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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 driver routine (version 3.1) --
  21:      /// Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
  22:      /// November 2006
  23:      /// Purpose
  24:      /// =======
  25:      /// 
  26:      /// DSBEVD computes all the eigenvalues and, optionally, eigenvectors of
  27:      /// a real symmetric band matrix A. If eigenvectors are desired, it uses
  28:      /// a divide and conquer algorithm.
  29:      /// 
  30:      /// The divide and conquer algorithm makes very mild assumptions about
  31:      /// floating point arithmetic. It will work on machines with a guard
  32:      /// digit in add/subtract, or on those binary machines without guard
  33:      /// digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
  34:      /// Cray-2. It could conceivably fail on hexadecimal or decimal machines
  35:      /// without guard digits, but we know of none.
  36:      /// 
  37:      ///</summary>
  38:      public class DSBEVD
  39:      {
  40:      
  41:   
  42:          #region Dependencies
  43:          
  44:          LSAME _lsame; DLAMCH _dlamch; DLANSB _dlansb; DGEMM _dgemm; DLACPY _dlacpy; DLASCL _dlascl; DSBTRD _dsbtrd; DSCAL _dscal; 
  45:          DSTEDC _dstedc;DSTERF _dsterf; XERBLA _xerbla; 
  46:   
  47:          #endregion
  48:   
  49:   
  50:          #region Fields
  51:          
  52:          const double ZERO = 0.0E+0; const double ONE = 1.0E+0; bool LOWER = false; bool LQUERY = false; bool WANTZ = false; 
  53:          int IINFO = 0;int INDE = 0; int INDWK2 = 0; int INDWRK = 0; int ISCALE = 0; int LIWMIN = 0; int LLWRK2 = 0; int LWMIN = 0; 
  54:          double ANRM = 0;double BIGNUM = 0; double EPS = 0; double RMAX = 0; double RMIN = 0; double SAFMIN = 0; double SIGMA = 0; 
  55:          double SMLNUM = 0;
  56:   
  57:          #endregion
  58:   
  59:          public DSBEVD(LSAME lsame, DLAMCH dlamch, DLANSB dlansb, DGEMM dgemm, DLACPY dlacpy, DLASCL dlascl, DSBTRD dsbtrd, DSCAL dscal, DSTEDC dstedc, DSTERF dsterf
  60:                        , XERBLA xerbla)
  61:          {
  62:      
  63:   
  64:              #region Set Dependencies
  65:              
  66:              this._lsame = lsame; this._dlamch = dlamch; this._dlansb = dlansb; this._dgemm = dgemm; this._dlacpy = dlacpy; 
  67:              this._dlascl = dlascl;this._dsbtrd = dsbtrd; this._dscal = dscal; this._dstedc = dstedc; this._dsterf = dsterf; 
  68:              this._xerbla = xerbla;
  69:   
  70:              #endregion
  71:   
  72:          }
  73:      
  74:          public DSBEVD()
  75:          {
  76:      
  77:   
  78:              #region Dependencies (Initialization)
  79:              
  80:              LSAME lsame = new LSAME();
  81:              DLAMC3 dlamc3 = new DLAMC3();
  82:              DLASSQ dlassq = new DLASSQ();
  83:              XERBLA xerbla = new XERBLA();
  84:              DLAR2V dlar2v = new DLAR2V();
  85:              DLARGV dlargv = new DLARGV();
  86:              DLARTV dlartv = new DLARTV();
  87:              DROT drot = new DROT();
  88:              DSCAL dscal = new DSCAL();
  89:              IEEECK ieeeck = new IEEECK();
  90:              IPARMQ iparmq = new IPARMQ();
  91:              DCOPY dcopy = new DCOPY();
  92:              IDAMAX idamax = new IDAMAX();
  93:              DLAPY2 dlapy2 = new DLAPY2();
  94:              DLAMRG dlamrg = new DLAMRG();
  95:              DNRM2 dnrm2 = new DNRM2();
  96:              DLAED5 dlaed5 = new DLAED5();
  97:              DLAE2 dlae2 = new DLAE2();
  98:              DLAEV2 dlaev2 = new DLAEV2();
  99:              DSWAP dswap = new DSWAP();
 100:              DLAMC1 dlamc1 = new DLAMC1(dlamc3);
 101:              DLAMC4 dlamc4 = new DLAMC4(dlamc3);
 102:              DLAMC5 dlamc5 = new DLAMC5(dlamc3);
 103:              DLAMC2 dlamc2 = new DLAMC2(dlamc3, dlamc1, dlamc4, dlamc5);
 104:              DLAMCH dlamch = new DLAMCH(lsame, dlamc2);
 105:              DLANSB dlansb = new DLANSB(dlassq, lsame);
 106:              DGEMM dgemm = new DGEMM(lsame, xerbla);
 107:              DLACPY dlacpy = new DLACPY(lsame);
 108:              DLASCL dlascl = new DLASCL(lsame, dlamch, xerbla);
 109:              DLARTG dlartg = new DLARTG(dlamch);
 110:              DLASET dlaset = new DLASET(lsame);
 111:              DSBTRD dsbtrd = new DSBTRD(dlar2v, dlargv, dlartg, dlartv, dlaset, drot, xerbla, lsame);
 112:              ILAENV ilaenv = new ILAENV(ieeeck, iparmq);
 113:              DLANST dlanst = new DLANST(lsame, dlassq);
 114:              DLAED2 dlaed2 = new DLAED2(idamax, dlamch, dlapy2, dcopy, dlacpy, dlamrg, drot, dscal, xerbla);
 115:              DLAED6 dlaed6 = new DLAED6(dlamch);
 116:              DLAED4 dlaed4 = new DLAED4(dlamch, dlaed5, dlaed6);
 117:              DLAED3 dlaed3 = new DLAED3(dlamc3, dnrm2, dcopy, dgemm, dlacpy, dlaed4, dlaset, xerbla);
 118:              DLAED1 dlaed1 = new DLAED1(dcopy, dlaed2, dlaed3, dlamrg, xerbla);
 119:              DLAED8 dlaed8 = new DLAED8(idamax, dlamch, dlapy2, dcopy, dlacpy, dlamrg, drot, dscal, xerbla);
 120:              DLAED9 dlaed9 = new DLAED9(dlamc3, dnrm2, dcopy, dlaed4, xerbla);
 121:              DGEMV dgemv = new DGEMV(lsame, xerbla);
 122:              DLAEDA dlaeda = new DLAEDA(dcopy, dgemv, drot, xerbla);
 123:              DLAED7 dlaed7 = new DLAED7(dgemm, dlaed8, dlaed9, dlaeda, dlamrg, xerbla);
 124:              DLASR dlasr = new DLASR(lsame, xerbla);
 125:              DLASRT dlasrt = new DLASRT(lsame, xerbla);
 126:              DSTEQR dsteqr = new DSTEQR(lsame, dlamch, dlanst, dlapy2, dlae2, dlaev2, dlartg, dlascl, dlaset, dlasr
 127:                                         , dlasrt, dswap, xerbla);
 128:              DLAED0 dlaed0 = new DLAED0(dcopy, dgemm, dlacpy, dlaed1, dlaed7, dsteqr, xerbla, ilaenv);
 129:              DSTERF dsterf = new DSTERF(dlamch, dlanst, dlapy2, dlae2, dlascl, dlasrt, xerbla);
 130:              DSTEDC dstedc = new DSTEDC(lsame, ilaenv, dlamch, dlanst, dgemm, dlacpy, dlaed0, dlascl, dlaset, dlasrt
 131:                                         , dsteqr, dsterf, dswap, xerbla);
 132:   
 133:              #endregion
 134:   
 135:   
 136:              #region Set Dependencies
 137:              
 138:              this._lsame = lsame; this._dlamch = dlamch; this._dlansb = dlansb; this._dgemm = dgemm; this._dlacpy = dlacpy; 
 139:              this._dlascl = dlascl;this._dsbtrd = dsbtrd; this._dscal = dscal; this._dstedc = dstedc; this._dsterf = dsterf; 
 140:              this._xerbla = xerbla;
 141:   
 142:              #endregion
 143:   
 144:          }
 145:          /// <summary>
 146:          /// Purpose
 147:          /// =======
 148:          /// 
 149:          /// DSBEVD computes all the eigenvalues and, optionally, eigenvectors of
 150:          /// a real symmetric band matrix A. If eigenvectors are desired, it uses
 151:          /// a divide and conquer algorithm.
 152:          /// 
 153:          /// The divide and conquer algorithm makes very mild assumptions about
 154:          /// floating point arithmetic. It will work on machines with a guard
 155:          /// digit in add/subtract, or on those binary machines without guard
 156:          /// digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
 157:          /// Cray-2. It could conceivably fail on hexadecimal or decimal machines
 158:          /// without guard digits, but we know of none.
 159:          /// 
 160:          ///</summary>
 161:          /// <param name="JOBZ">
 162:          /// (input) CHARACTER*1
 163:          /// = 'N':  Compute eigenvalues only;
 164:          /// = 'V':  Compute eigenvalues and eigenvectors.
 165:          ///</param>
 166:          /// <param name="UPLO">
 167:          /// (input) CHARACTER*1
 168:          /// = 'U':  Upper triangle of A is stored;
 169:          /// = 'L':  Lower triangle of A is stored.
 170:          ///</param>
 171:          /// <param name="N">
 172:          /// (input) INTEGER
 173:          /// The order of the matrix A.  N .GE. 0.
 174:          ///</param>
 175:          /// <param name="KD">
 176:          /// (input) INTEGER
 177:          /// The number of superdiagonals of the matrix A if UPLO = 'U',
 178:          /// or the number of subdiagonals if UPLO = 'L'.  KD .GE. 0.
 179:          ///</param>
 180:          /// <param name="AB">
 181:          /// (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
 182:          /// On entry, the upper or lower triangle of the symmetric band
 183:          /// matrix A, stored in the first KD+1 rows of the array.  The
 184:          /// j-th column of A is stored in the j-th column of the array AB
 185:          /// as follows:
 186:          /// if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd).LE.i.LE.j;
 187:          /// if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j.LE.i.LE.min(n,j+kd).
 188:          /// 
 189:          /// On exit, AB is overwritten by values generated during the
 190:          /// reduction to tridiagonal form.  If UPLO = 'U', the first
 191:          /// superdiagonal and the diagonal of the tridiagonal matrix T
 192:          /// are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
 193:          /// the diagonal and first subdiagonal of T are returned in the
 194:          /// first two rows of AB.
 195:          ///</param>
 196:          /// <param name="LDAB">
 197:          /// (input) INTEGER
 198:          /// The leading dimension of the array AB.  LDAB .GE. KD + 1.
 199:          ///</param>
 200:          /// <param name="W">
 201:          /// (output) DOUBLE PRECISION array, dimension (N)
 202:          /// If INFO = 0, the eigenvalues in ascending order.
 203:          ///</param>
 204:          /// <param name="Z">
 205:          /// (output) DOUBLE PRECISION array, dimension (LDZ, N)
 206:          /// If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
 207:          /// eigenvectors of the matrix A, with the i-th column of Z
 208:          /// holding the eigenvector associated with W(i).
 209:          /// If JOBZ = 'N', then Z is not referenced.
 210:          ///</param>
 211:          /// <param name="LDZ">
 212:          /// (input) INTEGER
 213:          /// The leading dimension of the array Z.  LDZ .GE. 1, and if
 214:          /// JOBZ = 'V', LDZ .GE. max(1,N).
 215:          ///</param>
 216:          /// <param name="WORK">
 217:          /// (workspace/output) DOUBLE PRECISION array,
 218:          /// dimension (LWORK)
 219:          /// On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 220:          ///</param>
 221:          /// <param name="LWORK">
 222:          /// (input) INTEGER
 223:          /// The dimension of the array WORK.
 224:          /// IF N .LE. 1,                LWORK must be at least 1.
 225:          /// If JOBZ  = 'N' and N .GT. 2, LWORK must be at least 2*N.
 226:          /// If JOBZ  = 'V' and N .GT. 2, LWORK must be at least
 227:          /// ( 1 + 5*N + 2*N**2 ).
 228:          /// 
 229:          /// If LWORK = -1, then a workspace query is assumed; the routine
 230:          /// only calculates the optimal sizes of the WORK and IWORK
 231:          /// arrays, returns these values as the first entries of the WORK
 232:          /// and IWORK arrays, and no error message related to LWORK or
 233:          /// LIWORK is issued by XERBLA.
 234:          ///</param>
 235:          /// <param name="IWORK">
 236:          /// (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
 237:          /// On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
 238:          ///</param>
 239:          /// <param name="LIWORK">
 240:          /// (input) INTEGER
 241:          /// The dimension of the array LIWORK.
 242:          /// If JOBZ  = 'N' or N .LE. 1, LIWORK must be at least 1.
 243:          /// If JOBZ  = 'V' and N .GT. 2, LIWORK must be at least 3 + 5*N.
 244:          /// 
 245:          /// If LIWORK = -1, then a workspace query is assumed; the
 246:          /// routine only calculates the optimal sizes of the WORK and
 247:          /// IWORK arrays, returns these values as the first entries of
 248:          /// the WORK and IWORK arrays, and no error message related to
 249:          /// LWORK or LIWORK is issued by XERBLA.
 250:          ///</param>
 251:          /// <param name="INFO">
 252:          /// (output) INTEGER
 253:          /// = 0:  successful exit
 254:          /// .LT. 0:  if INFO = -i, the i-th argument had an illegal value
 255:          /// .GT. 0:  if INFO = i, the algorithm failed to converge; i
 256:          /// off-diagonal elements of an intermediate tridiagonal
 257:          /// form did not converge to zero.
 258:          ///</param>
 259:          public void Run(string JOBZ, string UPLO, int N, int KD, ref double[] AB, int offset_ab, int LDAB
 260:                           , ref double[] W, int offset_w, ref double[] Z, int offset_z, int LDZ, ref double[] WORK, int offset_work, int LWORK, ref int[] IWORK, int offset_iwork
 261:                           , int LIWORK, ref int INFO)
 262:          {
 263:   
 264:              #region Array Index Correction
 265:              
 266:               int o_ab = -1 - LDAB + offset_ab;  int o_w = -1 + offset_w;  int o_z = -1 - LDZ + offset_z; 
 267:               int o_work = -1 + offset_work; int o_iwork = -1 + offset_iwork; 
 268:   
 269:              #endregion
 270:   
 271:   
 272:              #region Strings
 273:              
 274:              JOBZ = JOBZ.Substring(0, 1);  UPLO = UPLO.Substring(0, 1);  
 275:   
 276:              #endregion
 277:   
 278:   
 279:              #region Prolog
 280:              
 281:              // *
 282:              // *  -- LAPACK driver routine (version 3.1) --
 283:              // *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
 284:              // *     November 2006
 285:              // *
 286:              // *     .. Scalar Arguments ..
 287:              // *     ..
 288:              // *     .. Array Arguments ..
 289:              // *     ..
 290:              // *
 291:              // *  Purpose
 292:              // *  =======
 293:              // *
 294:              // *  DSBEVD computes all the eigenvalues and, optionally, eigenvectors of
 295:              // *  a real symmetric band matrix A. If eigenvectors are desired, it uses
 296:              // *  a divide and conquer algorithm.
 297:              // *
 298:              // *  The divide and conquer algorithm makes very mild assumptions about
 299:              // *  floating point arithmetic. It will work on machines with a guard
 300:              // *  digit in add/subtract, or on those binary machines without guard
 301:              // *  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
 302:              // *  Cray-2. It could conceivably fail on hexadecimal or decimal machines
 303:              // *  without guard digits, but we know of none.
 304:              // *
 305:              // *  Arguments
 306:              // *  =========
 307:              // *
 308:              // *  JOBZ    (input) CHARACTER*1
 309:              // *          = 'N':  Compute eigenvalues only;
 310:              // *          = 'V':  Compute eigenvalues and eigenvectors.
 311:              // *
 312:              // *  UPLO    (input) CHARACTER*1
 313:              // *          = 'U':  Upper triangle of A is stored;
 314:              // *          = 'L':  Lower triangle of A is stored.
 315:              // *
 316:              // *  N       (input) INTEGER
 317:              // *          The order of the matrix A.  N >= 0.
 318:              // *
 319:              // *  KD      (input) INTEGER
 320:              // *          The number of superdiagonals of the matrix A if UPLO = 'U',
 321:              // *          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
 322:              // *
 323:              // *  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
 324:              // *          On entry, the upper or lower triangle of the symmetric band
 325:              // *          matrix A, stored in the first KD+1 rows of the array.  The
 326:              // *          j-th column of A is stored in the j-th column of the array AB
 327:              // *          as follows:
 328:              // *          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
 329:              // *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
 330:              // *
 331:              // *          On exit, AB is overwritten by values generated during the
 332:              // *          reduction to tridiagonal form.  If UPLO = 'U', the first
 333:              // *          superdiagonal and the diagonal of the tridiagonal matrix T
 334:              // *          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
 335:              // *          the diagonal and first subdiagonal of T are returned in the
 336:              // *          first two rows of AB.
 337:              // *
 338:              // *  LDAB    (input) INTEGER
 339:              // *          The leading dimension of the array AB.  LDAB >= KD + 1.
 340:              // *
 341:              // *  W       (output) DOUBLE PRECISION array, dimension (N)
 342:              // *          If INFO = 0, the eigenvalues in ascending order.
 343:              // *
 344:              // *  Z       (output) DOUBLE PRECISION array, dimension (LDZ, N)
 345:              // *          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
 346:              // *          eigenvectors of the matrix A, with the i-th column of Z
 347:              // *          holding the eigenvector associated with W(i).
 348:              // *          If JOBZ = 'N', then Z is not referenced.
 349:              // *
 350:              // *  LDZ     (input) INTEGER
 351:              // *          The leading dimension of the array Z.  LDZ >= 1, and if
 352:              // *          JOBZ = 'V', LDZ >= max(1,N).
 353:              // *
 354:              // *  WORK    (workspace/output) DOUBLE PRECISION array,
 355:              // *                                         dimension (LWORK)
 356:              // *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 357:              // *
 358:              // *  LWORK   (input) INTEGER
 359:              // *          The dimension of the array WORK.
 360:              // *          IF N <= 1,                LWORK must be at least 1.
 361:              // *          If JOBZ  = 'N' and N > 2, LWORK must be at least 2*N.
 362:              // *          If JOBZ  = 'V' and N > 2, LWORK must be at least
 363:              // *                         ( 1 + 5*N + 2*N**2 ).
 364:              // *
 365:              // *          If LWORK = -1, then a workspace query is assumed; the routine
 366:              // *          only calculates the optimal sizes of the WORK and IWORK
 367:              // *          arrays, returns these values as the first entries of the WORK
 368:              // *          and IWORK arrays, and no error message related to LWORK or
 369:              // *          LIWORK is issued by XERBLA.
 370:              // *
 371:              // *  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
 372:              // *          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
 373:              // *
 374:              // *  LIWORK  (input) INTEGER
 375:              // *          The dimension of the array LIWORK.
 376:              // *          If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
 377:              // *          If JOBZ  = 'V' and N > 2, LIWORK must be at least 3 + 5*N.
 378:              // *
 379:              // *          If LIWORK = -1, then a workspace query is assumed; the
 380:              // *          routine only calculates the optimal sizes of the WORK and
 381:              // *          IWORK arrays, returns these values as the first entries of
 382:              // *          the WORK and IWORK arrays, and no error message related to
 383:              // *          LWORK or LIWORK is issued by XERBLA.
 384:              // *
 385:              // *  INFO    (output) INTEGER
 386:              // *          = 0:  successful exit
 387:              // *          < 0:  if INFO = -i, the i-th argument had an illegal value
 388:              // *          > 0:  if INFO = i, the algorithm failed to converge; i
 389:              // *                off-diagonal elements of an intermediate tridiagonal
 390:              // *                form did not converge to zero.
 391:              // *
 392:              // *  =====================================================================
 393:              // *
 394:              // *     .. Parameters ..
 395:              // *     ..
 396:              // *     .. Local Scalars ..
 397:              // *     ..
 398:              // *     .. External Functions ..
 399:              // *     ..
 400:              // *     .. External Subroutines ..
 401:              // *     ..
 402:              // *     .. Intrinsic Functions ..
 403:              //      INTRINSIC          SQRT;
 404:              // *     ..
 405:              // *     .. Executable Statements ..
 406:              // *
 407:              // *     Test the input parameters.
 408:              // *
 409:   
 410:              #endregion
 411:   
 412:   
 413:              #region Body
 414:              
 415:              WANTZ = this._lsame.Run(JOBZ, "V");
 416:              LOWER = this._lsame.Run(UPLO, "L");
 417:              LQUERY = (LWORK ==  - 1 || LIWORK ==  - 1);
 418:              // *
 419:              INFO = 0;
 420:              if (N <= 1)
 421:              {
 422:                  LIWMIN = 1;
 423:                  LWMIN = 1;
 424:              }
 425:              else
 426:              {
 427:                  if (WANTZ)
 428:                  {
 429:                      LIWMIN = 3 + 5 * N;
 430:                      LWMIN = 1 + 5 * N + 2 * (int)Math.Pow(N, 2);
 431:                  }
 432:                  else
 433:                  {
 434:                      LIWMIN = 1;
 435:                      LWMIN = 2 * N;
 436:                  }
 437:              }
 438:              if (!(WANTZ || this._lsame.Run(JOBZ, "N")))
 439:              {
 440:                  INFO =  - 1;
 441:              }
 442:              else
 443:              {
 444:                  if (!(LOWER || this._lsame.Run(UPLO, "U")))
 445:                  {
 446:                      INFO =  - 2;
 447:                  }
 448:                  else
 449:                  {
 450:                      if (N < 0)
 451:                      {
 452:                          INFO =  - 3;
 453:                      }
 454:                      else
 455:                      {
 456:                          if (KD < 0)
 457:                          {
 458:                              INFO =  - 4;
 459:                          }
 460:                          else
 461:                          {
 462:                              if (LDAB < KD + 1)
 463:                              {
 464:                                  INFO =  - 6;
 465:                              }
 466:                              else
 467:                              {
 468:                                  if (LDZ < 1 || (WANTZ && LDZ < N))
 469:                                  {
 470:                                      INFO =  - 9;
 471:                                  }
 472:                              }
 473:                          }
 474:                      }
 475:                  }
 476:              }
 477:              // *
 478:              if (INFO == 0)
 479:              {
 480:                  WORK[1 + o_work] = LWMIN;
 481:                  IWORK[1 + o_iwork] = LIWMIN;
 482:                  // *
 483:                  if (LWORK < LWMIN && !LQUERY)
 484:                  {
 485:                      INFO =  - 11;
 486:                  }
 487:                  else
 488:                  {
 489:                      if (LIWORK < LIWMIN && !LQUERY)
 490:                      {
 491:                          INFO =  - 13;
 492:                      }
 493:                  }
 494:              }
 495:              // *
 496:              if (INFO != 0)
 497:              {
 498:                  this._xerbla.Run("DSBEVD",  - INFO);
 499:                  return;
 500:              }
 501:              else
 502:              {
 503:                  if (LQUERY)
 504:                  {
 505:                      return;
 506:                  }
 507:              }
 508:              // *
 509:              // *     Quick return if possible
 510:              // *
 511:              if (N == 0) return;
 512:              // *
 513:              if (N == 1)
 514:              {
 515:                  W[1 + o_w] = AB[1+1 * LDAB + o_ab];
 516:                  if (WANTZ) Z[1+1 * LDZ + o_z] = ONE;
 517:                  return;
 518:              }
 519:              // *
 520:              // *     Get machine constants.
 521:              // *
 522:              SAFMIN = this._dlamch.Run("Safe minimum");
 523:              EPS = this._dlamch.Run("Precision");
 524:              SMLNUM = SAFMIN / EPS;
 525:              BIGNUM = ONE / SMLNUM;
 526:              RMIN = Math.Sqrt(SMLNUM);
 527:              RMAX = Math.Sqrt(BIGNUM);
 528:              // *
 529:              // *     Scale matrix to allowable range, if necessary.
 530:              // *
 531:              ANRM = this._dlansb.Run("M", UPLO, N, KD, AB, offset_ab, LDAB, ref WORK, offset_work);
 532:              ISCALE = 0;
 533:              if (ANRM > ZERO && ANRM < RMIN)
 534:              {
 535:                  ISCALE = 1;
 536:                  SIGMA = RMIN / ANRM;
 537:              }
 538:              else
 539:              {
 540:                  if (ANRM > RMAX)
 541:                  {
 542:                      ISCALE = 1;
 543:                      SIGMA = RMAX / ANRM;
 544:                  }
 545:              }
 546:              if (ISCALE == 1)
 547:              {
 548:                  if (LOWER)
 549:                  {
 550:                      this._dlascl.Run("B", KD, KD, ONE, SIGMA, N
 551:                                       , N, ref AB, offset_ab, LDAB, ref INFO);
 552:                  }
 553:                  else
 554:                  {
 555:                      this._dlascl.Run("Q", KD, KD, ONE, SIGMA, N
 556:                                       , N, ref AB, offset_ab, LDAB, ref INFO);
 557:                  }
 558:              }
 559:              // *
 560:              // *     Call DSBTRD to reduce symmetric band matrix to tridiagonal form.
 561:              // *
 562:              INDE = 1;
 563:              INDWRK = INDE + N;
 564:              INDWK2 = INDWRK + N * N;
 565:              LLWRK2 = LWORK - INDWK2 + 1;
 566:              this._dsbtrd.Run(JOBZ, UPLO, N, KD, ref AB, offset_ab, LDAB
 567:                               , ref W, offset_w, ref WORK, INDE + o_work, ref Z, offset_z, LDZ, ref WORK, INDWRK + o_work, ref IINFO);
 568:              // *
 569:              // *     For eigenvalues only, call DSTERF.  For eigenvectors, call SSTEDC.
 570:              // *
 571:              if (!WANTZ)
 572:              {
 573:                  this._dsterf.Run(N, ref W, offset_w, ref WORK, INDE + o_work, ref INFO);
 574:              }
 575:              else
 576:              {
 577:                  this._dstedc.Run("I", N, ref W, offset_w, ref WORK, INDE + o_work, ref WORK, INDWRK + o_work, N
 578:                                   , ref WORK, INDWK2 + o_work, LLWRK2, ref IWORK, offset_iwork, LIWORK, ref INFO);
 579:                  this._dgemm.Run("N", "N", N, N, N, ONE
 580:                                  , Z, offset_z, LDZ, WORK, INDWRK + o_work, N, ZERO, ref WORK, INDWK2 + o_work
 581:                                  , N);
 582:                  this._dlacpy.Run("A", N, N, WORK, INDWK2 + o_work, N, ref Z, offset_z
 583:                                   , LDZ);
 584:              }
 585:              // *
 586:              // *     If matrix was scaled, then rescale eigenvalues appropriately.
 587:              // *
 588:              if (ISCALE == 1) this._dscal.Run(N, ONE / SIGMA, ref W, offset_w, 1);
 589:              // *
 590:              WORK[1 + o_work] = LWMIN;
 591:              IWORK[1 + o_iwork] = LIWMIN;
 592:              return;
 593:              // *
 594:              // *     End of DSBEVD
 595:              // *
 596:   
 597:              #endregion
 598:   
 599:          }
 600:      }
 601:  }