basic_example1.py

# This example shows the use of the low level function tf.gradients() 
# [http://tensorflow.org/api_docs/python/train.html#gradients]
# The definiton of function R=R(x,y) is taken from the example on Wiki 
# [https://en.wikipedia.org/wiki/Gauss%E2%80%93Newton_algorithm]
# If you are interested in creating new Optimizers for Tensorflow 
#you may want to continue reading this example.
import tensorflow as tf

# define symbolic variables
x = tf.placeholder("float") 
y = tf.placeholder("float")

# define a function R=R(x,y)
R = 0.127-(x*0.194/(y+0.194))

# The derivative of R with respect to y
Rdy = tf.gradients(R, y); 

# Launch a session for the default graph to comput dR/dy at (x,y)=(0.362, 0.556)
sess = tf.Session()
result = sess.run(Rdy, {x:0.362,y:0.556})
print result
#[0.12484978]


# The above example actually is implemented in SymJava which provides symbolic-numeric
# computations with just-in-time (JIT) compilation.
# [https://github.com/yuemingl/SymJava/blob/master/src/symjava/examples/Example0.java]
# 
# public class Example0 {
# 	public static void main(String[] args) {
# 		Expr R = 0.127-(x*0.194/(y+0.194));
# 		Expr Rdy = R.diff(y);
# 		System.out.println(Rdy);
# 		//Just-In-Time compile the symbolic expression to native code
# 		BytecodeFunc func = JIT.compile(new Expr[]{x,y}, Rdy);
# 		System.out.println(func.apply(0.362, 0.556));
# 	}
# }