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123 .rm #[ #] #H #V #F C
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124 .\" ========================================================================
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125 .\"
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126 .IX Title "MATRIX 1"
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127 .TH MATRIX 1 "2015-03-29" "perl v5.14.2" "MayaChemTools"
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128 .\" For nroff, turn off justification. Always turn off hyphenation; it makes
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129 .\" way too many mistakes in technical documents.
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130 .if n .ad l
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131 .nh
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132 .SH "NAME"
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133 Matrix
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134 .SH "SYNOPSIS"
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135 .IX Header "SYNOPSIS"
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136 use Matrix;
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137 .PP
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138 use Matrix qw(:all);
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139 .SH "DESCRIPTION"
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140 .IX Header "DESCRIPTION"
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141 \&\fBMatrix\fR class provides the following methods:
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142 .PP
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143 new, AddColumnValues, AddRowValues, Copy, GetColumnValues,
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144 GetColumnValuesAsColumnMatrix, GetColumnValuesAsRowMatrix,
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145 GetColumnValuesAsString, GetColumnValuesAsVector, GetDiagonalValues,
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146 GetDiagonalValuesAsColumnMatrix, GetDiagonalValuesAsRowMatrix,
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147 GetDiagonalValuesAsString, GetDiagonalValuesAsVector, GetDimension,
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148 GetMatrixValuesReference, GetNumOfColumns, GetNumOfRows, GetRowValues,
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149 GetRowValuesAsColumnMatrix, GetRowValuesAsRowMatrix, GetRowValuesAsString,
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150 GetRowValuesAsVector, GetSize, GetValue, IdentityMatrix, IsAntiSymmetric,
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151 IsBiDiagonal, IsDiagonal, IsIdentity, IsLeftTriangular, IsLowerBiDiagonal,
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152 IsLowerTriangular, IsLowerUniTriangular, IsMatrix, IsNegative, IsPositive,
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153 IsRightTriangular, IsSkewSymmetric, IsSquare, IsStrictlyLowerTriangular,
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154 IsStrictlyUpperTriangular, IsSymmetric, IsTriDiagonal, IsUnit,
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155 IsUnitLowerTriangular, IsUnitUpperTriangular, IsUpperBiDiagonal,
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156 IsUpperTriangular, IsUpperUniTriangular, NewFromColumns, NewFromDiagonal,
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157 NewFromRows, One, SetAllValues, SetColumnValues, SetDiagonalValues,
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158 SetMatrixPrintStyle, SetRowValues, SetValue, SetValuePrintFormat, StringifyMatrix,
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159 Transpose, UnitMatrix, Zero, ZeroMatrix
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160 .PP
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161 The following functions are available:
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162 .PP
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163 IsMatrix, IdentityMatrix, NewFromRows, NewFromColumns, NewFromDiagonal,
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164 UnitMatrix, ZeroMatrix
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165 .PP
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166 The following operators are overloaded:
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167 .PP
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168 .Vb 6
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169 \& "" bool !
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170 \& @{}
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171 \& + \- * / ** %
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172 \& == != < <= > >=
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173 \& neg
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174 \& abs exp log sqrt cos sin
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175 .Ve
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176 .PP
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177 The matrix row and column indicies start from zero.
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178 .SS "\s-1FUNCTIONS\s0"
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179 .IX Subsection "FUNCTIONS"
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180 .IP "\fBnew\fR" 4
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181 .IX Item "new"
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182 .Vb 1
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183 \& $NewMatrix = $Matrix\->new($NumOfRows, $NumOfCols);
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184 .Ve
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185 .Sp
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186 Creates a new \fBMatrix\fR of size \fINumOfRows x NumOfCol\fR and returns \fBNewMatrix\fR
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187 object.
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188 .IP "\fBAddColumnValues\fR" 4
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189 .IX Item "AddColumnValues"
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190 .Vb 4
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191 \& $Matrix\->AddColumnValues(@Values);
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192 \& $Matrix\->AddColumnValues(\e@Values);
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193 \& $Matrix\->AddColumnValues($VectorObject);
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194 \& $Matrix\->AddColumnValues("Value1 Value2 Value3 ...");
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195 .Ve
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196 .Sp
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197 Adds column values to \fIMatrix\fR using an array, reference to an array, another vector, or space
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198 delimited value string and returns \fIMatrix\fR.
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199 .IP "\fBAddRowValues\fR" 4
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200 .IX Item "AddRowValues"
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201 .Vb 4
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202 \& $Matrix\->AddRowValues(@Values);
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203 \& $Matrix\->AddRowValues(\e@Values);
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204 \& $Matrix\->AddRowValues($VectorObject);
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205 \& $Matrix\->AddRowValues("Value1 Value2 Value3 ...");
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206 .Ve
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207 .Sp
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208 Adds row values to \fIMatrix\fR using an array, reference to an array, another vector, or space
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209 delimited value string and returns \fBMatrix\fR.
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210 .IP "\fBCopy\fR" 4
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211 .IX Item "Copy"
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212 .Vb 1
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213 \& $NewMatrix = $Matrix\->Copy();
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214 .Ve
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215 .Sp
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216 Creates a copy of \fIMatrix\fR and returns \fBNewMatrix\fR.
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217 .IP "\fBGetColumnValues\fR" 4
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218 .IX Item "GetColumnValues"
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219 .Vb 2
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220 \& @Values = $Matrix\->GetColumnValues($ColIndex);
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221 \& $ValueCount = $Matrix\->GetColumnValues($ColIndex);
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222 .Ve
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223 .Sp
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224 Returns an array containing column value specified using \fIColIndex\fR with column index
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225 starting at 0. In scalar context, number of column values is returned.
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226 .IP "\fBGetColumnValuesAsColumnMatrix\fR" 4
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227 .IX Item "GetColumnValuesAsColumnMatrix"
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228 .Vb 1
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229 \& $ColumnMatrix = $Matrix\->GetColumnValuesAsColumnMatrix($ColIndex);
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230 .Ve
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231 .Sp
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232 Returns a new \fBColumnMatrix\fR containing column values specified using \fIColIndex\fR with
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233 column index starting at 0.
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234 .IP "\fBGetColumnValuesAsRowMatrix\fR" 4
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235 .IX Item "GetColumnValuesAsRowMatrix"
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236 .Vb 1
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237 \& $RowMatrix = $Matrix\->GetColumnValuesAsRowMatrix($ColIndex);
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238 .Ve
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239 .Sp
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240 Returns a new \fBRowMatrix\fR containing column values specified using \fIColIndex\fR with
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241 column index starting at 0.
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242 .IP "\fBGetColumnValuesAsString\fR" 4
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243 .IX Item "GetColumnValuesAsString"
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244 .Vb 1
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245 \& $ColumnValuesString = $Matrix\->GetColumnValuesAsString($ColIndex);
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246 .Ve
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247 .Sp
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248 Returns a space delimited \fBColumnValuesString\fR column values specified using \fIColIndex\fR with
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249 column index starting at 0.
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250 .IP "\fBGetColumnValuesAsVector\fR" 4
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251 .IX Item "GetColumnValuesAsVector"
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252 .Vb 1
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253 \& $ColumnVector = $Matrix\->GetColumnValuesAsVector($ColIndex);
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254 .Ve
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255 .Sp
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256 Returns a new \fBColumnVector\fR column values specified using \fIRowIndex\fR with
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257 column index starting at 0.
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258 .IP "\fBGetDiagonalValues\fR" 4
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259 .IX Item "GetDiagonalValues"
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260 .Vb 2
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261 \& @Values = $Matrix\->GetDiagonalValues();
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262 \& $ValueCount = $Matrix\->GetDiagonalValues();
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263 .Ve
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264 .Sp
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265 Returns an array containing diagonal values. In scalar context, number of diagonal
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266 values is returned.
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267 .IP "\fBGetDiagonalValuesAsColumnMatrix\fR" 4
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268 .IX Item "GetDiagonalValuesAsColumnMatrix"
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269 .Vb 1
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270 \& $ColumnMatrix = $Matrix\->GetDiagonalValuesAsColumnMatrix();
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271 .Ve
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272 .Sp
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273 Returns a new \fBColumnMatrix\fR containing diagonal values corresponding to \fIMatrix\fR.
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274 .IP "\fBGetDiagonalValuesAsRowMatrix\fR" 4
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275 .IX Item "GetDiagonalValuesAsRowMatrix"
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276 .Vb 1
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277 \& $RowMatrix = $Matrix\->GetDiagonalValuesAsRowMatrix();
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278 .Ve
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279 .Sp
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280 Returns a new \fBRowMatrix\fR containing diagonal values corresponding to \fIMatrix\fR.
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281 .IP "\fBGetDiagonalValuesAsString\fR" 4
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282 .IX Item "GetDiagonalValuesAsString"
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283 .Vb 1
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284 \& $DiagonalValuesString = $Matrix\->GetDiagonalValuesAsString();
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285 .Ve
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286 .Sp
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287 Returns a space delimited \fBDiagonalValuesString\fR containing diagonal values corresponding to
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288 \&\fIMatrix\fR.
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289 .IP "\fBGetDiagonalValuesAsVector\fR" 4
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290 .IX Item "GetDiagonalValuesAsVector"
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291 .Vb 1
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292 \& $DiagonalVector = $Matrix\->GetDiagonalValuesAsVector();
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293 .Ve
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294 .Sp
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295 Returns a new \fBDiagonalVector\fR containing diagonal values corresponding to \fIMatrix\fR.
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296 .IP "\fBGetDimension\fR" 4
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297 .IX Item "GetDimension"
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298 .Vb 1
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299 \& ($NumOfRows, $NumOfCols) = $Matrix\->GetDimension();
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300 .Ve
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301 .Sp
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302 Returns size of \fIMatrix\fR.
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303 .IP "\fBGetMatrixValuesReference\fR" 4
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304 .IX Item "GetMatrixValuesReference"
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305 .Vb 1
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306 \& $ValuesRef = $Matrix\->GetMatrixValuesReference();
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307 .Ve
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308 .Sp
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309 Returns a reference to array containing rows and column values corresponding to \fIMatrix\fR.
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310 .IP "\fBGetNumOfColumns\fR" 4
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311 .IX Item "GetNumOfColumns"
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312 .Vb 1
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313 \& $NumOfCols = $Matrix\->GetNumOfColumns();
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314 .Ve
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315 .Sp
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316 Returns \fBNumOfCols\fR in \fIMatrix\fR.
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317 .IP "\fBGetNumOfRows\fR" 4
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318 .IX Item "GetNumOfRows"
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319 .Vb 1
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320 \& $NumOfRows = $Matrix\->GetNumOfRows();
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321 .Ve
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322 .Sp
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323 Returns \fBNumOfRows\fR in \fIMatrix\fR.
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324 .IP "\fBGetRowValues\fR" 4
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325 .IX Item "GetRowValues"
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326 .Vb 2
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327 \& @Values = $Matrix\->GetRowValues($RowIndex);
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328 \& $ValueCount = $Matrix\->GetRowValues($RowIndex);
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329 .Ve
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330 .Sp
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331 Returns an array containing row value specified using \fIRowIndex\fR with row index
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332 starting at 0. In scalar context, number of row values is returned.
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333 .IP "\fBGetRowValuesAsColumnMatrix\fR" 4
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334 .IX Item "GetRowValuesAsColumnMatrix"
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335 .Vb 1
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336 \& $ColumnMatrix = $Matrix\->GetRowValuesAsColumnMatrix($RowIndex);
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337 .Ve
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338 .Sp
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339 Returns a new \fBColumnMatrix\fR containing row values specified using \fIRowIndex\fR with
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340 column index starting at 0.
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341 .IP "\fBGetRowValuesAsRowMatrix\fR" 4
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342 .IX Item "GetRowValuesAsRowMatrix"
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343 .Vb 1
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344 \& $RowMatrix = $Matrix\->GetRowValuesAsRowMatrix($RowIndex);
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345 .Ve
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346 .Sp
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347 Returns a new \fBRowMatrix\fR containing row values specified using \fIRowIndex\fR with
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348 row index starting at 0.
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349 .IP "\fBGetRowValuesAsString\fR" 4
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350 .IX Item "GetRowValuesAsString"
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351 .Vb 1
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352 \& $RowValuesString = $Matrix\->GetRowValuesAsString($RowIndex);
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353 .Ve
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354 .Sp
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355 Returns a space delimited \fBRowValuesString\fR row values specified using \fIRowIndex\fR with
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356 row index starting at 0.
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357 .IP "\fBGetRowValuesAsVector\fR" 4
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358 .IX Item "GetRowValuesAsVector"
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|
|
359 .Vb 1
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|
|
360 \& $RowVector = $Matrix\->GetColumnValuesAsVector($RowIndex);
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|
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361 .Ve
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362 .Sp
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|
363 Returns a new \fBRowVector\fR row values specified using \fIRowIndex\fR with
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|
|
364 row index starting at 0.
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|
|
365 .IP "\fBGetSize\fR" 4
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|
|
366 .IX Item "GetSize"
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|
|
367 .Vb 1
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|
|
368 \& ($NumOfRows, $NumOfCols) = $Matrix\->GetSize();
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|
|
369 .Ve
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|
|
370 .Sp
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|
|
371 Returns size of \fIMatrix\fR.
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|
|
372 .IP "\fBGetValue\fR" 4
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|
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373 .IX Item "GetValue"
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|
|
374 .Vb 1
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|
|
375 \& $Value = $Matrix\->GetValue($RowIndex, $ColIndex, [$SkipIndexCheck]);
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|
|
376 .Ve
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|
377 .Sp
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|
|
378 Returns \fBValue\fR of \fIMatrix\fR element specified using \fIRowIndex\fR and \fIColIndex\fR with indicies
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|
|
379 starting at 0 with optional validation of specified index values.
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|
|
380 .IP "\fBIdentityMatrix\fR" 4
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|
|
381 .IX Item "IdentityMatrix"
|
|
|
382 .Vb 3
|
|
|
383 \& $NewIdentityMatrix = $Matrix\->IdentityMatrix($NumOfRows, $NumOfCols);
|
|
|
384 \& $NewIdentityMatrix = Matrix::IdentityMatrix($NumOfRows, $NumOfCols);
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|
|
385 \& $NewIdentityMatrix = Matrix::IdentityMatrix();
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|
|
386 .Ve
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|
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387 .Sp
|
|
|
388 Creates a new \fBIdentityMatrix\fR of specified size \fINumOfRows x NumOfCol\fR or of size 3 x 3 and
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|
|
389 returns \fBNewIdentityMatrix\fR object.
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|
|
390 .IP "\fBIsAntiSymmetric\fR" 4
|
|
|
391 .IX Item "IsAntiSymmetric"
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|
|
392 .Vb 1
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|
|
393 \& $Status = $Matrix\->IsAntiSymmetric();
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|
|
394 .Ve
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|
|
395 .Sp
|
|
|
396 Returns 1 or 0 based on whether \fIMatrix\fR is an anti symmetric matrix.
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|
|
397 .Sp
|
|
|
398 A matrix is an anti symmetric matrix:
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|
|
399 .Sp
|
|
|
400 .Vb 4
|
|
|
401 \& . It\*(Aqs a square matrix
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|
|
402 \& . Its elements are asymmetric with respect to main diagonal. In other words,
|
|
|
403 \& elements below the main diagonal are equal to the negative of elements above
|
|
|
404 \& the main diagonal.
|
|
|
405 .Ve
|
|
|
406 .Sp
|
|
|
407 Transpose of an anti symmetric matrix equals the negative of the matrix.
|
|
|
408 .IP "\fBIsBiDiagonal\fR" 4
|
|
|
409 .IX Item "IsBiDiagonal"
|
|
|
410 .Vb 1
|
|
|
411 \& $Status = $Matrix\->IsBiDiagonal();
|
|
|
412 .Ve
|
|
|
413 .Sp
|
|
|
414 Returns 1 or 0 based on whether \fIMatrix\fR is upper or lower bidiagonal matrix.
|
|
|
415 .IP "\fBIsDiagonal\fR" 4
|
|
|
416 .IX Item "IsDiagonal"
|
|
|
417 .Vb 1
|
|
|
418 \& $Status = $Matrix\->IsDiagonal();
|
|
|
419 .Ve
|
|
|
420 .Sp
|
|
|
421 Returns 1 or 0 based on whether \fIMatrix\fR is a diagonal matrix.
|
|
|
422 .Sp
|
|
|
423 A matrix is a diagonal matrix:
|
|
|
424 .Sp
|
|
|
425 .Vb 3
|
|
|
426 \& . It\*(Aqs a square matrix
|
|
|
427 \& . All its off\-diagonal elements are zeros and its diagonal elements may or may not
|
|
|
428 \& be zeros
|
|
|
429 .Ve
|
|
|
430 .IP "\fBIsIdentity\fR" 4
|
|
|
431 .IX Item "IsIdentity"
|
|
|
432 .Vb 1
|
|
|
433 \& $Status = $Matrix\->IsIdentity();
|
|
|
434 .Ve
|
|
|
435 .Sp
|
|
|
436 Returns 1 or 0 based on whether \fIMatrix\fR is an identity matrix.
|
|
|
437 .IP "\fBIsLeftTriangular\fR" 4
|
|
|
438 .IX Item "IsLeftTriangular"
|
|
|
439 .Vb 1
|
|
|
440 \& $Status = $Matrix\->IsLeftTriangular();
|
|
|
441 .Ve
|
|
|
442 .Sp
|
|
|
443 Returns 1 or 0 based on whether \fIMatrix\fR is a left or lower matrix.
|
|
|
444 .Sp
|
|
|
445 A matrix is a left triangular matrix:
|
|
|
446 .Sp
|
|
|
447 .Vb 2
|
|
|
448 \& . It\*(Aqs a square matrix
|
|
|
449 \& . All its entries above the main diagonal are zero
|
|
|
450 .Ve
|
|
|
451 .IP "\fBIsLowerBiDiagonal\fR" 4
|
|
|
452 .IX Item "IsLowerBiDiagonal"
|
|
|
453 .Vb 1
|
|
|
454 \& $Status = $Matrix\->IsLowerBiDiagonal();
|
|
|
455 .Ve
|
|
|
456 .Sp
|
|
|
457 Returns 1 or 0 based on whether \fIMatrix\fR is a lower bidiagonal matrix.
|
|
|
458 .Sp
|
|
|
459 A matrix is a lower bidiagonal matrix:
|
|
|
460 .Sp
|
|
|
461 .Vb 3
|
|
|
462 \& . It\*(Aqs a square matrix
|
|
|
463 \& . All its main diagonal and lower diagonal elements are non\-zeros and all its
|
|
|
464 \& other elements are zeros
|
|
|
465 .Ve
|
|
|
466 .IP "\fBIsLowerTriangular\fR" 4
|
|
|
467 .IX Item "IsLowerTriangular"
|
|
|
468 .Vb 1
|
|
|
469 \& $Status = $Matrix\->IsLowerTriangular();
|
|
|
470 .Ve
|
|
|
471 .Sp
|
|
|
472 Returns 1 or 0 based on whether \fIMatrix\fR is a left or lower triangular matrix.
|
|
|
473 .Sp
|
|
|
474 A matrix is a lower triangular matrix:
|
|
|
475 .Sp
|
|
|
476 .Vb 2
|
|
|
477 \& . It\*(Aqs a square matrix
|
|
|
478 \& . All its entries above the main diagonal are zero
|
|
|
479 .Ve
|
|
|
480 .IP "\fBIsLowerUniTriangular\fR" 4
|
|
|
481 .IX Item "IsLowerUniTriangular"
|
|
|
482 .Vb 1
|
|
|
483 \& $Status = $Matrix\->IsLowerUniTriangular();
|
|
|
484 .Ve
|
|
|
485 .Sp
|
|
|
486 Returns 1 or 0 based on whether \fIMatrix\fR is a lower triangular matrix.
|
|
|
487 .IP "\fBIsMatrix\fR" 4
|
|
|
488 .IX Item "IsMatrix"
|
|
|
489 .Vb 1
|
|
|
490 \& $Status = Matrix::IsMatrix($Object);
|
|
|
491 .Ve
|
|
|
492 .Sp
|
|
|
493 Returns 1 or 0 based on whether \fIObject\fR is a \fBMatrix\fR object.
|
|
|
494 .IP "\fBIsNegative\fR" 4
|
|
|
495 .IX Item "IsNegative"
|
|
|
496 .Vb 1
|
|
|
497 \& $Status = $Matrix\->IsNegative();
|
|
|
498 .Ve
|
|
|
499 .Sp
|
|
|
500 Returns 1 or 0 based on whether \fIMatrix\fR is a negative matrix containing only values
|
|
|
501 less than or equal to zero.
|
|
|
502 .IP "\fBIsPositive\fR" 4
|
|
|
503 .IX Item "IsPositive"
|
|
|
504 .Vb 1
|
|
|
505 \& $Status = $Matrix\->IsPositive();
|
|
|
506 .Ve
|
|
|
507 .Sp
|
|
|
508 Returns 1 or 0 based on whether \fIMatrix\fR is a negative matrix containing only values
|
|
|
509 greater than or equal to zero.
|
|
|
510 .IP "\fBIsRightTriangular\fR" 4
|
|
|
511 .IX Item "IsRightTriangular"
|
|
|
512 .Vb 1
|
|
|
513 \& $Status = $Matrix\->IsRightTriangular();
|
|
|
514 .Ve
|
|
|
515 .Sp
|
|
|
516 Returns 1 or 0 based on whether \fIMatrix\fR is a right or upper triangular matrix.
|
|
|
517 .IP "\fBIsSkewSymmetric\fR" 4
|
|
|
518 .IX Item "IsSkewSymmetric"
|
|
|
519 .Vb 1
|
|
|
520 \& $Status = $Matrix\->IsSkewSymmetric();
|
|
|
521 .Ve
|
|
|
522 .Sp
|
|
|
523 Returns 1 or 0 based on whether \fIMatrix\fR is a skew or anti symmetric matrix.
|
|
|
524 .IP "\fBIsSquare\fR" 4
|
|
|
525 .IX Item "IsSquare"
|
|
|
526 .Vb 1
|
|
|
527 \& $Status = $Matrix\->IsSquare();
|
|
|
528 .Ve
|
|
|
529 .Sp
|
|
|
530 Returns 1 or 0 based on whether \fIMatrix\fR is a square matrix containing equal
|
|
|
531 number of rows and columns.
|
|
|
532 .IP "\fBIsStrictlyLowerTriangular\fR" 4
|
|
|
533 .IX Item "IsStrictlyLowerTriangular"
|
|
|
534 .Vb 1
|
|
|
535 \& $Status = $Matrix\->IsStrictlyLowerTriangular();
|
|
|
536 .Ve
|
|
|
537 .Sp
|
|
|
538 Returns 1 or 0 based on whether \fIMatrix\fR is a strictly lower triangular matrix.
|
|
|
539 .Sp
|
|
|
540 A matrix is a strictly lower triangular matrix:
|
|
|
541 .Sp
|
|
|
542 .Vb 2
|
|
|
543 \& . It\*(Aqs a square matrix
|
|
|
544 \& . All its entries on and above the main diagonal are zero
|
|
|
545 .Ve
|
|
|
546 .IP "\fBIsStrictlyUpperTriangular\fR" 4
|
|
|
547 .IX Item "IsStrictlyUpperTriangular"
|
|
|
548 .Vb 1
|
|
|
549 \& $Status = $Matrix\->IsStrictlyUpperTriangular();
|
|
|
550 .Ve
|
|
|
551 .Sp
|
|
|
552 Returns 1 or 0 based on whether \fIMatrix\fR is a strictly upper triangular matrix.
|
|
|
553 .Sp
|
|
|
554 A matrix is a strictly upper triangular matrix:
|
|
|
555 .Sp
|
|
|
556 .Vb 2
|
|
|
557 \& . It\*(Aqs a square matrix
|
|
|
558 \& . All its entries on and below the main diagonal are zero
|
|
|
559 .Ve
|
|
|
560 .IP "\fBIsSymmetric\fR" 4
|
|
|
561 .IX Item "IsSymmetric"
|
|
|
562 .Vb 1
|
|
|
563 \& $Status = $Matrix\->IsSymmetric();
|
|
|
564 .Ve
|
|
|
565 .Sp
|
|
|
566 Returns 1 or 0 based on whether \fIMatrix\fR is a symmetric matrix.
|
|
|
567 .Sp
|
|
|
568 A matrix is a symmetric matrix:
|
|
|
569 .Sp
|
|
|
570 .Vb 4
|
|
|
571 \& . It\*(Aqs a square matrix
|
|
|
572 \& . Its elements are symmetric with respect to main diagonal. In other words,
|
|
|
573 \& elements below the main diagonal are equal to the elements above the main
|
|
|
574 \& diagonal.
|
|
|
575 .Ve
|
|
|
576 .Sp
|
|
|
577 Transpose of a symmetric matrix equals the matrix itself.
|
|
|
578 .IP "\fBIsTriDiagonal\fR" 4
|
|
|
579 .IX Item "IsTriDiagonal"
|
|
|
580 .Vb 1
|
|
|
581 \& $Status = $Matrix\->IsTriDiagonal();
|
|
|
582 .Ve
|
|
|
583 .Sp
|
|
|
584 Returns 1 or 0 based on whether \fIMatrix\fR is a tridiagonal matrix.
|
|
|
585 .Sp
|
|
|
586 A matrix is a tribidiagonal matrix:
|
|
|
587 .Sp
|
|
|
588 .Vb 3
|
|
|
589 \& . It\*(Aqs a square matrix
|
|
|
590 \& . All its main diagonal, upper diagonal, and lower diagonal elements are non\-zeros and all its
|
|
|
591 \& other elements are zeros
|
|
|
592 .Ve
|
|
|
593 .IP "\fBIsUnit\fR" 4
|
|
|
594 .IX Item "IsUnit"
|
|
|
595 .Vb 1
|
|
|
596 \& $Status = $Matrix\->IsUnit();
|
|
|
597 .Ve
|
|
|
598 .Sp
|
|
|
599 Returns 1 or 0 based on whether \fIMatrix\fR is a unit matrix.
|
|
|
600 .Sp
|
|
|
601 A matrix is a unit matrix:
|
|
|
602 .Sp
|
|
|
603 .Vb 2
|
|
|
604 \& . It\*(Aqs a square matrix
|
|
|
605 \& . All its diagonal elements are ones and its off\-diagonal elements are zeros
|
|
|
606 .Ve
|
|
|
607 .IP "\fBIsUnitLowerTriangular\fR" 4
|
|
|
608 .IX Item "IsUnitLowerTriangular"
|
|
|
609 .Vb 1
|
|
|
610 \& $Status = $Matrix\->IsUnitLowerTriangular();
|
|
|
611 .Ve
|
|
|
612 .Sp
|
|
|
613 Returns 1 or 0 based on whether \fIMatrix\fR is an unit lower triangular matrix.
|
|
|
614 .Sp
|
|
|
615 A matrix is an unit lower triangular matrix:
|
|
|
616 .Sp
|
|
|
617 .Vb 3
|
|
|
618 \& . It\*(Aqs a square matrix
|
|
|
619 \& . All its entries main diagonal are one
|
|
|
620 \& . All its entries above the main diagonal are zero
|
|
|
621 .Ve
|
|
|
622 .IP "\fBIsUnitUpperTriangular\fR" 4
|
|
|
623 .IX Item "IsUnitUpperTriangular"
|
|
|
624 .Vb 1
|
|
|
625 \& $Status = $Matrix\->IsUnitUpperTriangular();
|
|
|
626 .Ve
|
|
|
627 .Sp
|
|
|
628 Returns 1 or 0 based on whether \fIMatrix\fR is an unit upper triangular matrix.
|
|
|
629 .Sp
|
|
|
630 A matrix is an unit upper triangular matrix:
|
|
|
631 .Sp
|
|
|
632 .Vb 3
|
|
|
633 \& . It\*(Aqs a square matrix
|
|
|
634 \& . All its entries main diagonal are one
|
|
|
635 \& . All its entries below the main diagonal are zero
|
|
|
636 .Ve
|
|
|
637 .IP "\fBIsUpperBiDiagonal\fR" 4
|
|
|
638 .IX Item "IsUpperBiDiagonal"
|
|
|
639 .Vb 1
|
|
|
640 \& $Status = $Matrix\->IsUpperBiDiagonal();
|
|
|
641 .Ve
|
|
|
642 .Sp
|
|
|
643 Returns 1 or 0 based on whether \fIMatrix\fR is an upper bidiagonal matrix.
|
|
|
644 .Sp
|
|
|
645 A matrix is an upper bidiagonal matrix:
|
|
|
646 .Sp
|
|
|
647 .Vb 3
|
|
|
648 \& . It\*(Aqs a square matrix
|
|
|
649 \& . All its main diagonal and upper diagonal elements are non\-zeros and all its
|
|
|
650 \& other elements are zeros
|
|
|
651 .Ve
|
|
|
652 .IP "\fBIsUpperTriangular\fR" 4
|
|
|
653 .IX Item "IsUpperTriangular"
|
|
|
654 .Vb 1
|
|
|
655 \& $Status = $Matrix\->IsUpperTriangular();
|
|
|
656 .Ve
|
|
|
657 .Sp
|
|
|
658 Returns 1 or 0 based on whether \fIMatrix\fR is a right or upper triangular matrix.
|
|
|
659 .Sp
|
|
|
660 A matrix is an upper triangular matrix:
|
|
|
661 .Sp
|
|
|
662 .Vb 2
|
|
|
663 \& . It\*(Aqs a square matrix
|
|
|
664 \& . All its entries below the main diagonal are zero
|
|
|
665 .Ve
|
|
|
666 .IP "\fBIsUpperUniTriangular\fR" 4
|
|
|
667 .IX Item "IsUpperUniTriangular"
|
|
|
668 .Vb 1
|
|
|
669 \& $Status = $Matrix\->IsUpperUniTriangular();
|
|
|
670 .Ve
|
|
|
671 .Sp
|
|
|
672 Returns 1 or 0 based on whether \fIMatrix\fR is a right or upper triangular matrix.
|
|
|
673 .IP "\fBNewFromColumns\fR" 4
|
|
|
674 .IX Item "NewFromColumns"
|
|
|
675 .Vb 3
|
|
|
676 \& $NewMatrix = Matrix::NewFromColumns($Col1Vector, $Col2Vector, ...);
|
|
|
677 \& $NewMatrix = Matrix::NewFromColumns($Col1ValuesRef, $Col2ValuesRef, ...);
|
|
|
678 \& $NewMatrix = Matrix::NewFromColumns("Val1 Val2 ...", "Val1 Val2", ...);
|
|
|
679 \&
|
|
|
680 \& $NewMatrix = $Matrix\->NewFromColumns($Col1Vector, $Col2Vector, ...);
|
|
|
681 \& $NewMatrix = $Matrix\->NewFromColumns($Col1ValuesRef, $Col2ValuesRef, ...);
|
|
|
682 \& $NewMatrix = $Matrix\->NewFromColumns("Val1 Val2 ...", "Val1 Val2", ...);
|
|
|
683 .Ve
|
|
|
684 .Sp
|
|
|
685 Creates a new \fBMatrix\fR using specified column values and returns \fBNewMatrix\fR object.
|
|
|
686 .Sp
|
|
|
687 The column values can be specified in one of the following formats:
|
|
|
688 .Sp
|
|
|
689 .Vb 3
|
|
|
690 \& . List of vector objects
|
|
|
691 \& . References to list of values
|
|
|
692 \& . List of strings containing columns values delimited by space
|
|
|
693 .Ve
|
|
|
694 .Sp
|
|
|
695 Each column must contain the same number of values.
|
|
|
696 .IP "\fBNewFromDiagonal\fR" 4
|
|
|
697 .IX Item "NewFromDiagonal"
|
|
|
698 .Vb 3
|
|
|
699 \& $NewMatrix = Matrix::NewFromDiagonal($DiagonalVector);
|
|
|
700 \& $NewMatrix = Matrix::NewFromDiagonal($DiagonalValuesRef);
|
|
|
701 \& $NewMatrix = Matrix::NewFromDiagonal("Val1 Val2 ...");
|
|
|
702 \&
|
|
|
703 \& $NewMatrix = Matrix\->NewFromDiagonal($DiagonalVector);
|
|
|
704 \& $NewMatrix = Matrix\->NewFromDiagonal($DiagonalValuesRef);
|
|
|
705 \& $NewMatrix = Matrix\->NewFromDiagonal("Val1 Val2 ...");
|
|
|
706 .Ve
|
|
|
707 .Sp
|
|
|
708 Creates a new \fBMatrix\fR using specified diagonal values and returns \fBNewMatrix\fR object.
|
|
|
709 .Sp
|
|
|
710 The column values can be specified in one of the following formats:
|
|
|
711 .Sp
|
|
|
712 .Vb 3
|
|
|
713 \& . A vector object
|
|
|
714 \& . Reference to list of values
|
|
|
715 \& . Strings containing diagonal values delimited by space
|
|
|
716 .Ve
|
|
|
717 .IP "\fBNewFromRows\fR" 4
|
|
|
718 .IX Item "NewFromRows"
|
|
|
719 .Vb 3
|
|
|
720 \& $NewMatrix = Matrix::NewFromRows($Row1Vector, $RowVector, ...);
|
|
|
721 \& $NewMatrix = Matrix::NewFromRows($Row1ValuesRef, $Row2ValuesRef, ...);
|
|
|
722 \& $NewMatrix = Matrix::NewFromRows("Val1 Val2 ...", "Val1 Val2", ...);
|
|
|
723 \&
|
|
|
724 \& $NewMatrix = $Matrix\->NewFromRows($Row1Vector, $Row2Vector, ...);
|
|
|
725 \& $NewMatrix = $Matrix\->NewFromRows($Row1ValuesRef, $Row2ValuesRef, ...);
|
|
|
726 \& $NewMatrix = $Matrix\->NewFromRows("Val1 Val2 ...", "Val1 Val2", ...);
|
|
|
727 .Ve
|
|
|
728 .Sp
|
|
|
729 Creates a new \fBMatrix\fR using specified row values and returns \fBNewMatrix\fR object.
|
|
|
730 .Sp
|
|
|
731 The row values can be specified in one of the following formats:
|
|
|
732 .Sp
|
|
|
733 .Vb 3
|
|
|
734 \& . List of vector objects
|
|
|
735 \& . References to list of values
|
|
|
736 \& . List of strings containing columns values delimited by space
|
|
|
737 .Ve
|
|
|
738 .Sp
|
|
|
739 Each row must contain the same number of values.
|
|
|
740 .IP "\fBOne\fR" 4
|
|
|
741 .IX Item "One"
|
|
|
742 .Vb 1
|
|
|
743 \& $Matrix\->One();
|
|
|
744 .Ve
|
|
|
745 .Sp
|
|
|
746 Sets values of all \fIMatrix\fR elements to 1 and returns \fIMatrix\fR.
|
|
|
747 .IP "\fBSetAllValues\fR" 4
|
|
|
748 .IX Item "SetAllValues"
|
|
|
749 .Vb 1
|
|
|
750 \& $Matrix\->SetAllValues($Value);
|
|
|
751 .Ve
|
|
|
752 .Sp
|
|
|
753 Sets values of all \fIMatrix\fR elements to specified \fIValue\fR and returns \fIMatrix\fR.
|
|
|
754 .IP "\fBSetColumnValues\fR" 4
|
|
|
755 .IX Item "SetColumnValues"
|
|
|
756 .Vb 4
|
|
|
757 \& $Matrix\->SetColumnValues($ColIndex, @Values);
|
|
|
758 \& $Matrix\->SetColumnValues($ColIndex, \e@Values);
|
|
|
759 \& $Matrix\->SetColumnValues($ColIndex, $VectorObject);
|
|
|
760 \& $Matrix\->SetColumnValues($ColIndex, "Value1 Value2 Value3 ...");
|
|
|
761 .Ve
|
|
|
762 .Sp
|
|
|
763 Sets column values of a specified \fIColIndex\fR of \fIMatrix\fR using an array, reference to an array,
|
|
|
764 another vector, or space delimited value string and returns \fIMatrix\fR.
|
|
|
765 .IP "\fBSetDiagonalValues\fR" 4
|
|
|
766 .IX Item "SetDiagonalValues"
|
|
|
767 .Vb 4
|
|
|
768 \& $Matrix\->SetDiagonalValues(@Values);
|
|
|
769 \& $Matrix\->SetDiagonalValues(\e@Values);
|
|
|
770 \& $Matrix\->SetDiagonalValues($VectorObject);
|
|
|
771 \& $Matrix\->SetDiagonalValues("Value1 Value2 Value3 ...");
|
|
|
772 .Ve
|
|
|
773 .Sp
|
|
|
774 Sets values of the diagonal in square \fIMatrix\fR and returns \fIMatrix\fR.
|
|
|
775 .IP "\fBSetMatrixPrintStyle\fR" 4
|
|
|
776 .IX Item "SetMatrixPrintStyle"
|
|
|
777 .Vb 2
|
|
|
778 \& $Matrix\->SetMatrixPrintStyle($MatrixStyle);
|
|
|
779 \& $Matrix::SetMatrixPrintStyle($MatrixStyle);
|
|
|
780 .Ve
|
|
|
781 .Sp
|
|
|
782 Sets print style for matrix rows for an individual object or the whole class during StringifyMatrix
|
|
|
783 operation. Possible \fIMatrixStyle\fR values: \fIAllRowsInOneLine, OneRowPerLine\fR. Default:
|
|
|
784 \&\fIAllRowsInOneLine\fR.
|
|
|
785 .IP "\fBSetRowValues\fR" 4
|
|
|
786 .IX Item "SetRowValues"
|
|
|
787 .Vb 4
|
|
|
788 \& $Matrix\->SetRowValues($ColIndex, @Values);
|
|
|
789 \& $Matrix\->SetRowValues($ColIndex, \e@Values);
|
|
|
790 \& $Matrix\->SetRowValues($ColIndex, $VectorObjext);
|
|
|
791 \& $Matrix\->SetRowValues($ColIndex, "Value1 Value2 Value3 ...");
|
|
|
792 .Ve
|
|
|
793 .Sp
|
|
|
794 Sets row values of a specified \fIRowIndex\fR of \fIMatrix\fR using an array, reference to an array,
|
|
|
795 another vector, or space delimited value string and returns \fIMatrix\fR.
|
|
|
796 .IP "\fBSetValue\fR" 4
|
|
|
797 .IX Item "SetValue"
|
|
|
798 .Vb 1
|
|
|
799 \& $Matrix\->SetValue($RowIndex, $ColIndex, $Value, [$SkipIndexCheck]);
|
|
|
800 .Ve
|
|
|
801 .Sp
|
|
|
802 Sets \fBValue\fR of \fIMatrix\fR element specified using \fIRowIndex\fR and \fIColIndex\fR with indicies
|
|
|
803 starting at 0 with optional validation of specified index values and return \fIMatrix\fR.
|
|
|
804 .IP "\fBSetValuePrintFormat\fR" 4
|
|
|
805 .IX Item "SetValuePrintFormat"
|
|
|
806 .Vb 2
|
|
|
807 \& $Matrix\->SetValuePrintFormat($ValueFormat);
|
|
|
808 \& $Matrix::SetValuePrintFormat($ValueFormat);
|
|
|
809 .Ve
|
|
|
810 .Sp
|
|
|
811 Sets value print format for an individual object or the whole class during StringifyMatrix operation
|
|
|
812 and returns \fIMatrix\fR.
|
|
|
813 .IP "\fBStringifyMatrix\fR" 4
|
|
|
814 .IX Item "StringifyMatrix"
|
|
|
815 .Vb 1
|
|
|
816 \& $String = $Matrix\->StringifyMatrix();
|
|
|
817 .Ve
|
|
|
818 .Sp
|
|
|
819 Returns a string containing information about \fIMatrix\fR object.
|
|
|
820 .IP "\fBTranspose\fR" 4
|
|
|
821 .IX Item "Transpose"
|
|
|
822 .Vb 1
|
|
|
823 \& $Matrix\->Transpose();
|
|
|
824 .Ve
|
|
|
825 .Sp
|
|
|
826 Transposes \fIMatrix\fR by swaping rows with columns and returns \fIMatrix\fR.
|
|
|
827 .IP "\fBUnitMatrix\fR" 4
|
|
|
828 .IX Item "UnitMatrix"
|
|
|
829 .Vb 3
|
|
|
830 \& $NewUnitMatrix = $Matrix::UnitMatrix($NumOfRows, $NumOfCols);
|
|
|
831 \& $NewUnitMatrix = $Matrix::UnitMatrix();
|
|
|
832 \& $NewUnitMatrix = $Matrix\->UnitMatrix($NumOfRows, $NumOfCols);
|
|
|
833 .Ve
|
|
|
834 .Sp
|
|
|
835 Creates a new \fBUnitMatrix\fR of specified size \fINumOfRows x NumOfCol\fR or of size 3 x 3 and
|
|
|
836 returns \fBNewUnitMatrix\fR object.
|
|
|
837 .IP "\fBZero\fR" 4
|
|
|
838 .IX Item "Zero"
|
|
|
839 .Vb 1
|
|
|
840 \& $Matrix\->Zero();
|
|
|
841 .Ve
|
|
|
842 .Sp
|
|
|
843 Sets values of all \fIMatrix\fR elements to 0 and returns \fIMatrix\fR.
|
|
|
844 .IP "\fBZeroMatrix\fR" 4
|
|
|
845 .IX Item "ZeroMatrix"
|
|
|
846 .Vb 3
|
|
|
847 \& $NewZeroMatrix = $Matrix::ZeroMatrix($NumOfRows, $NumOfCols);
|
|
|
848 \& $NewZeroMatrix = $Matrix::ZeroMatrix();
|
|
|
849 \& $NewZeroMatrix = $Matrix\->ZeroMatrix($NumOfRows, $NumOfCols);
|
|
|
850 .Ve
|
|
|
851 .Sp
|
|
|
852 Creates a new \fBZeroMatrix\fR of specified size \fINumOfRows x NumOfCol\fR or of size 3 x 3 and
|
|
|
853 returns \fBNewZeroMatrix\fR object.
|
|
|
854 .SH "AUTHOR"
|
|
|
855 .IX Header "AUTHOR"
|
|
|
856 Manish Sud <msud@san.rr.com>
|
|
|
857 .SH "SEE ALSO"
|
|
|
858 .IX Header "SEE ALSO"
|
|
|
859 Vector.pm
|
|
|
860 .SH "COPYRIGHT"
|
|
|
861 .IX Header "COPYRIGHT"
|
|
|
862 Copyright (C) 2015 Manish Sud. All rights reserved.
|
|
|
863 .PP
|
|
|
864 This file is part of MayaChemTools.
|
|
|
865 .PP
|
|
|
866 MayaChemTools is free software; you can redistribute it and/or modify it under
|
|
|
867 the terms of the \s-1GNU\s0 Lesser General Public License as published by the Free
|
|
|
868 Software Foundation; either version 3 of the License, or (at your option)
|
|
|
869 any later version.
|
