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: /// DLAED2 merges the two sets of eigenvalues together into a single
27: /// sorted set. Then it tries to deflate the size of the problem.
28: /// There are two ways in which deflation can occur: when two or more
29: /// eigenvalues are close together or if there is a tiny entry in the
30: /// Z vector. For each such occurrence the order of the related secular
31: /// equation problem is reduced by one.
32: ///
33: ///</summary>
34: public class DLAED2
35: {
36:
37:
38: #region Dependencies
39:
40: IDAMAX _idamax; DLAMCH _dlamch; DLAPY2 _dlapy2; DCOPY _dcopy; DLACPY _dlacpy; DLAMRG _dlamrg; DROT _drot; DSCAL _dscal;
41: XERBLA _xerbla;
42:
43: #endregion
44:
45:
46: #region Fields
47:
48: const double MONE = - 1.0E0; const double ZERO = 0.0E0; const double ONE = 1.0E0; const double TWO = 2.0E0;
49: const double EIGHT = 8.0E0;int[] CTOT = new int[4]; int o_ctot = -1;
50: int[] PSM = new int[4]; int o_psm = -1;int CT = 0; int I = 0; int IMAX = 0; int IQ1 = 0; int IQ2 = 0;
51: int J = 0;int JMAX = 0; int JS = 0; int K2 = 0; int N1P1 = 0; int N2 = 0; int NJ = 0; int PJ = 0; double C = 0;
52: double EPS = 0;double S = 0; double T = 0; double TAU = 0; double TOL = 0;
53:
54: #endregion
55:
56: public DLAED2(IDAMAX idamax, DLAMCH dlamch, DLAPY2 dlapy2, DCOPY dcopy, DLACPY dlacpy, DLAMRG dlamrg, DROT drot, DSCAL dscal, XERBLA xerbla)
57: {
58:
59:
60: #region Set Dependencies
61:
62: this._idamax = idamax; this._dlamch = dlamch; this._dlapy2 = dlapy2; this._dcopy = dcopy; this._dlacpy = dlacpy;
63: this._dlamrg = dlamrg;this._drot = drot; this._dscal = dscal; this._xerbla = xerbla;
64:
65: #endregion
66:
67: }
68:
69: public DLAED2()
70: {
71:
72:
73: #region Dependencies (Initialization)
74:
75: IDAMAX idamax = new IDAMAX();
76: LSAME lsame = new LSAME();
77: DLAMC3 dlamc3 = new DLAMC3();
78: DLAPY2 dlapy2 = new DLAPY2();
79: DCOPY dcopy = new DCOPY();
80: DLAMRG dlamrg = new DLAMRG();
81: DROT drot = new DROT();
82: DSCAL dscal = new DSCAL();
83: XERBLA xerbla = new XERBLA();
84: DLAMC1 dlamc1 = new DLAMC1(dlamc3);
85: DLAMC4 dlamc4 = new DLAMC4(dlamc3);
86: DLAMC5 dlamc5 = new DLAMC5(dlamc3);
87: DLAMC2 dlamc2 = new DLAMC2(dlamc3, dlamc1, dlamc4, dlamc5);
88: DLAMCH dlamch = new DLAMCH(lsame, dlamc2);
89: DLACPY dlacpy = new DLACPY(lsame);
90:
91: #endregion
92:
93:
94: #region Set Dependencies
95:
96: this._idamax = idamax; this._dlamch = dlamch; this._dlapy2 = dlapy2; this._dcopy = dcopy; this._dlacpy = dlacpy;
97: this._dlamrg = dlamrg;this._drot = drot; this._dscal = dscal; this._xerbla = xerbla;
98:
99: #endregion
100:
101: }
102: /// <summary>
103: /// Purpose
104: /// =======
105: ///
106: /// DLAED2 merges the two sets of eigenvalues together into a single
107: /// sorted set. Then it tries to deflate the size of the problem.
108: /// There are two ways in which deflation can occur: when two or more
109: /// eigenvalues are close together or if there is a tiny entry in the
110: /// Z vector. For each such occurrence the order of the related secular
111: /// equation problem is reduced by one.
112: ///
113: ///</summary>
114: /// <param name="K">
115: /// (output) INTEGER
116: /// The number of non-deflated eigenvalues, and the order of the
117: /// related secular equation. 0 .LE. K .LE.N.
118: ///</param>
119: /// <param name="N">
120: /// (input) INTEGER
121: /// The dimension of the symmetric tridiagonal matrix. N .GE. 0.
122: ///</param>
123: /// <param name="N1">
124: /// (input) INTEGER
125: /// The location of the last eigenvalue in the leading sub-matrix.
126: /// min(1,N) .LE. N1 .LE. N/2.
127: ///</param>
128: /// <param name="D">
129: /// (input/output) DOUBLE PRECISION array, dimension (N)
130: /// On entry, D contains the eigenvalues of the two submatrices to
131: /// be combined.
132: /// On exit, D contains the trailing (N-K) updated eigenvalues
133: /// (those which were deflated) sorted into increasing order.
134: ///</param>
135: /// <param name="Q">
136: /// (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
137: /// On entry, Q contains the eigenvectors of two submatrices in
138: /// the two square blocks with corners at (1,1), (N1,N1)
139: /// and (N1+1, N1+1), (N,N).
140: /// On exit, Q contains the trailing (N-K) updated eigenvectors
141: /// (those which were deflated) in its last N-K columns.
142: ///</param>
143: /// <param name="LDQ">
144: /// (input) INTEGER
145: /// The leading dimension of the array Q. LDQ .GE. max(1,N).
146: ///</param>
147: /// <param name="INDXQ">
148: /// (input/output) INTEGER array, dimension (N)
149: /// The permutation which separately sorts the two sub-problems
150: /// in D into ascending order. Note that elements in the second
151: /// half of this permutation must first have N1 added to their
152: /// values. Destroyed on exit.
153: ///</param>
154: /// <param name="RHO">
155: /// (input/output) DOUBLE PRECISION
156: /// On entry, the off-diagonal element associated with the rank-1
157: /// cut which originally split the two submatrices which are now
158: /// being recombined.
159: /// On exit, RHO has been modified to the value required by
160: /// DLAED3.
161: ///</param>
162: /// <param name="Z">
163: /// (input) DOUBLE PRECISION array, dimension (N)
164: /// On entry, Z contains the updating vector (the last
165: /// row of the first sub-eigenvector matrix and the first row of
166: /// the second sub-eigenvector matrix).
167: /// On exit, the contents of Z have been destroyed by the updating
168: /// process.
169: ///</param>
170: /// <param name="DLAMDA">
171: /// (output) DOUBLE PRECISION array, dimension (N)
172: /// A copy of the first K eigenvalues which will be used by
173: /// DLAED3 to form the secular equation.
174: ///</param>
175: /// <param name="W">
176: /// (output) DOUBLE PRECISION array, dimension (N)
177: /// The first k values of the final deflation-altered z-vector
178: /// which will be passed to DLAED3.
179: ///</param>
180: /// <param name="Q2">
181: /// (output) DOUBLE PRECISION array, dimension (N1**2+(N-N1)**2)
182: /// A copy of the first K eigenvectors which will be used by
183: /// DLAED3 in a matrix multiply (DGEMM) to solve for the new
184: /// eigenvectors.
185: ///</param>
186: /// <param name="INDX">
187: /// (workspace) INTEGER array, dimension (N)
188: /// The permutation used to sort the contents of DLAMDA into
189: /// ascending order.
190: ///</param>
191: /// <param name="INDXC">
192: /// (output) INTEGER array, dimension (N)
193: /// The permutation used to arrange the columns of the deflated
194: /// Q matrix into three groups: the first group contains non-zero
195: /// elements only at and above N1, the second contains
196: /// non-zero elements only below N1, and the third is dense.
197: ///</param>
198: /// <param name="INDXP">
199: /// (workspace) INTEGER array, dimension (N)
200: /// The permutation used to place deflated values of D at the end
201: /// of the array. INDXP(1:K) points to the nondeflated D-values
202: /// and INDXP(K+1:N) points to the deflated eigenvalues.
203: ///</param>
204: /// <param name="COLTYP">
205: /// (workspace/output) INTEGER array, dimension (N)
206: /// During execution, a label which will indicate which of the
207: /// following types a column in the Q2 matrix is:
208: /// 1 : non-zero in the upper half only;
209: /// 2 : dense;
210: /// 3 : non-zero in the lower half only;
211: /// 4 : deflated.
212: /// On exit, COLTYP(i) is the number of columns of type i,
213: /// for i=1 to 4 only.
214: ///</param>
215: /// <param name="INFO">
216: /// (output) INTEGER
217: /// = 0: successful exit.
218: /// .LT. 0: if INFO = -i, the i-th argument had an illegal value.
219: ///</param>
220: public void Run(ref int K, int N, int N1, ref double[] D, int offset_d, ref double[] Q, int offset_q, int LDQ
221: , ref int[] INDXQ, int offset_indxq, ref double RHO, ref double[] Z, int offset_z, ref double[] DLAMDA, int offset_dlamda, ref double[] W, int offset_w, ref double[] Q2, int offset_q2
222: , ref int[] INDX, int offset_indx, ref int[] INDXC, int offset_indxc, ref int[] INDXP, int offset_indxp, ref int[] COLTYP, int offset_coltyp, ref int INFO)
223: {
224:
225: #region Array Index Correction
226:
227: int o_d = -1 + offset_d; int o_q = -1 - LDQ + offset_q; int o_indxq = -1 + offset_indxq; int o_z = -1 + offset_z;
228: int o_dlamda = -1 + offset_dlamda; int o_w = -1 + offset_w; int o_q2 = -1 + offset_q2;
229: int o_indx = -1 + offset_indx; int o_indxc = -1 + offset_indxc; int o_indxp = -1 + offset_indxp;
230: int o_coltyp = -1 + offset_coltyp;
231:
232: #endregion
233:
234:
235: #region Prolog
236:
237: // *
238: // * -- LAPACK routine (version 3.1) --
239: // * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
240: // * November 2006
241: // *
242: // * .. Scalar Arguments ..
243: // * ..
244: // * .. Array Arguments ..
245: // * ..
246: // *
247: // * Purpose
248: // * =======
249: // *
250: // * DLAED2 merges the two sets of eigenvalues together into a single
251: // * sorted set. Then it tries to deflate the size of the problem.
252: // * There are two ways in which deflation can occur: when two or more
253: // * eigenvalues are close together or if there is a tiny entry in the
254: // * Z vector. For each such occurrence the order of the related secular
255: // * equation problem is reduced by one.
256: // *
257: // * Arguments
258: // * =========
259: // *
260: // * K (output) INTEGER
261: // * The number of non-deflated eigenvalues, and the order of the
262: // * related secular equation. 0 <= K <=N.
263: // *
264: // * N (input) INTEGER
265: // * The dimension of the symmetric tridiagonal matrix. N >= 0.
266: // *
267: // * N1 (input) INTEGER
268: // * The location of the last eigenvalue in the leading sub-matrix.
269: // * min(1,N) <= N1 <= N/2.
270: // *
271: // * D (input/output) DOUBLE PRECISION array, dimension (N)
272: // * On entry, D contains the eigenvalues of the two submatrices to
273: // * be combined.
274: // * On exit, D contains the trailing (N-K) updated eigenvalues
275: // * (those which were deflated) sorted into increasing order.
276: // *
277: // * Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
278: // * On entry, Q contains the eigenvectors of two submatrices in
279: // * the two square blocks with corners at (1,1), (N1,N1)
280: // * and (N1+1, N1+1), (N,N).
281: // * On exit, Q contains the trailing (N-K) updated eigenvectors
282: // * (those which were deflated) in its last N-K columns.
283: // *
284: // * LDQ (input) INTEGER
285: // * The leading dimension of the array Q. LDQ >= max(1,N).
286: // *
287: // * INDXQ (input/output) INTEGER array, dimension (N)
288: // * The permutation which separately sorts the two sub-problems
289: // * in D into ascending order. Note that elements in the second
290: // * half of this permutation must first have N1 added to their
291: // * values. Destroyed on exit.
292: // *
293: // * RHO (input/output) DOUBLE PRECISION
294: // * On entry, the off-diagonal element associated with the rank-1
295: // * cut which originally split the two submatrices which are now
296: // * being recombined.
297: // * On exit, RHO has been modified to the value required by
298: // * DLAED3.
299: // *
300: // * Z (input) DOUBLE PRECISION array, dimension (N)
301: // * On entry, Z contains the updating vector (the last
302: // * row of the first sub-eigenvector matrix and the first row of
303: // * the second sub-eigenvector matrix).
304: // * On exit, the contents of Z have been destroyed by the updating
305: // * process.
306: // *
307: // * DLAMDA (output) DOUBLE PRECISION array, dimension (N)
308: // * A copy of the first K eigenvalues which will be used by
309: // * DLAED3 to form the secular equation.
310: // *
311: // * W (output) DOUBLE PRECISION array, dimension (N)
312: // * The first k values of the final deflation-altered z-vector
313: // * which will be passed to DLAED3.
314: // *
315: // * Q2 (output) DOUBLE PRECISION array, dimension (N1**2+(N-N1)**2)
316: // * A copy of the first K eigenvectors which will be used by
317: // * DLAED3 in a matrix multiply (DGEMM) to solve for the new
318: // * eigenvectors.
319: // *
320: // * INDX (workspace) INTEGER array, dimension (N)
321: // * The permutation used to sort the contents of DLAMDA into
322: // * ascending order.
323: // *
324: // * INDXC (output) INTEGER array, dimension (N)
325: // * The permutation used to arrange the columns of the deflated
326: // * Q matrix into three groups: the first group contains non-zero
327: // * elements only at and above N1, the second contains
328: // * non-zero elements only below N1, and the third is dense.
329: // *
330: // * INDXP (workspace) INTEGER array, dimension (N)
331: // * The permutation used to place deflated values of D at the end
332: // * of the array. INDXP(1:K) points to the nondeflated D-values
333: // * and INDXP(K+1:N) points to the deflated eigenvalues.
334: // *
335: // * COLTYP (workspace/output) INTEGER array, dimension (N)
336: // * During execution, a label which will indicate which of the
337: // * following types a column in the Q2 matrix is:
338: // * 1 : non-zero in the upper half only;
339: // * 2 : dense;
340: // * 3 : non-zero in the lower half only;
341: // * 4 : deflated.
342: // * On exit, COLTYP(i) is the number of columns of type i,
343: // * for i=1 to 4 only.
344: // *
345: // * INFO (output) INTEGER
346: // * = 0: successful exit.
347: // * < 0: if INFO = -i, the i-th argument had an illegal value.
348: // *
349: // * Further Details
350: // * ===============
351: // *
352: // * Based on contributions by
353: // * Jeff Rutter, Computer Science Division, University of California
354: // * at Berkeley, USA
355: // * Modified by Francoise Tisseur, University of Tennessee.
356: // *
357: // * =====================================================================
358: // *
359: // * .. Parameters ..
360: // * ..
361: // * .. Local Arrays ..
362: // * ..
363: // * .. Local Scalars ..
364: // * ..
365: // * .. External Functions ..
366: // * ..
367: // * .. External Subroutines ..
368: // * ..
369: // * .. Intrinsic Functions ..
370: // INTRINSIC ABS, MAX, MIN, SQRT;
371: // * ..
372: // * .. Executable Statements ..
373: // *
374: // * Test the input parameters.
375: // *
376:
377: #endregion
378:
379:
380: #region Body
381:
382: INFO = 0;
383: // *
384: if (N < 0)
385: {
386: INFO = - 2;
387: }
388: else
389: {
390: if (LDQ < Math.Max(1, N))
391: {
392: INFO = - 6;
393: }
394: else
395: {
396: if (Math.Min(1, (N / 2)) > N1 || (N / 2) < N1)
397: {
398: INFO = - 3;
399: }
400: }
401: }
402: if (INFO != 0)
403: {
404: this._xerbla.Run("DLAED2", - INFO);
405: return;
406: }
407: // *
408: // * Quick return if possible
409: // *
410: if (N == 0) return;
411: // *
412: N2 = N - N1;
413: N1P1 = N1 + 1;
414: // *
415: if (RHO < ZERO)
416: {
417: this._dscal.Run(N2, MONE, ref Z, N1P1 + o_z, 1);
418: }
419: // *
420: // * Normalize z so that norm(z) = 1. Since z is the concatenation of
421: // * two normalized vectors, norm2(z) = sqrt(2).
422: // *
423: T = ONE / Math.Sqrt(TWO);
424: this._dscal.Run(N, T, ref Z, offset_z, 1);
425: // *
426: // * RHO = ABS( norm(z)**2 * RHO )
427: // *
428: RHO = Math.Abs(TWO * RHO);
429: // *
430: // * Sort the eigenvalues into increasing order
431: // *
432: for (I = N1P1; I <= N; I++)
433: {
434: INDXQ[I + o_indxq] = INDXQ[I + o_indxq] + N1;
435: }
436: // *
437: // * re-integrate the deflated parts from the last pass
438: // *
439: for (I = 1; I <= N; I++)
440: {
441: DLAMDA[I + o_dlamda] = D[INDXQ[I + o_indxq] + o_d];
442: }
443: this._dlamrg.Run(N1, N2, DLAMDA, offset_dlamda, 1, 1, ref INDXC, offset_indxc);
444: for (I = 1; I <= N; I++)
445: {
446: INDX[I + o_indx] = INDXQ[INDXC[I + o_indxc] + o_indxq];
447: }
448: // *
449: // * Calculate the allowable deflation tolerance
450: // *
451: IMAX = this._idamax.Run(N, Z, offset_z, 1);
452: JMAX = this._idamax.Run(N, D, offset_d, 1);
453: EPS = this._dlamch.Run("Epsilon");
454: TOL = EIGHT * EPS * Math.Max(Math.Abs(D[JMAX + o_d]), Math.Abs(Z[IMAX + o_z]));
455: // *
456: // * If the rank-1 modifier is small enough, no more needs to be done
457: // * except to reorganize Q so that its columns correspond with the
458: // * elements in D.
459: // *
460: if (RHO * Math.Abs(Z[IMAX + o_z]) <= TOL)
461: {
462: K = 0;
463: IQ2 = 1;
464: for (J = 1; J <= N; J++)
465: {
466: I = INDX[J + o_indx];
467: this._dcopy.Run(N, Q, 1+I * LDQ + o_q, 1, ref Q2, IQ2 + o_q2, 1);
468: DLAMDA[J + o_dlamda] = D[I + o_d];
469: IQ2 = IQ2 + N;
470: }
471: this._dlacpy.Run("A", N, N, Q2, offset_q2, N, ref Q, offset_q
472: , LDQ);
473: this._dcopy.Run(N, DLAMDA, offset_dlamda, 1, ref D, offset_d, 1);
474: goto LABEL190;
475: }
476: // *
477: // * If there are multiple eigenvalues then the problem deflates. Here
478: // * the number of equal eigenvalues are found. As each equal
479: // * eigenvalue is found, an elementary reflector is computed to rotate
480: // * the corresponding eigensubspace so that the corresponding
481: // * components of Z are zero in this new basis.
482: // *
483: for (I = 1; I <= N1; I++)
484: {
485: COLTYP[I + o_coltyp] = 1;
486: }
487: for (I = N1P1; I <= N; I++)
488: {
489: COLTYP[I + o_coltyp] = 3;
490: }
491: // *
492: // *
493: K = 0;
494: K2 = N + 1;
495: for (J = 1; J <= N; J++)
496: {
497: NJ = INDX[J + o_indx];
498: if (RHO * Math.Abs(Z[NJ + o_z]) <= TOL)
499: {
500: // *
501: // * Deflate due to small z component.
502: // *
503: K2 = K2 - 1;
504: COLTYP[NJ + o_coltyp] = 4;
505: INDXP[K2 + o_indxp] = NJ;
506: if (J == N) goto LABEL100;
507: }
508: else
509: {
510: PJ = NJ;
511: goto LABEL80;
512: }
513: }
514: LABEL80:;
515: J = J + 1;
516: NJ = INDX[J + o_indx];
517: if (J > N) goto LABEL100;
518: if (RHO * Math.Abs(Z[NJ + o_z]) <= TOL)
519: {
520: // *
521: // * Deflate due to small z component.
522: // *
523: K2 = K2 - 1;
524: COLTYP[NJ + o_coltyp] = 4;
525: INDXP[K2 + o_indxp] = NJ;
526: }
527: else
528: {
529: // *
530: // * Check if eigenvalues are close enough to allow deflation.
531: // *
532: S = Z[PJ + o_z];
533: C = Z[NJ + o_z];
534: // *
535: // * Find sqrt(a**2+b**2) without overflow or
536: // * destructive underflow.
537: // *
538: TAU = this._dlapy2.Run(C, S);
539: T = D[NJ + o_d] - D[PJ + o_d];
540: C = C / TAU;
541: S = - S / TAU;
542: if (Math.Abs(T * C * S) <= TOL)
543: {
544: // *
545: // * Deflation is possible.
546: // *
547: Z[NJ + o_z] = TAU;
548: Z[PJ + o_z] = ZERO;
549: if (COLTYP[NJ + o_coltyp] != COLTYP[PJ + o_coltyp]) COLTYP[NJ + o_coltyp] = 2;
550: COLTYP[PJ + o_coltyp] = 4;
551: this._drot.Run(N, ref Q, 1+PJ * LDQ + o_q, 1, ref Q, 1+NJ * LDQ + o_q, 1, C
552: , S);
553: T = D[PJ + o_d] * Math.Pow(C,2) + D[NJ + o_d] * Math.Pow(S,2);
554: D[NJ + o_d] = D[PJ + o_d] * Math.Pow(S,2) + D[NJ + o_d] * Math.Pow(C,2);
555: D[PJ + o_d] = T;
556: K2 = K2 - 1;
557: I = 1;
558: LABEL90:;
559: if (K2 + I <= N)
560: {
561: if (D[PJ + o_d] < D[INDXP[K2 + I + o_indxp] + o_d])
562: {
563: INDXP[K2 + I - 1 + o_indxp] = INDXP[K2 + I + o_indxp];
564: INDXP[K2 + I + o_indxp] = PJ;
565: I = I + 1;
566: goto LABEL90;
567: }
568: else
569: {
570: INDXP[K2 + I - 1 + o_indxp] = PJ;
571: }
572: }
573: else
574: {
575: INDXP[K2 + I - 1 + o_indxp] = PJ;
576: }
577: PJ = NJ;
578: }
579: else
580: {
581: K = K + 1;
582: DLAMDA[K + o_dlamda] = D[PJ + o_d];
583: W[K + o_w] = Z[PJ + o_z];
584: INDXP[K + o_indxp] = PJ;
585: PJ = NJ;
586: }
587: }
588: goto LABEL80;
589: LABEL100:;
590: // *
591: // * Record the last eigenvalue.
592: // *
593: K = K + 1;
594: DLAMDA[K + o_dlamda] = D[PJ + o_d];
595: W[K + o_w] = Z[PJ + o_z];
596: INDXP[K + o_indxp] = PJ;
597: // *
598: // * Count up the total number of the various types of columns, then
599: // * form a permutation which positions the four column types into
600: // * four uniform groups (although one or more of these groups may be
601: // * empty).
602: // *
603: for (J = 1; J <= 4; J++)
604: {
605: CTOT[J + o_ctot] = 0;
606: }
607: for (J = 1; J <= N; J++)
608: {
609: CT = COLTYP[J + o_coltyp];
610: CTOT[CT + o_ctot] = CTOT[CT + o_ctot] + 1;
611: }
612: // *
613: // * PSM(*) = Position in SubMatrix (of types 1 through 4)
614: // *
615: PSM[1 + o_psm] = 1;
616: PSM[2 + o_psm] = 1 + CTOT[1 + o_ctot];
617: PSM[3 + o_psm] = PSM[2 + o_psm] + CTOT[2 + o_ctot];
618: PSM[4 + o_psm] = PSM[3 + o_psm] + CTOT[3 + o_ctot];
619: K = N - CTOT[4 + o_ctot];
620: // *
621: // * Fill out the INDXC array so that the permutation which it induces
622: // * will place all type-1 columns first, all type-2 columns next,
623: // * then all type-3's, and finally all type-4's.
624: // *
625: for (J = 1; J <= N; J++)
626: {
627: JS = INDXP[J + o_indxp];
628: CT = COLTYP[JS + o_coltyp];
629: INDX[PSM[CT + o_psm] + o_indx] = JS;
630: INDXC[PSM[CT + o_psm] + o_indxc] = J;
631: PSM[CT + o_psm] = PSM[CT + o_psm] + 1;
632: }
633: // *
634: // * Sort the eigenvalues and corresponding eigenvectors into DLAMDA
635: // * and Q2 respectively. The eigenvalues/vectors which were not
636: // * deflated go into the first K slots of DLAMDA and Q2 respectively,
637: // * while those which were deflated go into the last N - K slots.
638: // *
639: I = 1;
640: IQ1 = 1;
641: IQ2 = 1 + (CTOT[1 + o_ctot] + CTOT[2 + o_ctot]) * N1;
642: for (J = 1; J <= CTOT[1 + o_ctot]; J++)
643: {
644: JS = INDX[I + o_indx];
645: this._dcopy.Run(N1, Q, 1+JS * LDQ + o_q, 1, ref Q2, IQ1 + o_q2, 1);
646: Z[I + o_z] = D[JS + o_d];
647: I = I + 1;
648: IQ1 = IQ1 + N1;
649: }
650: // *
651: for (J = 1; J <= CTOT[2 + o_ctot]; J++)
652: {
653: JS = INDX[I + o_indx];
654: this._dcopy.Run(N1, Q, 1+JS * LDQ + o_q, 1, ref Q2, IQ1 + o_q2, 1);
655: this._dcopy.Run(N2, Q, N1 + 1+JS * LDQ + o_q, 1, ref Q2, IQ2 + o_q2, 1);
656: Z[I + o_z] = D[JS + o_d];
657: I = I + 1;
658: IQ1 = IQ1 + N1;
659: IQ2 = IQ2 + N2;
660: }
661: // *
662: for (J = 1; J <= CTOT[3 + o_ctot]; J++)
663: {
664: JS = INDX[I + o_indx];
665: this._dcopy.Run(N2, Q, N1 + 1+JS * LDQ + o_q, 1, ref Q2, IQ2 + o_q2, 1);
666: Z[I + o_z] = D[JS + o_d];
667: I = I + 1;
668: IQ2 = IQ2 + N2;
669: }
670: // *
671: IQ1 = IQ2;
672: for (J = 1; J <= CTOT[4 + o_ctot]; J++)
673: {
674: JS = INDX[I + o_indx];
675: this._dcopy.Run(N, Q, 1+JS * LDQ + o_q, 1, ref Q2, IQ2 + o_q2, 1);
676: IQ2 = IQ2 + N;
677: Z[I + o_z] = D[JS + o_d];
678: I = I + 1;
679: }
680: // *
681: // * The deflated eigenvalues and their corresponding vectors go back
682: // * into the last N - K slots of D and Q respectively.
683: // *
684: this._dlacpy.Run("A", N, CTOT[4 + o_ctot], Q2, IQ1 + o_q2, N, ref Q, 1+(K + 1) * LDQ + o_q
685: , LDQ);
686: this._dcopy.Run(N - K, Z, K + 1 + o_z, 1, ref D, K + 1 + o_d, 1);
687: // *
688: // * Copy CTOT into COLTYP for referencing in DLAED3.
689: // *
690: for (J = 1; J <= 4; J++)
691: {
692: COLTYP[J + o_coltyp] = CTOT[J + o_ctot];
693: }
694: // *
695: LABEL190:;
696: return;
697: // *
698: // * End of DLAED2
699: // *
700:
701: #endregion
702:
703: }
704: }
705: }