Annotation of rpl/lapack/lapack/dlaed1.f, revision 1.6
1.1 bertrand 1: SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK,
2: $ 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 CUTPNT, INFO, LDQ, N
11: DOUBLE PRECISION RHO
12: * ..
13: * .. Array Arguments ..
14: INTEGER INDXQ( * ), IWORK( * )
15: DOUBLE PRECISION D( * ), Q( LDQ, * ), WORK( * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * DLAED1 computes the updated eigensystem of a diagonal
22: * matrix after modification by a rank-one symmetric matrix. This
23: * routine is used only for the eigenproblem which requires all
24: * eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles
25: * the case in which eigenvalues only or eigenvalues and eigenvectors
26: * of a full symmetric matrix (which was reduced to tridiagonal form)
27: * are desired.
28: *
29: * T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)
30: *
31: * where Z = Q'u, u is a vector of length N with ones in the
32: * CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
33: *
34: * The eigenvectors of the original matrix are stored in Q, and the
35: * eigenvalues are in D. The algorithm consists of three stages:
36: *
37: * The first stage consists of deflating the size of the problem
38: * when there are multiple eigenvalues or if there is a zero in
39: * the Z vector. For each such occurence the dimension of the
40: * secular equation problem is reduced by one. This stage is
41: * performed by the routine DLAED2.
42: *
43: * The second stage consists of calculating the updated
44: * eigenvalues. This is done by finding the roots of the secular
45: * equation via the routine DLAED4 (as called by DLAED3).
46: * This routine also calculates the eigenvectors of the current
47: * problem.
48: *
49: * The final stage consists of computing the updated eigenvectors
50: * directly using the updated eigenvalues. The eigenvectors for
51: * the current problem are multiplied with the eigenvectors from
52: * the overall problem.
53: *
54: * Arguments
55: * =========
56: *
57: * N (input) INTEGER
58: * The dimension of the symmetric tridiagonal matrix. N >= 0.
59: *
60: * D (input/output) DOUBLE PRECISION array, dimension (N)
61: * On entry, the eigenvalues of the rank-1-perturbed matrix.
62: * On exit, the eigenvalues of the repaired matrix.
63: *
64: * Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N)
65: * On entry, the eigenvectors of the rank-1-perturbed matrix.
66: * On exit, the eigenvectors of the repaired tridiagonal matrix.
67: *
68: * LDQ (input) INTEGER
69: * The leading dimension of the array Q. LDQ >= max(1,N).
70: *
71: * INDXQ (input/output) INTEGER array, dimension (N)
72: * On entry, the permutation which separately sorts the two
73: * subproblems in D into ascending order.
74: * On exit, the permutation which will reintegrate the
75: * subproblems back into sorted order,
76: * i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.
77: *
78: * RHO (input) DOUBLE PRECISION
79: * The subdiagonal entry used to create the rank-1 modification.
80: *
81: * CUTPNT (input) INTEGER
82: * The location of the last eigenvalue in the leading sub-matrix.
83: * min(1,N) <= CUTPNT <= N/2.
84: *
85: * WORK (workspace) DOUBLE PRECISION array, dimension (4*N + N**2)
86: *
87: * IWORK (workspace) INTEGER array, dimension (4*N)
88: *
89: * INFO (output) INTEGER
90: * = 0: successful exit.
91: * < 0: if INFO = -i, the i-th argument had an illegal value.
92: * > 0: if INFO = 1, an eigenvalue did not converge
93: *
94: * Further Details
95: * ===============
96: *
97: * Based on contributions by
98: * Jeff Rutter, Computer Science Division, University of California
99: * at Berkeley, USA
100: * Modified by Francoise Tisseur, University of Tennessee.
101: *
102: * =====================================================================
103: *
104: * .. Local Scalars ..
105: INTEGER COLTYP, I, IDLMDA, INDX, INDXC, INDXP, IQ2, IS,
106: $ IW, IZ, K, N1, N2, ZPP1
107: * ..
108: * .. External Subroutines ..
109: EXTERNAL DCOPY, DLAED2, DLAED3, DLAMRG, XERBLA
110: * ..
111: * .. Intrinsic Functions ..
112: INTRINSIC MAX, MIN
113: * ..
114: * .. Executable Statements ..
115: *
116: * Test the input parameters.
117: *
118: INFO = 0
119: *
120: IF( N.LT.0 ) THEN
121: INFO = -1
122: ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
123: INFO = -4
124: ELSE IF( MIN( 1, N / 2 ).GT.CUTPNT .OR. ( N / 2 ).LT.CUTPNT ) THEN
125: INFO = -7
126: END IF
127: IF( INFO.NE.0 ) THEN
128: CALL XERBLA( 'DLAED1', -INFO )
129: RETURN
130: END IF
131: *
132: * Quick return if possible
133: *
134: IF( N.EQ.0 )
135: $ RETURN
136: *
137: * The following values are integer pointers which indicate
138: * the portion of the workspace
139: * used by a particular array in DLAED2 and DLAED3.
140: *
141: IZ = 1
142: IDLMDA = IZ + N
143: IW = IDLMDA + N
144: IQ2 = IW + N
145: *
146: INDX = 1
147: INDXC = INDX + N
148: COLTYP = INDXC + N
149: INDXP = COLTYP + N
150: *
151: *
152: * Form the z-vector which consists of the last row of Q_1 and the
153: * first row of Q_2.
154: *
155: CALL DCOPY( CUTPNT, Q( CUTPNT, 1 ), LDQ, WORK( IZ ), 1 )
156: ZPP1 = CUTPNT + 1
157: CALL DCOPY( N-CUTPNT, Q( ZPP1, ZPP1 ), LDQ, WORK( IZ+CUTPNT ), 1 )
158: *
159: * Deflate eigenvalues.
160: *
161: CALL DLAED2( K, N, CUTPNT, D, Q, LDQ, INDXQ, RHO, WORK( IZ ),
162: $ WORK( IDLMDA ), WORK( IW ), WORK( IQ2 ),
163: $ IWORK( INDX ), IWORK( INDXC ), IWORK( INDXP ),
164: $ IWORK( COLTYP ), INFO )
165: *
166: IF( INFO.NE.0 )
167: $ GO TO 20
168: *
169: * Solve Secular Equation.
170: *
171: IF( K.NE.0 ) THEN
172: IS = ( IWORK( COLTYP )+IWORK( COLTYP+1 ) )*CUTPNT +
173: $ ( IWORK( COLTYP+1 )+IWORK( COLTYP+2 ) )*( N-CUTPNT ) + IQ2
174: CALL DLAED3( K, N, CUTPNT, D, Q, LDQ, RHO, WORK( IDLMDA ),
175: $ WORK( IQ2 ), IWORK( INDXC ), IWORK( COLTYP ),
176: $ WORK( IW ), WORK( IS ), INFO )
177: IF( INFO.NE.0 )
178: $ GO TO 20
179: *
180: * Prepare the INDXQ sorting permutation.
181: *
182: N1 = K
183: N2 = N - K
184: CALL DLAMRG( N1, N2, D, 1, -1, INDXQ )
185: ELSE
186: DO 10 I = 1, N
187: INDXQ( I ) = I
188: 10 CONTINUE
189: END IF
190: *
191: 20 CONTINUE
192: RETURN
193: *
194: * End of DLAED1
195: *
196: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dlaed1.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack