Basic Tensorflow: Define Tensor variable using existing variables - tensorflow

Question

I have some very simple tensorflow code to rotate a vector:
import tensorflow as tf
import numpy as np
x = tf.placeholder(tf.float32, shape=(2, 1))
angle = tf.placeholder(tf.float32)
s_a = tf.sin(angle)
c_a = tf.cos(angle)
R = tf.Variable([[c_a, s_a], [-s_a, c_a]], tf.float32, expected_shape=(2,2))
#R = tf.Variable([[1.0, 0.0], [0.0, 1.0]], tf.float32)
rotated_v = tf.matmul(R,x)
init = tf.global_variables_initializer()
with tf.Session() as sess:
sess.run(init)
res = sess.run([init,rotated_v], feed_dict={x:np.array([[1.0],[1.0]]), angle:1.0})
print(res)
The code works fine when I hand-code the identity matrix. However, in its current form I get this error:
ValueError: initial_value must have a shape specified: Tensor("Variable/initial_value:0", dtype=float32)
I've tried specifying the shape in multiple ways, but I can't make this work.
What am I doing wrong?

Answer 1

I have figured out a way to achieve this (might not be the best way, but it works).
import tensorflow as tf
import numpy as np
x = tf.placeholder(tf.float32, shape=(2, 1))
angle = tf.placeholder(tf.float32)
s_a = tf.sin(angle)
c_a = tf.cos(angle)
R = tf.Variable([[1.0, 0.0], [0.0, 1.0]], tf.float32)
assignR = tf.assign(R, [[c_a, s_a], [-s_a, c_a]])
rotated_v = tf.matmul(R,x)
init = tf.global_variables_initializer()
with tf.Session() as sess:
sess.run(init)
newR = sess.run(assignR, feed_dict={angle:1.0})
print(newR)
print()
res = sess.run([rotated_v], feed_dict={x:np.array([[1.0],[1.0]])})
print(res)

Answer 2

This approach won't work, because s_a and c_a are the ops outputs, which values are uniquely determined by angle. You can't assign or update these nodes, so training them doesn't make any sense.
This line, on the other hand...
R = tf.Variable([[1.0, 0.0], [0.0, 1.0]], tf.float32)
... is a definition of an independent variable with initial value equal to identity matrix. This is perfectly valid. Since this variable is independent, you can assign a new value to it, which consists of s_a and c_a. Note that you can't initialize it with s_a and c_a, because the initializer is run before the values are fed into a session (so angle is unknown).