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   1:  #region Translated by Jose Antonio De Santiago-Castillo.
   2:   
   3:  //Translated by Jose Antonio De Santiago-Castillo. 
   4:  //E-mail:JAntonioDeSantiago@gmail.com
   5:  //Web: www.DotNumerics.com
   6:  //
   7:  //Fortran to C# Translation.
   8:  //Translated by:
   9:  //F2CSharp Version 0.71 (November 10, 2009)
  10:  //Code Optimizations: None
  11:  //
  12:  #endregion
  13:   
  14:  using System;
  15:  using DotNumerics.FortranLibrary;
  16:   
  17:  namespace DotNumerics.CSLapack
  18:  {
  19:      /// <summary>
  20:      /// -- LAPACK routine (version 3.1) --
  21:      /// Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
  22:      /// November 2006
  23:      /// Purpose
  24:      /// =======
  25:      /// 
  26:      /// DGGRQF computes a generalized RQ factorization of an M-by-N matrix A
  27:      /// and a P-by-N matrix B:
  28:      /// 
  29:      /// A = R*Q,        B = Z*T*Q,
  30:      /// 
  31:      /// where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal
  32:      /// matrix, and R and T assume one of the forms:
  33:      /// 
  34:      /// if M .LE. N,  R = ( 0  R12 ) M,   or if M .GT. N,  R = ( R11 ) M-N,
  35:      /// N-M  M                           ( R21 ) N
  36:      /// N
  37:      /// 
  38:      /// where R12 or R21 is upper triangular, and
  39:      /// 
  40:      /// if P .GE. N,  T = ( T11 ) N  ,   or if P .LT. N,  T = ( T11  T12 ) P,
  41:      /// (  0  ) P-N                         P   N-P
  42:      /// N
  43:      /// 
  44:      /// where T11 is upper triangular.
  45:      /// 
  46:      /// In particular, if B is square and nonsingular, the GRQ factorization
  47:      /// of A and B implicitly gives the RQ factorization of A*inv(B):
  48:      /// 
  49:      /// A*inv(B) = (R*inv(T))*Z'
  50:      /// 
  51:      /// where inv(B) denotes the inverse of the matrix B, and Z' denotes the
  52:      /// transpose of the matrix Z.
  53:      /// 
  54:      ///</summary>
  55:      public class DGGRQF
  56:      {
  57:      
  58:   
  59:          #region Dependencies
  60:          
  61:          DGEQRF _dgeqrf; DGERQF _dgerqf; DORMRQ _dormrq; XERBLA _xerbla; ILAENV _ilaenv; 
  62:   
  63:          #endregion
  64:   
  65:   
  66:          #region Fields
  67:          
  68:          bool LQUERY = false; int LOPT = 0; int LWKOPT = 0; int NB = 0; int NB1 = 0; int NB2 = 0; int NB3 = 0; 
  69:   
  70:          #endregion
  71:   
  72:          public DGGRQF(DGEQRF dgeqrf, DGERQF dgerqf, DORMRQ dormrq, XERBLA xerbla, ILAENV ilaenv)
  73:          {
  74:      
  75:   
  76:              #region Set Dependencies
  77:              
  78:              this._dgeqrf = dgeqrf; this._dgerqf = dgerqf; this._dormrq = dormrq; this._xerbla = xerbla; this._ilaenv = ilaenv; 
  79:   
  80:              #endregion
  81:   
  82:          }
  83:      
  84:          public DGGRQF()
  85:          {
  86:      
  87:   
  88:              #region Dependencies (Initialization)
  89:              
  90:              LSAME lsame = new LSAME();
  91:              XERBLA xerbla = new XERBLA();
  92:              DLAMC3 dlamc3 = new DLAMC3();
  93:              DLAPY2 dlapy2 = new DLAPY2();
  94:              DNRM2 dnrm2 = new DNRM2();
  95:              DSCAL dscal = new DSCAL();
  96:              DCOPY dcopy = new DCOPY();
  97:              IEEECK ieeeck = new IEEECK();
  98:              IPARMQ iparmq = new IPARMQ();
  99:              DGEMV dgemv = new DGEMV(lsame, xerbla);
 100:              DGER dger = new DGER(xerbla);
 101:              DLARF dlarf = new DLARF(dgemv, dger, lsame);
 102:              DLAMC1 dlamc1 = new DLAMC1(dlamc3);
 103:              DLAMC4 dlamc4 = new DLAMC4(dlamc3);
 104:              DLAMC5 dlamc5 = new DLAMC5(dlamc3);
 105:              DLAMC2 dlamc2 = new DLAMC2(dlamc3, dlamc1, dlamc4, dlamc5);
 106:              DLAMCH dlamch = new DLAMCH(lsame, dlamc2);
 107:              DLARFG dlarfg = new DLARFG(dlamch, dlapy2, dnrm2, dscal);
 108:              DGEQR2 dgeqr2 = new DGEQR2(dlarf, dlarfg, xerbla);
 109:              DGEMM dgemm = new DGEMM(lsame, xerbla);
 110:              DTRMM dtrmm = new DTRMM(lsame, xerbla);
 111:              DLARFB dlarfb = new DLARFB(lsame, dcopy, dgemm, dtrmm);
 112:              DTRMV dtrmv = new DTRMV(lsame, xerbla);
 113:              DLARFT dlarft = new DLARFT(dgemv, dtrmv, lsame);
 114:              ILAENV ilaenv = new ILAENV(ieeeck, iparmq);
 115:              DGEQRF dgeqrf = new DGEQRF(dgeqr2, dlarfb, dlarft, xerbla, ilaenv);
 116:              DGERQ2 dgerq2 = new DGERQ2(dlarf, dlarfg, xerbla);
 117:              DGERQF dgerqf = new DGERQF(dgerq2, dlarfb, dlarft, xerbla, ilaenv);
 118:              DORMR2 dormr2 = new DORMR2(lsame, dlarf, xerbla);
 119:              DORMRQ dormrq = new DORMRQ(lsame, ilaenv, dlarfb, dlarft, dormr2, xerbla);
 120:   
 121:              #endregion
 122:   
 123:   
 124:              #region Set Dependencies
 125:              
 126:              this._dgeqrf = dgeqrf; this._dgerqf = dgerqf; this._dormrq = dormrq; this._xerbla = xerbla; this._ilaenv = ilaenv; 
 127:   
 128:              #endregion
 129:   
 130:          }
 131:          /// <summary>
 132:          /// Purpose
 133:          /// =======
 134:          /// 
 135:          /// DGGRQF computes a generalized RQ factorization of an M-by-N matrix A
 136:          /// and a P-by-N matrix B:
 137:          /// 
 138:          /// A = R*Q,        B = Z*T*Q,
 139:          /// 
 140:          /// where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal
 141:          /// matrix, and R and T assume one of the forms:
 142:          /// 
 143:          /// if M .LE. N,  R = ( 0  R12 ) M,   or if M .GT. N,  R = ( R11 ) M-N,
 144:          /// N-M  M                           ( R21 ) N
 145:          /// N
 146:          /// 
 147:          /// where R12 or R21 is upper triangular, and
 148:          /// 
 149:          /// if P .GE. N,  T = ( T11 ) N  ,   or if P .LT. N,  T = ( T11  T12 ) P,
 150:          /// (  0  ) P-N                         P   N-P
 151:          /// N
 152:          /// 
 153:          /// where T11 is upper triangular.
 154:          /// 
 155:          /// In particular, if B is square and nonsingular, the GRQ factorization
 156:          /// of A and B implicitly gives the RQ factorization of A*inv(B):
 157:          /// 
 158:          /// A*inv(B) = (R*inv(T))*Z'
 159:          /// 
 160:          /// where inv(B) denotes the inverse of the matrix B, and Z' denotes the
 161:          /// transpose of the matrix Z.
 162:          /// 
 163:          ///</summary>
 164:          /// <param name="M">
 165:          /// (input) INTEGER
 166:          /// The number of rows of the matrix A.  M .GE. 0.
 167:          ///</param>
 168:          /// <param name="P">
 169:          /// (input) INTEGER
 170:          /// The number of rows of the matrix B.  P .GE. 0.
 171:          ///</param>
 172:          /// <param name="N">
 173:          /// (input) INTEGER
 174:          /// The number of columns of the matrices A and B. N .GE. 0.
 175:          ///</param>
 176:          /// <param name="A">
 177:          /// = R*Q,        B = Z*T*Q,
 178:          ///</param>
 179:          /// <param name="LDA">
 180:          /// (input) INTEGER
 181:          /// The leading dimension of the array A. LDA .GE. max(1,M).
 182:          ///</param>
 183:          /// <param name="TAUA">
 184:          /// (output) DOUBLE PRECISION array, dimension (min(M,N))
 185:          /// The scalar factors of the elementary reflectors which
 186:          /// represent the orthogonal matrix Q (see Further Details).
 187:          ///</param>
 188:          /// <param name="B">
 189:          /// (input/output) DOUBLE PRECISION array, dimension (LDB,N)
 190:          /// On entry, the P-by-N matrix B.
 191:          /// On exit, the elements on and above the diagonal of the array
 192:          /// contain the min(P,N)-by-N upper trapezoidal matrix T (T is
 193:          /// upper triangular if P .GE. N); the elements below the diagonal,
 194:          /// with the array TAUB, represent the orthogonal matrix Z as a
 195:          /// product of elementary reflectors (see Further Details).
 196:          ///</param>
 197:          /// <param name="LDB">
 198:          /// (input) INTEGER
 199:          /// The leading dimension of the array B. LDB .GE. max(1,P).
 200:          ///</param>
 201:          /// <param name="TAUB">
 202:          /// (output) DOUBLE PRECISION array, dimension (min(P,N))
 203:          /// The scalar factors of the elementary reflectors which
 204:          /// represent the orthogonal matrix Z (see Further Details).
 205:          ///</param>
 206:          /// <param name="WORK">
 207:          /// (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
 208:          /// On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 209:          ///</param>
 210:          /// <param name="LWORK">
 211:          /// (input) INTEGER
 212:          /// The dimension of the array WORK. LWORK .GE. max(1,N,M,P).
 213:          /// For optimum performance LWORK .GE. max(N,M,P)*max(NB1,NB2,NB3),
 214:          /// where NB1 is the optimal blocksize for the RQ factorization
 215:          /// of an M-by-N matrix, NB2 is the optimal blocksize for the
 216:          /// QR factorization of a P-by-N matrix, and NB3 is the optimal
 217:          /// blocksize for a call of DORMRQ.
 218:          /// 
 219:          /// If LWORK = -1, then a workspace query is assumed; the routine
 220:          /// only calculates the optimal size of the WORK array, returns
 221:          /// this value as the first entry of the WORK array, and no error
 222:          /// message related to LWORK is issued by XERBLA.
 223:          ///</param>
 224:          /// <param name="INFO">
 225:          /// (output) INTEGER
 226:          /// = 0:  successful exit
 227:          /// .LT. 0:  if INF0= -i, the i-th argument had an illegal value.
 228:          ///</param>
 229:          public void Run(int M, int P, int N, ref double[] A, int offset_a, int LDA, ref double[] TAUA, int offset_taua
 230:                           , ref double[] B, int offset_b, int LDB, ref double[] TAUB, int offset_taub, ref double[] WORK, int offset_work, int LWORK, ref int INFO)
 231:          {
 232:   
 233:              #region Array Index Correction
 234:              
 235:               int o_a = -1 - LDA + offset_a;  int o_taua = -1 + offset_taua;  int o_b = -1 - LDB + offset_b; 
 236:               int o_taub = -1 + offset_taub; int o_work = -1 + offset_work; 
 237:   
 238:              #endregion
 239:   
 240:   
 241:              #region Prolog
 242:              
 243:              // *
 244:              // *  -- LAPACK routine (version 3.1) --
 245:              // *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
 246:              // *     November 2006
 247:              // *
 248:              // *     .. Scalar Arguments ..
 249:              // *     ..
 250:              // *     .. Array Arguments ..
 251:              // *     ..
 252:              // *
 253:              // *  Purpose
 254:              // *  =======
 255:              // *
 256:              // *  DGGRQF computes a generalized RQ factorization of an M-by-N matrix A
 257:              // *  and a P-by-N matrix B:
 258:              // *
 259:              // *              A = R*Q,        B = Z*T*Q,
 260:              // *
 261:              // *  where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal
 262:              // *  matrix, and R and T assume one of the forms:
 263:              // *
 264:              // *  if M <= N,  R = ( 0  R12 ) M,   or if M > N,  R = ( R11 ) M-N,
 265:              // *                   N-M  M                           ( R21 ) N
 266:              // *                                                       N
 267:              // *
 268:              // *  where R12 or R21 is upper triangular, and
 269:              // *
 270:              // *  if P >= N,  T = ( T11 ) N  ,   or if P < N,  T = ( T11  T12 ) P,
 271:              // *                  (  0  ) P-N                         P   N-P
 272:              // *                     N
 273:              // *
 274:              // *  where T11 is upper triangular.
 275:              // *
 276:              // *  In particular, if B is square and nonsingular, the GRQ factorization
 277:              // *  of A and B implicitly gives the RQ factorization of A*inv(B):
 278:              // *
 279:              // *               A*inv(B) = (R*inv(T))*Z'
 280:              // *
 281:              // *  where inv(B) denotes the inverse of the matrix B, and Z' denotes the
 282:              // *  transpose of the matrix Z.
 283:              // *
 284:              // *  Arguments
 285:              // *  =========
 286:              // *
 287:              // *  M       (input) INTEGER
 288:              // *          The number of rows of the matrix A.  M >= 0.
 289:              // *
 290:              // *  P       (input) INTEGER
 291:              // *          The number of rows of the matrix B.  P >= 0.
 292:              // *
 293:              // *  N       (input) INTEGER
 294:              // *          The number of columns of the matrices A and B. N >= 0.
 295:              // *
 296:              // *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
 297:              // *          On entry, the M-by-N matrix A.
 298:              // *          On exit, if M <= N, the upper triangle of the subarray
 299:              // *          A(1:M,N-M+1:N) contains the M-by-M upper triangular matrix R;
 300:              // *          if M > N, the elements on and above the (M-N)-th subdiagonal
 301:              // *          contain the M-by-N upper trapezoidal matrix R; the remaining
 302:              // *          elements, with the array TAUA, represent the orthogonal
 303:              // *          matrix Q as a product of elementary reflectors (see Further
 304:              // *          Details).
 305:              // *
 306:              // *  LDA     (input) INTEGER
 307:              // *          The leading dimension of the array A. LDA >= max(1,M).
 308:              // *
 309:              // *  TAUA    (output) DOUBLE PRECISION array, dimension (min(M,N))
 310:              // *          The scalar factors of the elementary reflectors which
 311:              // *          represent the orthogonal matrix Q (see Further Details).
 312:              // *
 313:              // *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,N)
 314:              // *          On entry, the P-by-N matrix B.
 315:              // *          On exit, the elements on and above the diagonal of the array
 316:              // *          contain the min(P,N)-by-N upper trapezoidal matrix T (T is
 317:              // *          upper triangular if P >= N); the elements below the diagonal,
 318:              // *          with the array TAUB, represent the orthogonal matrix Z as a
 319:              // *          product of elementary reflectors (see Further Details).
 320:              // *
 321:              // *  LDB     (input) INTEGER
 322:              // *          The leading dimension of the array B. LDB >= max(1,P).
 323:              // *
 324:              // *  TAUB    (output) DOUBLE PRECISION array, dimension (min(P,N))
 325:              // *          The scalar factors of the elementary reflectors which
 326:              // *          represent the orthogonal matrix Z (see Further Details).
 327:              // *
 328:              // *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
 329:              // *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 330:              // *
 331:              // *  LWORK   (input) INTEGER
 332:              // *          The dimension of the array WORK. LWORK >= max(1,N,M,P).
 333:              // *          For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3),
 334:              // *          where NB1 is the optimal blocksize for the RQ factorization
 335:              // *          of an M-by-N matrix, NB2 is the optimal blocksize for the
 336:              // *          QR factorization of a P-by-N matrix, and NB3 is the optimal
 337:              // *          blocksize for a call of DORMRQ.
 338:              // *
 339:              // *          If LWORK = -1, then a workspace query is assumed; the routine
 340:              // *          only calculates the optimal size of the WORK array, returns
 341:              // *          this value as the first entry of the WORK array, and no error
 342:              // *          message related to LWORK is issued by XERBLA.
 343:              // *
 344:              // *  INFO    (output) INTEGER
 345:              // *          = 0:  successful exit
 346:              // *          < 0:  if INF0= -i, the i-th argument had an illegal value.
 347:              // *
 348:              // *  Further Details
 349:              // *  ===============
 350:              // *
 351:              // *  The matrix Q is represented as a product of elementary reflectors
 352:              // *
 353:              // *     Q = H(1) H(2) . . . H(k), where k = min(m,n).
 354:              // *
 355:              // *  Each H(i) has the form
 356:              // *
 357:              // *     H(i) = I - taua * v * v'
 358:              // *
 359:              // *  where taua is a real scalar, and v is a real vector with
 360:              // *  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
 361:              // *  A(m-k+i,1:n-k+i-1), and taua in TAUA(i).
 362:              // *  To form Q explicitly, use LAPACK subroutine DORGRQ.
 363:              // *  To use Q to update another matrix, use LAPACK subroutine DORMRQ.
 364:              // *
 365:              // *  The matrix Z is represented as a product of elementary reflectors
 366:              // *
 367:              // *     Z = H(1) H(2) . . . H(k), where k = min(p,n).
 368:              // *
 369:              // *  Each H(i) has the form
 370:              // *
 371:              // *     H(i) = I - taub * v * v'
 372:              // *
 373:              // *  where taub is a real scalar, and v is a real vector with
 374:              // *  v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i),
 375:              // *  and taub in TAUB(i).
 376:              // *  To form Z explicitly, use LAPACK subroutine DORGQR.
 377:              // *  To use Z to update another matrix, use LAPACK subroutine DORMQR.
 378:              // *
 379:              // *  =====================================================================
 380:              // *
 381:              // *     .. Local Scalars ..
 382:              // *     ..
 383:              // *     .. External Subroutines ..
 384:              // *     ..
 385:              // *     .. External Functions ..
 386:              // *     ..
 387:              // *     .. Intrinsic Functions ..
 388:              //      INTRINSIC          INT, MAX, MIN;
 389:              // *     ..
 390:              // *     .. Executable Statements ..
 391:              // *
 392:              // *     Test the input parameters
 393:              // *
 394:   
 395:              #endregion
 396:   
 397:   
 398:              #region Body
 399:              
 400:              INFO = 0;
 401:              NB1 = this._ilaenv.Run(1, "DGERQF", " ", M, N,  - 1,  - 1);
 402:              NB2 = this._ilaenv.Run(1, "DGEQRF", " ", P, N,  - 1,  - 1);
 403:              NB3 = this._ilaenv.Run(1, "DORMRQ", " ", M, N, P,  - 1);
 404:              NB = Math.Max(NB1, Math.Max(NB2, NB3));
 405:              LWKOPT = Math.Max(N, Math.Max(M, P)) * NB;
 406:              WORK[1 + o_work] = LWKOPT;
 407:              LQUERY = (LWORK ==  - 1);
 408:              if (M < 0)
 409:              {
 410:                  INFO =  - 1;
 411:              }
 412:              else
 413:              {
 414:                  if (P < 0)
 415:                  {
 416:                      INFO =  - 2;
 417:                  }
 418:                  else
 419:                  {
 420:                      if (N < 0)
 421:                      {
 422:                          INFO =  - 3;
 423:                      }
 424:                      else
 425:                      {
 426:                          if (LDA < Math.Max(1, M))
 427:                          {
 428:                              INFO =  - 5;
 429:                          }
 430:                          else
 431:                          {
 432:                              if (LDB < Math.Max(1, P))
 433:                              {
 434:                                  INFO =  - 8;
 435:                              }
 436:                              else
 437:                              {
 438:                                  if (LWORK < Math.Max(1, Math.Max(M, Math.Max(P, N))) && !LQUERY)
 439:                                  {
 440:                                      INFO =  - 11;
 441:                                  }
 442:                              }
 443:                          }
 444:                      }
 445:                  }
 446:              }
 447:              if (INFO != 0)
 448:              {
 449:                  this._xerbla.Run("DGGRQF",  - INFO);
 450:                  return;
 451:              }
 452:              else
 453:              {
 454:                  if (LQUERY)
 455:                  {
 456:                      return;
 457:                  }
 458:              }
 459:              // *
 460:              // *     RQ factorization of M-by-N matrix A: A = R*Q
 461:              // *
 462:              this._dgerqf.Run(M, N, ref A, offset_a, LDA, ref TAUA, offset_taua, ref WORK, offset_work
 463:                               , LWORK, ref INFO);
 464:              LOPT = (int)WORK[1 + o_work];
 465:              // *
 466:              // *     Update B := B*Q'
 467:              // *
 468:              this._dormrq.Run("Right", "Transpose", P, N, Math.Min(M, N), ref A, Math.Max(1, M - N + 1)+1 * LDA + o_a
 469:                               , LDA, TAUA, offset_taua, ref B, offset_b, LDB, ref WORK, offset_work, LWORK
 470:                               , ref INFO);
 471:              LOPT = Math.Max(LOPT, Convert.ToInt32(Math.Truncate(WORK[1 + o_work])));
 472:              // *
 473:              // *     QR factorization of P-by-N matrix B: B = Z*T
 474:              // *
 475:              this._dgeqrf.Run(P, N, ref B, offset_b, LDB, ref TAUB, offset_taub, ref WORK, offset_work
 476:                               , LWORK, ref INFO);
 477:              WORK[1 + o_work] = Math.Max(LOPT, Convert.ToInt32(Math.Truncate(WORK[1 + o_work])));
 478:              // *
 479:              return;
 480:              // *
 481:              // *     End of DGGRQF
 482:              // *
 483:   
 484:              #endregion
 485:   
 486:          }
 487:      }
 488:  }