Annotation of rpl/lapack/lapack/zlaed7.f, revision 1.6
1.1 bertrand 1: SUBROUTINE ZLAED7( N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q,
2: $ LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM,
3: $ GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK,
4: $ INFO )
5: *
6: * -- LAPACK routine (version 3.2) --
7: * -- LAPACK is a software package provided by Univ. of Tennessee, --
8: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
9: * November 2006
10: *
11: * .. Scalar Arguments ..
12: INTEGER CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ,
13: $ TLVLS
14: DOUBLE PRECISION RHO
15: * ..
16: * .. Array Arguments ..
17: INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ),
18: $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * )
19: DOUBLE PRECISION D( * ), GIVNUM( 2, * ), QSTORE( * ), RWORK( * )
20: COMPLEX*16 Q( LDQ, * ), WORK( * )
21: * ..
22: *
23: * Purpose
24: * =======
25: *
26: * ZLAED7 computes the updated eigensystem of a diagonal
27: * matrix after modification by a rank-one symmetric matrix. This
28: * routine is used only for the eigenproblem which requires all
29: * eigenvalues and optionally eigenvectors of a dense or banded
30: * Hermitian matrix that has been reduced to tridiagonal form.
31: *
32: * T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)
33: *
34: * where Z = Q'u, u is a vector of length N with ones in the
35: * CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
36: *
37: * The eigenvectors of the original matrix are stored in Q, and the
38: * eigenvalues are in D. The algorithm consists of three stages:
39: *
40: * The first stage consists of deflating the size of the problem
41: * when there are multiple eigenvalues or if there is a zero in
42: * the Z vector. For each such occurence the dimension of the
43: * secular equation problem is reduced by one. This stage is
44: * performed by the routine DLAED2.
45: *
46: * The second stage consists of calculating the updated
47: * eigenvalues. This is done by finding the roots of the secular
48: * equation via the routine DLAED4 (as called by SLAED3).
49: * This routine also calculates the eigenvectors of the current
50: * problem.
51: *
52: * The final stage consists of computing the updated eigenvectors
53: * directly using the updated eigenvalues. The eigenvectors for
54: * the current problem are multiplied with the eigenvectors from
55: * the overall problem.
56: *
57: * Arguments
58: * =========
59: *
60: * N (input) INTEGER
61: * The dimension of the symmetric tridiagonal matrix. N >= 0.
62: *
63: * CUTPNT (input) INTEGER
64: * Contains the location of the last eigenvalue in the leading
65: * sub-matrix. min(1,N) <= CUTPNT <= N.
66: *
67: * QSIZ (input) INTEGER
68: * The dimension of the unitary matrix used to reduce
69: * the full matrix to tridiagonal form. QSIZ >= N.
70: *
71: * TLVLS (input) INTEGER
72: * The total number of merging levels in the overall divide and
73: * conquer tree.
74: *
75: * CURLVL (input) INTEGER
76: * The current level in the overall merge routine,
77: * 0 <= curlvl <= tlvls.
78: *
79: * CURPBM (input) INTEGER
80: * The current problem in the current level in the overall
81: * merge routine (counting from upper left to lower right).
82: *
83: * D (input/output) DOUBLE PRECISION array, dimension (N)
84: * On entry, the eigenvalues of the rank-1-perturbed matrix.
85: * On exit, the eigenvalues of the repaired matrix.
86: *
87: * Q (input/output) COMPLEX*16 array, dimension (LDQ,N)
88: * On entry, the eigenvectors of the rank-1-perturbed matrix.
89: * On exit, the eigenvectors of the repaired tridiagonal matrix.
90: *
91: * LDQ (input) INTEGER
92: * The leading dimension of the array Q. LDQ >= max(1,N).
93: *
94: * RHO (input) DOUBLE PRECISION
95: * Contains the subdiagonal element used to create the rank-1
96: * modification.
97: *
98: * INDXQ (output) INTEGER array, dimension (N)
99: * This contains the permutation which will reintegrate the
100: * subproblem just solved back into sorted order,
101: * ie. D( INDXQ( I = 1, N ) ) will be in ascending order.
102: *
103: * IWORK (workspace) INTEGER array, dimension (4*N)
104: *
105: * RWORK (workspace) DOUBLE PRECISION array,
106: * dimension (3*N+2*QSIZ*N)
107: *
108: * WORK (workspace) COMPLEX*16 array, dimension (QSIZ*N)
109: *
110: * QSTORE (input/output) DOUBLE PRECISION array, dimension (N**2+1)
111: * Stores eigenvectors of submatrices encountered during
112: * divide and conquer, packed together. QPTR points to
113: * beginning of the submatrices.
114: *
115: * QPTR (input/output) INTEGER array, dimension (N+2)
116: * List of indices pointing to beginning of submatrices stored
117: * in QSTORE. The submatrices are numbered starting at the
118: * bottom left of the divide and conquer tree, from left to
119: * right and bottom to top.
120: *
121: * PRMPTR (input) INTEGER array, dimension (N lg N)
122: * Contains a list of pointers which indicate where in PERM a
123: * level's permutation is stored. PRMPTR(i+1) - PRMPTR(i)
124: * indicates the size of the permutation and also the size of
125: * the full, non-deflated problem.
126: *
127: * PERM (input) INTEGER array, dimension (N lg N)
128: * Contains the permutations (from deflation and sorting) to be
129: * applied to each eigenblock.
130: *
131: * GIVPTR (input) INTEGER array, dimension (N lg N)
132: * Contains a list of pointers which indicate where in GIVCOL a
133: * level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i)
134: * indicates the number of Givens rotations.
135: *
136: * GIVCOL (input) INTEGER array, dimension (2, N lg N)
137: * Each pair of numbers indicates a pair of columns to take place
138: * in a Givens rotation.
139: *
140: * GIVNUM (input) DOUBLE PRECISION array, dimension (2, N lg N)
141: * Each number indicates the S value to be used in the
142: * corresponding Givens rotation.
143: *
144: * INFO (output) INTEGER
145: * = 0: successful exit.
146: * < 0: if INFO = -i, the i-th argument had an illegal value.
147: * > 0: if INFO = 1, an eigenvalue did not converge
148: *
149: * =====================================================================
150: *
151: * .. Local Scalars ..
152: INTEGER COLTYP, CURR, I, IDLMDA, INDX,
153: $ INDXC, INDXP, IQ, IW, IZ, K, N1, N2, PTR
154: * ..
155: * .. External Subroutines ..
156: EXTERNAL DLAED9, DLAEDA, DLAMRG, XERBLA, ZLACRM, ZLAED8
157: * ..
158: * .. Intrinsic Functions ..
159: INTRINSIC MAX, MIN
160: * ..
161: * .. Executable Statements ..
162: *
163: * Test the input parameters.
164: *
165: INFO = 0
166: *
167: * IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN
168: * INFO = -1
169: * ELSE IF( N.LT.0 ) THEN
170: IF( N.LT.0 ) THEN
171: INFO = -1
172: ELSE IF( MIN( 1, N ).GT.CUTPNT .OR. N.LT.CUTPNT ) THEN
173: INFO = -2
174: ELSE IF( QSIZ.LT.N ) THEN
175: INFO = -3
176: ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
177: INFO = -9
178: END IF
179: IF( INFO.NE.0 ) THEN
180: CALL XERBLA( 'ZLAED7', -INFO )
181: RETURN
182: END IF
183: *
184: * Quick return if possible
185: *
186: IF( N.EQ.0 )
187: $ RETURN
188: *
189: * The following values are for bookkeeping purposes only. They are
190: * integer pointers which indicate the portion of the workspace
191: * used by a particular array in DLAED2 and SLAED3.
192: *
193: IZ = 1
194: IDLMDA = IZ + N
195: IW = IDLMDA + N
196: IQ = IW + N
197: *
198: INDX = 1
199: INDXC = INDX + N
200: COLTYP = INDXC + N
201: INDXP = COLTYP + N
202: *
203: * Form the z-vector which consists of the last row of Q_1 and the
204: * first row of Q_2.
205: *
206: PTR = 1 + 2**TLVLS
207: DO 10 I = 1, CURLVL - 1
208: PTR = PTR + 2**( TLVLS-I )
209: 10 CONTINUE
210: CURR = PTR + CURPBM
211: CALL DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR,
212: $ GIVCOL, GIVNUM, QSTORE, QPTR, RWORK( IZ ),
213: $ RWORK( IZ+N ), INFO )
214: *
215: * When solving the final problem, we no longer need the stored data,
216: * so we will overwrite the data from this level onto the previously
217: * used storage space.
218: *
219: IF( CURLVL.EQ.TLVLS ) THEN
220: QPTR( CURR ) = 1
221: PRMPTR( CURR ) = 1
222: GIVPTR( CURR ) = 1
223: END IF
224: *
225: * Sort and Deflate eigenvalues.
226: *
227: CALL ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, RWORK( IZ ),
228: $ RWORK( IDLMDA ), WORK, QSIZ, RWORK( IW ),
229: $ IWORK( INDXP ), IWORK( INDX ), INDXQ,
230: $ PERM( PRMPTR( CURR ) ), GIVPTR( CURR+1 ),
231: $ GIVCOL( 1, GIVPTR( CURR ) ),
232: $ GIVNUM( 1, GIVPTR( CURR ) ), INFO )
233: PRMPTR( CURR+1 ) = PRMPTR( CURR ) + N
234: GIVPTR( CURR+1 ) = GIVPTR( CURR+1 ) + GIVPTR( CURR )
235: *
236: * Solve Secular Equation.
237: *
238: IF( K.NE.0 ) THEN
239: CALL DLAED9( K, 1, K, N, D, RWORK( IQ ), K, RHO,
240: $ RWORK( IDLMDA ), RWORK( IW ),
241: $ QSTORE( QPTR( CURR ) ), K, INFO )
242: CALL ZLACRM( QSIZ, K, WORK, QSIZ, QSTORE( QPTR( CURR ) ), K, Q,
243: $ LDQ, RWORK( IQ ) )
244: QPTR( CURR+1 ) = QPTR( CURR ) + K**2
245: IF( INFO.NE.0 ) THEN
246: RETURN
247: END IF
248: *
249: * Prepare the INDXQ sorting premutation.
250: *
251: N1 = K
252: N2 = N - K
253: CALL DLAMRG( N1, N2, D, 1, -1, INDXQ )
254: ELSE
255: QPTR( CURR+1 ) = QPTR( CURR )
256: DO 20 I = 1, N
257: INDXQ( I ) = I
258: 20 CONTINUE
259: END IF
260: *
261: RETURN
262: *
263: * End of ZLAED7
264: *
265: END
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