org.netlib.lapack
Class DGTSVX
java.lang.Object
org.netlib.lapack.DGTSVX
public class DGTSVX
 extends java.lang.Object
DGTSVX is a simplified interface to the JLAPACK routine dgtsvx.
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
* =======
*
* DGTSVX uses the LU factorization to compute the solution to a real
* system of linear equations A * X = B or A**T * X = B,
* where A is a tridiagonal matrix of order N 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 LU decomposition is used to factor the matrix A
* as A = L * U, where L is a product of permutation and unit lower
* bidiagonal matrices and U is upper triangular with nonzeros in
* only the main diagonal and first two superdiagonals.
*
* 2. If some U(i,i)=0, so that U is exactly singular, 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': DLF, DF, DUF, DU2, and IPIV contain the factored
* form of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV
* will not be modified.
* = 'N': The matrix will be copied to DLF, DF, and DUF
* and factored.
*
* TRANS (input) CHARACTER*1
* Specifies the form of the system of equations:
* = 'N': A * X = B (No transpose)
* = 'T': A**T * X = B (Transpose)
* = 'C': A**H * X = B (Conjugate transpose = Transpose)
*
* 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 matrix B. NRHS >= 0.
*
* DL (input) DOUBLE PRECISION array, dimension (N1)
* The (n1) subdiagonal elements of A.
*
* D (input) DOUBLE PRECISION array, dimension (N)
* The n diagonal elements of A.
*
* DU (input) DOUBLE PRECISION array, dimension (N1)
* The (n1) superdiagonal elements of A.
*
* DLF (input or output) DOUBLE PRECISION array, dimension (N1)
* If FACT = 'F', then DLF is an input argument and on entry
* contains the (n1) multipliers that define the matrix L from
* the LU factorization of A as computed by DGTTRF.
*
* If FACT = 'N', then DLF is an output argument and on exit
* contains the (n1) multipliers that define the matrix L from
* the LU factorization of A.
*
* DF (input or output) DOUBLE PRECISION array, dimension (N)
* If FACT = 'F', then DF is an input argument and on entry
* contains the n diagonal elements of the upper triangular
* matrix U from the LU factorization of A.
*
* If FACT = 'N', then DF is an output argument and on exit
* contains the n diagonal elements of the upper triangular
* matrix U from the LU factorization of A.
*
* DUF (input or output) DOUBLE PRECISION array, dimension (N1)
* If FACT = 'F', then DUF is an input argument and on entry
* contains the (n1) elements of the first superdiagonal of U.
*
* If FACT = 'N', then DUF is an output argument and on exit
* contains the (n1) elements of the first superdiagonal of U.
*
* DU2 (input or output) DOUBLE PRECISION array, dimension (N2)
* If FACT = 'F', then DU2 is an input argument and on entry
* contains the (n2) elements of the second superdiagonal of
* U.
*
* If FACT = 'N', then DU2 is an output argument and on exit
* contains the (n2) elements of the second superdiagonal of
* U.
*
* IPIV (input or output) INTEGER array, dimension (N)
* If FACT = 'F', then IPIV is an input argument and on entry
* contains the pivot indices from the LU factorization of A as
* computed by DGTTRF.
*
* If FACT = 'N', then IPIV is an output argument and on exit
* contains the pivot indices from the LU factorization of A;
* row i of the matrix was interchanged with row IPIV(i).
* IPIV(i) will always be either i or i+1; IPIV(i) = i indicates
* a row interchange was not required.
*
* B (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS)
* If INFO = 0 or INFO = N+1, the NbyNRHS solution matrix X.
*
* LDX (input) INTEGER
* The leading dimension of the array X. LDX >= max(1,N).
*
* RCOND (output) DOUBLE PRECISION
* The estimate of 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) DOUBLE PRECISION array, dimension (NRHS)
* The estimated 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). The estimate is as reliable as
* the estimate for RCOND, and is almost always a slight
* overestimate of the true error.
*
* BERR (output) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (3*N)
*
* IWORK (workspace) INTEGER array, dimension (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: U(i,i) is exactly zero. The factorization
* has not been completed unless i = N, but the
* factor U is exactly singular, so the solution
* and error bounds could not be 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 
DGTSVX(java.lang.String fact,
java.lang.String trans,
int n,
int nrhs,
double[] dl,
double[] d,
double[] du,
double[] dlf,
double[] df,
double[] duf,
double[] du2,
int[] ipiv,
double[][] b,
double[][] x,
doubleW rcond,
double[] ferr,
double[] berr,
double[] work,
int[] iwork,
intW info)

Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
DGTSVX
public DGTSVX()
DGTSVX
public static void DGTSVX(java.lang.String fact,
java.lang.String trans,
int n,
int nrhs,
double[] dl,
double[] d,
double[] du,
double[] dlf,
double[] df,
double[] duf,
double[] du2,
int[] ipiv,
double[][] b,
double[][] x,
doubleW rcond,
double[] ferr,
double[] berr,
double[] work,
int[] iwork,
intW info)