org.netlib.lapack
Class SPTSVX
java.lang.Object
org.netlib.lapack.SPTSVX
public class SPTSVX
 extends java.lang.Object
SPTSVX is a simplified interface to the JLAPACK routine sptsvx.
This interface converts Javastyle 2D rowmajor arrays into
the 1D columnmajor 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
* =======
*
* SPTSVX uses the factorization A = L*D*L**T to compute the solution
* to a real system of linear equations A*X = B, where A is an NbyN
* symmetric positive definite tridiagonal matrix and X and B are
* NbyNRHS matrices.
*
* Error bounds on the solution and a condition estimate are also
* provided.
*
* Description
* ===========
*
* The following steps are performed:
*
* 1. If FACT = 'N', the matrix A is factored as A = L*D*L**T, where L
* is a unit lower bidiagonal matrix and D is diagonal. The
* factorization can also be regarded as having the form
* A = U**T*D*U.
*
* 2. If the leading ibyi principal minor is not positive definite,
* then the routine returns with INFO = i. Otherwise, the factored
* form of A is used to estimate the condition number of the matrix
* A. If the reciprocal of the condition number is less than machine
* precision, INFO = N+1 is returned as a warning, but the routine
* still goes on to solve for X and compute error bounds as
* described below.
*
* 3. The system of equations is solved for X using the factored form
* of A.
*
* 4. Iterative refinement is applied to improve the computed solution
* matrix and calculate error bounds and backward error estimates
* for it.
*
* Arguments
* =========
*
* FACT (input) CHARACTER*1
* Specifies whether or not the factored form of A has been
* supplied on entry.
* = 'F': On entry, DF and EF contain the factored form of A.
* D, E, DF, and EF will not be modified.
* = 'N': The matrix A will be copied to DF and EF and
* factored.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrices B and X. NRHS >= 0.
*
* D (input) REAL array, dimension (N)
* The n diagonal elements of the tridiagonal matrix A.
*
* E (input) REAL array, dimension (N1)
* The (n1) subdiagonal elements of the tridiagonal matrix A.
*
* DF (input or output) REAL array, dimension (N)
* If FACT = 'F', then DF is an input argument and on entry
* contains the n diagonal elements of the diagonal matrix D
* from the L*D*L**T factorization of A.
* If FACT = 'N', then DF is an output argument and on exit
* contains the n diagonal elements of the diagonal matrix D
* from the L*D*L**T factorization of A.
*
* EF (input or output) REAL array, dimension (N1)
* If FACT = 'F', then EF is an input argument and on entry
* contains the (n1) subdiagonal elements of the unit
* bidiagonal factor L from the L*D*L**T factorization of A.
* If FACT = 'N', then EF is an output argument and on exit
* contains the (n1) subdiagonal elements of the unit
* bidiagonal factor L from the L*D*L**T factorization of A.
*
* B (input) REAL array, dimension (LDB,NRHS)
* The NbyNRHS right hand side matrix B.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* X (output) REAL array, dimension (LDX,NRHS)
* If INFO = 0 of INFO = N+1, the NbyNRHS solution matrix X.
*
* LDX (input) INTEGER
* The leading dimension of the array X. LDX >= max(1,N).
*
* RCOND (output) REAL
* The reciprocal condition number of the matrix A. If RCOND
* is less than the machine precision (in particular, if
* RCOND = 0), the matrix is singular to working precision.
* This condition is indicated by a return code of INFO > 0.
*
* FERR (output) REAL array, dimension (NRHS)
* The forward error bound for each solution vector
* X(j) (the jth column of the solution matrix X).
* If XTRUE is the true solution corresponding to X(j), FERR(j)
* is an estimated upper bound for the magnitude of the largest
* element in (X(j)  XTRUE) divided by the magnitude of the
* largest element in X(j).
*
* BERR (output) REAL array, dimension (NRHS)
* The componentwise relative backward error of each solution
* vector X(j) (i.e., the smallest relative change in any
* element of A or B that makes X(j) an exact solution).
*
* WORK (workspace) REAL array, dimension (2*N)
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = i, the ith argument had an illegal value
* > 0: if INFO = i, and i is
* <= N: the leading minor of order i of A is
* not positive definite, so the factorization
* could not be completed, and the solution has not
* been computed. RCOND = 0 is returned.
* = N+1: U is nonsingular, but RCOND is less than machine
* precision, meaning that the matrix is singular
* to working precision. Nevertheless, the
* solution and error bounds are computed because
* there are a number of situations where the
* computed solution can be more accurate than the
* value of RCOND would suggest.
*
* =====================================================================
*
* .. Parameters ..
Method Summary 
static void 
SPTSVX(java.lang.String fact,
int n,
int nrhs,
float[] d,
float[] e,
float[] df,
float[] ef,
float[][] b,
float[][] x,
floatW rcond,
float[] ferr,
float[] berr,
float[] work,
intW info)

Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
SPTSVX
public SPTSVX()
SPTSVX
public static void SPTSVX(java.lang.String fact,
int n,
int nrhs,
float[] d,
float[] e,
float[] df,
float[] ef,
float[][] b,
float[][] x,
floatW rcond,
float[] ferr,
float[] berr,
float[] work,
intW info)