[9102] | 1 | ///
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| 2 | /// This file is part of ILNumerics Community Edition.
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| 3 | ///
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| 4 | /// ILNumerics Community Edition - high performance computing for applications.
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| 5 | /// Copyright (C) 2006 - 2012 Haymo Kutschbach, http://ilnumerics.net
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| 6 | ///
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| 7 | /// ILNumerics Community Edition is free software: you can redistribute it and/or modify
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| 8 | /// it under the terms of the GNU General Public License version 3 as published by
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| 9 | /// the Free Software Foundation.
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| 10 | ///
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| 11 | /// ILNumerics Community Edition is distributed in the hope that it will be useful,
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| 12 | /// but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 13 | /// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 14 | /// GNU General Public License for more details.
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| 15 | ///
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| 16 | /// You should have received a copy of the GNU General Public License
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| 17 | /// along with ILNumerics Community Edition. See the file License.txt in the root
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| 18 | /// of your distribution package. If not, see <http://www.gnu.org/licenses/>.
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| 19 | ///
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| 20 | /// In addition this software uses the following components and/or licenses:
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| 21 | ///
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| 22 | /// =================================================================================
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| 23 | /// The Open Toolkit Library License
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| 24 | ///
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| 25 | /// Copyright (c) 2006 - 2009 the Open Toolkit library.
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| 26 | ///
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| 27 | /// Permission is hereby granted, free of charge, to any person obtaining a copy
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| 28 | /// of this software and associated documentation files (the "Software"), to deal
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| 29 | /// in the Software without restriction, including without limitation the rights to
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| 30 | /// use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
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| 31 | /// the Software, and to permit persons to whom the Software is furnished to do
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| 32 | /// so, subject to the following conditions:
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| 33 | ///
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| 34 | /// The above copyright notice and this permission notice shall be included in all
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| 35 | /// copies or substantial portions of the Software.
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| 36 | ///
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| 37 | /// =================================================================================
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| 38 | ///
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| 39 |
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| 40 | using System;
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| 41 | using System.Collections.Generic;
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| 42 | using System.Text;
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| 43 | using ILNumerics.Storage;
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| 44 | using ILNumerics.Misc;
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| 45 | using ILNumerics.Exceptions;
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| 46 |
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| 47 |
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| 48 |
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| 49 | namespace ILNumerics {
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| 50 |
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| 51 | public partial class ILMath {
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| 52 |
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| 53 | |
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| 54 | /// <summary>
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| 55 | /// Vector or matrix norm
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| 56 | /// </summary>
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| 57 | /// <param name="A">Input matrix/ vector</param>
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| 58 | /// <param name="degree">[Optional] Degree of norm (default = 2). For vectors this must be one of:
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| 59 | /// <list type="bullet">
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| 60 | /// <item>arbitrary double value : returns sum(pow(abs(A),degree))^(1/degree)</item>
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| 61 | /// <item>System.double.PositiveInfinity: return Max(abs(A))</item>
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| 62 | /// <item>System.double.NegativeInfinity: return Min(abs(A))</item>
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| 63 | /// </list>
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| 64 | /// For matrices this must be one out of:
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| 65 | /// <list type="bullet">
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| 66 | /// <item>0: returns Frobenius norm: sqrt(sum(diag(multiply(A, A[1]))))</item>
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| 67 | /// <item>1: returns 1-norm, max(sum(abs(A)))</item>
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| 68 | /// <item>2: returns the largest singular value of A, max(svd(A))</item>
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| 69 | /// <item>PositiveInfinity: returns max(sum(abs(A), 2)), the largest value of the sums along the rows</item>
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| 70 | /// </list>
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| 71 | /// </param>
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| 72 | /// <returns>Array of same type as input array A</returns>
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| 73 | public static ILRetArray< double > norm(ILInArray< double > A, double degree = 2) {
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| 74 | using (ILScope.Enter(A)) {
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| 75 | if (Object.Equals(A, null) || !A.IsMatrix)
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| 76 | throw new ILArgumentSizeException("input array must be matrix or vector.");
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| 77 | if (A.IsEmpty)
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| 78 | return new ILRetArray< double>(ILSize.Scalar1_1);
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| 79 | else if (A.IsVector) {
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| 80 | if (degree == Double.PositiveInfinity) {
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| 81 | return max(abs(A));
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| 82 | } else if (degree == Double.NegativeInfinity) {
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| 83 | return min(abs(A));
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| 84 | } else {
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| 85 | if (degree == 0.0)
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| 86 | return array< double>( ( double)Double.PositiveInfinity , 1, 1);
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| 87 | return pow(sum(pow(abs(A), ( double)degree)), ( double)(1.0 / degree));
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| 88 | }
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| 89 | } else {
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| 90 | if (degree == 1.0) {
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| 91 | return max(sum(abs(A)));
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| 92 | } else if (degree == 2.0) {
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| 93 | return max(svd(A));
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| 94 | } else if (degree == Double.PositiveInfinity) {
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| 95 | return max(sum(abs(A), 2));
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| 96 | } else if (degree == 0.0) {
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| 97 |
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| 98 | return sqrt(sum(diag <double>(multiply(A, A[1]))));
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| 99 | } else {
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| 100 | throw new ILArgumentException("invalid argument 'degree' supplied. valid for matrices: 0,1,2,Double.PositiveInfinity");
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| 101 | }
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| 102 | }
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| 103 | }
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| 104 | }
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| 105 | |
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| 106 | #region HYCALPER AUTO GENERATED CODE
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| 107 | |
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| 108 | /// <summary>
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| 109 | /// Vector or matrix norm
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| 110 | /// </summary>
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| 111 | /// <param name="A">Input matrix/ vector</param>
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| 112 | /// <param name="degree">[Optional] Degree of norm (default = 2). For vectors this must be one of:
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| 113 | /// <list type="bullet">
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| 114 | /// <item>arbitrary double value : returns sum(pow(abs(A),degree))^(1/degree)</item>
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| 115 | /// <item>System.double.PositiveInfinity: return Max(abs(A))</item>
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| 116 | /// <item>System.double.NegativeInfinity: return Min(abs(A))</item>
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| 117 | /// </list>
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| 118 | /// For matrices this must be one out of:
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| 119 | /// <list type="bullet">
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| 120 | /// <item>0: returns Frobenius norm: sqrt(sum(diag(multiply(A, A[1]))))</item>
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| 121 | /// <item>1: returns 1-norm, max(sum(abs(A)))</item>
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| 122 | /// <item>2: returns the largest singular value of A, max(svd(A))</item>
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| 123 | /// <item>PositiveInfinity: returns max(sum(abs(A), 2)), the largest value of the sums along the rows</item>
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| 124 | /// </list>
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| 125 | /// </param>
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| 126 | /// <returns>Array of same type as input array A</returns>
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| 127 | public static ILRetArray< float > norm(ILInArray< fcomplex > A, double degree = 2) {
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| 128 | using (ILScope.Enter(A)) {
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| 129 | if (Object.Equals(A, null) || !A.IsMatrix)
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| 130 | throw new ILArgumentSizeException("input array must be matrix or vector.");
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| 131 | if (A.IsEmpty)
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| 132 | return new ILRetArray< float>(ILSize.Scalar1_1);
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| 133 | else if (A.IsVector) {
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| 134 | if (degree == Double.PositiveInfinity) {
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| 135 | return max(abs(A));
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| 136 | } else if (degree == Double.NegativeInfinity) {
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| 137 | return min(abs(A));
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| 138 | } else {
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| 139 | if (degree == 0.0)
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| 140 | return array< float>( ( float)Double.PositiveInfinity , 1, 1);
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| 141 | return pow(sum(pow(abs(A), ( float)degree)), ( float)(1.0 / degree));
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| 142 | }
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| 143 | } else {
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| 144 | if (degree == 1.0) {
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| 145 | return max(sum(abs(A)));
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| 146 | } else if (degree == 2.0) {
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| 147 | return max(svd(A));
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| 148 | } else if (degree == Double.PositiveInfinity) {
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| 149 | return max(sum(abs(A), 2));
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| 150 | } else if (degree == 0.0) {
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| 151 | return sqrt(sum(real(diag<fcomplex>(multiply(A, A[1])))));
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| 152 | } else {
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| 153 | throw new ILArgumentException("invalid argument 'degree' supplied. valid for matrices: 0,1,2,Double.PositiveInfinity");
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| 154 | }
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| 155 | }
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| 156 | }
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| 157 | }
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| 158 | /// <summary>
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| 159 | /// Vector or matrix norm
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| 160 | /// </summary>
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| 161 | /// <param name="A">Input matrix/ vector</param>
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| 162 | /// <param name="degree">[Optional] Degree of norm (default = 2). For vectors this must be one of:
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| 163 | /// <list type="bullet">
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| 164 | /// <item>arbitrary double value : returns sum(pow(abs(A),degree))^(1/degree)</item>
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| 165 | /// <item>System.double.PositiveInfinity: return Max(abs(A))</item>
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| 166 | /// <item>System.double.NegativeInfinity: return Min(abs(A))</item>
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| 167 | /// </list>
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| 168 | /// For matrices this must be one out of:
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| 169 | /// <list type="bullet">
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| 170 | /// <item>0: returns Frobenius norm: sqrt(sum(diag(multiply(A, A[1]))))</item>
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| 171 | /// <item>1: returns 1-norm, max(sum(abs(A)))</item>
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| 172 | /// <item>2: returns the largest singular value of A, max(svd(A))</item>
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| 173 | /// <item>PositiveInfinity: returns max(sum(abs(A), 2)), the largest value of the sums along the rows</item>
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| 174 | /// </list>
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| 175 | /// </param>
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| 176 | /// <returns>Array of same type as input array A</returns>
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| 177 | public static ILRetArray< float > norm(ILInArray< float > A, double degree = 2) {
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| 178 | using (ILScope.Enter(A)) {
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| 179 | if (Object.Equals(A, null) || !A.IsMatrix)
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| 180 | throw new ILArgumentSizeException("input array must be matrix or vector.");
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| 181 | if (A.IsEmpty)
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| 182 | return new ILRetArray< float>(ILSize.Scalar1_1);
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| 183 | else if (A.IsVector) {
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| 184 | if (degree == Double.PositiveInfinity) {
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| 185 | return max(abs(A));
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| 186 | } else if (degree == Double.NegativeInfinity) {
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| 187 | return min(abs(A));
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| 188 | } else {
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| 189 | if (degree == 0.0)
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| 190 | return array< float>( ( float)Double.PositiveInfinity , 1, 1);
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| 191 | return pow(sum(pow(abs(A), ( float)degree)), ( float)(1.0 / degree));
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| 192 | }
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| 193 | } else {
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| 194 | if (degree == 1.0) {
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| 195 | return max(sum(abs(A)));
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| 196 | } else if (degree == 2.0) {
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| 197 | return max(svd(A));
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| 198 | } else if (degree == Double.PositiveInfinity) {
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| 199 | return max(sum(abs(A), 2));
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| 200 | } else if (degree == 0.0) {
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| 201 | return sqrt(sum(diag<float>(multiply(A, A[1]))));
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| 202 | } else {
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| 203 | throw new ILArgumentException("invalid argument 'degree' supplied. valid for matrices: 0,1,2,Double.PositiveInfinity");
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| 204 | }
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| 205 | }
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| 206 | }
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| 207 | }
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| 208 | /// <summary>
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| 209 | /// Vector or matrix norm
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| 210 | /// </summary>
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| 211 | /// <param name="A">Input matrix/ vector</param>
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| 212 | /// <param name="degree">[Optional] Degree of norm (default = 2). For vectors this must be one of:
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| 213 | /// <list type="bullet">
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| 214 | /// <item>arbitrary double value : returns sum(pow(abs(A),degree))^(1/degree)</item>
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| 215 | /// <item>System.double.PositiveInfinity: return Max(abs(A))</item>
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| 216 | /// <item>System.double.NegativeInfinity: return Min(abs(A))</item>
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| 217 | /// </list>
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| 218 | /// For matrices this must be one out of:
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| 219 | /// <list type="bullet">
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| 220 | /// <item>0: returns Frobenius norm: sqrt(sum(diag(multiply(A, A[1]))))</item>
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| 221 | /// <item>1: returns 1-norm, max(sum(abs(A)))</item>
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| 222 | /// <item>2: returns the largest singular value of A, max(svd(A))</item>
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| 223 | /// <item>PositiveInfinity: returns max(sum(abs(A), 2)), the largest value of the sums along the rows</item>
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| 224 | /// </list>
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| 225 | /// </param>
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| 226 | /// <returns>Array of same type as input array A</returns>
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| 227 | public static ILRetArray< double > norm(ILInArray< complex > A, double degree = 2) {
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| 228 | using (ILScope.Enter(A)) {
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| 229 | if (Object.Equals(A, null) || !A.IsMatrix)
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| 230 | throw new ILArgumentSizeException("input array must be matrix or vector.");
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| 231 | if (A.IsEmpty)
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| 232 | return new ILRetArray< double>(ILSize.Scalar1_1);
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| 233 | else if (A.IsVector) {
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| 234 | if (degree == Double.PositiveInfinity) {
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| 235 | return max(abs(A));
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| 236 | } else if (degree == Double.NegativeInfinity) {
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| 237 | return min(abs(A));
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| 238 | } else {
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| 239 | if (degree == 0.0)
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| 240 | return array< double>( ( double)Double.PositiveInfinity , 1, 1);
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| 241 | return pow(sum(pow(abs(A), ( double)degree)), ( double)(1.0 / degree));
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| 242 | }
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| 243 | } else {
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| 244 | if (degree == 1.0) {
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| 245 | return max(sum(abs(A)));
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| 246 | } else if (degree == 2.0) {
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| 247 | return max(svd(A));
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| 248 | } else if (degree == Double.PositiveInfinity) {
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| 249 | return max(sum(abs(A), 2));
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| 250 | } else if (degree == 0.0) {
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| 251 | return sqrt(sum(real(diag<complex>(multiply(A, A[1])))));
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| 252 | } else {
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| 253 | throw new ILArgumentException("invalid argument 'degree' supplied. valid for matrices: 0,1,2,Double.PositiveInfinity");
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| 254 | }
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| 255 | }
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| 256 | }
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| 257 | }
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| 258 |
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| 259 | #endregion HYCALPER AUTO GENERATED CODE
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| 260 |
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| 261 | }
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| 262 |
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| 263 | }
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