org.netlib.lapack
Class SSBGVX
java.lang.Object
org.netlib.lapack.SSBGVX
public class SSBGVX
- extends java.lang.Object
SSBGVX is a simplified interface to the JLAPACK routine ssbgvx.
This interface converts Java-style 2D row-major arrays into
the 1D column-major linearized arrays expected by the lower
level JLAPACK routines. Using this interface also allows you
to omit offset and leading dimension arguments. However, because
of these conversions, these routines will be slower than the low
level ones. Following is the description from the original Fortran
source. Contact seymour@cs.utk.edu with any questions.
* ..
*
* Purpose
* =======
*
* 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.
*
* Arguments
* =========
*
* JOBZ (input) CHARACTER*1
* = 'N': Compute eigenvalues only;
* = 'V': Compute eigenvalues and eigenvectors.
*
* RANGE (input) 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.
*
* UPLO (input) CHARACTER*1
* = 'U': Upper triangles of A and B are stored;
* = 'L': Lower triangles of A and B are stored.
*
* N (input) INTEGER
* The order of the matrices A and B. N >= 0.
*
* KA (input) INTEGER
* The number of superdiagonals of the matrix A if UPLO = 'U',
* or the number of subdiagonals if UPLO = 'L'. KA >= 0.
*
* KB (input) INTEGER
* The number of superdiagonals of the matrix B if UPLO = 'U',
* or the number of subdiagonals if UPLO = 'L'. KB >= 0.
*
* AB (input/output) 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.
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDAB >= KA+1.
*
* BB (input/output) 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.
*
* LDBB (input) INTEGER
* The leading dimension of the array BB. LDBB >= KB+1.
*
* Q (output) 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.
*
* LDQ (input) INTEGER
* The leading dimension of the array Q. If JOBZ = 'N',
* LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N).
*
* VL (input) REAL
* VU (input) REAL
* If RANGE='V', the lower and upper bounds of the interval to
* be searched for eigenvalues. VL < VU.
* Not referenced if RANGE = 'A' or 'I'.
*
* IL (input) INTEGER
* IU (input) INTEGER
* If RANGE='I', the indices (in ascending order) of the
* smallest and largest eigenvalues 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'.
*
* ABSTOL (input) 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').
*
* M (output) INTEGER
* The total number of eigenvalues found. 0 <= M <= N.
* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
*
* W (output) REAL array, dimension (N)
* If INFO = 0, the eigenvalues in ascending order.
*
* Z (output) 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.
*
* LDZ (input) INTEGER
* The leading dimension of the array Z. LDZ >= 1, and if
* JOBZ = 'V', LDZ >= max(1,N).
*
* WORK (workspace/output) REAL array, dimension (7N)
*
* IWORK (workspace/output) INTEGER array, dimension (5N)
*
* IFAIL (input) 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.
*
* INFO (output) 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.
*
* Further Details
* ===============
*
* Based on contributions by
* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
*
* =====================================================================
*
* .. Parameters ..
|
Method Summary |
static void |
SSBGVX(java.lang.String jobz,
java.lang.String range,
java.lang.String uplo,
int n,
int ka,
int kb,
float[][] ab,
float[][] bb,
float[][] q,
float vl,
float vu,
int il,
int iu,
float abstol,
intW m,
float[] w,
float[][] z,
float[] work,
int[] iwork,
int[] ifail,
intW info)
|
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
SSBGVX
public SSBGVX()
SSBGVX
public static void SSBGVX(java.lang.String jobz,
java.lang.String range,
java.lang.String uplo,
int n,
int ka,
int kb,
float[][] ab,
float[][] bb,
float[][] q,
float vl,
float vu,
int il,
int iu,
float abstol,
intW m,
float[] w,
float[][] z,
float[] work,
int[] iwork,
int[] ifail,
intW info)