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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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| subroutine ssbgvx | ( | character | JOBZ, |
| character | RANGE, | ||
| character | UPLO, | ||
| integer | N, | ||
| integer | KA, | ||
| integer | KB, | ||
| real, dimension( ldab, * ) | AB, | ||
| integer | LDAB, | ||
| real, dimension( ldbb, * ) | BB, | ||
| integer | LDBB, | ||
| real, dimension( ldq, * ) | Q, | ||
| integer | LDQ, | ||
| real | VL, | ||
| real | VU, | ||
| integer | IL, | ||
| integer | IU, | ||
| real | ABSTOL, | ||
| integer | M, | ||
| real, dimension( * ) | W, | ||
| real, dimension( ldz, * ) | Z, | ||
| integer | LDZ, | ||
| real, dimension( * ) | WORK, | ||
| integer, dimension( * ) | IWORK, | ||
| integer, dimension( * ) | IFAIL, | ||
| integer | INFO | ||
| ) |
SSBGVX
Download SSBGVX + dependencies [TGZ] [ZIP] [TXT]
SSBGVX computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and banded, and B is also positive definite. Eigenvalues and eigenvectors can be selected by specifying either all eigenvalues, 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 triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored. |
| [in] | N | N is INTEGER
The order of the matrices A and B. N >= 0. |
| [in] | KA | KA is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KA >= 0. |
| [in] | KB | KB is INTEGER
The number of superdiagonals of the matrix B if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KB >= 0. |
| [in,out] | AB | AB is REAL array, dimension (LDAB, N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
On exit, the contents of AB are destroyed. |
| [in] | LDAB | LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KA+1. |
| [in,out] | BB | BB is REAL array, dimension (LDBB, N)
On entry, the upper or lower triangle of the symmetric band
matrix B, stored in the first kb+1 rows of the array. The
j-th column of B is stored in the j-th column of the array BB
as follows:
if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
On exit, the factor S from the split Cholesky factorization
B = S**T*S, as returned by SPBSTF. |
| [in] | LDBB | LDBB is INTEGER
The leading dimension of the array BB. LDBB >= KB+1. |
| [out] | Q | Q is REAL array, dimension (LDQ, N)
If JOBZ = 'V', the n-by-n matrix used in the reduction of
A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x,
and consequently C 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 = 'N',
LDQ >= 1. If JOBZ = 'V', 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 A 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'). |
| [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)
If INFO = 0, the eigenvalues in ascending order. |
| [out] | Z | Z is REAL array, dimension (LDZ, N)
If JOBZ = 'V', then 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 Z**T*B*Z = I.
If JOBZ = 'N', then Z is not referenced. |
| [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 REAL array, dimension (7*N) |
| [out] | IWORK | IWORK is INTEGER array, dimension (5*N) |
| [out] | IFAIL | IFAIL is INTEGER array, dimension (M)
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 eigenvalues 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
<= N: if INFO = i, then i eigenvectors failed to converge.
Their indices are stored in IFAIL.
> N: SPBSTF returned an error code; i.e.,
if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed. |
Definition at line 291 of file ssbgvx.f.
1.9.5