[2806] | 1 | /*************************************************************************
|
---|
| 2 | Copyright (c) 1992-2007 The University of Tennessee. All rights reserved.
|
---|
| 3 |
|
---|
| 4 | Contributors:
|
---|
| 5 | * Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
|
---|
| 6 | pseudocode.
|
---|
| 7 |
|
---|
| 8 | See subroutines comments for additional copyrights.
|
---|
| 9 |
|
---|
| 10 | >>> SOURCE LICENSE >>>
|
---|
| 11 | This program is free software; you can redistribute it and/or modify
|
---|
| 12 | it under the terms of the GNU General Public License as published by
|
---|
| 13 | the Free Software Foundation (www.fsf.org); either version 2 of the
|
---|
| 14 | License, or (at your option) any later version.
|
---|
| 15 |
|
---|
| 16 | This program is distributed in the hope that it will be useful,
|
---|
| 17 | but WITHOUT ANY WARRANTY; without even the implied warranty of
|
---|
| 18 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
---|
| 19 | GNU General Public License for more details.
|
---|
| 20 |
|
---|
| 21 | A copy of the GNU General Public License is available at
|
---|
| 22 | http://www.fsf.org/licensing/licenses
|
---|
| 23 |
|
---|
| 24 | >>> END OF LICENSE >>>
|
---|
| 25 | *************************************************************************/
|
---|
| 26 |
|
---|
| 27 | using System;
|
---|
| 28 |
|
---|
| 29 | namespace alglib
|
---|
| 30 | {
|
---|
| 31 | public class bidiagonal
|
---|
| 32 | {
|
---|
| 33 | /*************************************************************************
|
---|
| 34 | Reduction of a rectangular matrix to bidiagonal form
|
---|
| 35 |
|
---|
| 36 | The algorithm reduces the rectangular matrix A to bidiagonal form by
|
---|
| 37 | orthogonal transformations P and Q: A = Q*B*P.
|
---|
| 38 |
|
---|
| 39 | Input parameters:
|
---|
| 40 | A - source matrix. array[0..M-1, 0..N-1]
|
---|
| 41 | M - number of rows in matrix A.
|
---|
| 42 | N - number of columns in matrix A.
|
---|
| 43 |
|
---|
| 44 | Output parameters:
|
---|
| 45 | A - matrices Q, B, P in compact form (see below).
|
---|
| 46 | TauQ - scalar factors which are used to form matrix Q.
|
---|
| 47 | TauP - scalar factors which are used to form matrix P.
|
---|
| 48 |
|
---|
| 49 | The main diagonal and one of the secondary diagonals of matrix A are
|
---|
| 50 | replaced with bidiagonal matrix B. Other elements contain elementary
|
---|
| 51 | reflections which form MxM matrix Q and NxN matrix P, respectively.
|
---|
| 52 |
|
---|
| 53 | If M>=N, B is the upper bidiagonal MxN matrix and is stored in the
|
---|
| 54 | corresponding elements of matrix A. Matrix Q is represented as a
|
---|
| 55 | product of elementary reflections Q = H(0)*H(1)*...*H(n-1), where
|
---|
| 56 | H(i) = 1-tau*v*v'. Here tau is a scalar which is stored in TauQ[i], and
|
---|
| 57 | vector v has the following structure: v(0:i-1)=0, v(i)=1, v(i+1:m-1) is
|
---|
| 58 | stored in elements A(i+1:m-1,i). Matrix P is as follows: P =
|
---|
| 59 | G(0)*G(1)*...*G(n-2), where G(i) = 1 - tau*u*u'. Tau is stored in TauP[i],
|
---|
| 60 | u(0:i)=0, u(i+1)=1, u(i+2:n-1) is stored in elements A(i,i+2:n-1).
|
---|
| 61 |
|
---|
| 62 | If M<N, B is the lower bidiagonal MxN matrix and is stored in the
|
---|
| 63 | corresponding elements of matrix A. Q = H(0)*H(1)*...*H(m-2), where
|
---|
| 64 | H(i) = 1 - tau*v*v', tau is stored in TauQ, v(0:i)=0, v(i+1)=1, v(i+2:m-1)
|
---|
| 65 | is stored in elements A(i+2:m-1,i). P = G(0)*G(1)*...*G(m-1),
|
---|
| 66 | G(i) = 1-tau*u*u', tau is stored in TauP, u(0:i-1)=0, u(i)=1, u(i+1:n-1)
|
---|
| 67 | is stored in A(i,i+1:n-1).
|
---|
| 68 |
|
---|
| 69 | EXAMPLE:
|
---|
| 70 |
|
---|
| 71 | m=6, n=5 (m > n): m=5, n=6 (m < n):
|
---|
| 72 |
|
---|
| 73 | ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 )
|
---|
| 74 | ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 )
|
---|
| 75 | ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 )
|
---|
| 76 | ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 )
|
---|
| 77 | ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 )
|
---|
| 78 | ( v1 v2 v3 v4 v5 )
|
---|
| 79 |
|
---|
| 80 | Here vi and ui are vectors which form H(i) and G(i), and d and e -
|
---|
| 81 | are the diagonal and off-diagonal elements of matrix B.
|
---|
| 82 | *************************************************************************/
|
---|
| 83 | public static void rmatrixbd(ref double[,] a,
|
---|
| 84 | int m,
|
---|
| 85 | int n,
|
---|
| 86 | ref double[] tauq,
|
---|
| 87 | ref double[] taup)
|
---|
| 88 | {
|
---|
| 89 | double[] work = new double[0];
|
---|
| 90 | double[] t = new double[0];
|
---|
| 91 | int minmn = 0;
|
---|
| 92 | int maxmn = 0;
|
---|
| 93 | int i = 0;
|
---|
| 94 | double ltau = 0;
|
---|
| 95 | int i_ = 0;
|
---|
| 96 | int i1_ = 0;
|
---|
| 97 |
|
---|
| 98 |
|
---|
| 99 | //
|
---|
| 100 | // Prepare
|
---|
| 101 | //
|
---|
| 102 | if( n<=0 | m<=0 )
|
---|
| 103 | {
|
---|
| 104 | return;
|
---|
| 105 | }
|
---|
| 106 | minmn = Math.Min(m, n);
|
---|
| 107 | maxmn = Math.Max(m, n);
|
---|
| 108 | work = new double[maxmn+1];
|
---|
| 109 | t = new double[maxmn+1];
|
---|
| 110 | if( m>=n )
|
---|
| 111 | {
|
---|
| 112 | tauq = new double[n-1+1];
|
---|
| 113 | taup = new double[n-1+1];
|
---|
| 114 | }
|
---|
| 115 | else
|
---|
| 116 | {
|
---|
| 117 | tauq = new double[m-1+1];
|
---|
| 118 | taup = new double[m-1+1];
|
---|
| 119 | }
|
---|
| 120 | if( m>=n )
|
---|
| 121 | {
|
---|
| 122 |
|
---|
| 123 | //
|
---|
| 124 | // Reduce to upper bidiagonal form
|
---|
| 125 | //
|
---|
| 126 | for(i=0; i<=n-1; i++)
|
---|
| 127 | {
|
---|
| 128 |
|
---|
| 129 | //
|
---|
| 130 | // Generate elementary reflector H(i) to annihilate A(i+1:m-1,i)
|
---|
| 131 | //
|
---|
| 132 | i1_ = (i) - (1);
|
---|
| 133 | for(i_=1; i_<=m-i;i_++)
|
---|
| 134 | {
|
---|
| 135 | t[i_] = a[i_+i1_,i];
|
---|
| 136 | }
|
---|
| 137 | reflections.generatereflection(ref t, m-i, ref ltau);
|
---|
| 138 | tauq[i] = ltau;
|
---|
| 139 | i1_ = (1) - (i);
|
---|
| 140 | for(i_=i; i_<=m-1;i_++)
|
---|
| 141 | {
|
---|
| 142 | a[i_,i] = t[i_+i1_];
|
---|
| 143 | }
|
---|
| 144 | t[1] = 1;
|
---|
| 145 |
|
---|
| 146 | //
|
---|
| 147 | // Apply H(i) to A(i:m-1,i+1:n-1) from the left
|
---|
| 148 | //
|
---|
| 149 | reflections.applyreflectionfromtheleft(ref a, ltau, ref t, i, m-1, i+1, n-1, ref work);
|
---|
| 150 | if( i<n-1 )
|
---|
| 151 | {
|
---|
| 152 |
|
---|
| 153 | //
|
---|
| 154 | // Generate elementary reflector G(i) to annihilate
|
---|
| 155 | // A(i,i+2:n-1)
|
---|
| 156 | //
|
---|
| 157 | i1_ = (i+1) - (1);
|
---|
| 158 | for(i_=1; i_<=n-i-1;i_++)
|
---|
| 159 | {
|
---|
| 160 | t[i_] = a[i,i_+i1_];
|
---|
| 161 | }
|
---|
| 162 | reflections.generatereflection(ref t, n-1-i, ref ltau);
|
---|
| 163 | taup[i] = ltau;
|
---|
| 164 | i1_ = (1) - (i+1);
|
---|
| 165 | for(i_=i+1; i_<=n-1;i_++)
|
---|
| 166 | {
|
---|
| 167 | a[i,i_] = t[i_+i1_];
|
---|
| 168 | }
|
---|
| 169 | t[1] = 1;
|
---|
| 170 |
|
---|
| 171 | //
|
---|
| 172 | // Apply G(i) to A(i+1:m-1,i+1:n-1) from the right
|
---|
| 173 | //
|
---|
| 174 | reflections.applyreflectionfromtheright(ref a, ltau, ref t, i+1, m-1, i+1, n-1, ref work);
|
---|
| 175 | }
|
---|
| 176 | else
|
---|
| 177 | {
|
---|
| 178 | taup[i] = 0;
|
---|
| 179 | }
|
---|
| 180 | }
|
---|
| 181 | }
|
---|
| 182 | else
|
---|
| 183 | {
|
---|
| 184 |
|
---|
| 185 | //
|
---|
| 186 | // Reduce to lower bidiagonal form
|
---|
| 187 | //
|
---|
| 188 | for(i=0; i<=m-1; i++)
|
---|
| 189 | {
|
---|
| 190 |
|
---|
| 191 | //
|
---|
| 192 | // Generate elementary reflector G(i) to annihilate A(i,i+1:n-1)
|
---|
| 193 | //
|
---|
| 194 | i1_ = (i) - (1);
|
---|
| 195 | for(i_=1; i_<=n-i;i_++)
|
---|
| 196 | {
|
---|
| 197 | t[i_] = a[i,i_+i1_];
|
---|
| 198 | }
|
---|
| 199 | reflections.generatereflection(ref t, n-i, ref ltau);
|
---|
| 200 | taup[i] = ltau;
|
---|
| 201 | i1_ = (1) - (i);
|
---|
| 202 | for(i_=i; i_<=n-1;i_++)
|
---|
| 203 | {
|
---|
| 204 | a[i,i_] = t[i_+i1_];
|
---|
| 205 | }
|
---|
| 206 | t[1] = 1;
|
---|
| 207 |
|
---|
| 208 | //
|
---|
| 209 | // Apply G(i) to A(i+1:m-1,i:n-1) from the right
|
---|
| 210 | //
|
---|
| 211 | reflections.applyreflectionfromtheright(ref a, ltau, ref t, i+1, m-1, i, n-1, ref work);
|
---|
| 212 | if( i<m-1 )
|
---|
| 213 | {
|
---|
| 214 |
|
---|
| 215 | //
|
---|
| 216 | // Generate elementary reflector H(i) to annihilate
|
---|
| 217 | // A(i+2:m-1,i)
|
---|
| 218 | //
|
---|
| 219 | i1_ = (i+1) - (1);
|
---|
| 220 | for(i_=1; i_<=m-1-i;i_++)
|
---|
| 221 | {
|
---|
| 222 | t[i_] = a[i_+i1_,i];
|
---|
| 223 | }
|
---|
| 224 | reflections.generatereflection(ref t, m-1-i, ref ltau);
|
---|
| 225 | tauq[i] = ltau;
|
---|
| 226 | i1_ = (1) - (i+1);
|
---|
| 227 | for(i_=i+1; i_<=m-1;i_++)
|
---|
| 228 | {
|
---|
| 229 | a[i_,i] = t[i_+i1_];
|
---|
| 230 | }
|
---|
| 231 | t[1] = 1;
|
---|
| 232 |
|
---|
| 233 | //
|
---|
| 234 | // Apply H(i) to A(i+1:m-1,i+1:n-1) from the left
|
---|
| 235 | //
|
---|
| 236 | reflections.applyreflectionfromtheleft(ref a, ltau, ref t, i+1, m-1, i+1, n-1, ref work);
|
---|
| 237 | }
|
---|
| 238 | else
|
---|
| 239 | {
|
---|
| 240 | tauq[i] = 0;
|
---|
| 241 | }
|
---|
| 242 | }
|
---|
| 243 | }
|
---|
| 244 | }
|
---|
| 245 |
|
---|
| 246 |
|
---|
| 247 | /*************************************************************************
|
---|
| 248 | Unpacking matrix Q which reduces a matrix to bidiagonal form.
|
---|
| 249 |
|
---|
| 250 | Input parameters:
|
---|
| 251 | QP - matrices Q and P in compact form.
|
---|
| 252 | Output of ToBidiagonal subroutine.
|
---|
| 253 | M - number of rows in matrix A.
|
---|
| 254 | N - number of columns in matrix A.
|
---|
| 255 | TAUQ - scalar factors which are used to form Q.
|
---|
| 256 | Output of ToBidiagonal subroutine.
|
---|
| 257 | QColumns - required number of columns in matrix Q.
|
---|
| 258 | M>=QColumns>=0.
|
---|
| 259 |
|
---|
| 260 | Output parameters:
|
---|
| 261 | Q - first QColumns columns of matrix Q.
|
---|
| 262 | Array[0..M-1, 0..QColumns-1]
|
---|
| 263 | If QColumns=0, the array is not modified.
|
---|
| 264 |
|
---|
| 265 | -- ALGLIB --
|
---|
| 266 | Copyright 2005 by Bochkanov Sergey
|
---|
| 267 | *************************************************************************/
|
---|
| 268 | public static void rmatrixbdunpackq(ref double[,] qp,
|
---|
| 269 | int m,
|
---|
| 270 | int n,
|
---|
| 271 | ref double[] tauq,
|
---|
| 272 | int qcolumns,
|
---|
| 273 | ref double[,] q)
|
---|
| 274 | {
|
---|
| 275 | int i = 0;
|
---|
| 276 | int j = 0;
|
---|
| 277 |
|
---|
| 278 | System.Diagnostics.Debug.Assert(qcolumns<=m, "RMatrixBDUnpackQ: QColumns>M!");
|
---|
| 279 | System.Diagnostics.Debug.Assert(qcolumns>=0, "RMatrixBDUnpackQ: QColumns<0!");
|
---|
| 280 | if( m==0 | n==0 | qcolumns==0 )
|
---|
| 281 | {
|
---|
| 282 | return;
|
---|
| 283 | }
|
---|
| 284 |
|
---|
| 285 | //
|
---|
| 286 | // prepare Q
|
---|
| 287 | //
|
---|
| 288 | q = new double[m-1+1, qcolumns-1+1];
|
---|
| 289 | for(i=0; i<=m-1; i++)
|
---|
| 290 | {
|
---|
| 291 | for(j=0; j<=qcolumns-1; j++)
|
---|
| 292 | {
|
---|
| 293 | if( i==j )
|
---|
| 294 | {
|
---|
| 295 | q[i,j] = 1;
|
---|
| 296 | }
|
---|
| 297 | else
|
---|
| 298 | {
|
---|
| 299 | q[i,j] = 0;
|
---|
| 300 | }
|
---|
| 301 | }
|
---|
| 302 | }
|
---|
| 303 |
|
---|
| 304 | //
|
---|
| 305 | // Calculate
|
---|
| 306 | //
|
---|
| 307 | rmatrixbdmultiplybyq(ref qp, m, n, ref tauq, ref q, m, qcolumns, false, false);
|
---|
| 308 | }
|
---|
| 309 |
|
---|
| 310 |
|
---|
| 311 | /*************************************************************************
|
---|
| 312 | Multiplication by matrix Q which reduces matrix A to bidiagonal form.
|
---|
| 313 |
|
---|
| 314 | The algorithm allows pre- or post-multiply by Q or Q'.
|
---|
| 315 |
|
---|
| 316 | Input parameters:
|
---|
| 317 | QP - matrices Q and P in compact form.
|
---|
| 318 | Output of ToBidiagonal subroutine.
|
---|
| 319 | M - number of rows in matrix A.
|
---|
| 320 | N - number of columns in matrix A.
|
---|
| 321 | TAUQ - scalar factors which are used to form Q.
|
---|
| 322 | Output of ToBidiagonal subroutine.
|
---|
| 323 | Z - multiplied matrix.
|
---|
| 324 | array[0..ZRows-1,0..ZColumns-1]
|
---|
| 325 | ZRows - number of rows in matrix Z. If FromTheRight=False,
|
---|
| 326 | ZRows=M, otherwise ZRows can be arbitrary.
|
---|
| 327 | ZColumns - number of columns in matrix Z. If FromTheRight=True,
|
---|
| 328 | ZColumns=M, otherwise ZColumns can be arbitrary.
|
---|
| 329 | FromTheRight - pre- or post-multiply.
|
---|
| 330 | DoTranspose - multiply by Q or Q'.
|
---|
| 331 |
|
---|
| 332 | Output parameters:
|
---|
| 333 | Z - product of Z and Q.
|
---|
| 334 | Array[0..ZRows-1,0..ZColumns-1]
|
---|
| 335 | If ZRows=0 or ZColumns=0, the array is not modified.
|
---|
| 336 |
|
---|
| 337 | -- ALGLIB --
|
---|
| 338 | Copyright 2005 by Bochkanov Sergey
|
---|
| 339 | *************************************************************************/
|
---|
| 340 | public static void rmatrixbdmultiplybyq(ref double[,] qp,
|
---|
| 341 | int m,
|
---|
| 342 | int n,
|
---|
| 343 | ref double[] tauq,
|
---|
| 344 | ref double[,] z,
|
---|
| 345 | int zrows,
|
---|
| 346 | int zcolumns,
|
---|
| 347 | bool fromtheright,
|
---|
| 348 | bool dotranspose)
|
---|
| 349 | {
|
---|
| 350 | int i = 0;
|
---|
| 351 | int i1 = 0;
|
---|
| 352 | int i2 = 0;
|
---|
| 353 | int istep = 0;
|
---|
| 354 | double[] v = new double[0];
|
---|
| 355 | double[] work = new double[0];
|
---|
| 356 | int mx = 0;
|
---|
| 357 | int i_ = 0;
|
---|
| 358 | int i1_ = 0;
|
---|
| 359 |
|
---|
| 360 | if( m<=0 | n<=0 | zrows<=0 | zcolumns<=0 )
|
---|
| 361 | {
|
---|
| 362 | return;
|
---|
| 363 | }
|
---|
| 364 | System.Diagnostics.Debug.Assert(fromtheright & zcolumns==m | !fromtheright & zrows==m, "RMatrixBDMultiplyByQ: incorrect Z size!");
|
---|
| 365 |
|
---|
| 366 | //
|
---|
| 367 | // init
|
---|
| 368 | //
|
---|
| 369 | mx = Math.Max(m, n);
|
---|
| 370 | mx = Math.Max(mx, zrows);
|
---|
| 371 | mx = Math.Max(mx, zcolumns);
|
---|
| 372 | v = new double[mx+1];
|
---|
| 373 | work = new double[mx+1];
|
---|
| 374 | if( m>=n )
|
---|
| 375 | {
|
---|
| 376 |
|
---|
| 377 | //
|
---|
| 378 | // setup
|
---|
| 379 | //
|
---|
| 380 | if( fromtheright )
|
---|
| 381 | {
|
---|
| 382 | i1 = 0;
|
---|
| 383 | i2 = n-1;
|
---|
| 384 | istep = +1;
|
---|
| 385 | }
|
---|
| 386 | else
|
---|
| 387 | {
|
---|
| 388 | i1 = n-1;
|
---|
| 389 | i2 = 0;
|
---|
| 390 | istep = -1;
|
---|
| 391 | }
|
---|
| 392 | if( dotranspose )
|
---|
| 393 | {
|
---|
| 394 | i = i1;
|
---|
| 395 | i1 = i2;
|
---|
| 396 | i2 = i;
|
---|
| 397 | istep = -istep;
|
---|
| 398 | }
|
---|
| 399 |
|
---|
| 400 | //
|
---|
| 401 | // Process
|
---|
| 402 | //
|
---|
| 403 | i = i1;
|
---|
| 404 | do
|
---|
| 405 | {
|
---|
| 406 | i1_ = (i) - (1);
|
---|
| 407 | for(i_=1; i_<=m-i;i_++)
|
---|
| 408 | {
|
---|
| 409 | v[i_] = qp[i_+i1_,i];
|
---|
| 410 | }
|
---|
| 411 | v[1] = 1;
|
---|
| 412 | if( fromtheright )
|
---|
| 413 | {
|
---|
| 414 | reflections.applyreflectionfromtheright(ref z, tauq[i], ref v, 0, zrows-1, i, m-1, ref work);
|
---|
| 415 | }
|
---|
| 416 | else
|
---|
| 417 | {
|
---|
| 418 | reflections.applyreflectionfromtheleft(ref z, tauq[i], ref v, i, m-1, 0, zcolumns-1, ref work);
|
---|
| 419 | }
|
---|
| 420 | i = i+istep;
|
---|
| 421 | }
|
---|
| 422 | while( i!=i2+istep );
|
---|
| 423 | }
|
---|
| 424 | else
|
---|
| 425 | {
|
---|
| 426 |
|
---|
| 427 | //
|
---|
| 428 | // setup
|
---|
| 429 | //
|
---|
| 430 | if( fromtheright )
|
---|
| 431 | {
|
---|
| 432 | i1 = 0;
|
---|
| 433 | i2 = m-2;
|
---|
| 434 | istep = +1;
|
---|
| 435 | }
|
---|
| 436 | else
|
---|
| 437 | {
|
---|
| 438 | i1 = m-2;
|
---|
| 439 | i2 = 0;
|
---|
| 440 | istep = -1;
|
---|
| 441 | }
|
---|
| 442 | if( dotranspose )
|
---|
| 443 | {
|
---|
| 444 | i = i1;
|
---|
| 445 | i1 = i2;
|
---|
| 446 | i2 = i;
|
---|
| 447 | istep = -istep;
|
---|
| 448 | }
|
---|
| 449 |
|
---|
| 450 | //
|
---|
| 451 | // Process
|
---|
| 452 | //
|
---|
| 453 | if( m-1>0 )
|
---|
| 454 | {
|
---|
| 455 | i = i1;
|
---|
| 456 | do
|
---|
| 457 | {
|
---|
| 458 | i1_ = (i+1) - (1);
|
---|
| 459 | for(i_=1; i_<=m-i-1;i_++)
|
---|
| 460 | {
|
---|
| 461 | v[i_] = qp[i_+i1_,i];
|
---|
| 462 | }
|
---|
| 463 | v[1] = 1;
|
---|
| 464 | if( fromtheright )
|
---|
| 465 | {
|
---|
| 466 | reflections.applyreflectionfromtheright(ref z, tauq[i], ref v, 0, zrows-1, i+1, m-1, ref work);
|
---|
| 467 | }
|
---|
| 468 | else
|
---|
| 469 | {
|
---|
| 470 | reflections.applyreflectionfromtheleft(ref z, tauq[i], ref v, i+1, m-1, 0, zcolumns-1, ref work);
|
---|
| 471 | }
|
---|
| 472 | i = i+istep;
|
---|
| 473 | }
|
---|
| 474 | while( i!=i2+istep );
|
---|
| 475 | }
|
---|
| 476 | }
|
---|
| 477 | }
|
---|
| 478 |
|
---|
| 479 |
|
---|
| 480 | /*************************************************************************
|
---|
| 481 | Unpacking matrix P which reduces matrix A to bidiagonal form.
|
---|
| 482 | The subroutine returns transposed matrix P.
|
---|
| 483 |
|
---|
| 484 | Input parameters:
|
---|
| 485 | QP - matrices Q and P in compact form.
|
---|
| 486 | Output of ToBidiagonal subroutine.
|
---|
| 487 | M - number of rows in matrix A.
|
---|
| 488 | N - number of columns in matrix A.
|
---|
| 489 | TAUP - scalar factors which are used to form P.
|
---|
| 490 | Output of ToBidiagonal subroutine.
|
---|
| 491 | PTRows - required number of rows of matrix P^T. N >= PTRows >= 0.
|
---|
| 492 |
|
---|
| 493 | Output parameters:
|
---|
| 494 | PT - first PTRows columns of matrix P^T
|
---|
| 495 | Array[0..PTRows-1, 0..N-1]
|
---|
| 496 | If PTRows=0, the array is not modified.
|
---|
| 497 |
|
---|
| 498 | -- ALGLIB --
|
---|
| 499 | Copyright 2005-2007 by Bochkanov Sergey
|
---|
| 500 | *************************************************************************/
|
---|
| 501 | public static void rmatrixbdunpackpt(ref double[,] qp,
|
---|
| 502 | int m,
|
---|
| 503 | int n,
|
---|
| 504 | ref double[] taup,
|
---|
| 505 | int ptrows,
|
---|
| 506 | ref double[,] pt)
|
---|
| 507 | {
|
---|
| 508 | int i = 0;
|
---|
| 509 | int j = 0;
|
---|
| 510 |
|
---|
| 511 | System.Diagnostics.Debug.Assert(ptrows<=n, "RMatrixBDUnpackPT: PTRows>N!");
|
---|
| 512 | System.Diagnostics.Debug.Assert(ptrows>=0, "RMatrixBDUnpackPT: PTRows<0!");
|
---|
| 513 | if( m==0 | n==0 | ptrows==0 )
|
---|
| 514 | {
|
---|
| 515 | return;
|
---|
| 516 | }
|
---|
| 517 |
|
---|
| 518 | //
|
---|
| 519 | // prepare PT
|
---|
| 520 | //
|
---|
| 521 | pt = new double[ptrows-1+1, n-1+1];
|
---|
| 522 | for(i=0; i<=ptrows-1; i++)
|
---|
| 523 | {
|
---|
| 524 | for(j=0; j<=n-1; j++)
|
---|
| 525 | {
|
---|
| 526 | if( i==j )
|
---|
| 527 | {
|
---|
| 528 | pt[i,j] = 1;
|
---|
| 529 | }
|
---|
| 530 | else
|
---|
| 531 | {
|
---|
| 532 | pt[i,j] = 0;
|
---|
| 533 | }
|
---|
| 534 | }
|
---|
| 535 | }
|
---|
| 536 |
|
---|
| 537 | //
|
---|
| 538 | // Calculate
|
---|
| 539 | //
|
---|
| 540 | rmatrixbdmultiplybyp(ref qp, m, n, ref taup, ref pt, ptrows, n, true, true);
|
---|
| 541 | }
|
---|
| 542 |
|
---|
| 543 |
|
---|
| 544 | /*************************************************************************
|
---|
| 545 | Multiplication by matrix P which reduces matrix A to bidiagonal form.
|
---|
| 546 |
|
---|
| 547 | The algorithm allows pre- or post-multiply by P or P'.
|
---|
| 548 |
|
---|
| 549 | Input parameters:
|
---|
| 550 | QP - matrices Q and P in compact form.
|
---|
| 551 | Output of RMatrixBD subroutine.
|
---|
| 552 | M - number of rows in matrix A.
|
---|
| 553 | N - number of columns in matrix A.
|
---|
| 554 | TAUP - scalar factors which are used to form P.
|
---|
| 555 | Output of RMatrixBD subroutine.
|
---|
| 556 | Z - multiplied matrix.
|
---|
| 557 | Array whose indexes range within [0..ZRows-1,0..ZColumns-1].
|
---|
| 558 | ZRows - number of rows in matrix Z. If FromTheRight=False,
|
---|
| 559 | ZRows=N, otherwise ZRows can be arbitrary.
|
---|
| 560 | ZColumns - number of columns in matrix Z. If FromTheRight=True,
|
---|
| 561 | ZColumns=N, otherwise ZColumns can be arbitrary.
|
---|
| 562 | FromTheRight - pre- or post-multiply.
|
---|
| 563 | DoTranspose - multiply by P or P'.
|
---|
| 564 |
|
---|
| 565 | Output parameters:
|
---|
| 566 | Z - product of Z and P.
|
---|
| 567 | Array whose indexes range within [0..ZRows-1,0..ZColumns-1].
|
---|
| 568 | If ZRows=0 or ZColumns=0, the array is not modified.
|
---|
| 569 |
|
---|
| 570 | -- ALGLIB --
|
---|
| 571 | Copyright 2005-2007 by Bochkanov Sergey
|
---|
| 572 | *************************************************************************/
|
---|
| 573 | public static void rmatrixbdmultiplybyp(ref double[,] qp,
|
---|
| 574 | int m,
|
---|
| 575 | int n,
|
---|
| 576 | ref double[] taup,
|
---|
| 577 | ref double[,] z,
|
---|
| 578 | int zrows,
|
---|
| 579 | int zcolumns,
|
---|
| 580 | bool fromtheright,
|
---|
| 581 | bool dotranspose)
|
---|
| 582 | {
|
---|
| 583 | int i = 0;
|
---|
| 584 | double[] v = new double[0];
|
---|
| 585 | double[] work = new double[0];
|
---|
| 586 | int mx = 0;
|
---|
| 587 | int i1 = 0;
|
---|
| 588 | int i2 = 0;
|
---|
| 589 | int istep = 0;
|
---|
| 590 | int i_ = 0;
|
---|
| 591 | int i1_ = 0;
|
---|
| 592 |
|
---|
| 593 | if( m<=0 | n<=0 | zrows<=0 | zcolumns<=0 )
|
---|
| 594 | {
|
---|
| 595 | return;
|
---|
| 596 | }
|
---|
| 597 | System.Diagnostics.Debug.Assert(fromtheright & zcolumns==n | !fromtheright & zrows==n, "RMatrixBDMultiplyByP: incorrect Z size!");
|
---|
| 598 |
|
---|
| 599 | //
|
---|
| 600 | // init
|
---|
| 601 | //
|
---|
| 602 | mx = Math.Max(m, n);
|
---|
| 603 | mx = Math.Max(mx, zrows);
|
---|
| 604 | mx = Math.Max(mx, zcolumns);
|
---|
| 605 | v = new double[mx+1];
|
---|
| 606 | work = new double[mx+1];
|
---|
| 607 | v = new double[mx+1];
|
---|
| 608 | work = new double[mx+1];
|
---|
| 609 | if( m>=n )
|
---|
| 610 | {
|
---|
| 611 |
|
---|
| 612 | //
|
---|
| 613 | // setup
|
---|
| 614 | //
|
---|
| 615 | if( fromtheright )
|
---|
| 616 | {
|
---|
| 617 | i1 = n-2;
|
---|
| 618 | i2 = 0;
|
---|
| 619 | istep = -1;
|
---|
| 620 | }
|
---|
| 621 | else
|
---|
| 622 | {
|
---|
| 623 | i1 = 0;
|
---|
| 624 | i2 = n-2;
|
---|
| 625 | istep = +1;
|
---|
| 626 | }
|
---|
| 627 | if( !dotranspose )
|
---|
| 628 | {
|
---|
| 629 | i = i1;
|
---|
| 630 | i1 = i2;
|
---|
| 631 | i2 = i;
|
---|
| 632 | istep = -istep;
|
---|
| 633 | }
|
---|
| 634 |
|
---|
| 635 | //
|
---|
| 636 | // Process
|
---|
| 637 | //
|
---|
| 638 | if( n-1>0 )
|
---|
| 639 | {
|
---|
| 640 | i = i1;
|
---|
| 641 | do
|
---|
| 642 | {
|
---|
| 643 | i1_ = (i+1) - (1);
|
---|
| 644 | for(i_=1; i_<=n-1-i;i_++)
|
---|
| 645 | {
|
---|
| 646 | v[i_] = qp[i,i_+i1_];
|
---|
| 647 | }
|
---|
| 648 | v[1] = 1;
|
---|
| 649 | if( fromtheright )
|
---|
| 650 | {
|
---|
| 651 | reflections.applyreflectionfromtheright(ref z, taup[i], ref v, 0, zrows-1, i+1, n-1, ref work);
|
---|
| 652 | }
|
---|
| 653 | else
|
---|
| 654 | {
|
---|
| 655 | reflections.applyreflectionfromtheleft(ref z, taup[i], ref v, i+1, n-1, 0, zcolumns-1, ref work);
|
---|
| 656 | }
|
---|
| 657 | i = i+istep;
|
---|
| 658 | }
|
---|
| 659 | while( i!=i2+istep );
|
---|
| 660 | }
|
---|
| 661 | }
|
---|
| 662 | else
|
---|
| 663 | {
|
---|
| 664 |
|
---|
| 665 | //
|
---|
| 666 | // setup
|
---|
| 667 | //
|
---|
| 668 | if( fromtheright )
|
---|
| 669 | {
|
---|
| 670 | i1 = m-1;
|
---|
| 671 | i2 = 0;
|
---|
| 672 | istep = -1;
|
---|
| 673 | }
|
---|
| 674 | else
|
---|
| 675 | {
|
---|
| 676 | i1 = 0;
|
---|
| 677 | i2 = m-1;
|
---|
| 678 | istep = +1;
|
---|
| 679 | }
|
---|
| 680 | if( !dotranspose )
|
---|
| 681 | {
|
---|
| 682 | i = i1;
|
---|
| 683 | i1 = i2;
|
---|
| 684 | i2 = i;
|
---|
| 685 | istep = -istep;
|
---|
| 686 | }
|
---|
| 687 |
|
---|
| 688 | //
|
---|
| 689 | // Process
|
---|
| 690 | //
|
---|
| 691 | i = i1;
|
---|
| 692 | do
|
---|
| 693 | {
|
---|
| 694 | i1_ = (i) - (1);
|
---|
| 695 | for(i_=1; i_<=n-i;i_++)
|
---|
| 696 | {
|
---|
| 697 | v[i_] = qp[i,i_+i1_];
|
---|
| 698 | }
|
---|
| 699 | v[1] = 1;
|
---|
| 700 | if( fromtheright )
|
---|
| 701 | {
|
---|
| 702 | reflections.applyreflectionfromtheright(ref z, taup[i], ref v, 0, zrows-1, i, n-1, ref work);
|
---|
| 703 | }
|
---|
| 704 | else
|
---|
| 705 | {
|
---|
| 706 | reflections.applyreflectionfromtheleft(ref z, taup[i], ref v, i, n-1, 0, zcolumns-1, ref work);
|
---|
| 707 | }
|
---|
| 708 | i = i+istep;
|
---|
| 709 | }
|
---|
| 710 | while( i!=i2+istep );
|
---|
| 711 | }
|
---|
| 712 | }
|
---|
| 713 |
|
---|
| 714 |
|
---|
| 715 | /*************************************************************************
|
---|
| 716 | Unpacking of the main and secondary diagonals of bidiagonal decomposition
|
---|
| 717 | of matrix A.
|
---|
| 718 |
|
---|
| 719 | Input parameters:
|
---|
| 720 | B - output of RMatrixBD subroutine.
|
---|
| 721 | M - number of rows in matrix B.
|
---|
| 722 | N - number of columns in matrix B.
|
---|
| 723 |
|
---|
| 724 | Output parameters:
|
---|
| 725 | IsUpper - True, if the matrix is upper bidiagonal.
|
---|
| 726 | otherwise IsUpper is False.
|
---|
| 727 | D - the main diagonal.
|
---|
| 728 | Array whose index ranges within [0..Min(M,N)-1].
|
---|
| 729 | E - the secondary diagonal (upper or lower, depending on
|
---|
| 730 | the value of IsUpper).
|
---|
| 731 | Array index ranges within [0..Min(M,N)-1], the last
|
---|
| 732 | element is not used.
|
---|
| 733 |
|
---|
| 734 | -- ALGLIB --
|
---|
| 735 | Copyright 2005-2007 by Bochkanov Sergey
|
---|
| 736 | *************************************************************************/
|
---|
| 737 | public static void rmatrixbdunpackdiagonals(ref double[,] b,
|
---|
| 738 | int m,
|
---|
| 739 | int n,
|
---|
| 740 | ref bool isupper,
|
---|
| 741 | ref double[] d,
|
---|
| 742 | ref double[] e)
|
---|
| 743 | {
|
---|
| 744 | int i = 0;
|
---|
| 745 |
|
---|
| 746 | isupper = m>=n;
|
---|
| 747 | if( m<=0 | n<=0 )
|
---|
| 748 | {
|
---|
| 749 | return;
|
---|
| 750 | }
|
---|
| 751 | if( isupper )
|
---|
| 752 | {
|
---|
| 753 | d = new double[n-1+1];
|
---|
| 754 | e = new double[n-1+1];
|
---|
| 755 | for(i=0; i<=n-2; i++)
|
---|
| 756 | {
|
---|
| 757 | d[i] = b[i,i];
|
---|
| 758 | e[i] = b[i,i+1];
|
---|
| 759 | }
|
---|
| 760 | d[n-1] = b[n-1,n-1];
|
---|
| 761 | }
|
---|
| 762 | else
|
---|
| 763 | {
|
---|
| 764 | d = new double[m-1+1];
|
---|
| 765 | e = new double[m-1+1];
|
---|
| 766 | for(i=0; i<=m-2; i++)
|
---|
| 767 | {
|
---|
| 768 | d[i] = b[i,i];
|
---|
| 769 | e[i] = b[i+1,i];
|
---|
| 770 | }
|
---|
| 771 | d[m-1] = b[m-1,m-1];
|
---|
| 772 | }
|
---|
| 773 | }
|
---|
| 774 |
|
---|
| 775 |
|
---|
| 776 | public static void tobidiagonal(ref double[,] a,
|
---|
| 777 | int m,
|
---|
| 778 | int n,
|
---|
| 779 | ref double[] tauq,
|
---|
| 780 | ref double[] taup)
|
---|
| 781 | {
|
---|
| 782 | double[] work = new double[0];
|
---|
| 783 | double[] t = new double[0];
|
---|
| 784 | int minmn = 0;
|
---|
| 785 | int maxmn = 0;
|
---|
| 786 | int i = 0;
|
---|
| 787 | double ltau = 0;
|
---|
| 788 | int mmip1 = 0;
|
---|
| 789 | int nmi = 0;
|
---|
| 790 | int ip1 = 0;
|
---|
| 791 | int nmip1 = 0;
|
---|
| 792 | int mmi = 0;
|
---|
| 793 | int i_ = 0;
|
---|
| 794 | int i1_ = 0;
|
---|
| 795 |
|
---|
| 796 | minmn = Math.Min(m, n);
|
---|
| 797 | maxmn = Math.Max(m, n);
|
---|
| 798 | work = new double[maxmn+1];
|
---|
| 799 | t = new double[maxmn+1];
|
---|
| 800 | taup = new double[minmn+1];
|
---|
| 801 | tauq = new double[minmn+1];
|
---|
| 802 | if( m>=n )
|
---|
| 803 | {
|
---|
| 804 |
|
---|
| 805 | //
|
---|
| 806 | // Reduce to upper bidiagonal form
|
---|
| 807 | //
|
---|
| 808 | for(i=1; i<=n; i++)
|
---|
| 809 | {
|
---|
| 810 |
|
---|
| 811 | //
|
---|
| 812 | // Generate elementary reflector H(i) to annihilate A(i+1:m,i)
|
---|
| 813 | //
|
---|
| 814 | mmip1 = m-i+1;
|
---|
| 815 | i1_ = (i) - (1);
|
---|
| 816 | for(i_=1; i_<=mmip1;i_++)
|
---|
| 817 | {
|
---|
| 818 | t[i_] = a[i_+i1_,i];
|
---|
| 819 | }
|
---|
| 820 | reflections.generatereflection(ref t, mmip1, ref ltau);
|
---|
| 821 | tauq[i] = ltau;
|
---|
| 822 | i1_ = (1) - (i);
|
---|
| 823 | for(i_=i; i_<=m;i_++)
|
---|
| 824 | {
|
---|
| 825 | a[i_,i] = t[i_+i1_];
|
---|
| 826 | }
|
---|
| 827 | t[1] = 1;
|
---|
| 828 |
|
---|
| 829 | //
|
---|
| 830 | // Apply H(i) to A(i:m,i+1:n) from the left
|
---|
| 831 | //
|
---|
| 832 | reflections.applyreflectionfromtheleft(ref a, ltau, ref t, i, m, i+1, n, ref work);
|
---|
| 833 | if( i<n )
|
---|
| 834 | {
|
---|
| 835 |
|
---|
| 836 | //
|
---|
| 837 | // Generate elementary reflector G(i) to annihilate
|
---|
| 838 | // A(i,i+2:n)
|
---|
| 839 | //
|
---|
| 840 | nmi = n-i;
|
---|
| 841 | ip1 = i+1;
|
---|
| 842 | i1_ = (ip1) - (1);
|
---|
| 843 | for(i_=1; i_<=nmi;i_++)
|
---|
| 844 | {
|
---|
| 845 | t[i_] = a[i,i_+i1_];
|
---|
| 846 | }
|
---|
| 847 | reflections.generatereflection(ref t, nmi, ref ltau);
|
---|
| 848 | taup[i] = ltau;
|
---|
| 849 | i1_ = (1) - (ip1);
|
---|
| 850 | for(i_=ip1; i_<=n;i_++)
|
---|
| 851 | {
|
---|
| 852 | a[i,i_] = t[i_+i1_];
|
---|
| 853 | }
|
---|
| 854 | t[1] = 1;
|
---|
| 855 |
|
---|
| 856 | //
|
---|
| 857 | // Apply G(i) to A(i+1:m,i+1:n) from the right
|
---|
| 858 | //
|
---|
| 859 | reflections.applyreflectionfromtheright(ref a, ltau, ref t, i+1, m, i+1, n, ref work);
|
---|
| 860 | }
|
---|
| 861 | else
|
---|
| 862 | {
|
---|
| 863 | taup[i] = 0;
|
---|
| 864 | }
|
---|
| 865 | }
|
---|
| 866 | }
|
---|
| 867 | else
|
---|
| 868 | {
|
---|
| 869 |
|
---|
| 870 | //
|
---|
| 871 | // Reduce to lower bidiagonal form
|
---|
| 872 | //
|
---|
| 873 | for(i=1; i<=m; i++)
|
---|
| 874 | {
|
---|
| 875 |
|
---|
| 876 | //
|
---|
| 877 | // Generate elementary reflector G(i) to annihilate A(i,i+1:n)
|
---|
| 878 | //
|
---|
| 879 | nmip1 = n-i+1;
|
---|
| 880 | i1_ = (i) - (1);
|
---|
| 881 | for(i_=1; i_<=nmip1;i_++)
|
---|
| 882 | {
|
---|
| 883 | t[i_] = a[i,i_+i1_];
|
---|
| 884 | }
|
---|
| 885 | reflections.generatereflection(ref t, nmip1, ref ltau);
|
---|
| 886 | taup[i] = ltau;
|
---|
| 887 | i1_ = (1) - (i);
|
---|
| 888 | for(i_=i; i_<=n;i_++)
|
---|
| 889 | {
|
---|
| 890 | a[i,i_] = t[i_+i1_];
|
---|
| 891 | }
|
---|
| 892 | t[1] = 1;
|
---|
| 893 |
|
---|
| 894 | //
|
---|
| 895 | // Apply G(i) to A(i+1:m,i:n) from the right
|
---|
| 896 | //
|
---|
| 897 | reflections.applyreflectionfromtheright(ref a, ltau, ref t, i+1, m, i, n, ref work);
|
---|
| 898 | if( i<m )
|
---|
| 899 | {
|
---|
| 900 |
|
---|
| 901 | //
|
---|
| 902 | // Generate elementary reflector H(i) to annihilate
|
---|
| 903 | // A(i+2:m,i)
|
---|
| 904 | //
|
---|
| 905 | mmi = m-i;
|
---|
| 906 | ip1 = i+1;
|
---|
| 907 | i1_ = (ip1) - (1);
|
---|
| 908 | for(i_=1; i_<=mmi;i_++)
|
---|
| 909 | {
|
---|
| 910 | t[i_] = a[i_+i1_,i];
|
---|
| 911 | }
|
---|
| 912 | reflections.generatereflection(ref t, mmi, ref ltau);
|
---|
| 913 | tauq[i] = ltau;
|
---|
| 914 | i1_ = (1) - (ip1);
|
---|
| 915 | for(i_=ip1; i_<=m;i_++)
|
---|
| 916 | {
|
---|
| 917 | a[i_,i] = t[i_+i1_];
|
---|
| 918 | }
|
---|
| 919 | t[1] = 1;
|
---|
| 920 |
|
---|
| 921 | //
|
---|
| 922 | // Apply H(i) to A(i+1:m,i+1:n) from the left
|
---|
| 923 | //
|
---|
| 924 | reflections.applyreflectionfromtheleft(ref a, ltau, ref t, i+1, m, i+1, n, ref work);
|
---|
| 925 | }
|
---|
| 926 | else
|
---|
| 927 | {
|
---|
| 928 | tauq[i] = 0;
|
---|
| 929 | }
|
---|
| 930 | }
|
---|
| 931 | }
|
---|
| 932 | }
|
---|
| 933 |
|
---|
| 934 |
|
---|
| 935 | public static void unpackqfrombidiagonal(ref double[,] qp,
|
---|
| 936 | int m,
|
---|
| 937 | int n,
|
---|
| 938 | ref double[] tauq,
|
---|
| 939 | int qcolumns,
|
---|
| 940 | ref double[,] q)
|
---|
| 941 | {
|
---|
| 942 | int i = 0;
|
---|
| 943 | int j = 0;
|
---|
| 944 | int ip1 = 0;
|
---|
| 945 | double[] v = new double[0];
|
---|
| 946 | double[] work = new double[0];
|
---|
| 947 | int vm = 0;
|
---|
| 948 | int i_ = 0;
|
---|
| 949 | int i1_ = 0;
|
---|
| 950 |
|
---|
| 951 | System.Diagnostics.Debug.Assert(qcolumns<=m, "UnpackQFromBidiagonal: QColumns>M!");
|
---|
| 952 | if( m==0 | n==0 | qcolumns==0 )
|
---|
| 953 | {
|
---|
| 954 | return;
|
---|
| 955 | }
|
---|
| 956 |
|
---|
| 957 | //
|
---|
| 958 | // init
|
---|
| 959 | //
|
---|
| 960 | q = new double[m+1, qcolumns+1];
|
---|
| 961 | v = new double[m+1];
|
---|
| 962 | work = new double[qcolumns+1];
|
---|
| 963 |
|
---|
| 964 | //
|
---|
| 965 | // prepare Q
|
---|
| 966 | //
|
---|
| 967 | for(i=1; i<=m; i++)
|
---|
| 968 | {
|
---|
| 969 | for(j=1; j<=qcolumns; j++)
|
---|
| 970 | {
|
---|
| 971 | if( i==j )
|
---|
| 972 | {
|
---|
| 973 | q[i,j] = 1;
|
---|
| 974 | }
|
---|
| 975 | else
|
---|
| 976 | {
|
---|
| 977 | q[i,j] = 0;
|
---|
| 978 | }
|
---|
| 979 | }
|
---|
| 980 | }
|
---|
| 981 | if( m>=n )
|
---|
| 982 | {
|
---|
| 983 | for(i=Math.Min(n, qcolumns); i>=1; i--)
|
---|
| 984 | {
|
---|
| 985 | vm = m-i+1;
|
---|
| 986 | i1_ = (i) - (1);
|
---|
| 987 | for(i_=1; i_<=vm;i_++)
|
---|
| 988 | {
|
---|
| 989 | v[i_] = qp[i_+i1_,i];
|
---|
| 990 | }
|
---|
| 991 | v[1] = 1;
|
---|
| 992 | reflections.applyreflectionfromtheleft(ref q, tauq[i], ref v, i, m, 1, qcolumns, ref work);
|
---|
| 993 | }
|
---|
| 994 | }
|
---|
| 995 | else
|
---|
| 996 | {
|
---|
| 997 | for(i=Math.Min(m-1, qcolumns-1); i>=1; i--)
|
---|
| 998 | {
|
---|
| 999 | vm = m-i;
|
---|
| 1000 | ip1 = i+1;
|
---|
| 1001 | i1_ = (ip1) - (1);
|
---|
| 1002 | for(i_=1; i_<=vm;i_++)
|
---|
| 1003 | {
|
---|
| 1004 | v[i_] = qp[i_+i1_,i];
|
---|
| 1005 | }
|
---|
| 1006 | v[1] = 1;
|
---|
| 1007 | reflections.applyreflectionfromtheleft(ref q, tauq[i], ref v, i+1, m, 1, qcolumns, ref work);
|
---|
| 1008 | }
|
---|
| 1009 | }
|
---|
| 1010 | }
|
---|
| 1011 |
|
---|
| 1012 |
|
---|
| 1013 | public static void multiplybyqfrombidiagonal(ref double[,] qp,
|
---|
| 1014 | int m,
|
---|
| 1015 | int n,
|
---|
| 1016 | ref double[] tauq,
|
---|
| 1017 | ref double[,] z,
|
---|
| 1018 | int zrows,
|
---|
| 1019 | int zcolumns,
|
---|
| 1020 | bool fromtheright,
|
---|
| 1021 | bool dotranspose)
|
---|
| 1022 | {
|
---|
| 1023 | int i = 0;
|
---|
| 1024 | int ip1 = 0;
|
---|
| 1025 | int i1 = 0;
|
---|
| 1026 | int i2 = 0;
|
---|
| 1027 | int istep = 0;
|
---|
| 1028 | double[] v = new double[0];
|
---|
| 1029 | double[] work = new double[0];
|
---|
| 1030 | int vm = 0;
|
---|
| 1031 | int mx = 0;
|
---|
| 1032 | int i_ = 0;
|
---|
| 1033 | int i1_ = 0;
|
---|
| 1034 |
|
---|
| 1035 | if( m<=0 | n<=0 | zrows<=0 | zcolumns<=0 )
|
---|
| 1036 | {
|
---|
| 1037 | return;
|
---|
| 1038 | }
|
---|
| 1039 | System.Diagnostics.Debug.Assert(fromtheright & zcolumns==m | !fromtheright & zrows==m, "MultiplyByQFromBidiagonal: incorrect Z size!");
|
---|
| 1040 |
|
---|
| 1041 | //
|
---|
| 1042 | // init
|
---|
| 1043 | //
|
---|
| 1044 | mx = Math.Max(m, n);
|
---|
| 1045 | mx = Math.Max(mx, zrows);
|
---|
| 1046 | mx = Math.Max(mx, zcolumns);
|
---|
| 1047 | v = new double[mx+1];
|
---|
| 1048 | work = new double[mx+1];
|
---|
| 1049 | if( m>=n )
|
---|
| 1050 | {
|
---|
| 1051 |
|
---|
| 1052 | //
|
---|
| 1053 | // setup
|
---|
| 1054 | //
|
---|
| 1055 | if( fromtheright )
|
---|
| 1056 | {
|
---|
| 1057 | i1 = 1;
|
---|
| 1058 | i2 = n;
|
---|
| 1059 | istep = +1;
|
---|
| 1060 | }
|
---|
| 1061 | else
|
---|
| 1062 | {
|
---|
| 1063 | i1 = n;
|
---|
| 1064 | i2 = 1;
|
---|
| 1065 | istep = -1;
|
---|
| 1066 | }
|
---|
| 1067 | if( dotranspose )
|
---|
| 1068 | {
|
---|
| 1069 | i = i1;
|
---|
| 1070 | i1 = i2;
|
---|
| 1071 | i2 = i;
|
---|
| 1072 | istep = -istep;
|
---|
| 1073 | }
|
---|
| 1074 |
|
---|
| 1075 | //
|
---|
| 1076 | // Process
|
---|
| 1077 | //
|
---|
| 1078 | i = i1;
|
---|
| 1079 | do
|
---|
| 1080 | {
|
---|
| 1081 | vm = m-i+1;
|
---|
| 1082 | i1_ = (i) - (1);
|
---|
| 1083 | for(i_=1; i_<=vm;i_++)
|
---|
| 1084 | {
|
---|
| 1085 | v[i_] = qp[i_+i1_,i];
|
---|
| 1086 | }
|
---|
| 1087 | v[1] = 1;
|
---|
| 1088 | if( fromtheright )
|
---|
| 1089 | {
|
---|
| 1090 | reflections.applyreflectionfromtheright(ref z, tauq[i], ref v, 1, zrows, i, m, ref work);
|
---|
| 1091 | }
|
---|
| 1092 | else
|
---|
| 1093 | {
|
---|
| 1094 | reflections.applyreflectionfromtheleft(ref z, tauq[i], ref v, i, m, 1, zcolumns, ref work);
|
---|
| 1095 | }
|
---|
| 1096 | i = i+istep;
|
---|
| 1097 | }
|
---|
| 1098 | while( i!=i2+istep );
|
---|
| 1099 | }
|
---|
| 1100 | else
|
---|
| 1101 | {
|
---|
| 1102 |
|
---|
| 1103 | //
|
---|
| 1104 | // setup
|
---|
| 1105 | //
|
---|
| 1106 | if( fromtheright )
|
---|
| 1107 | {
|
---|
| 1108 | i1 = 1;
|
---|
| 1109 | i2 = m-1;
|
---|
| 1110 | istep = +1;
|
---|
| 1111 | }
|
---|
| 1112 | else
|
---|
| 1113 | {
|
---|
| 1114 | i1 = m-1;
|
---|
| 1115 | i2 = 1;
|
---|
| 1116 | istep = -1;
|
---|
| 1117 | }
|
---|
| 1118 | if( dotranspose )
|
---|
| 1119 | {
|
---|
| 1120 | i = i1;
|
---|
| 1121 | i1 = i2;
|
---|
| 1122 | i2 = i;
|
---|
| 1123 | istep = -istep;
|
---|
| 1124 | }
|
---|
| 1125 |
|
---|
| 1126 | //
|
---|
| 1127 | // Process
|
---|
| 1128 | //
|
---|
| 1129 | if( m-1>0 )
|
---|
| 1130 | {
|
---|
| 1131 | i = i1;
|
---|
| 1132 | do
|
---|
| 1133 | {
|
---|
| 1134 | vm = m-i;
|
---|
| 1135 | ip1 = i+1;
|
---|
| 1136 | i1_ = (ip1) - (1);
|
---|
| 1137 | for(i_=1; i_<=vm;i_++)
|
---|
| 1138 | {
|
---|
| 1139 | v[i_] = qp[i_+i1_,i];
|
---|
| 1140 | }
|
---|
| 1141 | v[1] = 1;
|
---|
| 1142 | if( fromtheright )
|
---|
| 1143 | {
|
---|
| 1144 | reflections.applyreflectionfromtheright(ref z, tauq[i], ref v, 1, zrows, i+1, m, ref work);
|
---|
| 1145 | }
|
---|
| 1146 | else
|
---|
| 1147 | {
|
---|
| 1148 | reflections.applyreflectionfromtheleft(ref z, tauq[i], ref v, i+1, m, 1, zcolumns, ref work);
|
---|
| 1149 | }
|
---|
| 1150 | i = i+istep;
|
---|
| 1151 | }
|
---|
| 1152 | while( i!=i2+istep );
|
---|
| 1153 | }
|
---|
| 1154 | }
|
---|
| 1155 | }
|
---|
| 1156 |
|
---|
| 1157 |
|
---|
| 1158 | public static void unpackptfrombidiagonal(ref double[,] qp,
|
---|
| 1159 | int m,
|
---|
| 1160 | int n,
|
---|
| 1161 | ref double[] taup,
|
---|
| 1162 | int ptrows,
|
---|
| 1163 | ref double[,] pt)
|
---|
| 1164 | {
|
---|
| 1165 | int i = 0;
|
---|
| 1166 | int j = 0;
|
---|
| 1167 | int ip1 = 0;
|
---|
| 1168 | double[] v = new double[0];
|
---|
| 1169 | double[] work = new double[0];
|
---|
| 1170 | int vm = 0;
|
---|
| 1171 | int i_ = 0;
|
---|
| 1172 | int i1_ = 0;
|
---|
| 1173 |
|
---|
| 1174 | System.Diagnostics.Debug.Assert(ptrows<=n, "UnpackPTFromBidiagonal: PTRows>N!");
|
---|
| 1175 | if( m==0 | n==0 | ptrows==0 )
|
---|
| 1176 | {
|
---|
| 1177 | return;
|
---|
| 1178 | }
|
---|
| 1179 |
|
---|
| 1180 | //
|
---|
| 1181 | // init
|
---|
| 1182 | //
|
---|
| 1183 | pt = new double[ptrows+1, n+1];
|
---|
| 1184 | v = new double[n+1];
|
---|
| 1185 | work = new double[ptrows+1];
|
---|
| 1186 |
|
---|
| 1187 | //
|
---|
| 1188 | // prepare PT
|
---|
| 1189 | //
|
---|
| 1190 | for(i=1; i<=ptrows; i++)
|
---|
| 1191 | {
|
---|
| 1192 | for(j=1; j<=n; j++)
|
---|
| 1193 | {
|
---|
| 1194 | if( i==j )
|
---|
| 1195 | {
|
---|
| 1196 | pt[i,j] = 1;
|
---|
| 1197 | }
|
---|
| 1198 | else
|
---|
| 1199 | {
|
---|
| 1200 | pt[i,j] = 0;
|
---|
| 1201 | }
|
---|
| 1202 | }
|
---|
| 1203 | }
|
---|
| 1204 | if( m>=n )
|
---|
| 1205 | {
|
---|
| 1206 | for(i=Math.Min(n-1, ptrows-1); i>=1; i--)
|
---|
| 1207 | {
|
---|
| 1208 | vm = n-i;
|
---|
| 1209 | ip1 = i+1;
|
---|
| 1210 | i1_ = (ip1) - (1);
|
---|
| 1211 | for(i_=1; i_<=vm;i_++)
|
---|
| 1212 | {
|
---|
| 1213 | v[i_] = qp[i,i_+i1_];
|
---|
| 1214 | }
|
---|
| 1215 | v[1] = 1;
|
---|
| 1216 | reflections.applyreflectionfromtheright(ref pt, taup[i], ref v, 1, ptrows, i+1, n, ref work);
|
---|
| 1217 | }
|
---|
| 1218 | }
|
---|
| 1219 | else
|
---|
| 1220 | {
|
---|
| 1221 | for(i=Math.Min(m, ptrows); i>=1; i--)
|
---|
| 1222 | {
|
---|
| 1223 | vm = n-i+1;
|
---|
| 1224 | i1_ = (i) - (1);
|
---|
| 1225 | for(i_=1; i_<=vm;i_++)
|
---|
| 1226 | {
|
---|
| 1227 | v[i_] = qp[i,i_+i1_];
|
---|
| 1228 | }
|
---|
| 1229 | v[1] = 1;
|
---|
| 1230 | reflections.applyreflectionfromtheright(ref pt, taup[i], ref v, 1, ptrows, i, n, ref work);
|
---|
| 1231 | }
|
---|
| 1232 | }
|
---|
| 1233 | }
|
---|
| 1234 |
|
---|
| 1235 |
|
---|
| 1236 | public static void multiplybypfrombidiagonal(ref double[,] qp,
|
---|
| 1237 | int m,
|
---|
| 1238 | int n,
|
---|
| 1239 | ref double[] taup,
|
---|
| 1240 | ref double[,] z,
|
---|
| 1241 | int zrows,
|
---|
| 1242 | int zcolumns,
|
---|
| 1243 | bool fromtheright,
|
---|
| 1244 | bool dotranspose)
|
---|
| 1245 | {
|
---|
| 1246 | int i = 0;
|
---|
| 1247 | int ip1 = 0;
|
---|
| 1248 | double[] v = new double[0];
|
---|
| 1249 | double[] work = new double[0];
|
---|
| 1250 | int vm = 0;
|
---|
| 1251 | int mx = 0;
|
---|
| 1252 | int i1 = 0;
|
---|
| 1253 | int i2 = 0;
|
---|
| 1254 | int istep = 0;
|
---|
| 1255 | int i_ = 0;
|
---|
| 1256 | int i1_ = 0;
|
---|
| 1257 |
|
---|
| 1258 | if( m<=0 | n<=0 | zrows<=0 | zcolumns<=0 )
|
---|
| 1259 | {
|
---|
| 1260 | return;
|
---|
| 1261 | }
|
---|
| 1262 | System.Diagnostics.Debug.Assert(fromtheright & zcolumns==n | !fromtheright & zrows==n, "MultiplyByQFromBidiagonal: incorrect Z size!");
|
---|
| 1263 |
|
---|
| 1264 | //
|
---|
| 1265 | // init
|
---|
| 1266 | //
|
---|
| 1267 | mx = Math.Max(m, n);
|
---|
| 1268 | mx = Math.Max(mx, zrows);
|
---|
| 1269 | mx = Math.Max(mx, zcolumns);
|
---|
| 1270 | v = new double[mx+1];
|
---|
| 1271 | work = new double[mx+1];
|
---|
| 1272 | v = new double[mx+1];
|
---|
| 1273 | work = new double[mx+1];
|
---|
| 1274 | if( m>=n )
|
---|
| 1275 | {
|
---|
| 1276 |
|
---|
| 1277 | //
|
---|
| 1278 | // setup
|
---|
| 1279 | //
|
---|
| 1280 | if( fromtheright )
|
---|
| 1281 | {
|
---|
| 1282 | i1 = n-1;
|
---|
| 1283 | i2 = 1;
|
---|
| 1284 | istep = -1;
|
---|
| 1285 | }
|
---|
| 1286 | else
|
---|
| 1287 | {
|
---|
| 1288 | i1 = 1;
|
---|
| 1289 | i2 = n-1;
|
---|
| 1290 | istep = +1;
|
---|
| 1291 | }
|
---|
| 1292 | if( !dotranspose )
|
---|
| 1293 | {
|
---|
| 1294 | i = i1;
|
---|
| 1295 | i1 = i2;
|
---|
| 1296 | i2 = i;
|
---|
| 1297 | istep = -istep;
|
---|
| 1298 | }
|
---|
| 1299 |
|
---|
| 1300 | //
|
---|
| 1301 | // Process
|
---|
| 1302 | //
|
---|
| 1303 | if( n-1>0 )
|
---|
| 1304 | {
|
---|
| 1305 | i = i1;
|
---|
| 1306 | do
|
---|
| 1307 | {
|
---|
| 1308 | vm = n-i;
|
---|
| 1309 | ip1 = i+1;
|
---|
| 1310 | i1_ = (ip1) - (1);
|
---|
| 1311 | for(i_=1; i_<=vm;i_++)
|
---|
| 1312 | {
|
---|
| 1313 | v[i_] = qp[i,i_+i1_];
|
---|
| 1314 | }
|
---|
| 1315 | v[1] = 1;
|
---|
| 1316 | if( fromtheright )
|
---|
| 1317 | {
|
---|
| 1318 | reflections.applyreflectionfromtheright(ref z, taup[i], ref v, 1, zrows, i+1, n, ref work);
|
---|
| 1319 | }
|
---|
| 1320 | else
|
---|
| 1321 | {
|
---|
| 1322 | reflections.applyreflectionfromtheleft(ref z, taup[i], ref v, i+1, n, 1, zcolumns, ref work);
|
---|
| 1323 | }
|
---|
| 1324 | i = i+istep;
|
---|
| 1325 | }
|
---|
| 1326 | while( i!=i2+istep );
|
---|
| 1327 | }
|
---|
| 1328 | }
|
---|
| 1329 | else
|
---|
| 1330 | {
|
---|
| 1331 |
|
---|
| 1332 | //
|
---|
| 1333 | // setup
|
---|
| 1334 | //
|
---|
| 1335 | if( fromtheright )
|
---|
| 1336 | {
|
---|
| 1337 | i1 = m;
|
---|
| 1338 | i2 = 1;
|
---|
| 1339 | istep = -1;
|
---|
| 1340 | }
|
---|
| 1341 | else
|
---|
| 1342 | {
|
---|
| 1343 | i1 = 1;
|
---|
| 1344 | i2 = m;
|
---|
| 1345 | istep = +1;
|
---|
| 1346 | }
|
---|
| 1347 | if( !dotranspose )
|
---|
| 1348 | {
|
---|
| 1349 | i = i1;
|
---|
| 1350 | i1 = i2;
|
---|
| 1351 | i2 = i;
|
---|
| 1352 | istep = -istep;
|
---|
| 1353 | }
|
---|
| 1354 |
|
---|
| 1355 | //
|
---|
| 1356 | // Process
|
---|
| 1357 | //
|
---|
| 1358 | i = i1;
|
---|
| 1359 | do
|
---|
| 1360 | {
|
---|
| 1361 | vm = n-i+1;
|
---|
| 1362 | i1_ = (i) - (1);
|
---|
| 1363 | for(i_=1; i_<=vm;i_++)
|
---|
| 1364 | {
|
---|
| 1365 | v[i_] = qp[i,i_+i1_];
|
---|
| 1366 | }
|
---|
| 1367 | v[1] = 1;
|
---|
| 1368 | if( fromtheright )
|
---|
| 1369 | {
|
---|
| 1370 | reflections.applyreflectionfromtheright(ref z, taup[i], ref v, 1, zrows, i, n, ref work);
|
---|
| 1371 | }
|
---|
| 1372 | else
|
---|
| 1373 | {
|
---|
| 1374 | reflections.applyreflectionfromtheleft(ref z, taup[i], ref v, i, n, 1, zcolumns, ref work);
|
---|
| 1375 | }
|
---|
| 1376 | i = i+istep;
|
---|
| 1377 | }
|
---|
| 1378 | while( i!=i2+istep );
|
---|
| 1379 | }
|
---|
| 1380 | }
|
---|
| 1381 |
|
---|
| 1382 |
|
---|
| 1383 | public static void unpackdiagonalsfrombidiagonal(ref double[,] b,
|
---|
| 1384 | int m,
|
---|
| 1385 | int n,
|
---|
| 1386 | ref bool isupper,
|
---|
| 1387 | ref double[] d,
|
---|
| 1388 | ref double[] e)
|
---|
| 1389 | {
|
---|
| 1390 | int i = 0;
|
---|
| 1391 |
|
---|
| 1392 | isupper = m>=n;
|
---|
| 1393 | if( m==0 | n==0 )
|
---|
| 1394 | {
|
---|
| 1395 | return;
|
---|
| 1396 | }
|
---|
| 1397 | if( isupper )
|
---|
| 1398 | {
|
---|
| 1399 | d = new double[n+1];
|
---|
| 1400 | e = new double[n+1];
|
---|
| 1401 | for(i=1; i<=n-1; i++)
|
---|
| 1402 | {
|
---|
| 1403 | d[i] = b[i,i];
|
---|
| 1404 | e[i] = b[i,i+1];
|
---|
| 1405 | }
|
---|
| 1406 | d[n] = b[n,n];
|
---|
| 1407 | }
|
---|
| 1408 | else
|
---|
| 1409 | {
|
---|
| 1410 | d = new double[m+1];
|
---|
| 1411 | e = new double[m+1];
|
---|
| 1412 | for(i=1; i<=m-1; i++)
|
---|
| 1413 | {
|
---|
| 1414 | d[i] = b[i,i];
|
---|
| 1415 | e[i] = b[i+1,i];
|
---|
| 1416 | }
|
---|
| 1417 | d[m] = b[m,m];
|
---|
| 1418 | }
|
---|
| 1419 | }
|
---|
| 1420 | }
|
---|
| 1421 | }
|
---|