Annotation of rpl/lapack/lapack/dspevd.f, revision 1.7
1.1 bertrand 1: SUBROUTINE DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
2: $ IWORK, LIWORK, INFO )
3: *
4: * -- LAPACK driver 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: CHARACTER JOBZ, UPLO
11: INTEGER INFO, LDZ, LIWORK, LWORK, N
12: * ..
13: * .. Array Arguments ..
14: INTEGER IWORK( * )
15: DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * DSPEVD computes all the eigenvalues and, optionally, eigenvectors
22: * of a real symmetric matrix A in packed storage. If eigenvectors are
23: * desired, it uses a divide and conquer algorithm.
24: *
25: * The divide and conquer algorithm makes very mild assumptions about
26: * floating point arithmetic. It will work on machines with a guard
27: * digit in add/subtract, or on those binary machines without guard
28: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
29: * Cray-2. It could conceivably fail on hexadecimal or decimal machines
30: * without guard digits, but we know of none.
31: *
32: * Arguments
33: * =========
34: *
35: * JOBZ (input) CHARACTER*1
36: * = 'N': Compute eigenvalues only;
37: * = 'V': Compute eigenvalues and eigenvectors.
38: *
39: * UPLO (input) CHARACTER*1
40: * = 'U': Upper triangle of A is stored;
41: * = 'L': Lower triangle of A is stored.
42: *
43: * N (input) INTEGER
44: * The order of the matrix A. N >= 0.
45: *
46: * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
47: * On entry, the upper or lower triangle of the symmetric matrix
48: * A, packed columnwise in a linear array. The j-th column of A
49: * is stored in the array AP as follows:
50: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
51: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
52: *
53: * On exit, AP is overwritten by values generated during the
54: * reduction to tridiagonal form. If UPLO = 'U', the diagonal
55: * and first superdiagonal of the tridiagonal matrix T overwrite
56: * the corresponding elements of A, and if UPLO = 'L', the
57: * diagonal and first subdiagonal of T overwrite the
58: * corresponding elements of A.
59: *
60: * W (output) DOUBLE PRECISION array, dimension (N)
61: * If INFO = 0, the eigenvalues in ascending order.
62: *
63: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
64: * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
65: * eigenvectors of the matrix A, with the i-th column of Z
66: * holding the eigenvector associated with W(i).
67: * If JOBZ = 'N', then Z is not referenced.
68: *
69: * LDZ (input) INTEGER
70: * The leading dimension of the array Z. LDZ >= 1, and if
71: * JOBZ = 'V', LDZ >= max(1,N).
72: *
73: * WORK (workspace/output) DOUBLE PRECISION array,
74: * dimension (LWORK)
75: * On exit, if INFO = 0, WORK(1) returns the required LWORK.
76: *
77: * LWORK (input) INTEGER
78: * The dimension of the array WORK.
79: * If N <= 1, LWORK must be at least 1.
80: * If JOBZ = 'N' and N > 1, LWORK must be at least 2*N.
81: * If JOBZ = 'V' and N > 1, LWORK must be at least
82: * 1 + 6*N + N**2.
83: *
84: * If LWORK = -1, then a workspace query is assumed; the routine
85: * only calculates the required sizes of the WORK and IWORK
86: * arrays, returns these values as the first entries of the WORK
87: * and IWORK arrays, and no error message related to LWORK or
88: * LIWORK is issued by XERBLA.
89: *
90: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
91: * On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
92: *
93: * LIWORK (input) INTEGER
94: * The dimension of the array IWORK.
95: * If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
96: * If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
97: *
98: * If LIWORK = -1, then a workspace query is assumed; the
99: * routine only calculates the required sizes of the WORK and
100: * IWORK arrays, returns these values as the first entries of
101: * the WORK and IWORK arrays, and no error message related to
102: * LWORK or LIWORK is issued by XERBLA.
103: *
104: * INFO (output) INTEGER
105: * = 0: successful exit
106: * < 0: if INFO = -i, the i-th argument had an illegal value.
107: * > 0: if INFO = i, the algorithm failed to converge; i
108: * off-diagonal elements of an intermediate tridiagonal
109: * form did not converge to zero.
110: *
111: * =====================================================================
112: *
113: * .. Parameters ..
114: DOUBLE PRECISION ZERO, ONE
115: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
116: * ..
117: * .. Local Scalars ..
118: LOGICAL LQUERY, WANTZ
119: INTEGER IINFO, INDE, INDTAU, INDWRK, ISCALE, LIWMIN,
120: $ LLWORK, LWMIN
121: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
122: $ SMLNUM
123: * ..
124: * .. External Functions ..
125: LOGICAL LSAME
126: DOUBLE PRECISION DLAMCH, DLANSP
127: EXTERNAL LSAME, DLAMCH, DLANSP
128: * ..
129: * .. External Subroutines ..
130: EXTERNAL DOPMTR, DSCAL, DSPTRD, DSTEDC, DSTERF, XERBLA
131: * ..
132: * .. Intrinsic Functions ..
133: INTRINSIC SQRT
134: * ..
135: * .. Executable Statements ..
136: *
137: * Test the input parameters.
138: *
139: WANTZ = LSAME( JOBZ, 'V' )
140: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
141: *
142: INFO = 0
143: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
144: INFO = -1
145: ELSE IF( .NOT.( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) )
146: $ THEN
147: INFO = -2
148: ELSE IF( N.LT.0 ) THEN
149: INFO = -3
150: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
151: INFO = -7
152: END IF
153: *
154: IF( INFO.EQ.0 ) THEN
155: IF( N.LE.1 ) THEN
156: LIWMIN = 1
157: LWMIN = 1
158: ELSE
159: IF( WANTZ ) THEN
160: LIWMIN = 3 + 5*N
161: LWMIN = 1 + 6*N + N**2
162: ELSE
163: LIWMIN = 1
164: LWMIN = 2*N
165: END IF
166: END IF
167: IWORK( 1 ) = LIWMIN
168: WORK( 1 ) = LWMIN
169: *
170: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
171: INFO = -9
172: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
173: INFO = -11
174: END IF
175: END IF
176: *
177: IF( INFO.NE.0 ) THEN
178: CALL XERBLA( 'DSPEVD', -INFO )
179: RETURN
180: ELSE IF( LQUERY ) THEN
181: RETURN
182: END IF
183: *
184: * Quick return if possible
185: *
186: IF( N.EQ.0 )
187: $ RETURN
188: *
189: IF( N.EQ.1 ) THEN
190: W( 1 ) = AP( 1 )
191: IF( WANTZ )
192: $ Z( 1, 1 ) = ONE
193: RETURN
194: END IF
195: *
196: * Get machine constants.
197: *
198: SAFMIN = DLAMCH( 'Safe minimum' )
199: EPS = DLAMCH( 'Precision' )
200: SMLNUM = SAFMIN / EPS
201: BIGNUM = ONE / SMLNUM
202: RMIN = SQRT( SMLNUM )
203: RMAX = SQRT( BIGNUM )
204: *
205: * Scale matrix to allowable range, if necessary.
206: *
207: ANRM = DLANSP( 'M', UPLO, N, AP, WORK )
208: ISCALE = 0
209: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
210: ISCALE = 1
211: SIGMA = RMIN / ANRM
212: ELSE IF( ANRM.GT.RMAX ) THEN
213: ISCALE = 1
214: SIGMA = RMAX / ANRM
215: END IF
216: IF( ISCALE.EQ.1 ) THEN
217: CALL DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
218: END IF
219: *
220: * Call DSPTRD to reduce symmetric packed matrix to tridiagonal form.
221: *
222: INDE = 1
223: INDTAU = INDE + N
224: CALL DSPTRD( UPLO, N, AP, W, WORK( INDE ), WORK( INDTAU ), IINFO )
225: *
226: * For eigenvalues only, call DSTERF. For eigenvectors, first call
227: * DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
228: * tridiagonal matrix, then call DOPMTR to multiply it by the
229: * Householder transformations represented in AP.
230: *
231: IF( .NOT.WANTZ ) THEN
232: CALL DSTERF( N, W, WORK( INDE ), INFO )
233: ELSE
234: INDWRK = INDTAU + N
235: LLWORK = LWORK - INDWRK + 1
236: CALL DSTEDC( 'I', N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
237: $ LLWORK, IWORK, LIWORK, INFO )
238: CALL DOPMTR( 'L', UPLO, 'N', N, N, AP, WORK( INDTAU ), Z, LDZ,
239: $ WORK( INDWRK ), IINFO )
240: END IF
241: *
242: * If matrix was scaled, then rescale eigenvalues appropriately.
243: *
244: IF( ISCALE.EQ.1 )
245: $ CALL DSCAL( N, ONE / SIGMA, W, 1 )
246: *
247: WORK( 1 ) = LWMIN
248: IWORK( 1 ) = LIWMIN
249: RETURN
250: *
251: * End of DSPEVD
252: *
253: END
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