Annotation of rpl/lapack/lapack/zlaed0.f, revision 1.6
1.1 bertrand 1: SUBROUTINE ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK,
2: $ IWORK, INFO )
3: *
4: * -- LAPACK routine (version 3.2) --
5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7: * November 2006
8: *
9: * .. Scalar Arguments ..
10: INTEGER INFO, LDQ, LDQS, N, QSIZ
11: * ..
12: * .. Array Arguments ..
13: INTEGER IWORK( * )
14: DOUBLE PRECISION D( * ), E( * ), RWORK( * )
15: COMPLEX*16 Q( LDQ, * ), QSTORE( LDQS, * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * Using the divide and conquer method, ZLAED0 computes all eigenvalues
22: * of a symmetric tridiagonal matrix which is one diagonal block of
23: * those from reducing a dense or band Hermitian matrix and
24: * corresponding eigenvectors of the dense or band matrix.
25: *
26: * Arguments
27: * =========
28: *
29: * QSIZ (input) INTEGER
30: * The dimension of the unitary matrix used to reduce
31: * the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
32: *
33: * N (input) INTEGER
34: * The dimension of the symmetric tridiagonal matrix. N >= 0.
35: *
36: * D (input/output) DOUBLE PRECISION array, dimension (N)
37: * On entry, the diagonal elements of the tridiagonal matrix.
38: * On exit, the eigenvalues in ascending order.
39: *
40: * E (input/output) DOUBLE PRECISION array, dimension (N-1)
41: * On entry, the off-diagonal elements of the tridiagonal matrix.
42: * On exit, E has been destroyed.
43: *
44: * Q (input/output) COMPLEX*16 array, dimension (LDQ,N)
45: * On entry, Q must contain an QSIZ x N matrix whose columns
46: * unitarily orthonormal. It is a part of the unitary matrix
47: * that reduces the full dense Hermitian matrix to a
48: * (reducible) symmetric tridiagonal matrix.
49: *
50: * LDQ (input) INTEGER
51: * The leading dimension of the array Q. LDQ >= max(1,N).
52: *
53: * IWORK (workspace) INTEGER array,
54: * the dimension of IWORK must be at least
55: * 6 + 6*N + 5*N*lg N
56: * ( lg( N ) = smallest integer k
57: * such that 2^k >= N )
58: *
59: * RWORK (workspace) DOUBLE PRECISION array,
60: * dimension (1 + 3*N + 2*N*lg N + 3*N**2)
61: * ( lg( N ) = smallest integer k
62: * such that 2^k >= N )
63: *
64: * QSTORE (workspace) COMPLEX*16 array, dimension (LDQS, N)
65: * Used to store parts of
66: * the eigenvector matrix when the updating matrix multiplies
67: * take place.
68: *
69: * LDQS (input) INTEGER
70: * The leading dimension of the array QSTORE.
71: * LDQS >= max(1,N).
72: *
73: * INFO (output) INTEGER
74: * = 0: successful exit.
75: * < 0: if INFO = -i, the i-th argument had an illegal value.
76: * > 0: The algorithm failed to compute an eigenvalue while
77: * working on the submatrix lying in rows and columns
78: * INFO/(N+1) through mod(INFO,N+1).
79: *
80: * =====================================================================
81: *
82: * Warning: N could be as big as QSIZ!
83: *
84: * .. Parameters ..
85: DOUBLE PRECISION TWO
86: PARAMETER ( TWO = 2.D+0 )
87: * ..
88: * .. Local Scalars ..
89: INTEGER CURLVL, CURPRB, CURR, I, IGIVCL, IGIVNM,
90: $ IGIVPT, INDXQ, IPERM, IPRMPT, IQ, IQPTR, IWREM,
91: $ J, K, LGN, LL, MATSIZ, MSD2, SMLSIZ, SMM1,
92: $ SPM1, SPM2, SUBMAT, SUBPBS, TLVLS
93: DOUBLE PRECISION TEMP
94: * ..
95: * .. External Subroutines ..
96: EXTERNAL DCOPY, DSTEQR, XERBLA, ZCOPY, ZLACRM, ZLAED7
97: * ..
98: * .. External Functions ..
99: INTEGER ILAENV
100: EXTERNAL ILAENV
101: * ..
102: * .. Intrinsic Functions ..
103: INTRINSIC ABS, DBLE, INT, LOG, MAX
104: * ..
105: * .. Executable Statements ..
106: *
107: * Test the input parameters.
108: *
109: INFO = 0
110: *
111: * IF( ICOMPQ .LT. 0 .OR. ICOMPQ .GT. 2 ) THEN
112: * INFO = -1
113: * ELSE IF( ( ICOMPQ .EQ. 1 ) .AND. ( QSIZ .LT. MAX( 0, N ) ) )
114: * $ THEN
115: IF( QSIZ.LT.MAX( 0, N ) ) THEN
116: INFO = -1
117: ELSE IF( N.LT.0 ) THEN
118: INFO = -2
119: ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
120: INFO = -6
121: ELSE IF( LDQS.LT.MAX( 1, N ) ) THEN
122: INFO = -8
123: END IF
124: IF( INFO.NE.0 ) THEN
125: CALL XERBLA( 'ZLAED0', -INFO )
126: RETURN
127: END IF
128: *
129: * Quick return if possible
130: *
131: IF( N.EQ.0 )
132: $ RETURN
133: *
134: SMLSIZ = ILAENV( 9, 'ZLAED0', ' ', 0, 0, 0, 0 )
135: *
136: * Determine the size and placement of the submatrices, and save in
137: * the leading elements of IWORK.
138: *
139: IWORK( 1 ) = N
140: SUBPBS = 1
141: TLVLS = 0
142: 10 CONTINUE
143: IF( IWORK( SUBPBS ).GT.SMLSIZ ) THEN
144: DO 20 J = SUBPBS, 1, -1
145: IWORK( 2*J ) = ( IWORK( J )+1 ) / 2
146: IWORK( 2*J-1 ) = IWORK( J ) / 2
147: 20 CONTINUE
148: TLVLS = TLVLS + 1
149: SUBPBS = 2*SUBPBS
150: GO TO 10
151: END IF
152: DO 30 J = 2, SUBPBS
153: IWORK( J ) = IWORK( J ) + IWORK( J-1 )
154: 30 CONTINUE
155: *
156: * Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1
157: * using rank-1 modifications (cuts).
158: *
159: SPM1 = SUBPBS - 1
160: DO 40 I = 1, SPM1
161: SUBMAT = IWORK( I ) + 1
162: SMM1 = SUBMAT - 1
163: D( SMM1 ) = D( SMM1 ) - ABS( E( SMM1 ) )
164: D( SUBMAT ) = D( SUBMAT ) - ABS( E( SMM1 ) )
165: 40 CONTINUE
166: *
167: INDXQ = 4*N + 3
168: *
169: * Set up workspaces for eigenvalues only/accumulate new vectors
170: * routine
171: *
172: TEMP = LOG( DBLE( N ) ) / LOG( TWO )
173: LGN = INT( TEMP )
174: IF( 2**LGN.LT.N )
175: $ LGN = LGN + 1
176: IF( 2**LGN.LT.N )
177: $ LGN = LGN + 1
178: IPRMPT = INDXQ + N + 1
179: IPERM = IPRMPT + N*LGN
180: IQPTR = IPERM + N*LGN
181: IGIVPT = IQPTR + N + 2
182: IGIVCL = IGIVPT + N*LGN
183: *
184: IGIVNM = 1
185: IQ = IGIVNM + 2*N*LGN
186: IWREM = IQ + N**2 + 1
187: * Initialize pointers
188: DO 50 I = 0, SUBPBS
189: IWORK( IPRMPT+I ) = 1
190: IWORK( IGIVPT+I ) = 1
191: 50 CONTINUE
192: IWORK( IQPTR ) = 1
193: *
194: * Solve each submatrix eigenproblem at the bottom of the divide and
195: * conquer tree.
196: *
197: CURR = 0
198: DO 70 I = 0, SPM1
199: IF( I.EQ.0 ) THEN
200: SUBMAT = 1
201: MATSIZ = IWORK( 1 )
202: ELSE
203: SUBMAT = IWORK( I ) + 1
204: MATSIZ = IWORK( I+1 ) - IWORK( I )
205: END IF
206: LL = IQ - 1 + IWORK( IQPTR+CURR )
207: CALL DSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ),
208: $ RWORK( LL ), MATSIZ, RWORK, INFO )
209: CALL ZLACRM( QSIZ, MATSIZ, Q( 1, SUBMAT ), LDQ, RWORK( LL ),
210: $ MATSIZ, QSTORE( 1, SUBMAT ), LDQS,
211: $ RWORK( IWREM ) )
212: IWORK( IQPTR+CURR+1 ) = IWORK( IQPTR+CURR ) + MATSIZ**2
213: CURR = CURR + 1
214: IF( INFO.GT.0 ) THEN
215: INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1
216: RETURN
217: END IF
218: K = 1
219: DO 60 J = SUBMAT, IWORK( I+1 )
220: IWORK( INDXQ+J ) = K
221: K = K + 1
222: 60 CONTINUE
223: 70 CONTINUE
224: *
225: * Successively merge eigensystems of adjacent submatrices
226: * into eigensystem for the corresponding larger matrix.
227: *
228: * while ( SUBPBS > 1 )
229: *
230: CURLVL = 1
231: 80 CONTINUE
232: IF( SUBPBS.GT.1 ) THEN
233: SPM2 = SUBPBS - 2
234: DO 90 I = 0, SPM2, 2
235: IF( I.EQ.0 ) THEN
236: SUBMAT = 1
237: MATSIZ = IWORK( 2 )
238: MSD2 = IWORK( 1 )
239: CURPRB = 0
240: ELSE
241: SUBMAT = IWORK( I ) + 1
242: MATSIZ = IWORK( I+2 ) - IWORK( I )
243: MSD2 = MATSIZ / 2
244: CURPRB = CURPRB + 1
245: END IF
246: *
247: * Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2)
248: * into an eigensystem of size MATSIZ. ZLAED7 handles the case
249: * when the eigenvectors of a full or band Hermitian matrix (which
250: * was reduced to tridiagonal form) are desired.
251: *
252: * I am free to use Q as a valuable working space until Loop 150.
253: *
254: CALL ZLAED7( MATSIZ, MSD2, QSIZ, TLVLS, CURLVL, CURPRB,
255: $ D( SUBMAT ), QSTORE( 1, SUBMAT ), LDQS,
256: $ E( SUBMAT+MSD2-1 ), IWORK( INDXQ+SUBMAT ),
257: $ RWORK( IQ ), IWORK( IQPTR ), IWORK( IPRMPT ),
258: $ IWORK( IPERM ), IWORK( IGIVPT ),
259: $ IWORK( IGIVCL ), RWORK( IGIVNM ),
260: $ Q( 1, SUBMAT ), RWORK( IWREM ),
261: $ IWORK( SUBPBS+1 ), INFO )
262: IF( INFO.GT.0 ) THEN
263: INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1
264: RETURN
265: END IF
266: IWORK( I / 2+1 ) = IWORK( I+2 )
267: 90 CONTINUE
268: SUBPBS = SUBPBS / 2
269: CURLVL = CURLVL + 1
270: GO TO 80
271: END IF
272: *
273: * end while
274: *
275: * Re-merge the eigenvalues/vectors which were deflated at the final
276: * merge step.
277: *
278: DO 100 I = 1, N
279: J = IWORK( INDXQ+I )
280: RWORK( I ) = D( J )
281: CALL ZCOPY( QSIZ, QSTORE( 1, J ), 1, Q( 1, I ), 1 )
282: 100 CONTINUE
283: CALL DCOPY( N, RWORK, 1, D, 1 )
284: *
285: RETURN
286: *
287: * End of ZLAED0
288: *
289: END
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