`   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 driver routine (version 3.1) --`
`  21:      /// Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..`
`  22:      /// November 2006`
`  23:      /// Purpose`
`  24:      /// =======`
`  25:      /// `
`  26:      /// DGGGLM solves a general Gauss-Markov linear model (GLM) problem:`
`  27:      /// `
`  28:      /// minimize || y ||_2   subject to   d = A*x + B*y`
`  29:      /// x`
`  30:      /// `
`  31:      /// where A is an N-by-M matrix, B is an N-by-P matrix, and d is a`
`  32:      /// given N-vector. It is assumed that M .LE. N .LE. M+P, and`
`  33:      /// `
`  34:      /// rank(A) = M    and    rank( A B ) = N.`
`  35:      /// `
`  36:      /// Under these assumptions, the constrained equation is always`
`  37:      /// consistent, and there is a unique solution x and a minimal 2-norm`
`  38:      /// solution y, which is obtained using a generalized QR factorization`
`  39:      /// of the matrices (A, B) given by`
`  40:      /// `
`  41:      /// A = Q*(R),   B = Q*T*Z.`
`  42:      /// (0)`
`  43:      /// `
`  44:      /// In particular, if matrix B is square nonsingular, then the problem`
`  45:      /// GLM is equivalent to the following weighted linear least squares`
`  46:      /// problem`
`  47:      /// `
`  48:      /// minimize || inv(B)*(d-A*x) ||_2`
`  49:      /// x`
`  50:      /// `
`  51:      /// where inv(B) denotes the inverse of B.`
`  52:      /// `
`  53:      ///</summary>`
`  54:      public class DGGGLM`
`  55:      {`
`  56:      `
`  57:   `
`  58:          #region Dependencies`
`  59:          `
`  60:          DCOPY _dcopy; DGEMV _dgemv; DGGQRF _dggqrf; DORMQR _dormqr; DORMRQ _dormrq; DTRTRS _dtrtrs; XERBLA _xerbla; `
`  61:          ILAENV _ilaenv;`
`  62:   `
`  63:          #endregion`
`  64:   `
`  65:   `
`  66:          #region Fields`
`  67:          `
`  68:          const double ZERO = 0.0E+0; const double ONE = 1.0E+0; bool LQUERY = false; int I = 0; int LOPT = 0; int LWKMIN = 0; `
`  69:          int LWKOPT = 0;int NB = 0; int NB1 = 0; int NB2 = 0; int NB3 = 0; int NB4 = 0; int NP = 0; `
`  70:   `
`  71:          #endregion`
`  72:   `
`  73:          public DGGGLM(DCOPY dcopy, DGEMV dgemv, DGGQRF dggqrf, DORMQR dormqr, DORMRQ dormrq, DTRTRS dtrtrs, XERBLA xerbla, ILAENV ilaenv)`
`  74:          {`
`  75:      `
`  76:   `
`  77:              #region Set Dependencies`
`  78:              `
`  79:              this._dcopy = dcopy; this._dgemv = dgemv; this._dggqrf = dggqrf; this._dormqr = dormqr; this._dormrq = dormrq; `
`  80:              this._dtrtrs = dtrtrs;this._xerbla = xerbla; this._ilaenv = ilaenv; `
`  81:   `
`  82:              #endregion`
`  83:   `
`  84:          }`
`  85:      `
`  86:          public DGGGLM()`
`  87:          {`
`  88:      `
`  89:   `
`  90:              #region Dependencies (Initialization)`
`  91:              `
`  92:              DCOPY dcopy = new DCOPY();`
`  93:              LSAME lsame = new LSAME();`
`  94:              XERBLA xerbla = new XERBLA();`
`  95:              DLAMC3 dlamc3 = new DLAMC3();`
`  96:              DLAPY2 dlapy2 = new DLAPY2();`
`  97:              DNRM2 dnrm2 = new DNRM2();`
`  98:              DSCAL dscal = new DSCAL();`
`  99:              IEEECK ieeeck = new IEEECK();`
` 100:              IPARMQ iparmq = new IPARMQ();`
` 101:              DGEMV dgemv = new DGEMV(lsame, xerbla);`
` 102:              DGER dger = new DGER(xerbla);`
` 103:              DLARF dlarf = new DLARF(dgemv, dger, lsame);`
` 104:              DLAMC1 dlamc1 = new DLAMC1(dlamc3);`
` 105:              DLAMC4 dlamc4 = new DLAMC4(dlamc3);`
` 106:              DLAMC5 dlamc5 = new DLAMC5(dlamc3);`
` 107:              DLAMC2 dlamc2 = new DLAMC2(dlamc3, dlamc1, dlamc4, dlamc5);`
` 108:              DLAMCH dlamch = new DLAMCH(lsame, dlamc2);`
` 109:              DLARFG dlarfg = new DLARFG(dlamch, dlapy2, dnrm2, dscal);`
` 110:              DGEQR2 dgeqr2 = new DGEQR2(dlarf, dlarfg, xerbla);`
` 111:              DGEMM dgemm = new DGEMM(lsame, xerbla);`
` 112:              DTRMM dtrmm = new DTRMM(lsame, xerbla);`
` 113:              DLARFB dlarfb = new DLARFB(lsame, dcopy, dgemm, dtrmm);`
` 114:              DTRMV dtrmv = new DTRMV(lsame, xerbla);`
` 115:              DLARFT dlarft = new DLARFT(dgemv, dtrmv, lsame);`
` 116:              ILAENV ilaenv = new ILAENV(ieeeck, iparmq);`
` 117:              DGEQRF dgeqrf = new DGEQRF(dgeqr2, dlarfb, dlarft, xerbla, ilaenv);`
` 118:              DGERQ2 dgerq2 = new DGERQ2(dlarf, dlarfg, xerbla);`
` 119:              DGERQF dgerqf = new DGERQF(dgerq2, dlarfb, dlarft, xerbla, ilaenv);`
` 120:              DORM2R dorm2r = new DORM2R(lsame, dlarf, xerbla);`
` 121:              DORMQR dormqr = new DORMQR(lsame, ilaenv, dlarfb, dlarft, dorm2r, xerbla);`
` 122:              DGGQRF dggqrf = new DGGQRF(dgeqrf, dgerqf, dormqr, xerbla, ilaenv);`
` 123:              DORMR2 dormr2 = new DORMR2(lsame, dlarf, xerbla);`
` 124:              DORMRQ dormrq = new DORMRQ(lsame, ilaenv, dlarfb, dlarft, dormr2, xerbla);`
` 125:              DTRSM dtrsm = new DTRSM(lsame, xerbla);`
` 126:              DTRTRS dtrtrs = new DTRTRS(lsame, dtrsm, xerbla);`
` 127:   `
` 128:              #endregion`
` 129:   `
` 130:   `
` 131:              #region Set Dependencies`
` 132:              `
` 133:              this._dcopy = dcopy; this._dgemv = dgemv; this._dggqrf = dggqrf; this._dormqr = dormqr; this._dormrq = dormrq; `
` 134:              this._dtrtrs = dtrtrs;this._xerbla = xerbla; this._ilaenv = ilaenv; `
` 135:   `
` 136:              #endregion`
` 137:   `
` 138:          }`
` 139:          /// <summary>`
` 140:          /// Purpose`
` 141:          /// =======`
` 142:          /// `
` 143:          /// DGGGLM solves a general Gauss-Markov linear model (GLM) problem:`
` 144:          /// `
` 145:          /// minimize || y ||_2   subject to   d = A*x + B*y`
` 146:          /// x`
` 147:          /// `
` 148:          /// where A is an N-by-M matrix, B is an N-by-P matrix, and d is a`
` 149:          /// given N-vector. It is assumed that M .LE. N .LE. M+P, and`
` 150:          /// `
` 151:          /// rank(A) = M    and    rank( A B ) = N.`
` 152:          /// `
` 153:          /// Under these assumptions, the constrained equation is always`
` 154:          /// consistent, and there is a unique solution x and a minimal 2-norm`
` 155:          /// solution y, which is obtained using a generalized QR factorization`
` 156:          /// of the matrices (A, B) given by`
` 157:          /// `
` 158:          /// A = Q*(R),   B = Q*T*Z.`
` 159:          /// (0)`
` 160:          /// `
` 161:          /// In particular, if matrix B is square nonsingular, then the problem`
` 162:          /// GLM is equivalent to the following weighted linear least squares`
` 163:          /// problem`
` 164:          /// `
` 165:          /// minimize || inv(B)*(d-A*x) ||_2`
` 166:          /// x`
` 167:          /// `
` 168:          /// where inv(B) denotes the inverse of B.`
` 169:          /// `
` 170:          ///</summary>`
` 171:          /// <param name="N">`
` 172:          /// (input) INTEGER`
` 173:          /// The number of rows of the matrices A and B.  N .GE. 0.`
` 174:          ///</param>`
` 175:          /// <param name="M">`
` 176:          /// (input) INTEGER`
` 177:          /// The number of columns of the matrix A.  0 .LE. M .LE. N.`
` 178:          ///</param>`
` 179:          /// <param name="P">`
` 180:          /// (input) INTEGER`
` 181:          /// The number of columns of the matrix B.  P .GE. N-M.`
` 182:          ///</param>`
` 183:          /// <param name="A">`
` 184:          /// = Q*(R),   B = Q*T*Z.`
` 185:          /// (0)`
` 186:          ///</param>`
` 187:          /// <param name="LDA">`
` 188:          /// (input) INTEGER`
` 189:          /// The leading dimension of the array A. LDA .GE. max(1,N).`
` 190:          ///</param>`
` 191:          /// <param name="B">`
` 192:          /// (input/output) DOUBLE PRECISION array, dimension (LDB,P)`
` 193:          /// On entry, the N-by-P matrix B.`
` 194:          /// On exit, if N .LE. P, the upper triangle of the subarray`
` 195:          /// B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;`
` 196:          /// if N .GT. P, the elements on and above the (N-P)th subdiagonal`
` 197:          /// contain the N-by-P upper trapezoidal matrix T.`
` 198:          ///</param>`
` 199:          /// <param name="LDB">`
` 200:          /// (input) INTEGER`
` 201:          /// The leading dimension of the array B. LDB .GE. max(1,N).`
` 202:          ///</param>`
` 203:          /// <param name="D">`
` 204:          /// (input/output) DOUBLE PRECISION array, dimension (N)`
` 205:          /// On entry, D is the left hand side of the GLM equation.`
` 206:          /// On exit, D is destroyed.`
` 207:          ///</param>`
` 208:          /// <param name="X">`
` 209:          /// (output) DOUBLE PRECISION array, dimension (M)`
` 210:          ///</param>`
` 211:          /// <param name="Y">`
` 212:          /// (output) DOUBLE PRECISION array, dimension (P)`
` 213:          /// On exit, X and Y are the solutions of the GLM problem.`
` 214:          ///</param>`
` 215:          /// <param name="WORK">`
` 216:          /// (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))`
` 217:          /// On exit, if INFO = 0, WORK(1) returns the optimal LWORK.`
` 218:          ///</param>`
` 219:          /// <param name="LWORK">`
` 220:          /// (input) INTEGER`
` 221:          /// The dimension of the array WORK. LWORK .GE. max(1,N+M+P).`
` 222:          /// For optimum performance, LWORK .GE. M+min(N,P)+max(N,P)*NB,`
` 223:          /// where NB is an upper bound for the optimal blocksizes for`
` 224:          /// DGEQRF, SGERQF, DORMQR and SORMRQ.`
` 225:          /// `
` 226:          /// If LWORK = -1, then a workspace query is assumed; the routine`
` 227:          /// only calculates the optimal size of the WORK array, returns`
` 228:          /// this value as the first entry of the WORK array, and no error`
` 229:          /// message related to LWORK is issued by XERBLA.`
` 230:          ///</param>`
` 231:          /// <param name="INFO">`
` 232:          /// (output) INTEGER`
` 233:          /// = 0:  successful exit.`
` 234:          /// .LT. 0:  if INFO = -i, the i-th argument had an illegal value.`
` 235:          /// = 1:  the upper triangular factor R associated with A in the`
` 236:          /// generalized QR factorization of the pair (A, B) is`
` 237:          /// singular, so that rank(A) .LT. M; the least squares`
` 238:          /// solution could not be computed.`
` 239:          /// = 2:  the bottom (N-M) by (N-M) part of the upper trapezoidal`
` 240:          /// factor T associated with B in the generalized QR`
` 241:          /// factorization of the pair (A, B) is singular, so that`
` 242:          /// rank( A B ) .LT. N; the least squares solution could not`
` 243:          /// be computed.`
` 244:          ///</param>`
` 245:          public void Run(int N, int M, int P, ref double[] A, int offset_a, int LDA, ref double[] B, int offset_b`
` 246:                           , int LDB, ref double[] D, int offset_d, ref double[] X, int offset_x, ref double[] Y, int offset_y, ref double[] WORK, int offset_work, int LWORK`
` 247:                           , ref int INFO)`
` 248:          {`
` 249:   `
` 250:              #region Array Index Correction`
` 251:              `
` 252:               int o_a = -1 - LDA + offset_a;  int o_b = -1 - LDB + offset_b;  int o_d = -1 + offset_d;  int o_x = -1 + offset_x; `
` 253:               int o_y = -1 + offset_y; int o_work = -1 + offset_work; `
` 254:   `
` 255:              #endregion`
` 256:   `
` 257:   `
` 258:              #region Prolog`
` 259:              `
` 260:              // *`
` 261:              // *  -- LAPACK driver routine (version 3.1) --`
` 262:              // *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..`
` 263:              // *     November 2006`
` 264:              // *`
` 265:              // *     .. Scalar Arguments ..`
` 266:              // *     ..`
` 267:              // *     .. Array Arguments ..`
` 268:              // *     ..`
` 269:              // *`
` 270:              // *  Purpose`
` 271:              // *  =======`
` 272:              // *`
` 273:              // *  DGGGLM solves a general Gauss-Markov linear model (GLM) problem:`
` 274:              // *`
` 275:              // *          minimize || y ||_2   subject to   d = A*x + B*y`
` 276:              // *              x`
` 277:              // *`
` 278:              // *  where A is an N-by-M matrix, B is an N-by-P matrix, and d is a`
` 279:              // *  given N-vector. It is assumed that M <= N <= M+P, and`
` 280:              // *`
` 281:              // *             rank(A) = M    and    rank( A B ) = N.`
` 282:              // *`
` 283:              // *  Under these assumptions, the constrained equation is always`
` 284:              // *  consistent, and there is a unique solution x and a minimal 2-norm`
` 285:              // *  solution y, which is obtained using a generalized QR factorization`
` 286:              // *  of the matrices (A, B) given by`
` 287:              // *`
` 288:              // *     A = Q*(R),   B = Q*T*Z.`
` 289:              // *           (0)`
` 290:              // *`
` 291:              // *  In particular, if matrix B is square nonsingular, then the problem`
` 292:              // *  GLM is equivalent to the following weighted linear least squares`
` 293:              // *  problem`
` 294:              // *`
` 295:              // *               minimize || inv(B)*(d-A*x) ||_2`
` 296:              // *                   x`
` 297:              // *`
` 298:              // *  where inv(B) denotes the inverse of B.`
` 299:              // *`
` 300:              // *  Arguments`
` 301:              // *  =========`
` 302:              // *`
` 303:              // *  N       (input) INTEGER`
` 304:              // *          The number of rows of the matrices A and B.  N >= 0.`
` 305:              // *`
` 306:              // *  M       (input) INTEGER`
` 307:              // *          The number of columns of the matrix A.  0 <= M <= N.`
` 308:              // *`
` 309:              // *  P       (input) INTEGER`
` 310:              // *          The number of columns of the matrix B.  P >= N-M.`
` 311:              // *`
` 312:              // *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,M)`
` 313:              // *          On entry, the N-by-M matrix A.`
` 314:              // *          On exit, the upper triangular part of the array A contains`
` 315:              // *          the M-by-M upper triangular matrix R.`
` 316:              // *`
` 317:              // *  LDA     (input) INTEGER`
` 318:              // *          The leading dimension of the array A. LDA >= max(1,N).`
` 319:              // *`
` 320:              // *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,P)`
` 321:              // *          On entry, the N-by-P matrix B.`
` 322:              // *          On exit, if N <= P, the upper triangle of the subarray`
` 323:              // *          B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;`
` 324:              // *          if N > P, the elements on and above the (N-P)th subdiagonal`
` 325:              // *          contain the N-by-P upper trapezoidal matrix T.`
` 326:              // *`
` 327:              // *  LDB     (input) INTEGER`
` 328:              // *          The leading dimension of the array B. LDB >= max(1,N).`
` 329:              // *`
` 330:              // *  D       (input/output) DOUBLE PRECISION array, dimension (N)`
` 331:              // *          On entry, D is the left hand side of the GLM equation.`
` 332:              // *          On exit, D is destroyed.`
` 333:              // *`
` 334:              // *  X       (output) DOUBLE PRECISION array, dimension (M)`
` 335:              // *  Y       (output) DOUBLE PRECISION array, dimension (P)`
` 336:              // *          On exit, X and Y are the solutions of the GLM problem.`
` 337:              // *`
` 338:              // *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))`
` 339:              // *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.`
` 340:              // *`
` 341:              // *  LWORK   (input) INTEGER`
` 342:              // *          The dimension of the array WORK. LWORK >= max(1,N+M+P).`
` 343:              // *          For optimum performance, LWORK >= M+min(N,P)+max(N,P)*NB,`
` 344:              // *          where NB is an upper bound for the optimal blocksizes for`
` 345:              // *          DGEQRF, SGERQF, DORMQR and SORMRQ.`
` 346:              // *`
` 347:              // *          If LWORK = -1, then a workspace query is assumed; the routine`
` 348:              // *          only calculates the optimal size of the WORK array, returns`
` 349:              // *          this value as the first entry of the WORK array, and no error`
` 350:              // *          message related to LWORK is issued by XERBLA.`
` 351:              // *`
` 352:              // *  INFO    (output) INTEGER`
` 353:              // *          = 0:  successful exit.`
` 354:              // *          < 0:  if INFO = -i, the i-th argument had an illegal value.`
` 355:              // *          = 1:  the upper triangular factor R associated with A in the`
` 356:              // *                generalized QR factorization of the pair (A, B) is`
` 357:              // *                singular, so that rank(A) < M; the least squares`
` 358:              // *                solution could not be computed.`
` 359:              // *          = 2:  the bottom (N-M) by (N-M) part of the upper trapezoidal`
` 360:              // *                factor T associated with B in the generalized QR`
` 361:              // *                factorization of the pair (A, B) is singular, so that`
` 362:              // *                rank( A B ) < N; the least squares solution could not`
` 363:              // *                be computed.`
` 364:              // *`
` 365:              // *  ===================================================================`
` 366:              // *`
` 367:              // *     .. Parameters ..`
` 368:              // *     ..`
` 369:              // *     .. Local Scalars ..`
` 370:              // *     ..`
` 371:              // *     .. External Subroutines ..`
` 372:              // *     ..`
` 373:              // *     .. External Functions ..`
` 374:              // *     ..`
` 375:              // *     .. Intrinsic Functions ..`
` 376:              //      INTRINSIC          INT, MAX, MIN;`
` 377:              // *     ..`
` 378:              // *     .. Executable Statements ..`
` 379:              // *`
` 380:              // *     Test the input parameters`
` 381:              // *`
` 382:   `
` 383:              #endregion`
` 384:   `
` 385:   `
` 386:              #region Body`
` 387:              `
` 388:              INFO = 0;`
` 389:              NP = Math.Min(N, P);`
` 390:              LQUERY = (LWORK ==  - 1);`
` 391:              if (N < 0)`
` 392:              {`
` 393:                  INFO =  - 1;`
` 394:              }`
` 395:              else`
` 396:              {`
` 397:                  if (M < 0 || M > N)`
` 398:                  {`
` 399:                      INFO =  - 2;`
` 400:                  }`
` 401:                  else`
` 402:                  {`
` 403:                      if (P < 0 || P < N - M)`
` 404:                      {`
` 405:                          INFO =  - 3;`
` 406:                      }`
` 407:                      else`
` 408:                      {`
` 409:                          if (LDA < Math.Max(1, N))`
` 410:                          {`
` 411:                              INFO =  - 5;`
` 412:                          }`
` 413:                          else`
` 414:                          {`
` 415:                              if (LDB < Math.Max(1, N))`
` 416:                              {`
` 417:                                  INFO =  - 7;`
` 418:                              }`
` 419:                          }`
` 420:                      }`
` 421:                  }`
` 422:              }`
` 423:              // *`
` 424:              // *     Calculate workspace`
` 425:              // *`
` 426:              if (INFO == 0)`
` 427:              {`
` 428:                  if (N == 0)`
` 429:                  {`
` 430:                      LWKMIN = 1;`
` 431:                      LWKOPT = 1;`
` 432:                  }`
` 433:                  else`
` 434:                  {`
` 435:                      NB1 = this._ilaenv.Run(1, "DGEQRF", " ", N, M,  - 1,  - 1);`
` 436:                      NB2 = this._ilaenv.Run(1, "DGERQF", " ", N, M,  - 1,  - 1);`
` 437:                      NB3 = this._ilaenv.Run(1, "DORMQR", " ", N, M, P,  - 1);`
` 438:                      NB4 = this._ilaenv.Run(1, "DORMRQ", " ", N, M, P,  - 1);`
` 439:                      NB = Math.Max(NB1, Math.Max(NB2, Math.Max(NB3, NB4)));`
` 440:                      LWKMIN = M + N + P;`
` 441:                      LWKOPT = M + NP + Math.Max(N, P) * NB;`
` 442:                  }`
` 443:                  WORK[1 + o_work] = LWKOPT;`
` 444:                  // *`
` 445:                  if (LWORK < LWKMIN && !LQUERY)`
` 446:                  {`
` 447:                      INFO =  - 12;`
` 448:                  }`
` 449:              }`
` 450:              // *`
` 451:              if (INFO != 0)`
` 452:              {`
` 453:                  this._xerbla.Run("DGGGLM",  - INFO);`
` 454:                  return;`
` 455:              }`
` 456:              else`
` 457:              {`
` 458:                  if (LQUERY)`
` 459:                  {`
` 460:                      return;`
` 461:                  }`
` 462:              }`
` 463:              // *`
` 464:              // *     Quick return if possible`
` 465:              // *`
` 466:              if (N == 0) return;`
` 467:              // *`
` 468:              // *     Compute the GQR factorization of matrices A and B:`
` 469:              // *`
` 470:              // *            Q'*A = ( R11 ) M,    Q'*B*Z' = ( T11   T12 ) M`
` 471:              // *                   (  0  ) N-M             (  0    T22 ) N-M`
` 472:              // *                      M                     M+P-N  N-M`
` 473:              // *`
` 474:              // *     where R11 and T22 are upper triangular, and Q and Z are`
` 475:              // *     orthogonal.`
` 476:              // *`
` 477:              this._dggqrf.Run(N, M, P, ref A, offset_a, LDA, ref WORK, offset_work`
` 478:                               , ref B, offset_b, LDB, ref WORK, M + 1 + o_work, ref WORK, M + NP + 1 + o_work, LWORK - M - NP, ref INFO);`
` 479:              LOPT = (int)WORK[M + NP + 1 + o_work];`
` 480:              // *`
` 481:              // *     Update left-hand-side vector d = Q'*d = ( d1 ) M`
` 482:              // *                                             ( d2 ) N-M`
` 483:              // *`
` 484:              this._dormqr.Run("Left", "Transpose", N, 1, M, ref A, offset_a`
` 485:                               , LDA, WORK, offset_work, ref D, offset_d, Math.Max(1, N), ref WORK, M + NP + 1 + o_work, LWORK - M - NP`
` 486:                               , ref INFO);`
` 487:              LOPT = Math.Max(LOPT, Convert.ToInt32(Math.Truncate(WORK[M + NP + 1 + o_work])));`
` 488:              // *`
` 489:              // *     Solve T22*y2 = d2 for y2`
` 490:              // *`
` 491:              if (N > M)`
` 492:              {`
` 493:                  this._dtrtrs.Run("Upper", "No transpose", "Non unit", N - M, 1, B, M + 1+(M + P - N + 1) * LDB + o_b`
` 494:                                   , LDB, ref D, M + 1 + o_d, N - M, ref INFO);`
` 495:                  // *`
` 496:                  if (INFO > 0)`
` 497:                  {`
` 498:                      INFO = 1;`
` 499:                      return;`
` 500:                  }`
` 501:                  // *`
` 502:                  this._dcopy.Run(N - M, D, M + 1 + o_d, 1, ref Y, M + P - N + 1 + o_y, 1);`
` 503:              }`
` 504:              // *`
` 505:              // *     Set y1 = 0`
` 506:              // *`
` 507:              for (I = 1; I <= M + P - N; I++)`
` 508:              {`
` 509:                  Y[I + o_y] = ZERO;`
` 510:              }`
` 511:              // *`
` 512:              // *     Update d1 = d1 - T12*y2`
` 513:              // *`
` 514:              this._dgemv.Run("No transpose", M, N - M,  - ONE, B, 1+(M + P - N + 1) * LDB + o_b, LDB`
` 515:                              , Y, M + P - N + 1 + o_y, 1, ONE, ref D, offset_d, 1);`
` 516:              // *`
` 517:              // *     Solve triangular system: R11*x = d1`
` 518:              // *`
` 519:              if (M > 0)`
` 520:              {`
` 521:                  this._dtrtrs.Run("Upper", "No Transpose", "Non unit", M, 1, A, offset_a`
` 522:                                   , LDA, ref D, offset_d, M, ref INFO);`
` 523:                  // *`
` 524:                  if (INFO > 0)`
` 525:                  {`
` 526:                      INFO = 2;`
` 527:                      return;`
` 528:                  }`
` 529:                  // *`
` 530:                  // *        Copy D to X`
` 531:                  // *`
` 532:                  this._dcopy.Run(M, D, offset_d, 1, ref X, offset_x, 1);`
` 533:              }`
` 534:              // *`
` 535:              // *     Backward transformation y = Z'*y`
` 536:              // *`
` 537:              this._dormrq.Run("Left", "Transpose", P, 1, NP, ref B, Math.Max(1, N - P + 1)+1 * LDB + o_b`
` 538:                               , LDB, WORK, M + 1 + o_work, ref Y, offset_y, Math.Max(1, P), ref WORK, M + NP + 1 + o_work, LWORK - M - NP`
` 539:                               , ref INFO);`
` 540:              WORK[1 + o_work] = M + NP + Math.Max(LOPT, Convert.ToInt32(Math.Truncate(WORK[M + NP + 1 + o_work])));`
` 541:              // *`
` 542:              return;`
` 543:              // *`
` 544:              // *     End of DGGGLM`
` 545:              // *`
` 546:   `
` 547:              #endregion`
` 548:   `
` 549:          }`
` 550:      }`
` 551:  }`