`   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:      /// This subroutine computes the I-th eigenvalue of a symmetric rank-one`
`  27:      /// modification of a 2-by-2 diagonal matrix`
`  28:      /// `
`  29:      /// diag( D )  +  RHO *  Z * transpose(Z) .`
`  30:      /// `
`  31:      /// The diagonal elements in the array D are assumed to satisfy`
`  32:      /// `
`  33:      /// D(i) .LT. D(j)  for  i .LT. j .`
`  34:      /// `
`  35:      /// We also assume RHO .GT. 0 and that the Euclidean norm of the vector`
`  36:      /// Z is one.`
`  37:      /// `
`  38:      ///</summary>`
`  39:      public class DLAED5`
`  40:      {`
`  41:      `
`  42:   `
`  43:          #region Fields`
`  44:          `
`  45:          const double ZERO = 0.0E0; const double ONE = 1.0E0; const double TWO = 2.0E0; const double FOUR = 4.0E0; double B = 0; `
`  46:          double C = 0;double DEL = 0; double TAU = 0; double TEMP = 0; double W = 0; `
`  47:   `
`  48:          #endregion`
`  49:   `
`  50:          public DLAED5()`
`  51:          {`
`  52:      `
`  53:          }`
`  54:      `
`  55:          /// <summary>`
`  56:          /// Purpose`
`  57:          /// =======`
`  58:          /// `
`  59:          /// This subroutine computes the I-th eigenvalue of a symmetric rank-one`
`  60:          /// modification of a 2-by-2 diagonal matrix`
`  61:          /// `
`  62:          /// diag( D )  +  RHO *  Z * transpose(Z) .`
`  63:          /// `
`  64:          /// The diagonal elements in the array D are assumed to satisfy`
`  65:          /// `
`  66:          /// D(i) .LT. D(j)  for  i .LT. j .`
`  67:          /// `
`  68:          /// We also assume RHO .GT. 0 and that the Euclidean norm of the vector`
`  69:          /// Z is one.`
`  70:          /// `
`  71:          ///</summary>`
`  72:          /// <param name="I">`
`  73:          /// (input) INTEGER`
`  74:          /// The index of the eigenvalue to be computed.  I = 1 or I = 2.`
`  75:          ///</param>`
`  76:          /// <param name="D">`
`  77:          /// (input) DOUBLE PRECISION array, dimension (2)`
`  78:          /// The original eigenvalues.  We assume D(1) .LT. D(2).`
`  79:          ///</param>`
`  80:          /// <param name="Z">`
`  81:          /// (input) DOUBLE PRECISION array, dimension (2)`
`  82:          /// The components of the updating vector.`
`  83:          ///</param>`
`  84:          /// <param name="DELTA">`
`  85:          /// (output) DOUBLE PRECISION array, dimension (2)`
`  86:          /// The vector DELTA contains the information necessary`
`  87:          /// to construct the eigenvectors.`
`  88:          ///</param>`
`  89:          /// <param name="RHO">`
`  90:          /// (input) DOUBLE PRECISION`
`  91:          /// The scalar in the symmetric updating formula.`
`  92:          ///</param>`
`  93:          /// <param name="DLAM">`
`  94:          /// (output) DOUBLE PRECISION`
`  95:          /// The computed lambda_I, the I-th updated eigenvalue.`
`  96:          ///</param>`
`  97:          public void Run(int I, double[] D, int offset_d, double[] Z, int offset_z, ref double[] DELTA, int offset_delta, double RHO, ref double DLAM)`
`  98:          {`
`  99:   `
` 100:              #region Array Index Correction`
` 101:              `
` 102:               int o_d = -1 + offset_d;  int o_z = -1 + offset_z;  int o_delta = -1 + offset_delta; `
` 103:   `
` 104:              #endregion`
` 105:   `
` 106:   `
` 107:              #region Prolog`
` 108:              `
` 109:              // *`
` 110:              // *  -- LAPACK routine (version 3.1) --`
` 111:              // *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..`
` 112:              // *     November 2006`
` 113:              // *`
` 114:              // *     .. Scalar Arguments ..`
` 115:              // *     ..`
` 116:              // *     .. Array Arguments ..`
` 117:              // *     ..`
` 118:              // *`
` 119:              // *  Purpose`
` 120:              // *  =======`
` 121:              // *`
` 122:              // *  This subroutine computes the I-th eigenvalue of a symmetric rank-one`
` 123:              // *  modification of a 2-by-2 diagonal matrix`
` 124:              // *`
` 125:              // *             diag( D )  +  RHO *  Z * transpose(Z) .`
` 126:              // *`
` 127:              // *  The diagonal elements in the array D are assumed to satisfy`
` 128:              // *`
` 129:              // *             D(i) < D(j)  for  i < j .`
` 130:              // *`
` 131:              // *  We also assume RHO > 0 and that the Euclidean norm of the vector`
` 132:              // *  Z is one.`
` 133:              // *`
` 134:              // *  Arguments`
` 135:              // *  =========`
` 136:              // *`
` 137:              // *  I      (input) INTEGER`
` 138:              // *         The index of the eigenvalue to be computed.  I = 1 or I = 2.`
` 139:              // *`
` 140:              // *  D      (input) DOUBLE PRECISION array, dimension (2)`
` 141:              // *         The original eigenvalues.  We assume D(1) < D(2).`
` 142:              // *`
` 143:              // *  Z      (input) DOUBLE PRECISION array, dimension (2)`
` 144:              // *         The components of the updating vector.`
` 145:              // *`
` 146:              // *  DELTA  (output) DOUBLE PRECISION array, dimension (2)`
` 147:              // *         The vector DELTA contains the information necessary`
` 148:              // *         to construct the eigenvectors.`
` 149:              // *`
` 150:              // *  RHO    (input) DOUBLE PRECISION`
` 151:              // *         The scalar in the symmetric updating formula.`
` 152:              // *`
` 153:              // *  DLAM   (output) DOUBLE PRECISION`
` 154:              // *         The computed lambda_I, the I-th updated eigenvalue.`
` 155:              // *`
` 156:              // *  Further Details`
` 157:              // *  ===============`
` 158:              // *`
` 159:              // *  Based on contributions by`
` 160:              // *     Ren-Cang Li, Computer Science Division, University of California`
` 161:              // *     at Berkeley, USA`
` 162:              // *`
` 163:              // *  =====================================================================`
` 164:              // *`
` 165:              // *     .. Parameters ..`
` 166:              // *     ..`
` 167:              // *     .. Local Scalars ..`
` 168:              // *     ..`
` 169:              // *     .. Intrinsic Functions ..`
` 170:              //      INTRINSIC          ABS, SQRT;`
` 171:              // *     ..`
` 172:              // *     .. Executable Statements ..`
` 173:              // *`
` 174:   `
` 175:              #endregion`
` 176:   `
` 177:   `
` 178:              #region Body`
` 179:              `
` 180:              DEL = D[2 + o_d] - D[1 + o_d];`
` 181:              if (I == 1)`
` 182:              {`
` 183:                  W = ONE + TWO * RHO * (Z[2 + o_z] * Z[2 + o_z] - Z[1 + o_z] * Z[1 + o_z]) / DEL;`
` 184:                  if (W > ZERO)`
` 185:                  {`
` 186:                      B = DEL + RHO * (Z[1 + o_z] * Z[1 + o_z] + Z[2 + o_z] * Z[2 + o_z]);`
` 187:                      C = RHO * Z[1 + o_z] * Z[1 + o_z] * DEL;`
` 188:                      // *`
` 189:                      // *           B > ZERO, always`
` 190:                      // *`
` 191:                      TAU = TWO * C / (B + Math.Sqrt(Math.Abs(B * B - FOUR * C)));`
` 192:                      DLAM = D[1 + o_d] + TAU;`
` 193:                      DELTA[1 + o_delta] =  - Z[1 + o_z] / TAU;`
` 194:                      DELTA[2 + o_delta] = Z[2 + o_z] / (DEL - TAU);`
` 195:                  }`
` 196:                  else`
` 197:                  {`
` 198:                      B =  - DEL + RHO * (Z[1 + o_z] * Z[1 + o_z] + Z[2 + o_z] * Z[2 + o_z]);`
` 199:                      C = RHO * Z[2 + o_z] * Z[2 + o_z] * DEL;`
` 200:                      if (B > ZERO)`
` 201:                      {`
` 202:                          TAU =  - TWO * C / (B + Math.Sqrt(B * B + FOUR * C));`
` 203:                      }`
` 204:                      else`
` 205:                      {`
` 206:                          TAU = (B - Math.Sqrt(B * B + FOUR * C)) / TWO;`
` 207:                      }`
` 208:                      DLAM = D[2 + o_d] + TAU;`
` 209:                      DELTA[1 + o_delta] =  - Z[1 + o_z] / (DEL + TAU);`
` 210:                      DELTA[2 + o_delta] =  - Z[2 + o_z] / TAU;`
` 211:                  }`
` 212:                  TEMP = Math.Sqrt(DELTA[1 + o_delta] * DELTA[1 + o_delta] + DELTA[2 + o_delta] * DELTA[2 + o_delta]);`
` 213:                  DELTA[1 + o_delta] = DELTA[1 + o_delta] / TEMP;`
` 214:                  DELTA[2 + o_delta] = DELTA[2 + o_delta] / TEMP;`
` 215:              }`
` 216:              else`
` 217:              {`
` 218:                  // *`
` 219:                  // *     Now I=2`
` 220:                  // *`
` 221:                  B =  - DEL + RHO * (Z[1 + o_z] * Z[1 + o_z] + Z[2 + o_z] * Z[2 + o_z]);`
` 222:                  C = RHO * Z[2 + o_z] * Z[2 + o_z] * DEL;`
` 223:                  if (B > ZERO)`
` 224:                  {`
` 225:                      TAU = (B + Math.Sqrt(B * B + FOUR * C)) / TWO;`
` 226:                  }`
` 227:                  else`
` 228:                  {`
` 229:                      TAU = TWO * C / ( - B + Math.Sqrt(B * B + FOUR * C));`
` 230:                  }`
` 231:                  DLAM = D[2 + o_d] + TAU;`
` 232:                  DELTA[1 + o_delta] =  - Z[1 + o_z] / (DEL + TAU);`
` 233:                  DELTA[2 + o_delta] =  - Z[2 + o_z] / TAU;`
` 234:                  TEMP = Math.Sqrt(DELTA[1 + o_delta] * DELTA[1 + o_delta] + DELTA[2 + o_delta] * DELTA[2 + o_delta]);`
` 235:                  DELTA[1 + o_delta] = DELTA[1 + o_delta] / TEMP;`
` 236:                  DELTA[2 + o_delta] = DELTA[2 + o_delta] / TEMP;`
` 237:              }`
` 238:              return;`
` 239:              // *`
` 240:              // *     End OF DLAED5`
` 241:              // *`
` 242:   `
` 243:              #endregion`
` 244:   `
` 245:          }`
` 246:      }`
` 247:  }`