1DSPEVD(1) LAPACK driver routine (version 3.2) DSPEVD(1)
2
6 DSPEVD - computes all the eigenvalues and, optionally, eigenvectors of
7 a real symmetric matrix A in packed storage
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10 SUBROUTINE DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK,
11 LIWORK, INFO )
12 CHARACTER JOBZ, UPLO
14 INTEGER INFO, LDZ, LIWORK, LWORK, N
16 INTEGER IWORK( * )
18 DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
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22 DSPEVD computes all the eigenvalues and, optionally, eigenvectors of a
23 real symmetric matrix A in packed storage. If eigenvectors are desired,
24 it uses a divide and conquer algorithm.
25 The divide and conquer algorithm makes very mild assumptions about
26 floating point arithmetic. It will work on machines with a guard digit
27 in add/subtract, or on those binary machines without guard digits which
28 subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
29 conceivably fail on hexadecimal or decimal machines without guard dig‐
30 its, but we know of none.
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33 JOBZ (input) CHARACTER*1
34 = 'N': Compute eigenvalues only;
35 = 'V': Compute eigenvalues and eigenvectors.
36 UPLO (input) CHARACTER*1
38 = 'U': Upper triangle of A is stored;
39 = 'L': Lower triangle of A is stored.
40 N (input) INTEGER
42 The order of the matrix A. N >= 0.
43 AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
45 On entry, the upper or lower triangle of the symmetric matrix
46 A, packed columnwise in a linear array. The j-th column of A
47 is stored in the array AP as follows: if UPLO = 'U', AP(i +
48 (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
49 (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, AP is over‐
50 written by values generated during the reduction to tridiagonal
51 form. If UPLO = 'U', the diagonal and first superdiagonal of
52 the tridiagonal matrix T overwrite the corresponding elements
53 of A, and if UPLO = 'L', the diagonal and first subdiagonal of
54 T overwrite the corresponding elements of A.
55 W (output) DOUBLE PRECISION array, dimension (N)
57 If INFO = 0, the eigenvalues in ascending order.
58 Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
60 If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
61 eigenvectors of the matrix A, with the i-th column of Z holding
62 the eigenvector associated with W(i). If JOBZ = 'N', then Z is
63 not referenced.
64 LDZ (input) INTEGER
66 The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
67 'V', LDZ >= max(1,N).
68 WORK (workspace/output) DOUBLE PRECISION array,
70 dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the
71 required LWORK.
72 LWORK (input) INTEGER
74 The dimension of the array WORK. If N <= 1,
75 LWORK must be at least 1. If JOBZ = 'N' and N > 1, LWORK must
76 be at least 2*N. If JOBZ = 'V' and N > 1, LWORK must be at
77 least 1 + 6*N + N**2. If LWORK = -1, then a workspace query is
78 assumed; the routine only calculates the required sizes of the
79 WORK and IWORK arrays, returns these values as the first
80 entries of the WORK and IWORK arrays, and no error message
81 related to LWORK or LIWORK is issued by XERBLA.
82 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
84 On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
85 LIWORK (input) INTEGER
87 The dimension of the array IWORK. If JOBZ = 'N' or N <= 1,
88 LIWORK must be at least 1. If JOBZ = 'V' and N > 1, LIWORK
89 must be at least 3 + 5*N. If LIWORK = -1, then a workspace
90 query is assumed; the routine only calculates the required
91 sizes of the WORK and IWORK arrays, returns these values as the
92 first entries of the WORK and IWORK arrays, and no error mes‐
93 sage related to LWORK or LIWORK is issued by XERBLA.
94 INFO (output) INTEGER
96 = 0: successful exit
97 < 0: if INFO = -i, the i-th argument had an illegal value.
98 > 0: if INFO = i, the algorithm failed to converge; i off-
99 diagonal elements of an intermediate tridiagonal form did not
100 converge to zero.
101 LAPACK driver routine (version 3.N2o)vember 2008 DSPEVD(1)