between 3rd hidden layer and output layer
# b4_out   String   ---   File to store bias between 3rd hidden layer and output layer
# HIDDEN   String   " "   File to store the hidden (2nd) layer representation if needed
# ---------------------------------------------------------------------------------------------
#
# INVOCATION:
# -f autoencoder_2layer.dml --nvargs X=<input file> H1=500 H2=2 EPOCH=1 fmt="csv" 
#                                    W1_out=<weights from input to 1st hidden layer> b1_out=<bias from input to 1st hidden layer> 
#									 W2_out=<weights from 1st hidden layer to 2nd hidden layer> b2_out=<bias from 1st hidden layer to 2nd hidden layer> 
#									 W3_out=<weights from 2nd hidden layer to 3rd hidden layer> b3_out=<bias from 2nd hidden layer to 3rd hidden layer> 
#									 W4_out=<weights from 3rd hidden layer to output> b4_out=<bias from 3rd hidden layer to output>
#

#implements tanh
#to use another activation fn, implement a DML-bodied function with 
#function name 'func' and comment out this one
func = function(Matrix[Double] X) return(Matrix[Double] Y, Matrix[Double] Y_prime){
     Y = (exp(2*X) - 1)/(exp(2*X) + 1)
     Y_prime = 1 - Y^2
}

feedForward = function(Matrix[Double] X, 
	               Matrix[Double] W1, Matrix[Double] b1, 
	               Matrix[Double] W2, Matrix[Double] b2, 
	               Matrix[Double] W3, Matrix[Double] b3, 
	               Matrix[Double] W4, Matrix[Double] b4, 
		       Matrix[Double] Y)
      	      return(Matrix[Double] H1, Matrix[Double] H1_prime,
	     	     Matrix[Double] H2, Matrix[Double] H2_prime,
	     	     Matrix[Double] H3, Matrix[Double] H3_prime,
	     	     Matrix[Double] Yhat, Matrix[Double] Yhat_prime,
	     	     Matrix[Double] E){
      H1_in = t(W1 %*% t(X) + b1)
      [H1, H1_prime] = func(H1_in)

      H2_in = t(W2 %*% t(H1) + b2)
      [H2, H2_prime] = func(H2_in)

      H3_in = t(W3 %*% t(H2) + b3)
      [H3, H3_prime] = func(H3_in)

      Yhat_in = t(W4 %*% t(H3) + b4)
      [Yhat, Yhat_prime] = func(Yhat_in)
      E = Yhat - Y
}

grad = function(Matrix[Double] X, 
       		Matrix[Double] H1, Matrix[Double] H1_prime,
       		Matrix[Double] H2, Matrix[Double] H2_prime,
       		Matrix[Double] H3, Matrix[Double] H3_prime,
		Matrix[Double] Yhat_prime,
		Matrix[Double] E,
		Matrix[Double] W1, Matrix[Double] W2, Matrix[Double] W3, Matrix[Double] W4)
       return(Matrix[Double] W1_grad, Matrix[Double] b1_grad,
              Matrix[Double] W2_grad, Matrix[Double] b2_grad,
	      Matrix[Double] W3_grad, Matrix[Double] b3_grad,
	      Matrix[Double] W4_grad, Matrix[Double] b4_grad){
      #backprop
      delta4 = E * Yhat_prime
      delta3 = H3_prime * (delta4 %*% W4)
      delta2 = H2_prime * (delta3 %*% W3)
      delta1 = H1_prime * (delta2 %*% W2)

      #compute gradients
      b4_grad = t(colSums(delta4))
      b3_grad = t(colSums(delta3))
      b2_grad = t(colSums(delta2))
      b1_grad = t(colSums(delta1))

      W4_grad = t(delta4) %*% H3
      W3_grad = t(delta3) %*% H2
      W2_grad = t(delta2) %*% H1
      W1_grad = t(delta1) %*% X
}

obj = function(Matrix[Double] E) return(Double val){
    val = 0.5 * sum(E^2)
}

batch_size = ifdef($BATCH, 256)
mu = ifdef($MOMENTUM, 0.9)
step = ifdef($STEP, 1e-5)
decay = ifdef($DECAY, 0.95)
hfile = ifdef($HIDDEN, " ")
fmt = ifdef($fmt, "text")
full_obj = ifdef($OBJ, FALSE)

X = read($X)
num_hidden1 = $H1
num_hidden2 = $H2
max_epochs = $EPOCH

n = nrow(X)
m = ncol(X)

#randomly reordering rows
permut = table(seq(1,n,1), order(target=Rand(rows=n, cols=1, min=0, max=1, pdf="uniform"), by=1, index.return=TRUE), n, n)
X = permut %*% X

#z-transform, whitening operator is better
means = colSums(X)/n
stds = sqrt((colSums(X^2)/n - means*means)*n/(n-1)) + 1e-17
X = (X - means)/stds

W1 = sqrt(6)/sqrt(m + num_hidden1) * Rand(rows=num_hidden1, cols=m, min=-1, max=1, pdf="uniform")
b1 = matrix(0, rows=num_hidden1, cols=1)
W2 = sqrt(6)/sqrt(num_hidden1 + num_hidden2) * Rand(rows=num_hidden2, cols=num_hidden1, min=-1, max=1, pdf="uniform")
b2 = matrix(0, rows=num_hidden2, cols=1)
W3 = sqrt(6)/sqrt(num_hidden2 + num_hidden1) * Rand(rows=num_hidden1, cols=num_hidden2, min=-1, max=1, pdf="uniform")
b3 = matrix(0, rows=num_hidden1, cols=1)
W4 = sqrt(6)/sqrt(num_hidden2 + m) * Rand(rows=m, cols=num_hidden1, min=-1, max=1, pdf="uniform")
b4 = matrix(0, rows=m, cols=1)

upd_W1 = matrix(0, rows=nrow(W1), cols=ncol(W1))
upd_b1 = matrix(0, rows=nrow(b1), cols=ncol(b1))
upd_W2 = matrix(0, rows=nrow(W2), cols=ncol(W2))
upd_b2 = matrix(0, rows=nrow(b2), cols=ncol(b2))
upd_W3 = matrix(0, rows=nrow(W3), cols=ncol(W3))
upd_b3 = matrix(0, rows=nrow(b3), cols=ncol(b3))
upd_W4 = matrix(0, rows=nrow(W4), cols=ncol(W4))
upd_b4 = matrix(0, rows=nrow(b4), cols=ncol(b4))

if( full_obj ){
      [full_H1, full_H1_prime, full_H2, full_H2_prime, full_H3, full_H3_prime, full_Yhat, full_Yhat_prime, full_E] = feedForward(X, W1, b1, W2, b2, W3, b3, W4, b4, X)
      full_o = obj(full_E)
      print("EPOCHS=" + 0 + " OBJ (FULL DATA): " + full_o)
}

iter = 0
num_iters_per_epoch = ceil(n / batch_size)
max_iterations = max_epochs * num_iters_per_epoch
#print("num_iters_per_epoch=" + num_iters_per_epoch + " max_iterations=" + max_iterations)
beg = 1
while( iter < max_iterations ){
      end = beg + batch_size - 1
      if(end > n) end = n
      X_batch = X[beg:end,]

      [H1, H1_prime, H2, H2_prime, H3, H3_prime, Yhat, Yhat_prime, E] = feedForward(X_batch, W1, b1, W2, b2, W3, b3, W4, b4, X_batch)
      [W1_grad, b1_grad, W2_grad, b2_grad, W3_grad, b3_grad, W4_grad, b4_grad] = grad(X_batch, H1, H1_prime, H2, H2_prime, H3, H3_prime, Yhat_prime, E, W1, W2, W3, W4)

      o = obj(E)
      print("epochs=%5.4f BATCH beg=%d end=%d obj=%f", (iter / num_iters_per_epoch), beg, end, o)

      #update
      local_step = step / nrow(X_batch)
      upd_W1 = mu * upd_W1 - local_step * W1_grad
      upd_b1 = mu * upd_b1 - local_step * b1
      upd_W2 = mu * upd_W2 - local_step * W2_grad
      upd_b2 = mu * upd_b2 - local_step * b2
      upd_W3 = mu * upd_W3 - local_step * W3_grad
      upd_b3 = mu * upd_b3 - local_step * b3
      upd_W4 = mu * upd_W4 - local_step * W4_grad
      upd_b4 = mu * upd_b4 - local_step * b4
      W1 = W1 + upd_W1
      b1 = b1 + upd_b1
      W2 = W2 + upd_W2
      b2 = b2 + upd_b2
      W3 = W3 + upd_W3
      b3 = b3 + upd_b3
      W4 = W4 + upd_W4
      b4 = b4 + upd_b4

      iter = iter + 1
      if(end == n) beg = 1
      else beg = end + 1

      if( iter %% num_iters_per_epoch == 0 ) step = step * decay

      if( full_obj & iter %% num_iters_per_epoch == 0 ){
      	  [full_H1, full_H1_prime, full_H2, full_H2_prime, full_H3, full_H3_prime, full_Yhat, full_Yhat_prime, full_E] = feedForward(X, W1, b1, W2, b2, W3, b3, W4, b4, X)
          full_o = obj(full_E)
      	  epochs = iter %/% num_iters_per_epoch
          print("EPOCHS=" + epochs + " iter=" + iter + " OBJ (FULL DATA)=" + full_o)
      }
}

write(W1, $W1_out, format=fmt)
write(b1, $b1_out, format=fmt)
write(W2, $W2_out, format=fmt)
write(b2, $b2_out, format=fmt)
write(W3, $W3_out, format=fmt)
write(b3, $b3_out, format=fmt)
write(W4, $W4_out, format=fmt)
write(b4, $b4_out, format=fmt)

if( hfile != " " ){
      [full_H1, full_H1_prime, full_H2, full_H2_prime, full_H3, full_H3_prime, full_Yhat, full_Yhat_prime, full_E] = feedForward(X, W1, b1, W2, b2, W3, b3, W4, b4, X)
      reordered_H = t(permut) %*% full_H2
      write(reordered_H, hfile, format=fmt)
}