org.netlib.lapack
Class DSPGVX
java.lang.Object
org.netlib.lapack.DSPGVX
public class DSPGVX
- extends java.lang.Object
DSPGVX is a simplified interface to the JLAPACK routine dspgvx.
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
* =======
*
* DSPGVX computes selected eigenvalues, and optionally, eigenvectors
* of a real generalized symmetric-definite eigenproblem, of the form
* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A
* and B are assumed to be symmetric, stored in packed storage, and B
* is also positive definite. Eigenvalues and eigenvectors can be
* selected by specifying either a range of values or a range of indices
* for the desired eigenvalues.
*
* Arguments
* =========
*
* ITYPE (input) INTEGER
* Specifies the problem type to be solved:
* = 1: A*x = (lambda)*B*x
* = 2: A*B*x = (lambda)*x
* = 3: B*A*x = (lambda)*x
*
* 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 triangle of A and B are stored;
* = 'L': Lower triangle of A and B are stored.
*
* N (input) INTEGER
* The order of the matrix pencil (A,B). N >= 0.
*
* AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
* On entry, the upper or lower triangle of the symmetric matrix
* A, packed columnwise in a linear array. The j-th column of A
* is stored in the array AP as follows:
* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
*
* On exit, the contents of AP are destroyed.
*
* BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
* On entry, the upper or lower triangle of the symmetric matrix
* B, packed columnwise in a linear array. The j-th column of B
* is stored in the array BP as follows:
* if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
* if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
*
* On exit, the triangular factor U or L from the Cholesky
* factorization B = U**T*U or B = L*L**T, in the same storage
* format as B.
*
* VL (input) DOUBLE PRECISION
* VU (input) DOUBLE PRECISION
* 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) DOUBLE PRECISION
* 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*DLAMCH('S'), not zero.
* If this routine returns with INFO>0, indicating that some
* eigenvectors did not converge, try setting ABSTOL to
* 2*DLAMCH('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) DOUBLE PRECISION array, dimension (N)
* On normal exit, the first M elements contain the selected
* eigenvalues in ascending order.
*
* Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M))
* If JOBZ = 'N', then Z is not referenced.
* 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).
* The eigenvectors are normalized as follows:
* if ITYPE = 1 or 2, Z**T*B*Z = I;
* if ITYPE = 3, Z**T*inv(B)*Z = 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.
* 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.
*
* LDZ (input) INTEGER
* The leading dimension of the array Z. LDZ >= 1, and if
* JOBZ = 'V', LDZ >= max(1,N).
*
* WORK (workspace) DOUBLE PRECISION array, dimension (8*N)
*
* IWORK (workspace) INTEGER array, dimension (5*N)
*
* IFAIL (output) 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.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
* > 0: DPPTRF or DSPEVX returned an error code:
* <= N: if INFO = i, DSPEVX failed to converge;
* i eigenvectors failed to converge. Their indices
* are stored in array IFAIL.
* > N: 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
*
* =====================================================================
*
* .. Local Scalars ..
|
Method Summary |
static void |
DSPGVX(int itype,
java.lang.String jobz,
java.lang.String range,
java.lang.String uplo,
int n,
double[] ap,
double[] bp,
double vl,
double vu,
int il,
int iu,
double abstol,
intW m,
double[] w,
double[][] z,
double[] 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 |
DSPGVX
public DSPGVX()
DSPGVX
public static void DSPGVX(int itype,
java.lang.String jobz,
java.lang.String range,
java.lang.String uplo,
int n,
double[] ap,
double[] bp,
double vl,
double vu,
int il,
int iu,
double abstol,
intW m,
double[] w,
double[][] z,
double[] work,
int[] iwork,
int[] ifail,
intW info)