1: *> \brief \b ZPTEQR
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZPTEQR + dependencies
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11: *> [TGZ]</a>
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpteqr.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER COMPZ
25: * INTEGER INFO, LDZ, N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION D( * ), E( * ), WORK( * )
29: * COMPLEX*16 Z( LDZ, * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZPTEQR computes all eigenvalues and, optionally, eigenvectors of a
39: *> symmetric positive definite tridiagonal matrix by first factoring the
40: *> matrix using DPTTRF and then calling ZBDSQR to compute the singular
41: *> values of the bidiagonal factor.
42: *>
43: *> This routine computes the eigenvalues of the positive definite
44: *> tridiagonal matrix to high relative accuracy. This means that if the
45: *> eigenvalues range over many orders of magnitude in size, then the
46: *> small eigenvalues and corresponding eigenvectors will be computed
47: *> more accurately than, for example, with the standard QR method.
48: *>
49: *> The eigenvectors of a full or band positive definite Hermitian matrix
50: *> can also be found if ZHETRD, ZHPTRD, or ZHBTRD has been used to
51: *> reduce this matrix to tridiagonal form. (The reduction to
52: *> tridiagonal form, however, may preclude the possibility of obtaining
53: *> high relative accuracy in the small eigenvalues of the original
54: *> matrix, if these eigenvalues range over many orders of magnitude.)
55: *> \endverbatim
56: *
57: * Arguments:
58: * ==========
59: *
60: *> \param[in] COMPZ
61: *> \verbatim
62: *> COMPZ is CHARACTER*1
63: *> = 'N': Compute eigenvalues only.
64: *> = 'V': Compute eigenvectors of original Hermitian
65: *> matrix also. Array Z contains the unitary matrix
66: *> used to reduce the original matrix to tridiagonal
67: *> form.
68: *> = 'I': Compute eigenvectors of tridiagonal matrix also.
69: *> \endverbatim
70: *>
71: *> \param[in] N
72: *> \verbatim
73: *> N is INTEGER
74: *> The order of the matrix. N >= 0.
75: *> \endverbatim
76: *>
77: *> \param[in,out] D
78: *> \verbatim
79: *> D is DOUBLE PRECISION array, dimension (N)
80: *> On entry, the n diagonal elements of the tridiagonal matrix.
81: *> On normal exit, D contains the eigenvalues, in descending
82: *> order.
83: *> \endverbatim
84: *>
85: *> \param[in,out] E
86: *> \verbatim
87: *> E is DOUBLE PRECISION array, dimension (N-1)
88: *> On entry, the (n-1) subdiagonal elements of the tridiagonal
89: *> matrix.
90: *> On exit, E has been destroyed.
91: *> \endverbatim
92: *>
93: *> \param[in,out] Z
94: *> \verbatim
95: *> Z is COMPLEX*16 array, dimension (LDZ, N)
96: *> On entry, if COMPZ = 'V', the unitary matrix used in the
97: *> reduction to tridiagonal form.
98: *> On exit, if COMPZ = 'V', the orthonormal eigenvectors of the
99: *> original Hermitian matrix;
100: *> if COMPZ = 'I', the orthonormal eigenvectors of the
101: *> tridiagonal matrix.
102: *> If INFO > 0 on exit, Z contains the eigenvectors associated
103: *> with only the stored eigenvalues.
104: *> If COMPZ = 'N', then Z is not referenced.
105: *> \endverbatim
106: *>
107: *> \param[in] LDZ
108: *> \verbatim
109: *> LDZ is INTEGER
110: *> The leading dimension of the array Z. LDZ >= 1, and if
111: *> COMPZ = 'V' or 'I', LDZ >= max(1,N).
112: *> \endverbatim
113: *>
114: *> \param[out] WORK
115: *> \verbatim
116: *> WORK is DOUBLE PRECISION array, dimension (4*N)
117: *> \endverbatim
118: *>
119: *> \param[out] INFO
120: *> \verbatim
121: *> INFO is INTEGER
122: *> = 0: successful exit.
123: *> < 0: if INFO = -i, the i-th argument had an illegal value.
124: *> > 0: if INFO = i, and i is:
125: *> <= N the Cholesky factorization of the matrix could
126: *> not be performed because the i-th principal minor
127: *> was not positive definite.
128: *> > N the SVD algorithm failed to converge;
129: *> if INFO = N+i, i off-diagonal elements of the
130: *> bidiagonal factor did not converge to zero.
131: *> \endverbatim
132: *
133: * Authors:
134: * ========
135: *
136: *> \author Univ. of Tennessee
137: *> \author Univ. of California Berkeley
138: *> \author Univ. of Colorado Denver
139: *> \author NAG Ltd.
140: *
141: *> \ingroup complex16PTcomputational
142: *
143: * =====================================================================
144: SUBROUTINE ZPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
145: *
146: * -- LAPACK computational routine --
147: * -- LAPACK is a software package provided by Univ. of Tennessee, --
148: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
149: *
150: * .. Scalar Arguments ..
151: CHARACTER COMPZ
152: INTEGER INFO, LDZ, N
153: * ..
154: * .. Array Arguments ..
155: DOUBLE PRECISION D( * ), E( * ), WORK( * )
156: COMPLEX*16 Z( LDZ, * )
157: * ..
158: *
159: * ====================================================================
160: *
161: * .. Parameters ..
162: COMPLEX*16 CZERO, CONE
163: PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
164: $ CONE = ( 1.0D+0, 0.0D+0 ) )
165: * ..
166: * .. External Functions ..
167: LOGICAL LSAME
168: EXTERNAL LSAME
169: * ..
170: * .. External Subroutines ..
171: EXTERNAL DPTTRF, XERBLA, ZBDSQR, ZLASET
172: * ..
173: * .. Local Arrays ..
174: COMPLEX*16 C( 1, 1 ), VT( 1, 1 )
175: * ..
176: * .. Local Scalars ..
177: INTEGER I, ICOMPZ, NRU
178: * ..
179: * .. Intrinsic Functions ..
180: INTRINSIC MAX, SQRT
181: * ..
182: * .. Executable Statements ..
183: *
184: * Test the input parameters.
185: *
186: INFO = 0
187: *
188: IF( LSAME( COMPZ, 'N' ) ) THEN
189: ICOMPZ = 0
190: ELSE IF( LSAME( COMPZ, 'V' ) ) THEN
191: ICOMPZ = 1
192: ELSE IF( LSAME( COMPZ, 'I' ) ) THEN
193: ICOMPZ = 2
194: ELSE
195: ICOMPZ = -1
196: END IF
197: IF( ICOMPZ.LT.0 ) THEN
198: INFO = -1
199: ELSE IF( N.LT.0 ) THEN
200: INFO = -2
201: ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1,
202: $ N ) ) ) THEN
203: INFO = -6
204: END IF
205: IF( INFO.NE.0 ) THEN
206: CALL XERBLA( 'ZPTEQR', -INFO )
207: RETURN
208: END IF
209: *
210: * Quick return if possible
211: *
212: IF( N.EQ.0 )
213: $ RETURN
214: *
215: IF( N.EQ.1 ) THEN
216: IF( ICOMPZ.GT.0 )
217: $ Z( 1, 1 ) = CONE
218: RETURN
219: END IF
220: IF( ICOMPZ.EQ.2 )
221: $ CALL ZLASET( 'Full', N, N, CZERO, CONE, Z, LDZ )
222: *
223: * Call DPTTRF to factor the matrix.
224: *
225: CALL DPTTRF( N, D, E, INFO )
226: IF( INFO.NE.0 )
227: $ RETURN
228: DO 10 I = 1, N
229: D( I ) = SQRT( D( I ) )
230: 10 CONTINUE
231: DO 20 I = 1, N - 1
232: E( I ) = E( I )*D( I )
233: 20 CONTINUE
234: *
235: * Call ZBDSQR to compute the singular values/vectors of the
236: * bidiagonal factor.
237: *
238: IF( ICOMPZ.GT.0 ) THEN
239: NRU = N
240: ELSE
241: NRU = 0
242: END IF
243: CALL ZBDSQR( 'Lower', N, 0, NRU, 0, D, E, VT, 1, Z, LDZ, C, 1,
244: $ WORK, INFO )
245: *
246: * Square the singular values.
247: *
248: IF( INFO.EQ.0 ) THEN
249: DO 30 I = 1, N
250: D( I ) = D( I )*D( I )
251: 30 CONTINUE
252: ELSE
253: INFO = N + INFO
254: END IF
255: *
256: RETURN
257: *
258: * End of ZPTEQR
259: *
260: END
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