Annotation of rpl/lapack/lapack/zpteqr.f, revision 1.4
1.1 bertrand 1: SUBROUTINE ZPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
2: *
3: * -- LAPACK routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: CHARACTER COMPZ
10: INTEGER INFO, LDZ, N
11: * ..
12: * .. Array Arguments ..
13: DOUBLE PRECISION D( * ), E( * ), WORK( * )
14: COMPLEX*16 Z( LDZ, * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * ZPTEQR computes all eigenvalues and, optionally, eigenvectors of a
21: * symmetric positive definite tridiagonal matrix by first factoring the
22: * matrix using DPTTRF and then calling ZBDSQR to compute the singular
23: * values of the bidiagonal factor.
24: *
25: * This routine computes the eigenvalues of the positive definite
26: * tridiagonal matrix to high relative accuracy. This means that if the
27: * eigenvalues range over many orders of magnitude in size, then the
28: * small eigenvalues and corresponding eigenvectors will be computed
29: * more accurately than, for example, with the standard QR method.
30: *
31: * The eigenvectors of a full or band positive definite Hermitian matrix
32: * can also be found if ZHETRD, ZHPTRD, or ZHBTRD has been used to
33: * reduce this matrix to tridiagonal form. (The reduction to
34: * tridiagonal form, however, may preclude the possibility of obtaining
35: * high relative accuracy in the small eigenvalues of the original
36: * matrix, if these eigenvalues range over many orders of magnitude.)
37: *
38: * Arguments
39: * =========
40: *
41: * COMPZ (input) CHARACTER*1
42: * = 'N': Compute eigenvalues only.
43: * = 'V': Compute eigenvectors of original Hermitian
44: * matrix also. Array Z contains the unitary matrix
45: * used to reduce the original matrix to tridiagonal
46: * form.
47: * = 'I': Compute eigenvectors of tridiagonal matrix also.
48: *
49: * N (input) INTEGER
50: * The order of the matrix. N >= 0.
51: *
52: * D (input/output) DOUBLE PRECISION array, dimension (N)
53: * On entry, the n diagonal elements of the tridiagonal matrix.
54: * On normal exit, D contains the eigenvalues, in descending
55: * order.
56: *
57: * E (input/output) DOUBLE PRECISION array, dimension (N-1)
58: * On entry, the (n-1) subdiagonal elements of the tridiagonal
59: * matrix.
60: * On exit, E has been destroyed.
61: *
62: * Z (input/output) COMPLEX*16 array, dimension (LDZ, N)
63: * On entry, if COMPZ = 'V', the unitary matrix used in the
64: * reduction to tridiagonal form.
65: * On exit, if COMPZ = 'V', the orthonormal eigenvectors of the
66: * original Hermitian matrix;
67: * if COMPZ = 'I', the orthonormal eigenvectors of the
68: * tridiagonal matrix.
69: * If INFO > 0 on exit, Z contains the eigenvectors associated
70: * with only the stored eigenvalues.
71: * If COMPZ = 'N', then Z is not referenced.
72: *
73: * LDZ (input) INTEGER
74: * The leading dimension of the array Z. LDZ >= 1, and if
75: * COMPZ = 'V' or 'I', LDZ >= max(1,N).
76: *
77: * WORK (workspace) DOUBLE PRECISION array, dimension (4*N)
78: *
79: * INFO (output) INTEGER
80: * = 0: successful exit.
81: * < 0: if INFO = -i, the i-th argument had an illegal value.
82: * > 0: if INFO = i, and i is:
83: * <= N the Cholesky factorization of the matrix could
84: * not be performed because the i-th principal minor
85: * was not positive definite.
86: * > N the SVD algorithm failed to converge;
87: * if INFO = N+i, i off-diagonal elements of the
88: * bidiagonal factor did not converge to zero.
89: *
90: * ====================================================================
91: *
92: * .. Parameters ..
93: COMPLEX*16 CZERO, CONE
94: PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
95: $ CONE = ( 1.0D+0, 0.0D+0 ) )
96: * ..
97: * .. External Functions ..
98: LOGICAL LSAME
99: EXTERNAL LSAME
100: * ..
101: * .. External Subroutines ..
102: EXTERNAL DPTTRF, XERBLA, ZBDSQR, ZLASET
103: * ..
104: * .. Local Arrays ..
105: COMPLEX*16 C( 1, 1 ), VT( 1, 1 )
106: * ..
107: * .. Local Scalars ..
108: INTEGER I, ICOMPZ, NRU
109: * ..
110: * .. Intrinsic Functions ..
111: INTRINSIC MAX, SQRT
112: * ..
113: * .. Executable Statements ..
114: *
115: * Test the input parameters.
116: *
117: INFO = 0
118: *
119: IF( LSAME( COMPZ, 'N' ) ) THEN
120: ICOMPZ = 0
121: ELSE IF( LSAME( COMPZ, 'V' ) ) THEN
122: ICOMPZ = 1
123: ELSE IF( LSAME( COMPZ, 'I' ) ) THEN
124: ICOMPZ = 2
125: ELSE
126: ICOMPZ = -1
127: END IF
128: IF( ICOMPZ.LT.0 ) THEN
129: INFO = -1
130: ELSE IF( N.LT.0 ) THEN
131: INFO = -2
132: ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1,
133: $ N ) ) ) THEN
134: INFO = -6
135: END IF
136: IF( INFO.NE.0 ) THEN
137: CALL XERBLA( 'ZPTEQR', -INFO )
138: RETURN
139: END IF
140: *
141: * Quick return if possible
142: *
143: IF( N.EQ.0 )
144: $ RETURN
145: *
146: IF( N.EQ.1 ) THEN
147: IF( ICOMPZ.GT.0 )
148: $ Z( 1, 1 ) = CONE
149: RETURN
150: END IF
151: IF( ICOMPZ.EQ.2 )
152: $ CALL ZLASET( 'Full', N, N, CZERO, CONE, Z, LDZ )
153: *
154: * Call DPTTRF to factor the matrix.
155: *
156: CALL DPTTRF( N, D, E, INFO )
157: IF( INFO.NE.0 )
158: $ RETURN
159: DO 10 I = 1, N
160: D( I ) = SQRT( D( I ) )
161: 10 CONTINUE
162: DO 20 I = 1, N - 1
163: E( I ) = E( I )*D( I )
164: 20 CONTINUE
165: *
166: * Call ZBDSQR to compute the singular values/vectors of the
167: * bidiagonal factor.
168: *
169: IF( ICOMPZ.GT.0 ) THEN
170: NRU = N
171: ELSE
172: NRU = 0
173: END IF
174: CALL ZBDSQR( 'Lower', N, 0, NRU, 0, D, E, VT, 1, Z, LDZ, C, 1,
175: $ WORK, INFO )
176: *
177: * Square the singular values.
178: *
179: IF( INFO.EQ.0 ) THEN
180: DO 30 I = 1, N
181: D( I ) = D( I )*D( I )
182: 30 CONTINUE
183: ELSE
184: INFO = N + INFO
185: END IF
186: *
187: RETURN
188: *
189: * End of ZPTEQR
190: *
191: END
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