import theano
from theano import tensor, scalar
import numpy

############
#
# SCALAR OPS
#

class ScalarSigmoid(scalar.UnaryScalarOp):
    @staticmethod
    def st_impl(x):
        if x < -30.0:
            return 0.0
        if x > 30.0:
            return 1.0 
        return 1.0 / (1.0 + numpy.exp(-x))
    def impl(self, x):
        return ScalarSigmoid.st_impl(x)
    def grad(self, (x,), (gz,)):
        y = scalar_sigmoid(x)
        return [gz * y * (1.0 - y)]
    def c_code(self, node, name, (x,), (z,), sub):
        if node.inputs[0].type in [scalar.float32, scalar.float64]:
            return """%(z)s =
                %(x)s < -30.0 
                ? 0.0 
                : %(x)s > 30.0 
                   ? 1.0
                   : 1.0 /(1.0+exp(-%(x)s));""" % locals()
        raise NotImplementedError('only floatingpoint is implemented')
scalar_sigmoid = ScalarSigmoid(scalar.upgrade_to_float, name='scalar_sigmoid')
sigmoid = tensor.Elemwise(scalar_sigmoid, name='sigmoid')

class ScalarSoftplus(scalar.UnaryScalarOp):
    @staticmethod
    def static_impl(x):
        if x < -30.0:
            return 0.0
        if x > 30.0:
            return x
        return numpy.log1p(numpy.exp(x))
    def impl(self, x):
        return ScalarSoftplus.static_impl(x)
    def grad(self, (x,), (gz,)):
        return [gz * scalar_sigmoid(x)]
    def c_code(self, node, name, (x,), (z,), sub):
        if node.inputs[0].type in [scalar.float32, scalar.float64]:
            return """%(z)s =
                %(x)s < -30.0 
                ? 0.0 
                : %(x)s > 30.0 
                   ? %(x)s
                   : log1p(exp(%(x)s));""" % locals()
        raise NotImplementedError('only floating point x is implemented')
scalar_softplus = ScalarSoftplus(scalar.upgrade_to_float, name='scalar_softplus')
softplus = tensor.Elemwise(scalar_softplus, name='softplus')


############
#
# TENSOR OPS
#

class CrossentropySoftmax1HotWithBias(theano.Op):
    """A special compound L{Op} for the output of neural-net classifiers.

    @type x: is a matrix of floats (32 or 64)
    @type b: is a [row] vector of floats (32 or 64), length is number of cols in x
    @type y_idx: a [column] vector of int (32 or 64), length is number of rows in x

    @precondition: every entry in y_idx is a valid (non-negative) column index into x

    This L{Op} has two outputs:
     - KL(softmax(x+b), y)
     - softmax(x+b)

    
    softmax(x[i]) is the i'th distribution over len(x[i]) options

    y_idx[i] is an integer index, encoding a 1-hot distribution. 
    
    In practice, when we're trying to do classification, we have one row in x
    and y_idx per example, and y[i] is the index of the (correct) class of the
    i'th example.

    """
    nin=3
    nout=2
    def __init__(self, **kwargs):
        theano.Op.__init__(self, **kwargs)

    def make_node(self, x, b, y_idx):
        x = tensor.as_tensor(x)
        b = tensor.as_tensor(b)
        y_idx = tensor.as_tensor(y_idx)
        if x.type.ndim != 2 \
                or x.type.dtype not in ['float32', 'float64']:
            raise ValueError('x must be 2-d tensor of floats')
        if b.type.ndim != 1 \
                or x.type.dtype not in ['float32', 'float64']:
            raise ValueError('b must be 1-d tensor of floats')
        if y_idx.type.ndim != 1 \
                or y_idx.type.dtype not in ['int8', 'int16', 'int32', 'int64']:
            raise ValueError('y_idx must be 1-d tensor of ints')

#       TODO: Is this correct? It used to be y, not y_idx
        nll = tensor.Tensor(x.type.dtype, 
                y_idx.type.broadcastable).make_result()
#        nll = Tensor(x.dtype, y.broadcastable)
        sm = x.type.make_result()
        return theano.Apply(self, [x, b, y_idx], [nll, sm])
    def perform(self, node, input_storage, output_storage):
        x, b, y_idx = input_storage
        if b.shape[0] != x.shape[1]:
            raise ValueError('b must have same number of columns as x')
        if y_idx.shape[0] != x.shape[0]:
            raise ValueError('y_idx must have same number of rows as x')

        sm = numpy.zeros_like(x) # softmax
        nll = numpy.zeros(x.shape[0]) #nll(y | softmax(x))
        for i in xrange(sm.shape[0]):
            row = x[i] + b
            sm[i] = numpy.exp(row - numpy.max(row)) #softmax
            sm[i] *= 1.0 / numpy.sum(sm[i]) #vector scale
            nll[i] = -numpy.log( sm[i, y_idx[i]]) #cross-entropy
        output_storage[0][0] = nll
        output_storage[1][0] = sm
    def grad(self, (x, b, y_idx), (g_nll, g_sm)):
        if g_sm is not None:
            raise NotImplementedError()
        nll, sm = crossentropy_softmax_1hot_with_bias(x, b, y_idx)
        dx = CrossentropySoftmax1HotWithBiasDx()(g_nll, sm, y_idx)
        db = tensor.sum(dx, axis = [0])
        return dx, db, None

    def c_headers(self): return ['<iostream>']
    def c_code(self, node, name, (x, b, y_idx), (nll, sm), sub):
        # this implementation was lifted from
        # /u/bergstrj/cvs/bergstrj/src/feb07/nn.cxx

        #TODO: put this into a templated function, in the support code
        #TODO: declare the max of each row as an Op output

        #TODO: set error messages for failures in this code

        #TODO: use this to accept float32 and int32: node.inputs[0].type.dtype_specs()[1]
        y_idx_type = node.inputs[2].type.dtype_specs()[1]

        return """
        npy_intp* Nx = %(x)s->dimensions;

        if (%(x)s->nd != 2)
        {
            PyErr_SetString(PyExc_ValueError, "a not 2d tensor");
            %(fail)s;
        }
        if (%(b)s->nd != 1)
        {
            PyErr_SetString(PyExc_ValueError, "b not 1d tensor");
            %(fail)s;
        }
        if (%(y_idx)s->nd != 1)
        {
            PyErr_SetString(PyExc_ValueError, "y_idx not 1d tensor");
            %(fail)s;
        }
        if (%(x)s->descr->type_num != PyArray_DOUBLE)
        {
            PyErr_SetString(PyExc_TypeError, "a not float64");
            %(fail)s;
        }
        if (%(b)s->descr->type_num != PyArray_DOUBLE)
        {
            PyErr_SetString(PyExc_TypeError, "b not float64");
            %(fail)s;
        }
        if ((%(y_idx)s->descr->type_num != PyArray_INT64)
            && (%(y_idx)s->descr->type_num != PyArray_INT32)
            && (%(y_idx)s->descr->type_num != PyArray_INT16)
            && (%(y_idx)s->descr->type_num != PyArray_INT8))
        {
            PyErr_SetString(PyExc_TypeError, "y_idx not int8, int16, int32, or int64");
            %(fail)s;
        }
        if ((%(x)s->dimensions[1] != %(b)s->dimensions[0])
         || (%(x)s->dimensions[0] != %(y_idx)s->dimensions[0]))
        {
            PyErr_SetString(PyExc_ValueError, "dimension mismatch in arguments");
            %(fail)s;
        }

        if ((NULL == %(nll)s) //initial condition
            || (%(nll)s->dimensions[0] != %(y_idx)s->dimensions[0]))
        {
            if (NULL != %(nll)s) Py_XDECREF(%(nll)s);
            %(nll)s = (PyArrayObject*)PyArray_SimpleNew(1, PyArray_DIMS(%(y_idx)s), type_num_%(x)s);
            if(!%(nll)s)
            {
                PyErr_SetString(PyExc_MemoryError, "failed to alloc nll output");
                %(fail)s;
            }
        }
        if ((NULL == %(sm)s)
            || (%(sm)s->dimensions[0] != %(x)s->dimensions[0])
            || (%(sm)s->dimensions[1] != %(x)s->dimensions[1]))
        {
            if (NULL != %(sm)s) Py_XDECREF(%(sm)s);
            %(sm)s = (PyArrayObject*)PyArray_SimpleNew(2, PyArray_DIMS(%(x)s), type_num_%(x)s);
            if(!%(sm)s) {
                // The normal cleanup code will take care of %(nll)s
                // Py_XDECREF(%(nll)s); %(nll)s=NULL;
                PyErr_SetString(PyExc_MemoryError, "failed to alloc sm output");
                %(fail)s
            }
        }

        for (size_t i = 0; i < Nx[0]; ++i)
        {
            size_t j;
            double sum = 0.0;
            bool  discount_max = false;

            const double* __restrict__ x_i = (double*)(%(x)s->data + %(x)s->strides[0] * i);
            const double* __restrict__ b_i = (double*)(%(b)s->data);
            const %(y_idx_type)s y_i = ((%(y_idx_type)s*)(%(y_idx)s->data + %(y_idx)s->strides[0] * i))[0];
            double* __restrict__ sm_i = (double*)(%(sm)s->data + %(sm)s->strides[0] * i);
            double* __restrict__ nll_i = (double*)(%(nll)s->data + %(nll)s->strides[0] * i);

            npy_intp Sx = %(x)s->strides[1]/sizeof(double);
            npy_intp Sb = %(b)s->strides[0]/sizeof(double);
            npy_intp Ssm = %(sm)s->strides[1]/sizeof(double);

            size_t row_max_j=0;
            double row_max = x_i[0] + b_i[0];
            //try to compute sum and sm the easy way
            for (j = 0; j < Nx[1]; ++j)
            {
                double row_ij = x_i[j * Sx] +  b_i[j * Sb];
                row_max_j = (row_ij > row_max) ? j : row_max_j;
                row_max   = (row_ij > row_max) ? row_ij : row_max;

                double sm_ij = exp(row_ij);
                sum += sm_ij;
                sm_i[j * Ssm] = sm_ij;
            }
            if ((0.0 == sum) || (isinf(sum))) 
            {
                //our cheap trick didn't work... try again and do it better.
                discount_max = true;
                sum = 0.0; //reset sum and recompute....
                for (j = 0; j < Nx[1]; ++j)
                {
                    double row_ij = x_i[j * Sx] +  b_i[j * Sb];

                    double sm_ij = exp(row_ij - row_max);
                    sum += sm_ij;
                    sm_i[j * Ssm] = sm_ij;
                }
                if ( (0.0 == sum) || (isinf(sum)))
                { 
                    //that was our best... 
                    %(fail)s;
                }
                //if we still can't sum it up, we're screwed.
                //So far, this assertion has never failed...
            }

            //cblas_dscal(x.N, 1.0 / sum, &mat_at(s,i,0), s.n);
            double sum_inv = 1.0 / sum;
            for (j = 0; j < Nx[1]; ++j)
            {
                sm_i[j * Ssm] *= sum_inv;
            }

            if (y_i >= Nx[1])
            {
                %(fail)s;
            }

            nll_i[0] = - x_i[y_i*Sx] 
                       - b_i[y_i*Sb]
                       + (discount_max ? row_max : 0.0)
                       + log(sum);
              //mat_at(y,i,0) = -log( mat_at(s,i,t[i]));  //less accurate?
              //mat_at(y,i,0) =  - mat_at(x,i,t[i]) - mat_at(b,0,t[i]) + (discount_max ? maxi : 0.0) + log(sum);
        }
        """ % dict(locals(), **sub)
crossentropy_softmax_1hot_with_bias = CrossentropySoftmax1HotWithBias()

class CrossentropySoftmax1HotWithBiasDx (theano.Op):
    nin=3
    nout=1
    """Gradient wrt x of the CrossentropySoftmax1Hot Op"""
    def __init__(self, **kwargs):
        theano.Op.__init__(self,**kwargs)
    def make_node(self, dy, sm, y_idx,**kwargs):
        dy = tensor.as_tensor(dy)
        sm = tensor.as_tensor(sm)
        y_idx = tensor.as_tensor(y_idx)
        return theano.Apply(self, [dy, sm, y_idx],[sm.type.make_result()])
    def perform(self, node, input_storage, output_storage):
        dy,sm,y_idx = input_storage
        dx = numpy.zeros_like(sm)
        for i in xrange(sm.shape[0]):
            dx[i] = dy[i] * sm[i] #vector scale
            dx[i, y_idx[i]] -= dy[i] #scalar decrement
        output_storage[0][0] = dx
    def grad(self, *args):
        raise NotImplementedError()
    def c_code(self, node, name, (dnll, sm, y_idx), (dx,), sub):
        y_idx_type = node.inputs[2].type.dtype_specs()[1]
        return """

        if ((%(dnll)s->descr->type_num != PyArray_DOUBLE)
            || (%(sm)s->descr->type_num != PyArray_DOUBLE)
            )
        {
            PyErr_SetString(PyExc_TypeError, "types should be float64, float64, int64");
            %(fail)s;
        }
        if ((%(y_idx)s->descr->type_num != PyArray_INT64)
            && (%(y_idx)s->descr->type_num != PyArray_INT32)
            && (%(y_idx)s->descr->type_num != PyArray_INT16)
            && (%(y_idx)s->descr->type_num != PyArray_INT8))
        {
            PyErr_SetString(PyExc_TypeError, "y_idx not int8, int16, int32, or int64");
            %(fail)s;
        }
        if ((%(dnll)s->nd != 1)
            || (%(sm)s->nd != 2)
            || (%(y_idx)s->nd != 1))
        {
            PyErr_SetString(PyExc_ValueError, "rank error");
            %(fail)s;
        }
        if ((%(dnll)s->dimensions[0] != %(sm)s->dimensions[0])
            || (%(dnll)s->dimensions[0] != %(y_idx)s->dimensions[0]))
        {
            PyErr_SetString(PyExc_ValueError, "dimension mismatch");
            %(fail)s;
        }
        if ((NULL == %(dx)s)
            || (%(dx)s->dimensions[0] != %(sm)s->dimensions[0])
            || (%(dx)s->dimensions[1] != %(sm)s->dimensions[1]))
        {
            if (NULL != %(dx)s) Py_XDECREF(%(dx)s);
            %(dx)s = (PyArrayObject*)PyArray_SimpleNew(2, PyArray_DIMS(%(sm)s), type_num_%(sm)s);
            if(!%(dx)s) {
                PyErr_SetString(PyExc_MemoryError, "failed to alloc dx output");
                %(fail)s
            }
        }

        for (size_t i = 0; i < %(dx)s->dimensions[0]; ++i)
        {
            const double dnll_i = ((double*)(%(dnll)s->data + %(dnll)s->strides[0] * i))[0];

            const %(y_idx_type)s y_i = ((%(y_idx_type)s*)(%(y_idx)s->data + %(y_idx)s->strides[0] * i))[0];

            const double* __restrict__ sm_i = (double*)(%(sm)s->data + %(sm)s->strides[0] * i);
            npy_intp Ssm = %(sm)s->strides[1]/sizeof(double);

            double* __restrict__ dx_i = (double*)(%(dx)s->data + %(dx)s->strides[0] * i);
            npy_intp Sdx = %(dx)s->strides[1]/sizeof(double);

            for (size_t j = 0; j < %(dx)s->dimensions[1]; ++j)
            {
                dx_i[j * Sdx] = dnll_i * sm_i[j * Ssm];
            }
            if (y_i >= %(dx)s->dimensions[1])
            {
                %(fail)s;
            }
            dx_i[y_i * Sdx] -= dnll_i;
        }
        """ % dict(locals(), **sub)

def crossentropy_softmax_1hot(x, y_idx, **kwargs):
    b = tensor.zeros_like(x[0,:])
    return crossentropy_softmax_1hot_with_bias(x, b, y_idx, **kwargs)

def binary_crossentropy(output, target):
    """
    Compute the crossentropy of binary output wrt binary target.
    @note: We do not sum, crossentropy is computed by component.
    @todo: Rewrite as a scalar, and then broadcast to tensor.
    """
    return -(target * tensor.log(output) + (1 - target) * tensor.log(1 - output))