1ZLAED0(1) LAPACK routine (version 3.2) ZLAED0(1)
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6 ZLAED0 - the divide and conquer method, ZLAED0 computes all eigenvalues
7 of a symmetric tridiagonal matrix which is one diagonal block of those
8 from reducing a dense or band Hermitian matrix and corresponding eigen‐
9 vectors of the dense or band matrix
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12 SUBROUTINE ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, IWORK,
13 INFO )
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15 INTEGER INFO, LDQ, LDQS, N, QSIZ
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17 INTEGER IWORK( * )
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19 DOUBLE PRECISION D( * ), E( * ), RWORK( * )
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21 COMPLEX*16 Q( LDQ, * ), QSTORE( LDQS, * )
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24 Using the divide and conquer method, ZLAED0 computes all eigenvalues of
25 a symmetric tridiagonal matrix which is one diagonal block of those
26 from reducing a dense or band Hermitian matrix and corresponding eigen‐
27 vectors of the dense or band matrix.
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30 QSIZ (input) INTEGER
31 The dimension of the unitary matrix used to reduce the full
32 matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
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34 N (input) INTEGER
35 The dimension of the symmetric tridiagonal matrix. N >= 0.
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37 D (input/output) DOUBLE PRECISION array, dimension (N)
38 On entry, the diagonal elements of the tridiagonal matrix. On
39 exit, the eigenvalues in ascending order.
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41 E (input/output) DOUBLE PRECISION array, dimension (N-1)
42 On entry, the off-diagonal elements of the tridiagonal matrix.
43 On exit, E has been destroyed.
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45 Q (input/output) COMPLEX*16 array, dimension (LDQ,N)
46 On entry, Q must contain an QSIZ x N matrix whose columns uni‐
47 tarily orthonormal. It is a part of the unitary matrix that
48 reduces the full dense Hermitian matrix to a (reducible) symmet‐
49 ric tridiagonal matrix.
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51 LDQ (input) INTEGER
52 The leading dimension of the array Q. LDQ >= max(1,N).
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54 IWORK (workspace) INTEGER array,
55 the dimension of IWORK must be at least 6 + 6*N + 5*N*lg N ( lg(
56 N ) = smallest integer k such that 2^k >= N )
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58 RWORK (workspace) DOUBLE PRECISION array,
59 dimension (1 + 3*N + 2*N*lg N + 3*N**2) ( lg( N ) = smallest
60 integer k such that 2^k >= N ) QSTORE (workspace) COMPLEX*16
61 array, dimension (LDQS, N) Used to store parts of the eigenvec‐
62 tor matrix when the updating matrix multiplies take place.
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64 LDQS (input) INTEGER
65 The leading dimension of the array QSTORE. LDQS >= max(1,N).
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67 INFO (output) INTEGER
68 = 0: successful exit.
69 < 0: if INFO = -i, the i-th argument had an illegal value.
70 > 0: The algorithm failed to compute an eigenvalue while work‐
71 ing on the submatrix lying in rows and columns INFO/(N+1)
72 through mod(INFO,N+1).
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76 LAPACK routine (version 3.2) November 2008 ZLAED0(1)