R1DL_Spark.py

import argparse
import functools
import numpy as np
import os.path
import scipy.linalg as sla
import sys
import datetime
import os
import psutil

from pyspark import SparkContext, SparkConf
from pyspark.mllib.linalg import SparseVector

###################################
# Utility functions
###################################

def select_topr(vct_input, r):
    """
    Returns the R-th greatest elements indices
    in input vector and store them in idxs_n.
    """
    temp = np.argpartition(-vct_input, r)
    idxs_n = temp[:r]
    return idxs_n

def input_to_rowmatrix(raw_rdd, norm):
    """
    Utility function for reading the matrix data
    """
    # Parse each line of the input into a numpy array of floats. This requires
    # several steps.
    #  1: Split each string into a list of strings.
    #  2: Convert each string to a float.
    #  3: Convert each list to a numpy array.
    p_and_n = functools.partial(parse_and_normalize, norm = norm)
    numpy_rdd = raw_rdd \
        .zipWithIndex() \
        .map(lambda x: (x[1], p_and_n(x[0])))
    return numpy_rdd

###################################
# Spark helper functions
###################################

def parse_and_normalize(line, norm):
    """
    Utility function. Parses a line of text into a floating point array, then
    whitens the array.
    """
    x = np.array([float(c) for c in line.strip().split()])
    if norm:
        x -= x.mean()  # 0-mean.
        x /= sla.norm(x)  # Unit norm.
    return x

def vector_matrix(row):
    """
    Applies u * S by row-wise multiplication, followed by a reduction on
    each column into a single vector.
    """
    row_index, vector = row     # Split up the [key, value] pair.
    u = _U_.value       # Extract the broadcasted vector "u".

    # This means we're in the first iteration and we just want a random
    # vector. To ensure all the workers generate the same random vector,
    # we have to seed the RNG identically.
    if type(u) == tuple:
        T, seed = u
        np.random.seed(seed)
        u = np.random.random(T)
        u -= u.mean()
        u /= sla.norm(u)
    u = u[row_index]

    # Generate a list of [key, value] output pairs, one for each nonzero
    # element of vector.
    out = []
    for i in range(vector.shape[0]):
        out.append([i, u * vector[i]])
    return out

def matrix_vector(row):
    """
    Applies S * v by row-wise multiplication. No reduction needed, as all the
    summations are performed within this very function.
    """
    k, row = row  # Extract the broadcast variables.
    v = _V_.value

    # Perform the multiplication using the specified indices in both arrays.
    innerprod = np.dot(row[v.indices], v.values)

    # That's it! Return the [row, inner product] tuple.
    return [k, innerprod]

def deflate(row):
    """
    Deflates the data matrix by subtracting off the outer product of the
    broadcasted vectors and returning the modified row.
    """
    k, vector = row
    # It's important to keep order of operations in mind: we are computing
    # (and subtracting from S) the outer product of u * v. As we are operating
    # on a row-distributed matrix, we therefore will only iterate over the
    # elements of v, and use the single element of u that corresponds to the
    # index of the current row of S.
    # Got all that? Good! Explain it to me.
    u, v = _U_.value, _V_.value
    vector[v.indices] -= (u[k] * v.values)
    return [k, vector]

if __name__ == "__main__":
    parser = argparse.ArgumentParser(description = 'PySpark Dictionary Learning',
        add_help = 'How to use', prog = 'python R1DL_Spark.py <args>')

    # Inputs.
    parser.add_argument("-i", "--input", required = True,
        help = "Input file containing the matrix S.")
    parser.add_argument("-T", "--rows", type = int, required = True,
        help = "Number of rows (observations) in the input matrix S.")
    parser.add_argument("-P", "--cols", type = int, required = True,
        help = "Number of columns (features) in the input matrix S.")

    # Optional.
    parser.add_argument("-r", "--pnonzero", type = float, default = 0.07,
        help = "Percentage of non-zero elements. [DEFAULT: 0.07]")
    parser.add_argument("-m", "--dictatoms", type = int, default = 5,
        help = "Number of the dictionary atoms. [DEFAULT: 5]")
    parser.add_argument("-e", "--epsilon", type = float, default = 0.01,
        help = "The convergence criteria in the ALS step. [DEFAULT: 0.01]")
    parser.add_argument("--normalize", action = "store_true",
        help = "If set, normalizes input data.")
    parser.add_argument("--debug", action = "store_true",
        help = "If set, turns out debug output.")

    # Spark options.
    parser.add_argument("--partitions", type = int, default = None,
        help = "Number of RDD partitions to use. [DEFAULT: 4 * CPUs]")
    parser.add_argument("--execmem", default = "8g",
        help = "Amount of memory for each executor. [DEFAULT: 8g]")

    # Outputs.
    parser.add_argument("-d", "--dictionary", required = True,
        help = "Output path to dictionary file.(file_D)")
    parser.add_argument("-o", "--output", required = True,
        help = "Output path to z matrix.(file_z)")
    parser.add_argument("--prefix", required = True,
        help = "Prefix strings to the output files")

    args = vars(parser.parse_args())

    if args['debug']: print(datetime.datetime.now())

    # Initialize the SparkContext. This is where you can create RDDs,
    # the Spark abstraction for distributed data sets.
    conf = SparkConf()
    conf.set("spark.executor.memory", args['execmem'])
    sc = SparkContext(conf = conf)
    partitions = args['partitions'] if args['partitions'] is not None else (4 * sc.defaultParallelism)

    # Read the data and convert it into a thunder RowMatrix.
    raw_rdd = sc.textFile(args['input'], minPartitions = partitions)
    S = input_to_rowmatrix(raw_rdd, args['normalize'])
    S.cache()

    ##################################################################
    # Here's where the real fun begins.
    #
    # First, we're going to initialize some variables we'll need for the
    # following operations. Next, we'll start the optimization loops. Finally,
    # we'll perform the stepping and deflation operations until convergence.
    #
    # Sound like fun?
    ##################################################################

    T = args['rows']
    P = args['cols']

    epsilon = args['epsilon']       # convergence stopping criterion
    M = args['dictatoms']            # dimensionality of the learned dictionary
    R = args['pnonzero'] * P        # enforces sparsity
    u_new = np.zeros(T)             # atom updates at each iteration
    v = np.zeros(P)

    max_iterations = P * 10
    file_D = os.path.join(args['dictionary'], "{}_D.txt".format(args["prefix"]))
    file_z = os.path.join(args['output'], "{}_z.txt".format(args["prefix"]))

    # Start the loop!
    for m in range(M):
        # In lieu of generating a dense random vector and broadcasting it, we
        # instead compute a random seed. Randomly, of course.
        seed = np.random.randint(max_iterations + 1, high = 4294967295)
        np.random.seed(seed)
        u_old = np.random.random(T)
        num_iterations = 0
        delta = 2 * epsilon

        # Start the inner loop: this learns a single atom.
        while num_iterations < max_iterations and delta > epsilon:
            # P2: Vector-matrix multiplication step. Computes v.
            _U_ = sc.broadcast(u_old) if num_iterations > 0 else sc.broadcast((T, seed))
            v = S \
                .flatMap(vector_matrix) \
                .reduceByKey(lambda x, y: x + y) \
                .collect()
            v = np.take(sorted(v), indices = 1, axis = 1)

            # Use our previous method to select the top R.
            indices = np.sort(select_topr(v, R))
            sv = SparseVector(P, indices, v[indices])

            # Broadcast the sparse vector.
            _V_ = sc.broadcast(sv)

            # P1: Matrix-vector multiplication step. Computes u.
            u_new = S \
                .map(matrix_vector) \
                .collect()
            u_new = np.take(sorted(u_new), indices = 1, axis = 1)

            # Subtract off the mean and normalize.
            u_new -= u_new.mean()
            u_new /= sla.norm(u_new)

            # Update for the next iteration.
            delta = sla.norm(u_old - u_new)
            u_old = u_new
            num_iterations += 1

        # Save the newly-computed u and v to the output files;
        with open(file_D, "a+") as fD:
            np.savetxt(fD, u_new, fmt = "%.6f", newline = " ")
            fD.write("\n")
        with open(file_z, "a+") as fz:
            np.savetxt(fz, sv.toArray(), fmt = "%.6f", newline = " ")
            fz.write("\n")

        # P4: Deflation step. Update the primary data matrix S.
        _U_ = sc.broadcast(u_new)
        _V_ = sc.broadcast(sv)

        if args['debug']: print(m)

        S = S.map(deflate).reduceByKey(lambda x, y: x + y)
        S.cache()

    if args['debug']: print(datetime.datetime.now())
    process = psutil.Process(os.getpid())
    print(process.memory_info().rss)