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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine chbevx | ( | character | JOBZ, |
character | RANGE, | ||
character | UPLO, | ||
integer | N, | ||
integer | KD, | ||
complex, dimension( ldab, * ) | AB, | ||
integer | LDAB, | ||
complex, dimension( ldq, * ) | Q, | ||
integer | LDQ, | ||
real | VL, | ||
real | VU, | ||
integer | IL, | ||
integer | IU, | ||
real | ABSTOL, | ||
integer | M, | ||
real, dimension( * ) | W, | ||
complex, dimension( ldz, * ) | Z, | ||
integer | LDZ, | ||
complex, dimension( * ) | WORK, | ||
real, dimension( * ) | RWORK, | ||
integer, dimension( * ) | IWORK, | ||
integer, dimension( * ) | IFAIL, | ||
integer | INFO | ||
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CHBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
Download CHBEVX + dependencies [TGZ] [ZIP] [TXT]
CHBEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
[in] | JOBZ | JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. |
[in] | RANGE | RANGE is CHARACTER*1 = 'A': all eigenvalues will be found; = 'V': all eigenvalues in the half-open interval (VL,VU] will be found; = 'I': the IL-th through IU-th eigenvalues will be found. |
[in] | UPLO | UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. |
[in] | N | N is INTEGER The order of the matrix A. N >= 0. |
[in] | KD | KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. |
[in,out] | AB | AB is COMPLEX array, dimension (LDAB, N) On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, AB is overwritten by values generated during the reduction to tridiagonal form. |
[in] | LDAB | LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD + 1. |
[out] | Q | Q is COMPLEX array, dimension (LDQ, N) If JOBZ = 'V', the N-by-N unitary matrix used in the reduction to tridiagonal form. If JOBZ = 'N', the array Q is not referenced. |
[in] | LDQ | LDQ is INTEGER The leading dimension of the array Q. If JOBZ = 'V', then LDQ >= max(1,N). |
[in] | VL | VL is REAL If RANGE='V', the lower bound of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'. |
[in] | VU | VU is REAL If RANGE='V', the upper bound of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'. |
[in] | IL | IL is INTEGER If RANGE='I', the index of the smallest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'. |
[in] | IU | IU is INTEGER If RANGE='I', the index of the largest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'. |
[in] | ABSTOL | ABSTOL is REAL The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( |a|,|b| ) , where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing AB to tridiagonal form. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*SLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*SLAMCH('S'). See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3. |
[out] | M | M is INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. |
[out] | W | W is REAL array, dimension (N) The first M elements contain the selected eigenvalues in ascending order. |
[out] | Z | Z is COMPLEX array, dimension (LDZ, max(1,M)) If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. If JOBZ = 'N', then Z is not referenced. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = 'V', the exact value of M is not known in advance and an upper bound must be used. |
[in] | LDZ | LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). |
[out] | WORK | WORK is COMPLEX array, dimension (N) |
[out] | RWORK | RWORK is REAL array, dimension (7*N) |
[out] | IWORK | IWORK is INTEGER array, dimension (5*N) |
[out] | IFAIL | IFAIL is INTEGER array, dimension (N) If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = 'N', then IFAIL is not referenced. |
[out] | INFO | INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, then i eigenvectors failed to converge. Their indices are stored in array IFAIL. |
Definition at line 269 of file chbevx.f.