org.netlib.lapack
Class Sgtsvx
java.lang.Object
org.netlib.lapack.Sgtsvx
public class Sgtsvx
 extends java.lang.Object
Following is the description from the original
Fortran source. For each array argument, the Java
version will include an integer offset parameter, so
the arguments may not match the description exactly.
Contact seymour@cs.utk.edu with any questions.
* ..
*
* Purpose
* =======
*
* SGTSVX 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) REAL array, dimension (N1)
* The (n1) subdiagonal elements of A.
*
* D (input) REAL array, dimension (N)
* The n diagonal elements of A.
*
* DU (input) REAL array, dimension (N1)
* The (n1) superdiagonal elements of A.
*
* DLF (input or output) REAL 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 SGTTRF.
*
* 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) REAL 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) REAL 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) REAL 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 SGTTRF.
*
* 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) 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 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) REAL
* 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) REAL 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) 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 (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 
sgtsvx(java.lang.String fact,
java.lang.String trans,
int n,
int nrhs,
float[] dl,
int _dl_offset,
float[] d,
int _d_offset,
float[] du,
int _du_offset,
float[] dlf,
int _dlf_offset,
float[] df,
int _df_offset,
float[] duf,
int _duf_offset,
float[] du2,
int _du2_offset,
int[] ipiv,
int _ipiv_offset,
float[] b,
int _b_offset,
int ldb,
float[] x,
int _x_offset,
int ldx,
floatW rcond,
float[] ferr,
int _ferr_offset,
float[] berr,
int _berr_offset,
float[] work,
int _work_offset,
int[] iwork,
int _iwork_offset,
intW info)

Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Sgtsvx
public Sgtsvx()
sgtsvx
public static void sgtsvx(java.lang.String fact,
java.lang.String trans,
int n,
int nrhs,
float[] dl,
int _dl_offset,
float[] d,
int _d_offset,
float[] du,
int _du_offset,
float[] dlf,
int _dlf_offset,
float[] df,
int _df_offset,
float[] duf,
int _duf_offset,
float[] du2,
int _du2_offset,
int[] ipiv,
int _ipiv_offset,
float[] b,
int _b_offset,
int ldb,
float[] x,
int _x_offset,
int ldx,
floatW rcond,
float[] ferr,
int _ferr_offset,
float[] berr,
int _berr_offset,
float[] work,
int _work_offset,
int[] iwork,
int _iwork_offset,
intW info)