Annotation of rpl/lapack/lapack/zhpevd.f, revision 1.6
1.1 bertrand 1: SUBROUTINE ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
2: $ RWORK, LRWORK, 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, LRWORK, LWORK, N
12: * ..
13: * .. Array Arguments ..
14: INTEGER IWORK( * )
15: DOUBLE PRECISION RWORK( * ), W( * )
16: COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
17: * ..
18: *
19: * Purpose
20: * =======
21: *
22: * ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of
23: * a complex Hermitian matrix A in packed storage. If eigenvectors are
24: * desired, it uses a divide and conquer algorithm.
25: *
26: * The divide and conquer algorithm makes very mild assumptions about
27: * floating point arithmetic. It will work on machines with a guard
28: * digit in add/subtract, or on those binary machines without guard
29: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
30: * Cray-2. It could conceivably fail on hexadecimal or decimal machines
31: * without guard digits, but we know of none.
32: *
33: * Arguments
34: * =========
35: *
36: * JOBZ (input) CHARACTER*1
37: * = 'N': Compute eigenvalues only;
38: * = 'V': Compute eigenvalues and eigenvectors.
39: *
40: * UPLO (input) CHARACTER*1
41: * = 'U': Upper triangle of A is stored;
42: * = 'L': Lower triangle of A is stored.
43: *
44: * N (input) INTEGER
45: * The order of the matrix A. N >= 0.
46: *
47: * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
48: * On entry, the upper or lower triangle of the Hermitian matrix
49: * A, packed columnwise in a linear array. The j-th column of A
50: * is stored in the array AP as follows:
51: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
52: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
53: *
54: * On exit, AP is overwritten by values generated during the
55: * reduction to tridiagonal form. If UPLO = 'U', the diagonal
56: * and first superdiagonal of the tridiagonal matrix T overwrite
57: * the corresponding elements of A, and if UPLO = 'L', the
58: * diagonal and first subdiagonal of T overwrite the
59: * corresponding elements of A.
60: *
61: * W (output) DOUBLE PRECISION array, dimension (N)
62: * If INFO = 0, the eigenvalues in ascending order.
63: *
64: * Z (output) COMPLEX*16 array, dimension (LDZ, N)
65: * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
66: * eigenvectors of the matrix A, with the i-th column of Z
67: * holding the eigenvector associated with W(i).
68: * If JOBZ = 'N', then Z is not referenced.
69: *
70: * LDZ (input) INTEGER
71: * The leading dimension of the array Z. LDZ >= 1, and if
72: * JOBZ = 'V', LDZ >= max(1,N).
73: *
74: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
75: * On exit, if INFO = 0, WORK(1) returns the required LWORK.
76: *
77: * LWORK (input) INTEGER
78: * The dimension of array WORK.
79: * If N <= 1, LWORK must be at least 1.
80: * If JOBZ = 'N' and N > 1, LWORK must be at least N.
81: * If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.
82: *
83: * If LWORK = -1, then a workspace query is assumed; the routine
84: * only calculates the required sizes of the WORK, RWORK and
85: * IWORK arrays, returns these values as the first entries of
86: * the WORK, RWORK and IWORK arrays, and no error message
87: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
88: *
89: * RWORK (workspace/output) DOUBLE PRECISION array,
90: * dimension (LRWORK)
91: * On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
92: *
93: * LRWORK (input) INTEGER
94: * The dimension of array RWORK.
95: * If N <= 1, LRWORK must be at least 1.
96: * If JOBZ = 'N' and N > 1, LRWORK must be at least N.
97: * If JOBZ = 'V' and N > 1, LRWORK must be at least
98: * 1 + 5*N + 2*N**2.
99: *
100: * If LRWORK = -1, then a workspace query is assumed; the
101: * routine only calculates the required sizes of the WORK, RWORK
102: * and IWORK arrays, returns these values as the first entries
103: * of the WORK, RWORK and IWORK arrays, and no error message
104: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
105: *
106: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
107: * On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
108: *
109: * LIWORK (input) INTEGER
110: * The dimension of array IWORK.
111: * If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
112: * If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
113: *
114: * If LIWORK = -1, then a workspace query is assumed; the
115: * routine only calculates the required sizes of the WORK, RWORK
116: * and IWORK arrays, returns these values as the first entries
117: * of the WORK, RWORK and IWORK arrays, and no error message
118: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
119: *
120: * INFO (output) INTEGER
121: * = 0: successful exit
122: * < 0: if INFO = -i, the i-th argument had an illegal value.
123: * > 0: if INFO = i, the algorithm failed to converge; i
124: * off-diagonal elements of an intermediate tridiagonal
125: * form did not converge to zero.
126: *
127: * =====================================================================
128: *
129: * .. Parameters ..
130: DOUBLE PRECISION ZERO, ONE
131: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
132: COMPLEX*16 CONE
133: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
134: * ..
135: * .. Local Scalars ..
136: LOGICAL LQUERY, WANTZ
137: INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWRK,
138: $ ISCALE, LIWMIN, LLRWK, LLWRK, LRWMIN, LWMIN
139: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
140: $ SMLNUM
141: * ..
142: * .. External Functions ..
143: LOGICAL LSAME
144: DOUBLE PRECISION DLAMCH, ZLANHP
145: EXTERNAL LSAME, DLAMCH, ZLANHP
146: * ..
147: * .. External Subroutines ..
148: EXTERNAL DSCAL, DSTERF, XERBLA, ZDSCAL, ZHPTRD, ZSTEDC,
149: $ ZUPMTR
150: * ..
151: * .. Intrinsic Functions ..
152: INTRINSIC SQRT
153: * ..
154: * .. Executable Statements ..
155: *
156: * Test the input parameters.
157: *
158: WANTZ = LSAME( JOBZ, 'V' )
159: LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
160: *
161: INFO = 0
162: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
163: INFO = -1
164: ELSE IF( .NOT.( LSAME( UPLO, 'L' ) .OR. LSAME( UPLO, 'U' ) ) )
165: $ THEN
166: INFO = -2
167: ELSE IF( N.LT.0 ) THEN
168: INFO = -3
169: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
170: INFO = -7
171: END IF
172: *
173: IF( INFO.EQ.0 ) THEN
174: IF( N.LE.1 ) THEN
175: LWMIN = 1
176: LIWMIN = 1
177: LRWMIN = 1
178: ELSE
179: IF( WANTZ ) THEN
180: LWMIN = 2*N
181: LRWMIN = 1 + 5*N + 2*N**2
182: LIWMIN = 3 + 5*N
183: ELSE
184: LWMIN = N
185: LRWMIN = N
186: LIWMIN = 1
187: END IF
188: END IF
189: WORK( 1 ) = LWMIN
190: RWORK( 1 ) = LRWMIN
191: IWORK( 1 ) = LIWMIN
192: *
193: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
194: INFO = -9
195: ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
196: INFO = -11
197: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
198: INFO = -13
199: END IF
200: END IF
201: *
202: IF( INFO.NE.0 ) THEN
203: CALL XERBLA( 'ZHPEVD', -INFO )
204: RETURN
205: ELSE IF( LQUERY ) THEN
206: RETURN
207: END IF
208: *
209: * Quick return if possible
210: *
211: IF( N.EQ.0 )
212: $ RETURN
213: *
214: IF( N.EQ.1 ) THEN
215: W( 1 ) = AP( 1 )
216: IF( WANTZ )
217: $ Z( 1, 1 ) = CONE
218: RETURN
219: END IF
220: *
221: * Get machine constants.
222: *
223: SAFMIN = DLAMCH( 'Safe minimum' )
224: EPS = DLAMCH( 'Precision' )
225: SMLNUM = SAFMIN / EPS
226: BIGNUM = ONE / SMLNUM
227: RMIN = SQRT( SMLNUM )
228: RMAX = SQRT( BIGNUM )
229: *
230: * Scale matrix to allowable range, if necessary.
231: *
232: ANRM = ZLANHP( 'M', UPLO, N, AP, RWORK )
233: ISCALE = 0
234: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
235: ISCALE = 1
236: SIGMA = RMIN / ANRM
237: ELSE IF( ANRM.GT.RMAX ) THEN
238: ISCALE = 1
239: SIGMA = RMAX / ANRM
240: END IF
241: IF( ISCALE.EQ.1 ) THEN
242: CALL ZDSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
243: END IF
244: *
245: * Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form.
246: *
247: INDE = 1
248: INDTAU = 1
249: INDRWK = INDE + N
250: INDWRK = INDTAU + N
251: LLWRK = LWORK - INDWRK + 1
252: LLRWK = LRWORK - INDRWK + 1
253: CALL ZHPTRD( UPLO, N, AP, W, RWORK( INDE ), WORK( INDTAU ),
254: $ IINFO )
255: *
256: * For eigenvalues only, call DSTERF. For eigenvectors, first call
257: * ZUPGTR to generate the orthogonal matrix, then call ZSTEDC.
258: *
259: IF( .NOT.WANTZ ) THEN
260: CALL DSTERF( N, W, RWORK( INDE ), INFO )
261: ELSE
262: CALL ZSTEDC( 'I', N, W, RWORK( INDE ), Z, LDZ, WORK( INDWRK ),
263: $ LLWRK, RWORK( INDRWK ), LLRWK, IWORK, LIWORK,
264: $ INFO )
265: CALL ZUPMTR( 'L', UPLO, 'N', N, N, AP, WORK( INDTAU ), Z, LDZ,
266: $ WORK( INDWRK ), IINFO )
267: END IF
268: *
269: * If matrix was scaled, then rescale eigenvalues appropriately.
270: *
271: IF( ISCALE.EQ.1 ) THEN
272: IF( INFO.EQ.0 ) THEN
273: IMAX = N
274: ELSE
275: IMAX = INFO - 1
276: END IF
277: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
278: END IF
279: *
280: WORK( 1 ) = LWMIN
281: RWORK( 1 ) = LRWMIN
282: IWORK( 1 ) = LIWMIN
283: RETURN
284: *
285: * End of ZHPEVD
286: *
287: END
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