Add erfinv operator for calculating inverse error function

docs/api/python/ndarray/ndarray.md

@@ -659,6 +659,7 @@ The `ndarray` package provides several classes:
     relu
     sigmoid
     erf
+    erfinv
 ```
 
 ### More

docs/api/python/symbol/symbol.md

@@ -659,6 +659,7 @@ Composite multiple symbols into a new one by an operator.
     relu
     sigmoid
     erf
+    erfinv
 ```
 
 ### More

src/operator/mshadow_op.h

@@ -169,6 +169,93 @@ struct softrelu : public mxnet_op::tunable {
 
 MXNET_UNARY_MATH_OP(softrelu_grad, -math::expm1(-a));
 
+
+/* The next function is taken from 
+https://github.com/antelopeusersgroup/antelope_contrib/blob/master/lib/location/libgenloc/erfinv.c.
+Below is the copyright. Output was modified to be inf or -inf when input is 1 or -1.
+
+    Copyright (c) 2014 Indiana University
+    All rights reserved.
+    Written by Prof. Gary L. Pavlis, Dept. of Geol. Sci.,
+            Indiana University, Bloomington, IN
+    This software is licensed under the New BSD license:
+    Redistribution and use in source and binary forms,
+    with or without modification, are permitted provided
+    that the following conditions are met:
+    Redistributions of source code must retain the above
+    copyright notice, this list of conditions and the
+    following disclaimer.
+    Redistributions in binary form must reproduce the
+    above copyright notice, this list of conditions and
+    the following disclaimer in the documentation and/or
+    other materials provided with the distribution.
+    Neither the name of Indiana University nor
+    the names of its contributors may be used to endorse
+    or promote products derived from this software without
+    specific prior written permission.
+    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
+    CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED
+    WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+    WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
+    PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
+    THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY
+    DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+    CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+    PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
+    USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+    HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER
+    IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+    NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
+    USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+    POSSIBILITY OF SUCH DAMAGE.
+*/
+
+#define CENTRAL_RANGE 0.7
+/*! \brief inverse gauss error function */
+struct erfinv : public mxnet_op::tunable {
+  template<typename DType>
+  MSHADOW_XINLINE static DType Map(DType v) {
+    /* Function to calculate inverse error function.  Rational approximation
+    is used to generate an initial approximation, which is then improved to
+    full accuracy by two steps of Newton's method.  Code is a direct
+    translation of the erfinv m file in matlab version 2.0.
+    Author:  Gary L. Pavlis, Indiana University
+    Date:  February 1996
+    */
+    double y = static_cast<double>(v);
+    double x,z,num,dem; /*working variables */
+    /* coefficients in rational expansion */
+    double a[4]={ 0.886226899, -1.645349621,  0.914624893, -0.140543331};
+    double b[4]={-2.118377725,  1.442710462, -0.329097515,  0.012229801};
+    double c[4]={-1.970840454, -1.624906493,  3.429567803,  1.641345311};
+    double d[2]={ 3.543889200,  1.637067800};
+    if(fabs(y) > 1.0) return DType(atof("NaN"));  /* This needs IEEE constant*/
+    if(fabs(y) == 1.0) return DType((copysign(1.0,y))*atof("INFINITY"));
+    if(fabs(y) <= CENTRAL_RANGE )
+    {
+            z = y*y;
+            num = (((a[3]*z + a[2])*z + a[1])*z + a[0]);
+            dem = ((((b[3]*z + b[2])*z + b[1])*z +b[0])*z + 1.0);
+            x = y*num/dem;
+    }
+    else if( (fabs(y) > CENTRAL_RANGE) && (fabs(y) < 1.0) )
+    {
+            z = sqrt(-log((1.0-fabs(y))/2.0));
+            num = ((c[3]*z + c[2])*z + c[1])*z + c[0];
+            dem = (d[1]*z + d[0])*z + 1.0;
+            x = (copysign(1.0,y))*num/dem;
+    }
+    /* Two steps of Newton-Raphson correction */
+    x = x - (erf(x) - y)/( (2.0/sqrt(M_PI))*exp(-x*x));
+    x = x - (erf(x) - y)/( (2.0/sqrt(M_PI))*exp(-x*x));
+
+    return DType(x);
+  }
+};
+#undef CENTRAL_RANGE
+
+MXNET_UNARY_MATH_OP(erfinv_grad, 0.5 * math::sqrt(PI) * math::exp(math::sqr(mshadow_op::erfinv::Map(a))));
+
 MXNET_UNARY_MATH_OP(erf_grad, 2.0 / math::sqrt(PI) * math::exp(-(a * a)));
 
 MXNET_SIMPLE_UNARY_MATH_OP(erf);

src/operator/operator_tune.cc

@@ -234,9 +234,11 @@ IMPLEMENT_UNARY_WORKLOAD_FWD(mxnet::op::mshadow_op::log2);  // NOLINT()
 IMPLEMENT_UNARY_WORKLOAD_BWD(mxnet::op::mshadow_op::log2_grad);  // NOLINT()
 IMPLEMENT_UNARY_WORKLOAD_FWD(mxnet::op::mshadow_op::log10);  // NOLINT()
 IMPLEMENT_UNARY_WORKLOAD_BWD(mxnet::op::mshadow_op::log10_grad);  // NOLINT()
-IMPLEMENT_UNARY_WORKLOAD_FWD(mxnet::op::mshadow_op::sin);  // NOLINT()
 IMPLEMENT_UNARY_WORKLOAD_FWD(mxnet::op::mshadow_op::erf);  // NOLINT()
 IMPLEMENT_UNARY_WORKLOAD_BWD(mxnet::op::mshadow_op::erf_grad);  // NOLINT()
+IMPLEMENT_UNARY_WORKLOAD_FWD(mxnet::op::mshadow_op::erfinv);  // NOLINT()
+IMPLEMENT_UNARY_WORKLOAD_BWD(mxnet::op::mshadow_op::erfinv_grad);  // NOLINT()
+IMPLEMENT_UNARY_WORKLOAD_FWD(mxnet::op::mshadow_op::sin);  // NOLINT()
 IMPLEMENT_UNARY_WORKLOAD_BWD(mxnet::op::mshadow_op::sin_grad);  // NOLINT()
 IMPLEMENT_UNARY_WORKLOAD_FWD(mxnet::op::mshadow_op::sinh);  // NOLINT()
 IMPLEMENT_UNARY_WORKLOAD_BWD(mxnet::op::mshadow_op::sinh_grad);  // NOLINT()

src/operator/tensor/elemwise_unary_op_basic.cc

@@ -916,6 +916,22 @@ MXNET_OPERATOR_REGISTER_BINARY(_backward_erf)
 .set_attr<FCompute>("FCompute<cpu>",
                     ElemwiseBinaryOp::Compute<cpu, unary_bwd<mshadow_op::erf_grad>>);
 
+// erfinv
+MXNET_OPERATOR_REGISTER_UNARY(erfinv)
+.describe(R"code(Returns element-wise inverse gauss error function of the input.
+
+Example::
+
+   erfinv([0, 0.5., -1.]) = [0., 0.4769, -inf]
+
+)code" ADD_FILELINE)
+.set_attr<FCompute>("FCompute<cpu>", UnaryOp::Compute<cpu, mshadow_op::erfinv>)
+.set_attr<nnvm::FGradient>("FGradient", ElemwiseGradUseIn{"_backward_erfinv"});
+
+MXNET_OPERATOR_REGISTER_BINARY(_backward_erfinv)
+.set_attr<FCompute>("FCompute<cpu>",
+                    ElemwiseBinaryOp::Compute<cpu, unary_bwd<mshadow_op::erfinv_grad>>);
+
 // rcbrt
 MXNET_OPERATOR_REGISTER_UNARY(rcbrt)
 .describe(R"code(Returns element-wise inverse cube-root value of the input.

src/operator/tensor/elemwise_unary_op_basic.cu

@@ -62,6 +62,14 @@ NNVM_REGISTER_OP(_backward_erf)
 .set_attr<FCompute>("FCompute<gpu>",
                     ElemwiseBinaryOp::Compute<gpu, unary_bwd<mshadow_op::erf_grad>>);
 
+// erfinv
+NNVM_REGISTER_OP(erfinv)
+.set_attr<FCompute>("FCompute<gpu>", UnaryOp::Compute<gpu, mshadow_op::erfinv>);
+
+NNVM_REGISTER_OP(_backward_erfinv)
+.set_attr<FCompute>("FCompute<gpu>",
+                    ElemwiseBinaryOp::Compute<gpu, unary_bwd<mshadow_op::erfinv_grad>>);
+
 // copy
 NNVM_REGISTER_OP(_copy)
 .set_attr<FCompute>("FCompute<gpu>", UnaryOp::IdentityCompute<gpu>)

tests/python/unittest/test_operator.py

@@ -3500,7 +3500,11 @@ def test_special_functions_using_scipy():
 
     # erf
     mathematical_core("erf", lambda x: mx.sym.erf(x), lambda x: scipy_special.erf(x),
-                     lambda x: 2.0 / math.sqrt(math.pi) * math.exp(-(x ** 2)), 0.5, 0.5)
+                     lambda x: 2.0 / math.sqrt(math.pi) * np.exp(-(x ** 2)), 0.5, 0.5)
+
+    # erfinv
+    mathematical_core("erfinv", lambda x: mx.sym.erfinv(x), lambda x: scipy_special.erfinv(x),
+                     lambda x: 0.5 * math.sqrt(math.pi) * np.exp(scipy_special.erfinv(x) ** 2), 0.5, 0.5)
 
 
 def rounding(name, forward_mxnet_call, forward_numpy_call, data_init=5., grad_init=2.):