/*
    * Licensed to the Apache Software Foundation (ASF) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * The ASF licenses this file to You under the Apache License, Version 2.0
    * (the "License"); you may not use this file except in compliance with
    * the License.  You may obtain a copy of the License at
    *
    *      https://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  
  /*
   * This is not the original file distributed by the Apache Software Foundation
   * It has been modified by the Hipparchus project
   */
  package org.hipparchus.exception;
  
  import java.util.Locale;
  import java.util.MissingResourceException;
  import java.util.ResourceBundle;
  
  /**
   * Enumeration for localized messages formats used in exceptions messages.
   * <p>
   * The constants in this enumeration represent the available
   * formats as localized strings. These formats are intended to be
   * localized using simple properties files, using the constant
   * name as the key and the property value as the message format.
   * The source English format is provided in the constants themselves
   * to serve both as a reminder for developers to understand the parameters
   * needed by each format, as a basis for translators to create
   * localized properties files, and as a default format if some
   * translation is missing.
   * </p>
   */
  public enum LocalizedCoreFormats implements Localizable {
  
      /** ARRAY_SIZE_EXCEEDS_MAX_VARIABLES. */
      ARRAY_SIZE_EXCEEDS_MAX_VARIABLES("array size cannot be greater than {0}"),
  
      /** ARRAY_SIZES_SHOULD_HAVE_DIFFERENCE_1. */
      ARRAY_SIZES_SHOULD_HAVE_DIFFERENCE_1("array sizes should have difference 1 ({0} != {1} + 1)"),
  
      /** ARRAY_SUMS_TO_ZERO. */
      ARRAY_SUMS_TO_ZERO("array sums to zero"),
  
      /** AT_LEAST_ONE_COLUMN. */
      AT_LEAST_ONE_COLUMN("matrix must have at least one column"),
  
      /** AT_LEAST_ONE_ROW. */
      AT_LEAST_ONE_ROW("matrix must have at least one row"),
  
      /** BANDWIDTH. */
      BANDWIDTH("bandwidth ({0})"),
  
      /** BESSEL_FUNCTION_BAD_ARGUMENT. */
      BESSEL_FUNCTION_BAD_ARGUMENT("Bessel function of order {0} cannot be computed for x = {1}"),
  
      /** BESSEL_FUNCTION_FAILED_CONVERGENCE. */
      BESSEL_FUNCTION_FAILED_CONVERGENCE("Bessel function of order {0} failed to converge for x = {1}"),
  
      /** BINOMIAL_INVALID_PARAMETERS_ORDER. */
      BINOMIAL_INVALID_PARAMETERS_ORDER("must have n >= k for binomial coefficient (n, k), got k = {0}, n = {1}"),
  
      /** BINOMIAL_NEGATIVE_PARAMETER. */
      BINOMIAL_NEGATIVE_PARAMETER("must have n >= 0 for binomial coefficient (n, k), got n = {0}"),
  
      /** CANNOT_COMPUTE_0TH_ROOT_OF_UNITY. */
      CANNOT_COMPUTE_0TH_ROOT_OF_UNITY("cannot compute 0-th root of unity, indefinite result"),
  
      /** CANNOT_COMPUTE_BETA_DENSITY_AT_0_FOR_SOME_ALPHA. */
      CANNOT_COMPUTE_BETA_DENSITY_AT_0_FOR_SOME_ALPHA("cannot compute beta density at 0 when alpha = {0,number}"),
  
      /** CANNOT_COMPUTE_BETA_DENSITY_AT_1_FOR_SOME_BETA. */
      CANNOT_COMPUTE_BETA_DENSITY_AT_1_FOR_SOME_BETA("cannot compute beta density at 1 when beta = %.3g"),
  
      /** CANNOT_COMPUTE_NTH_ROOT_FOR_NEGATIVE_N. */
      CANNOT_COMPUTE_NTH_ROOT_FOR_NEGATIVE_N("cannot compute nth root for null or negative n: {0}"),
  
      /** CANNOT_DISCARD_NEGATIVE_NUMBER_OF_ELEMENTS. */
      CANNOT_DISCARD_NEGATIVE_NUMBER_OF_ELEMENTS("cannot discard a negative number of elements ({0})"),
  
      /** CANNOT_FORMAT_INSTANCE_AS_COMPLEX. */
      CANNOT_FORMAT_INSTANCE_AS_COMPLEX("cannot format a {0} instance as a complex number"),
  
      /** CANNOT_FORMAT_OBJECT_TO_FRACTION. */
      CANNOT_FORMAT_OBJECT_TO_FRACTION("cannot format given object as a fraction number"),
  
      /** CANNOT_SUBSTITUTE_ELEMENT_FROM_EMPTY_ARRAY. */
      CANNOT_SUBSTITUTE_ELEMENT_FROM_EMPTY_ARRAY("cannot substitute an element from an empty array"),
  
      /** COLUMN_INDEX. */
      COLUMN_INDEX("column index ({0})"), /* keep */
 
     /** COMPLEX_CANNOT_BE_CONSIDERED_A_REAL_NUMBER. */
     COMPLEX_CANNOT_BE_CONSIDERED_A_REAL_NUMBER("complex number ({0},{1}) cannot be considered to be a real number"),
 
     /** CONSTRAINT. */
     CONSTRAINT("constraint"), /* keep */
 
     /** CONTINUED_FRACTION_INFINITY_DIVERGENCE. */
     CONTINUED_FRACTION_INFINITY_DIVERGENCE("Continued fraction convergents diverged to +/- infinity for value {0}"),
 
     /** CONTINUED_FRACTION_NAN_DIVERGENCE. */
     CONTINUED_FRACTION_NAN_DIVERGENCE("Continued fraction diverged to NaN for value {0}"),
 
     /** CONTRACTION_CRITERIA_SMALLER_THAN_EXPANSION_FACTOR. */
     CONTRACTION_CRITERIA_SMALLER_THAN_EXPANSION_FACTOR("contraction criteria ({0}) smaller than the expansion factor ({1}).  This would lead to a never ending loop of expansion and contraction as a newly expanded internal storage array would immediately satisfy the criteria for contraction."),
 
     /** CONTRACTION_CRITERIA_SMALLER_THAN_ONE. */
     CONTRACTION_CRITERIA_SMALLER_THAN_ONE("contraction criteria smaller than one ({0}).  This would lead to a never ending loop of expansion and contraction as an internal storage array length equal to the number of elements would satisfy the contraction criteria."),
 
     /** CONVERGENCE_FAILED. */
     CONVERGENCE_FAILED("convergence failed"), /* keep */
 
     /** CUMULATIVE_PROBABILITY_RETURNED_NAN. */
     CUMULATIVE_PROBABILITY_RETURNED_NAN("Cumulative probability function returned NaN for argument {0} p = {1}"),
 
     /** DERIVATION_ORDER_NOT_ALLOWED. */
     DERIVATION_ORDER_NOT_ALLOWED("derivation order {0} is not allowed here"),
 
     /** DIFFERENT_ROWS_LENGTHS. */
     DIFFERENT_ROWS_LENGTHS("some rows have length {0} while others have length {1}"),
 
     /** DIGEST_NOT_INITIALIZED. */
     DIGEST_NOT_INITIALIZED("digest not initialized"),
 
     /** DIMENSIONS_MISMATCH_2x2. */
     DIMENSIONS_MISMATCH_2x2("got {0}x{1} but expected {2}x{3}"), /* keep */
 
     /** DIMENSIONS_MISMATCH. */
     DIMENSIONS_MISMATCH("inconsistent dimensions: {0} != {1}"), /* keep */
 
     /** DISCRETE_CUMULATIVE_PROBABILITY_RETURNED_NAN. */
     DISCRETE_CUMULATIVE_PROBABILITY_RETURNED_NAN("Discrete cumulative probability function returned NaN for argument {0}"),
 
     /** DISTRIBUTION_NOT_LOADED. */
     DISTRIBUTION_NOT_LOADED("distribution not loaded"),
 
     /** DUPLICATED_ABSCISSA_DIVISION_BY_ZERO. */
     DUPLICATED_ABSCISSA_DIVISION_BY_ZERO("duplicated abscissa {0} causes division by zero"),
 
     /** EMPTY_INTERPOLATION_SAMPLE. */
     EMPTY_INTERPOLATION_SAMPLE("sample for interpolation is empty"),
 
     /** EMPTY_POLYNOMIALS_COEFFICIENTS_ARRAY. */
     EMPTY_POLYNOMIALS_COEFFICIENTS_ARRAY("empty polynomials coefficients array"), /* keep */
 
     /** EMPTY_SELECTED_COLUMN_INDEX_ARRAY. */
     EMPTY_SELECTED_COLUMN_INDEX_ARRAY("empty selected column index array"),
 
     /** EMPTY_SELECTED_ROW_INDEX_ARRAY. */
     EMPTY_SELECTED_ROW_INDEX_ARRAY("empty selected row index array"),
 
     /** ENDPOINTS_NOT_AN_INTERVAL. */
     ENDPOINTS_NOT_AN_INTERVAL("endpoints do not specify an interval: [{0}, {1}]"),
 
     /** EVALUATION. */
     EVALUATION("evaluation"), /* keep */
 
     /** EXPANSION_FACTOR_SMALLER_THAN_ONE. */
     EXPANSION_FACTOR_SMALLER_THAN_ONE("expansion factor smaller than one ({0})"),
 
     /** FACTORIAL_NEGATIVE_PARAMETER. */
     FACTORIAL_NEGATIVE_PARAMETER("must have n >= 0 for n!, got n = {0}"),
 
     /** FAILED_BRACKETING. */
     FAILED_BRACKETING("number of iterations={4}, maximum iterations={5}, initial={6}, lower bound={7}, upper bound={8}, final a value={0}, final b value={1}, f(a)={2}, f(b)={3}"),
 
     /** FAILED_DECOMPOSITION. */
     FAILED_DECOMPOSITION("failed decomposition of a {0}x{1} matrix"),
 
     /** FAILED_FRACTION_CONVERSION. */
     FAILED_FRACTION_CONVERSION("Unable to convert {0} to fraction after {1} iterations"),
 
     /** FIRST_COLUMNS_NOT_INITIALIZED_YET. */
     FIRST_COLUMNS_NOT_INITIALIZED_YET("first {0} columns are not initialized yet"),
 
     /** FIRST_ROWS_NOT_INITIALIZED_YET. */
     FIRST_ROWS_NOT_INITIALIZED_YET("first {0} rows are not initialized yet"),
 
     /** FRACTION_CONVERSION_OVERFLOW. */
     FRACTION_CONVERSION_OVERFLOW("Overflow trying to convert {0} to fraction ({1}/{2})"),
 
     /** GCD_OVERFLOW_32_BITS. */
     GCD_OVERFLOW_32_BITS("overflow: gcd({0}, {1}) is 2^31"),
 
     /** GCD_OVERFLOW_64_BITS. */
     GCD_OVERFLOW_64_BITS("overflow: gcd({0}, {1}) is 2^63"),
 
     /** ILL_CONDITIONED_OPERATOR. */
     ILL_CONDITIONED_OPERATOR("condition number {1} is too high "),
 
     /** INDEX_LARGER_THAN_MAX. */
     INDEX_LARGER_THAN_MAX("the index specified: {0} is larger than the current maximal index {1}"),
 
     /** INDEX_NOT_POSITIVE. */
     INDEX_NOT_POSITIVE("index ({0}) is not positive"),
 
     /** INDEX. */
     INDEX("index ({0})"), /* keep */
 
     /** NOT_FINITE_NUMBER. */
     NOT_FINITE_NUMBER("{0} is not a finite number"), /* keep */
 
     /** INFINITE_BOUND. */
     INFINITE_BOUND("interval bounds must be finite"),
 
     /** ARRAY_ELEMENT. */
     ARRAY_ELEMENT("value {0} at index {1}"), /* keep */
 
     /** INFINITE_ARRAY_ELEMENT. */
     INFINITE_ARRAY_ELEMENT("Array contains an infinite element, {0} at index {1}"),
 
     /** INFINITE_VALUE_CONVERSION. */
     INFINITE_VALUE_CONVERSION("cannot convert infinite value"),
 
     /** INITIAL_CAPACITY_NOT_POSITIVE. */
     INITIAL_CAPACITY_NOT_POSITIVE("initial capacity ({0}) is not positive"),
 
     /** INITIAL_COLUMN_AFTER_FINAL_COLUMN. */
     INITIAL_COLUMN_AFTER_FINAL_COLUMN("initial column {1} after final column {0}"),
 
     /** INITIAL_ROW_AFTER_FINAL_ROW. */
     INITIAL_ROW_AFTER_FINAL_ROW("initial row {1} after final row {0}"),
 
     /** INSUFFICIENT_DATA. */
     INSUFFICIENT_DATA("insufficient data"),
 
     /** INSUFFICIENT_DIMENSION. */
     INSUFFICIENT_DIMENSION("insufficient dimension {0}, must be at least {1}"),
 
     /** DIMENSION. */
     DIMENSION("dimension ({0})"), /* keep */
 
     /** INSUFFICIENT_OBSERVED_POINTS_IN_SAMPLE. */
     INSUFFICIENT_OBSERVED_POINTS_IN_SAMPLE("sample contains {0} observed points, at least {1} are required"),
 
     /** INSUFFICIENT_ROWS_AND_COLUMNS. */
     INSUFFICIENT_ROWS_AND_COLUMNS("insufficient data: only {0} rows and {1} columns."),
 
     /** INTERNAL_ERROR. */
     INTERNAL_ERROR("internal error, please fill a bug report at {0}"),
 
     /** INVALID_MAX_ITERATIONS. */
     INVALID_MAX_ITERATIONS("bad value for maximum iterations number: {0}"),
 
     /** ITERATIONS. */
     ITERATIONS("iterations"), /* keep */
 
     /** LCM_OVERFLOW_32_BITS. */
     LCM_OVERFLOW_32_BITS("overflow: lcm({0}, {1}) is 2^31"),
 
     /** LCM_OVERFLOW_64_BITS. */
     LCM_OVERFLOW_64_BITS("overflow: lcm({0}, {1}) is 2^63"),
 
     /** LOWER_BOUND_NOT_BELOW_UPPER_BOUND. */
     LOWER_BOUND_NOT_BELOW_UPPER_BOUND("lower bound ({0}) must be strictly less than upper bound ({1})"), /* keep */
 
     /** LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT. */
     LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT("lower endpoint ({0}) must be less than or equal to upper endpoint ({1})"),
 
     /** EVALUATIONS. */
     EVALUATIONS("evaluations"), /* keep */
 
     /** MAX_COUNT_EXCEEDED. */
     MAX_COUNT_EXCEEDED("maximal count ({0}) exceeded"), /* keep */
 
     /** NAN_ELEMENT_AT_INDEX. */
     NAN_ELEMENT_AT_INDEX("element {0} is NaN"),
 
     /** NAN_VALUE_CONVERSION. */
     NAN_VALUE_CONVERSION("cannot convert NaN value"),
 
     /** NEGATIVE_DEFINITE_MATRIX. */
     NEGATIVE_DEFINITE_MATRIX("negative definite matrix"),
 
     /** NEGATIVE_COMPLEX_MODULE. */
     NEGATIVE_COMPLEX_MODULE("negative complex module {0}"),
 
     /** NEGATIVE_ELEMENT_AT_INDEX. */
     NEGATIVE_ELEMENT_AT_INDEX("element {0} is negative: {1}"),
 
     /** NUMBER_OF_SUCCESSES. */
     NUMBER_OF_SUCCESSES("number of successes ({0})"), /* keep */
 
     /** NUMBER_OF_INTERPOLATION_POINTS. */
     NUMBER_OF_INTERPOLATION_POINTS("number of interpolation points ({0})"), /* keep */
 
     /** NUMBER_OF_TRIALS. */
     NUMBER_OF_TRIALS("number of trials ({0})"),
 
     /** ROBUSTNESS_ITERATIONS. */
     ROBUSTNESS_ITERATIONS("number of robustness iterations ({0})"),
 
     /** START_POSITION. */
     START_POSITION("start position ({0})"), /* keep */
 
     /** NON_CONVERGENT_CONTINUED_FRACTION. */
     NON_CONVERGENT_CONTINUED_FRACTION("Continued fraction convergents failed to converge (in less than {0} iterations) for value {1}"),
 
     /** NON_SQUARE_MATRIX. */
     NON_SQUARE_MATRIX("non square ({0}x{1}) matrix"),
 
     /** NORM. */
     NORM("Norm ({0})"), /* keep */
 
     /** NORMALIZE_INFINITE. */
     NORMALIZE_INFINITE("Cannot normalize to an infinite value"),
 
     /** NORMALIZE_NAN. */
     NORMALIZE_NAN("Cannot normalize to NaN"),
 
     /** NOT_DECREASING_SEQUENCE. */
     NOT_DECREASING_SEQUENCE("points {3} and {2} are not decreasing ({1} < {0})"), /* keep */
 
     /** NOT_ENOUGH_POINTS_IN_SPLINE_PARTITION. */
     NOT_ENOUGH_POINTS_IN_SPLINE_PARTITION("spline partition must have at least {0} points, got {1}"),
 
     /** NOT_INCREASING_SEQUENCE. */
     NOT_INCREASING_SEQUENCE("points {3} and {2} are not increasing ({1} > {0})"), /* keep */
 
     /** NOT_POSITIVE_DEFINITE_MATRIX. */
     NOT_POSITIVE_DEFINITE_MATRIX("not positive definite matrix"), /* keep */
 
     /** NON_POSITIVE_DEFINITE_OPERATOR. */
     NON_POSITIVE_DEFINITE_OPERATOR("non positive definite linear operator"), /* keep */
 
     /** NON_SELF_ADJOINT_OPERATOR. */
     NON_SELF_ADJOINT_OPERATOR("non self-adjoint linear operator"), /* keep */
 
     /** NON_SQUARE_OPERATOR. */
     NON_SQUARE_OPERATOR("non square ({0}x{1}) linear operator"), /* keep */
 
     /** DEGREES_OF_FREEDOM. */
     DEGREES_OF_FREEDOM("degrees of freedom ({0})"), /* keep */
 
     /** NOT_POSITIVE_EXPONENT. */
     NOT_POSITIVE_EXPONENT("invalid exponent {0} (must be positive)"),
 
     /** NUMBER_OF_ELEMENTS_SHOULD_BE_POSITIVE. */
     NUMBER_OF_ELEMENTS_SHOULD_BE_POSITIVE("number of elements should be positive ({0})"),
 
     /** BASE. */
     BASE("base ({0})"), /* keep */
 
     /** EXPONENT. */
     EXPONENT("exponent ({0})"), /* keep */
 
     /** LENGTH. */
     LENGTH("length ({0})"), /* keep */
 
     /** MEAN. */
     MEAN("mean ({0})"), /* keep */
 
     /** NOT_POSITIVE_NUMBER_OF_SAMPLES. */
     NOT_POSITIVE_NUMBER_OF_SAMPLES("number of sample is not positive: {0}"),
 
     /** NUMBER_OF_SAMPLES. */
     NUMBER_OF_SAMPLES("number of samples ({0})"), /* keep */
 
     /** PERMUTATION_SIZE. */
     PERMUTATION_SIZE("permutation size ({0}"), /* keep */
 
     /** POPULATION_SIZE. */
     POPULATION_SIZE("population size ({0})"), /* keep */
 
     /** NOT_POSITIVE_SCALE. */
     NOT_POSITIVE_SCALE("scale must be positive ({0})"),
 
     /** SCALE. */
     SCALE("scale ({0})"), /* keep */
 
     /** SHAPE. */
     SHAPE("shape ({0})"), /* keep */
 
     /** STANDARD_DEVIATION. */
     STANDARD_DEVIATION("standard deviation ({0})"), /* keep */
 
     /** NOT_POSITIVE_WINDOW_SIZE. */
     NOT_POSITIVE_WINDOW_SIZE("window size must be positive ({0})"),
 
     /** NOT_STRICTLY_DECREASING_SEQUENCE. */
     NOT_STRICTLY_DECREASING_SEQUENCE("points {3} and {2} are not strictly decreasing ({1} <= {0})"), /* keep */
 
     /** NOT_STRICTLY_INCREASING_SEQUENCE. */
     NOT_STRICTLY_INCREASING_SEQUENCE("points {3} and {2} are not strictly increasing ({1} >= {0})"), /* keep */
 
     /** NON_SYMMETRIC_MATRIX. */
     NON_SYMMETRIC_MATRIX("non symmetric matrix: the difference between entries at ({0},{1}) and ({1},{0}) is larger than {2}"), /* keep */
 
     /** NO_CONVERGENCE_WITH_ANY_START_POINT. */
     NO_CONVERGENCE_WITH_ANY_START_POINT("none of the {0} start points lead to convergence"), /* keep */
 
     /** NO_DATA. */
     NO_DATA("no data"), /* keep */
 
     /** NO_OPTIMUM_COMPUTED_YET. */
     NO_OPTIMUM_COMPUTED_YET("no optimum computed yet"), /* keep */
 
     /** NAN_NOT_ALLOWED. */
     NAN_NOT_ALLOWED("NaN is not allowed"),
 
     /** NULL_NOT_ALLOWED. */
     NULL_NOT_ALLOWED("null is not allowed"), /* keep */
 
     /** ARRAY_ZERO_LENGTH_OR_NULL_NOT_ALLOWED. */
     ARRAY_ZERO_LENGTH_OR_NULL_NOT_ALLOWED("a null or zero length array not allowed"),
 
     /** DENOMINATOR. */
     DENOMINATOR("denominator"), /* keep */
 
     /** DENOMINATOR_FORMAT. */
     DENOMINATOR_FORMAT("denominator format"), /* keep */
 
     /** FRACTION. */
     FRACTION("fraction"), /* keep */
 
     /** FUNCTION. */
     FUNCTION("function"), /* keep */
 
     /** IMAGINARY_FORMAT. */
     IMAGINARY_FORMAT("imaginary format"), /* keep */
 
     /** INPUT_ARRAY. */
     INPUT_ARRAY("input array"), /* keep */
 
     /** NUMERATOR. */
     NUMERATOR("numerator"), /* keep */
 
     /** NUMERATOR_FORMAT. */
     NUMERATOR_FORMAT("numerator format"), /* keep */
 
     /** REAL_FORMAT. */
     REAL_FORMAT("real format"), /* keep */
 
     /** WHOLE_FORMAT. */
     WHOLE_FORMAT("whole format"), /* keep */
 
     /** NUMBER_TOO_LARGE. */
     NUMBER_TOO_LARGE("{0} is larger than the maximum ({1})"), /* keep */
 
     /** NUMBER_TOO_SMALL. */
     NUMBER_TOO_SMALL("{0} is smaller than the minimum ({1})"), /* keep */
 
     /** NUMBER_TOO_LARGE_BOUND_EXCLUDED. */
     NUMBER_TOO_LARGE_BOUND_EXCLUDED("{0} is larger than, or equal to, the maximum ({1})"), /* keep */
 
     /** NUMBER_TOO_SMALL_BOUND_EXCLUDED. */
     NUMBER_TOO_SMALL_BOUND_EXCLUDED("{0} is smaller than, or equal to, the minimum ({1})"), /* keep */
 
     /** NUMBER_OF_SUCCESS_LARGER_THAN_POPULATION_SIZE. */
     NUMBER_OF_SUCCESS_LARGER_THAN_POPULATION_SIZE("number of successes ({0}) must be less than or equal to population size ({1})"),
 
     /** NUMERATOR_OVERFLOW_AFTER_MULTIPLY. */
     NUMERATOR_OVERFLOW_AFTER_MULTIPLY("overflow, numerator too large after multiply: {0}"),
 
     /** OBSERVED_COUNTS_BOTTH_ZERO_FOR_ENTRY. */
     OBSERVED_COUNTS_BOTTH_ZERO_FOR_ENTRY("observed counts are both zero for entry {0}"),
 
     /** OUT_OF_RANGE_ROOT_OF_UNITY_INDEX. */
     OUT_OF_RANGE_ROOT_OF_UNITY_INDEX("out of range root of unity index {0} (must be in [{1};{2}])"),
 
     /** OUT_OF_RANGE. */
     OUT_OF_RANGE("out of range"), /* keep */
 
     /** OUT_OF_RANGE_SIMPLE. */
     OUT_OF_RANGE_SIMPLE("{0} out of [{1}, {2}] range"), /* keep */
 
     /** OUT_OF_RANGE_LEFT. */
     OUT_OF_RANGE_LEFT("{0} out of ({1}, {2}] range"),
 
     /** OVERFLOW. */
     OVERFLOW("overflow"), /* keep */
 
     /** OVERFLOW_IN_FRACTION. */
     OVERFLOW_IN_FRACTION("overflow in fraction {0}/{1}, cannot negate"),
 
     /** OVERFLOW_IN_ADDITION. */
     OVERFLOW_IN_ADDITION("overflow in addition: {0} + {1}"),
 
     /** OVERFLOW_IN_SUBTRACTION. */
     OVERFLOW_IN_SUBTRACTION("overflow in subtraction: {0} - {1}"),
 
     /** OVERFLOW_IN_MULTIPLICATION. */
     OVERFLOW_IN_MULTIPLICATION("overflow in multiplication: {0} * {1}"),
 
     /** PERMUTATION_EXCEEDS_N. */
     PERMUTATION_EXCEEDS_N("permutation size ({0}) exceeds permuation domain ({1})"), /* keep */
 
     /** POLYNOMIAL. */
     POLYNOMIAL("polynomial"), /* keep */
 
     /** ROOTS_OF_UNITY_NOT_COMPUTED_YET. */
     ROOTS_OF_UNITY_NOT_COMPUTED_YET("roots of unity have not been computed yet"),
 
     /** ROW_INDEX. */
     ROW_INDEX("row index ({0})"), /* keep */
 
     /** NOT_BRACKETING_INTERVAL. */
     NOT_BRACKETING_INTERVAL("interval does not bracket a root: f({0,number,##0.################E0}) = {2,number,##0.################E0}, f({1,number,##0.################E0}) = {3,number,##0.################E0}"),
 
     /** START_POINT_NOT_IN_INTERVAL. */
     START_POINT_NOT_IN_INTERVAL("The start point {0} is not in the interval [{1}, {2}]"),
 
     /** SAMPLE_SIZE_EXCEEDS_COLLECTION_SIZE. */
     SAMPLE_SIZE_EXCEEDS_COLLECTION_SIZE("sample size ({0}) exceeds collection size ({1})"), /* keep */
 
     /** SAMPLE_SIZE_LARGER_THAN_POPULATION_SIZE. */
     SAMPLE_SIZE_LARGER_THAN_POPULATION_SIZE("sample size ({0}) must be less than or equal to population size ({1})"),
 
     /** SIMPLE_MESSAGE. */
     SIMPLE_MESSAGE("{0}"),
 
     /** SINGULAR_MATRIX. */
     SINGULAR_MATRIX("matrix is singular"), /* keep */
 
     /** SINGULAR_OPERATOR. */
     SINGULAR_OPERATOR("operator is singular"),
 
     /** SUBARRAY_ENDS_AFTER_ARRAY_END. */
     SUBARRAY_ENDS_AFTER_ARRAY_END("subarray ends after array end"),
 
     /** TOO_LARGE_CUTOFF_SINGULAR_VALUE. */
     TOO_LARGE_CUTOFF_SINGULAR_VALUE("cutoff singular value is {0}, should be at most {1}"),
 
     /** TOO_MANY_ELEMENTS_TO_DISCARD_FROM_ARRAY. */
     TOO_MANY_ELEMENTS_TO_DISCARD_FROM_ARRAY("cannot discard {0} elements from a {1} elements array"),
 
     /** UNKNOWN_MODE. */
     UNKNOWN_MODE("unknown mode {0}, known modes: {1} ({2}), {3} ({4}), {5} ({6}), {7} ({8}), {9} ({10}) and {11} ({12})"),
 
     /** CANNOT_PARSE_AS_TYPE. */
     CANNOT_PARSE_AS_TYPE("string \"{0}\" unparseable (from position {1}) as an object of type {2}"), /* keep */
 
     /** CANNOT_PARSE. */
     CANNOT_PARSE("string \"{0}\" unparseable (from position {1})"), /* keep */
 
     /** UNSUPPORTED_OPERATION. */
     UNSUPPORTED_OPERATION("unsupported operation"), /* keep */
 
     /** ARITHMETIC_EXCEPTION. */
     ARITHMETIC_EXCEPTION("arithmetic exception"), /* keep */
 
     /** ILLEGAL_STATE. */
     ILLEGAL_STATE("illegal state"), /* keep */
 
     /** USER_EXCEPTION. */
     USER_EXCEPTION("exception generated in user code"), /* keep */
 
     /** URL_CONTAINS_NO_DATA. */
     URL_CONTAINS_NO_DATA("URL {0} contains no data"),
 
     /** VECTOR_MUST_HAVE_AT_LEAST_ONE_ELEMENT. */
     VECTOR_MUST_HAVE_AT_LEAST_ONE_ELEMENT("vector must have at least one element"),
 
     /** WEIGHT_AT_LEAST_ONE_NON_ZERO. */
     WEIGHT_AT_LEAST_ONE_NON_ZERO("weight array must contain at least one non-zero value"),
 
     /** WRONG_NUMBER_OF_POINTS. */
     WRONG_NUMBER_OF_POINTS("{0} points are required, got only {1}"),
 
     /** NUMBER_OF_POINTS. */
     NUMBER_OF_POINTS("number of points ({0})"), /* keep */
 
     /** ZERO_DENOMINATOR. */
     ZERO_DENOMINATOR("denominator must be different from 0"), /* keep */
 
     /** ZERO_DENOMINATOR_IN_FRACTION. */
     ZERO_DENOMINATOR_IN_FRACTION("zero denominator in fraction {0}/{1}"),
 
     /** ZERO_FRACTION_TO_DIVIDE_BY. */
     ZERO_FRACTION_TO_DIVIDE_BY("the fraction to divide by must not be zero: {0}/{1}"),
 
     /** ZERO_NORM. */
     ZERO_NORM("zero norm"),
 
     /** ZERO_NOT_ALLOWED. */
     ZERO_NOT_ALLOWED("zero not allowed here"),
 
     /** ZERO_STATE_SIZE. */
     ZERO_STATE_SIZE("state dimension must be different from 0"),
 
     /** RIGHT_EDGE_GREATER_THAN_LEFT_EDGE. */
     RIGHT_EDGE_GREATER_THAN_LEFT_EDGE("left edge {0} should be smaller than right edge {1}"),
 
     /** INPUT_EXPECTED_BETWEEN_ZERO_AND_ONE_INCLUDED. */
     INPUT_EXPECTED_BETWEEN_ZERO_AND_ONE_INCLUDED("input {0} is expected to be between [0:1]");
 
     /** Source English format. */
     private final String sourceFormat;
 
     /** Simple constructor.
      * @param sourceFormat source English format to use when no
      * localized version is available
      */
     LocalizedCoreFormats(final String sourceFormat) {
         this.sourceFormat = sourceFormat;
     }
 
     /** {@inheritDoc} */
     @Override
     public String getSourceString() {
         return sourceFormat;
     }
 
     /** {@inheritDoc} */
     @Override
     public String getLocalizedString(final Locale locale) {
         try {
             final String path = LocalizedCoreFormats.class.getName().replaceAll("\\.", "/");
             ResourceBundle bundle =
                     ResourceBundle.getBundle("assets/" + path, locale, new UTF8Control());
             if (bundle.getLocale().getLanguage().equals(locale.getLanguage())) {
                 final String translated = bundle.getString(name());
                 if ((translated != null) &&
                     (translated.length() > 0) &&
                     (!translated.toLowerCase(locale).contains("missing translation"))) {
                     // the value of the resource is the translated format
                     return translated;
                 }
             }
 
         } catch (MissingResourceException mre) { // NOPMD
             // do nothing here
         }
 
         // either the locale is not supported or the resource is unknown
         // don't translate and fall back to using the source format
         return sourceFormat;
 
     }
 
 }