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◆ zhbgv()
| void zhbgv |
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char |
jobz, |
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char |
uplo, |
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int |
n, |
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int |
ka, |
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int |
kb, |
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int |
ldab, |
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doublecomplex |
ab[], |
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int |
ldbb, |
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doublecomplex |
bb[], |
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double |
w[], |
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int |
ldz, |
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doublecomplex |
z[], |
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doublecomplex |
work[], |
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double |
rwork[], |
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int * |
info |
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(Simple driver) Generalized eigenvalue problem of Hermitian band matrices
- Purpose
- This routine computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form Here A and B are assumed to be Hermitian and banded, and B is also positive definite.
- Parameters
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| [in] | jobz | = 'N': Compute eigenvalues only.
= 'V': Compute eigenvalues and eigenvectors. |
| [in] | uplo | = 'U': Upper triangles of A and B are stored.
= 'L': Lower triangles of A and B are stored. |
| [in] | n | Order of the matrices A and B. (n >= 0) (If n = 0, returns without computation) |
| [in] | ka | Number of super-diagonals of the matrix A if uplo = 'U' or the number of sub-diagonals if uplo = 'L'. (ka >= 0) |
| [in] | kb | Number of super-diagonals of the matrix B if uplo = 'U' or the number of sub-diagonals if uplo = 'L'. (kb >= 0) |
| [in] | ldab | Leading dimension of the two dimensional array ab[][]. (ldab >= ka + 1) |
| [in,out] | ab[][] | Array ab[lab][ldab] (lab >= n)
[in] The upper or lower triangle of the Hermitian band matrix A, stored in the first ka+1 columns of the array. The j-th column of A is stored in the j-th row of the array ab as follows.
uplo = 'U': ab[j][ka + i - j] = Aij for max(0, j - ka - 1) <= i <= j <= n - 1.
uplo = 'L': ab[j][i - j] = Aij for 0 <= j <= i <= min(n - 1, j + ka - 1).
[out] The contents of ab[][] are destroyed. |
| [in] | ldbb | Leading dimension of the two dimensional array bb[][]. (ldbb >= kb + 1) |
| [in,out] | bb[][] | Array bb[lbb][ldbb] (lbb >= n)
[in] The upper or lower triangle of the Hermitian positive definite band matrix B, stored in the first kb+1 columns of the array. The j-th column of B is stored in the j-th row of the array bb as follows.
uplo = 'U': bb[j][kb + i - j] = Bij for max(0, j - kb - 1) <= i <= j <= n - 1.
uplo = 'L': bb[j][i - j] = Bij for 0 <= j <= i <= min(n - 1, j + kb - 1).
[out] The factor S from the split Cholesky factorization B = S^H*S, as returned by zpbstf. |
| [out] | w[] | Array w[lw] (lw >= n)
If info = 0, the eigenvalues in ascending order. |
| [in] | ldz | Leading dimension of the two dimensional array z[][]. (ldz >= 1 if jobz = 'N', ldz >= max(1, n) if jobz = 'V') |
| [out] | z[][] | Array z[lz][ldz] (lz >= n)
jobz = 'V': If info = 0, z[][] contains the matrix Z of eigenvectors, with the i-th column of Z holding the eigenvector associated with w[i]. The eigenvectors are normalized so that Z^H*B*Z = I.
jobz = 'N': z[][] is not referenced. |
| [out] | work[] | Array work[lwork] (lwork >= n)
Complex work array. |
| [out] | rwork[] | Array rwork[lrwork] (lrwork >= 3*n)
Work array. |
| [out] | info | = 0: Successful exit
= -1: The argument jobz had an illegal value (jobz != 'V' nor 'N')
= -2: The argument uplo had an illegal value (uplo != 'U' nor 'L')
= -3: The argument n had an illegal value (n < 0)
= -4: The argument ka had an illegal value (ka < 0)
= -5: The argument kb had an illegal value (kb < 0 or kb > ka)
= -6: The argument ldab had an illegal value (ldab < ka + 1)
= -8: The argument ldbb had an illegal value (ldbb < kb + 1)
= -11: The argument ldz had an illegal value (ldz too small)
= i (0 < i <= n): The algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.
= i (i > n): zpbstf returned info = i-n. B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. |
- Reference
- LAPACK
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1.9.7