Add derivative to pow with scalar base (pytorch#12450)

Summary:
Fixes: pytorch#12426

Thank you, DriesSmit, for the report!
Pull Request resolved: pytorch#12450

Differential Revision: D10238556

Pulled By: soumith

fbshipit-source-id: 8bf71467c6734ecc5ff30f15500304d731f7e155

Author: t-vi

test/test_autograd.py

@@ -2150,6 +2150,10 @@ def run_test(input_size, exponent):
         run_test((10, 10), torch.zeros(10, 10))
         run_test((10,), 0)
 
+    def test_pow_scalar_base(self):
+        a = torch.arange(1, 13, dtype=torch.double).view(3, 4).requires_grad_()
+        gradcheck(lambda a: torch.pow(2, a), (a,))
+
     @skipIfRocm
     def test_pinverse(self):
         # Why is pinverse tested this way, and not ordinarily as other linear algebra methods?

tools/autograd/derivatives.yaml

@@ -559,6 +559,9 @@
   self: pow_backward_self(grad, self, exponent)
   exponent: pow_backward_exponent(grad, self, exponent)
 
+- name: pow(Scalar base, Tensor self)
+  self: pow_backward_exponent(grad, base, self)
+
 - name: _prod(Tensor self, int64_t dim, bool keepdim)
   self: prod_backward(grad, self, result, dim, keepdim)
 

tools/autograd/templates/Functions.cpp

@@ -130,6 +130,10 @@ Tensor pow_backward_exponent(Tensor grad, const Tensor & self, const Tensor & ex
   return grad * self.pow(exponent) * self.log();
 }
 
+Tensor pow_backward_exponent(Tensor grad, const Scalar & base, const Tensor & exponent) {
+  return grad * at::pow(base, exponent) * std::log(base.toDouble());
+}
+
 Tensor mvlgamma_backward(Tensor grad, const Tensor & self, int64_t p) {
   Tensor args = at::arange(-p + 1, 1, -1, self.options()).div_(2.);
   args = args.add(self.unsqueeze(-1));