Annotation of rpl/lapack/lapack/dspev.f, revision 1.2
1.1 bertrand 1: SUBROUTINE DSPEV( JOBZ, UPLO, N, AP, W, 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, UPLO
10: INTEGER INFO, LDZ, N
11: * ..
12: * .. Array Arguments ..
13: DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DSPEV computes all the eigenvalues and, optionally, eigenvectors of a
20: * real symmetric matrix A in packed storage.
21: *
22: * Arguments
23: * =========
24: *
25: * JOBZ (input) CHARACTER*1
26: * = 'N': Compute eigenvalues only;
27: * = 'V': Compute eigenvalues and eigenvectors.
28: *
29: * UPLO (input) CHARACTER*1
30: * = 'U': Upper triangle of A is stored;
31: * = 'L': Lower triangle of A is stored.
32: *
33: * N (input) INTEGER
34: * The order of the matrix A. N >= 0.
35: *
36: * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
37: * On entry, the upper or lower triangle of the symmetric matrix
38: * A, packed columnwise in a linear array. The j-th column of A
39: * is stored in the array AP as follows:
40: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
41: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
42: *
43: * On exit, AP is overwritten by values generated during the
44: * reduction to tridiagonal form. If UPLO = 'U', the diagonal
45: * and first superdiagonal of the tridiagonal matrix T overwrite
46: * the corresponding elements of A, and if UPLO = 'L', the
47: * diagonal and first subdiagonal of T overwrite the
48: * corresponding elements of A.
49: *
50: * W (output) DOUBLE PRECISION array, dimension (N)
51: * If INFO = 0, the eigenvalues in ascending order.
52: *
53: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
54: * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
55: * eigenvectors of the matrix A, with the i-th column of Z
56: * holding the eigenvector associated with W(i).
57: * If JOBZ = 'N', then Z is not referenced.
58: *
59: * LDZ (input) INTEGER
60: * The leading dimension of the array Z. LDZ >= 1, and if
61: * JOBZ = 'V', LDZ >= max(1,N).
62: *
63: * WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
64: *
65: * INFO (output) INTEGER
66: * = 0: successful exit.
67: * < 0: if INFO = -i, the i-th argument had an illegal value.
68: * > 0: if INFO = i, the algorithm failed to converge; i
69: * off-diagonal elements of an intermediate tridiagonal
70: * form did not converge to zero.
71: *
72: * =====================================================================
73: *
74: * .. Parameters ..
75: DOUBLE PRECISION ZERO, ONE
76: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
77: * ..
78: * .. Local Scalars ..
79: LOGICAL WANTZ
80: INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE
81: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
82: $ SMLNUM
83: * ..
84: * .. External Functions ..
85: LOGICAL LSAME
86: DOUBLE PRECISION DLAMCH, DLANSP
87: EXTERNAL LSAME, DLAMCH, DLANSP
88: * ..
89: * .. External Subroutines ..
90: EXTERNAL DOPGTR, DSCAL, DSPTRD, DSTEQR, DSTERF, XERBLA
91: * ..
92: * .. Intrinsic Functions ..
93: INTRINSIC SQRT
94: * ..
95: * .. Executable Statements ..
96: *
97: * Test the input parameters.
98: *
99: WANTZ = LSAME( JOBZ, 'V' )
100: *
101: INFO = 0
102: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
103: INFO = -1
104: ELSE IF( .NOT.( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) )
105: $ THEN
106: INFO = -2
107: ELSE IF( N.LT.0 ) THEN
108: INFO = -3
109: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
110: INFO = -7
111: END IF
112: *
113: IF( INFO.NE.0 ) THEN
114: CALL XERBLA( 'DSPEV ', -INFO )
115: RETURN
116: END IF
117: *
118: * Quick return if possible
119: *
120: IF( N.EQ.0 )
121: $ RETURN
122: *
123: IF( N.EQ.1 ) THEN
124: W( 1 ) = AP( 1 )
125: IF( WANTZ )
126: $ Z( 1, 1 ) = ONE
127: RETURN
128: END IF
129: *
130: * Get machine constants.
131: *
132: SAFMIN = DLAMCH( 'Safe minimum' )
133: EPS = DLAMCH( 'Precision' )
134: SMLNUM = SAFMIN / EPS
135: BIGNUM = ONE / SMLNUM
136: RMIN = SQRT( SMLNUM )
137: RMAX = SQRT( BIGNUM )
138: *
139: * Scale matrix to allowable range, if necessary.
140: *
141: ANRM = DLANSP( 'M', UPLO, N, AP, WORK )
142: ISCALE = 0
143: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
144: ISCALE = 1
145: SIGMA = RMIN / ANRM
146: ELSE IF( ANRM.GT.RMAX ) THEN
147: ISCALE = 1
148: SIGMA = RMAX / ANRM
149: END IF
150: IF( ISCALE.EQ.1 ) THEN
151: CALL DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
152: END IF
153: *
154: * Call DSPTRD to reduce symmetric packed matrix to tridiagonal form.
155: *
156: INDE = 1
157: INDTAU = INDE + N
158: CALL DSPTRD( UPLO, N, AP, W, WORK( INDE ), WORK( INDTAU ), IINFO )
159: *
160: * For eigenvalues only, call DSTERF. For eigenvectors, first call
161: * DOPGTR to generate the orthogonal matrix, then call DSTEQR.
162: *
163: IF( .NOT.WANTZ ) THEN
164: CALL DSTERF( N, W, WORK( INDE ), INFO )
165: ELSE
166: INDWRK = INDTAU + N
167: CALL DOPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ,
168: $ WORK( INDWRK ), IINFO )
169: CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDTAU ),
170: $ INFO )
171: END IF
172: *
173: * If matrix was scaled, then rescale eigenvalues appropriately.
174: *
175: IF( ISCALE.EQ.1 ) THEN
176: IF( INFO.EQ.0 ) THEN
177: IMAX = N
178: ELSE
179: IMAX = INFO - 1
180: END IF
181: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
182: END IF
183: *
184: RETURN
185: *
186: * End of DSPEV
187: *
188: END
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