Annotation of rpl/lapack/lapack/dstev.f, revision 1.6
1.1 bertrand 1: SUBROUTINE DSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
2: *
3: * -- LAPACK driver 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 JOBZ
10: INTEGER INFO, LDZ, N
11: * ..
12: * .. Array Arguments ..
13: DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DSTEV computes all eigenvalues and, optionally, eigenvectors of a
20: * real symmetric tridiagonal matrix A.
21: *
22: * Arguments
23: * =========
24: *
25: * JOBZ (input) CHARACTER*1
26: * = 'N': Compute eigenvalues only;
27: * = 'V': Compute eigenvalues and eigenvectors.
28: *
29: * N (input) INTEGER
30: * The order of the matrix. N >= 0.
31: *
32: * D (input/output) DOUBLE PRECISION array, dimension (N)
33: * On entry, the n diagonal elements of the tridiagonal matrix
34: * A.
35: * On exit, if INFO = 0, the eigenvalues in ascending order.
36: *
37: * E (input/output) DOUBLE PRECISION array, dimension (N-1)
38: * On entry, the (n-1) subdiagonal elements of the tridiagonal
39: * matrix A, stored in elements 1 to N-1 of E.
40: * On exit, the contents of E are destroyed.
41: *
42: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
43: * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
44: * eigenvectors of the matrix A, with the i-th column of Z
45: * holding the eigenvector associated with D(i).
46: * If JOBZ = 'N', then Z is not referenced.
47: *
48: * LDZ (input) INTEGER
49: * The leading dimension of the array Z. LDZ >= 1, and if
50: * JOBZ = 'V', LDZ >= max(1,N).
51: *
52: * WORK (workspace) DOUBLE PRECISION array, dimension (max(1,2*N-2))
53: * If JOBZ = 'N', WORK is not referenced.
54: *
55: * INFO (output) INTEGER
56: * = 0: successful exit
57: * < 0: if INFO = -i, the i-th argument had an illegal value
58: * > 0: if INFO = i, the algorithm failed to converge; i
59: * off-diagonal elements of E did not converge to zero.
60: *
61: * =====================================================================
62: *
63: * .. Parameters ..
64: DOUBLE PRECISION ZERO, ONE
65: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
66: * ..
67: * .. Local Scalars ..
68: LOGICAL WANTZ
69: INTEGER IMAX, ISCALE
70: DOUBLE PRECISION BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
71: $ TNRM
72: * ..
73: * .. External Functions ..
74: LOGICAL LSAME
75: DOUBLE PRECISION DLAMCH, DLANST
76: EXTERNAL LSAME, DLAMCH, DLANST
77: * ..
78: * .. External Subroutines ..
79: EXTERNAL DSCAL, DSTEQR, DSTERF, XERBLA
80: * ..
81: * .. Intrinsic Functions ..
82: INTRINSIC SQRT
83: * ..
84: * .. Executable Statements ..
85: *
86: * Test the input parameters.
87: *
88: WANTZ = LSAME( JOBZ, 'V' )
89: *
90: INFO = 0
91: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
92: INFO = -1
93: ELSE IF( N.LT.0 ) THEN
94: INFO = -2
95: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
96: INFO = -6
97: END IF
98: *
99: IF( INFO.NE.0 ) THEN
100: CALL XERBLA( 'DSTEV ', -INFO )
101: RETURN
102: END IF
103: *
104: * Quick return if possible
105: *
106: IF( N.EQ.0 )
107: $ RETURN
108: *
109: IF( N.EQ.1 ) THEN
110: IF( WANTZ )
111: $ Z( 1, 1 ) = ONE
112: RETURN
113: END IF
114: *
115: * Get machine constants.
116: *
117: SAFMIN = DLAMCH( 'Safe minimum' )
118: EPS = DLAMCH( 'Precision' )
119: SMLNUM = SAFMIN / EPS
120: BIGNUM = ONE / SMLNUM
121: RMIN = SQRT( SMLNUM )
122: RMAX = SQRT( BIGNUM )
123: *
124: * Scale matrix to allowable range, if necessary.
125: *
126: ISCALE = 0
127: TNRM = DLANST( 'M', N, D, E )
128: IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
129: ISCALE = 1
130: SIGMA = RMIN / TNRM
131: ELSE IF( TNRM.GT.RMAX ) THEN
132: ISCALE = 1
133: SIGMA = RMAX / TNRM
134: END IF
135: IF( ISCALE.EQ.1 ) THEN
136: CALL DSCAL( N, SIGMA, D, 1 )
137: CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
138: END IF
139: *
140: * For eigenvalues only, call DSTERF. For eigenvalues and
141: * eigenvectors, call DSTEQR.
142: *
143: IF( .NOT.WANTZ ) THEN
144: CALL DSTERF( N, D, E, INFO )
145: ELSE
146: CALL DSTEQR( 'I', N, D, E, Z, LDZ, WORK, INFO )
147: END IF
148: *
149: * If matrix was scaled, then rescale eigenvalues appropriately.
150: *
151: IF( ISCALE.EQ.1 ) THEN
152: IF( INFO.EQ.0 ) THEN
153: IMAX = N
154: ELSE
155: IMAX = INFO - 1
156: END IF
157: CALL DSCAL( IMAX, ONE / SIGMA, D, 1 )
158: END IF
159: *
160: RETURN
161: *
162: * End of DSTEV
163: *
164: END
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