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Class org.netlib.lapack.DGESVX
java.lang.Object
|
+----org.netlib.lapack.DGESVX
- public class DGESVX
- extends Object
DGESVX is a simplified interface to the JLAPACK routine dgesvx.
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
* =======
*
* DGESVX uses the LU factorization to compute the solution to a real
* system of linear equations
* A * X = B,
* where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
*
* Error bounds on the solution and a condition estimate are also
* provided.
*
* Description
* ===========
*
* The following steps are performed:
*
* 1. If FACT = 'E', real scaling factors are computed to equilibrate
* the system:
* TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
* TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
* TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
* Whether or not the system will be equilibrated depends on the
* scaling of the matrix A, but if equilibration is used, A is
* overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
* or diag(C)*B (if TRANS = 'T' or 'C').
*
* 2. If FACT = 'N' or 'E', the LU decomposition is used to factor the
* matrix A (after equilibration if FACT = 'E') as
* A = P * L * U,
* where P is a permutation matrix, L is a unit lower triangular
* matrix, and U is upper triangular.
*
* 3. 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, steps 4-6 are skipped.
*
* 4. The system of equations is solved for X using the factored form
* of A.
*
* 5. Iterative refinement is applied to improve the computed solution
* matrix and calculate error bounds and backward error estimates
* for it.
*
* 6. If equilibration was used, the matrix X is premultiplied by
* diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
* that it solves the original system before equilibration.
*
* Arguments
* =========
*
* FACT (input) CHARACTER*1
* Specifies whether or not the factored form of the matrix A is
* supplied on entry, and if not, whether the matrix A should be
* equilibrated before it is factored.
* = 'F': On entry, AF and IPIV contain the factored form of A.
* If EQUED is not 'N', the matrix A has been
* equilibrated with scaling factors given by R and C.
* A, AF, and IPIV are not modified.
* = 'N': The matrix A will be copied to AF and factored.
* = 'E': The matrix A will be equilibrated if necessary, then
* copied to AF 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 (Transpose)
*
* N (input) INTEGER
* The number of linear equations, i.e., 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.
*
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
* On entry, the N-by-N matrix A. If FACT = 'F' and EQUED is
* not 'N', then A must have been equilibrated by the scaling
* factors in R and/or C. A is not modified if FACT = 'F' or
* 'N', or if FACT = 'E' and EQUED = 'N' on exit.
*
* On exit, if EQUED .ne. 'N', A is scaled as follows:
* EQUED = 'R': A := diag(R) * A
* EQUED = 'C': A := A * diag(C)
* EQUED = 'B': A := diag(R) * A * diag(C).
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* AF (input or output) DOUBLE PRECISION array, dimension (LDAF,N)
* If FACT = 'F', then AF is an input argument and on entry
* contains the factors L and U from the factorization
* A = P*L*U as computed by DGETRF. If EQUED .ne. 'N', then
* AF is the factored form of the equilibrated matrix A.
*
* If FACT = 'N', then AF is an output argument and on exit
* returns the factors L and U from the factorization A = P*L*U
* of the original matrix A.
*
* If FACT = 'E', then AF is an output argument and on exit
* returns the factors L and U from the factorization A = P*L*U
* of the equilibrated matrix A (see the description of A for
* the form of the equilibrated matrix).
*
* LDAF (input) INTEGER
* The leading dimension of the array AF. LDAF >= max(1,N).
*
* 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 factorization A = P*L*U
* as computed by DGETRF; row i of the matrix was interchanged
* with row IPIV(i).
*
* If FACT = 'N', then IPIV is an output argument and on exit
* contains the pivot indices from the factorization A = P*L*U
* of the original matrix A.
*
* If FACT = 'E', then IPIV is an output argument and on exit
* contains the pivot indices from the factorization A = P*L*U
* of the equilibrated matrix A.
*
* EQUED (input or output) CHARACTER*1
* Specifies the form of equilibration that was done.
* = 'N': No equilibration (always true if FACT = 'N').
* = 'R': Row equilibration, i.e., A has been premultiplied by
* diag(R).
* = 'C': Column equilibration, i.e., A has been postmultiplied
* by diag(C).
* = 'B': Both row and column equilibration, i.e., A has been
* replaced by diag(R) * A * diag(C).
* EQUED is an input argument if FACT = 'F'; otherwise, it is an
* output argument.
*
* R (input or output) DOUBLE PRECISION array, dimension (N)
* The row scale factors for A. If EQUED = 'R' or 'B', A is
* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R
* is not accessed. R is an input argument if FACT = 'F';
* otherwise, R is an output argument. If FACT = 'F' and
* EQUED = 'R' or 'B', each element of R must be positive.
*
* C (input or output) DOUBLE PRECISION array, dimension (N)
* The column scale factors for A. If EQUED = 'C' or 'B', A is
* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C
* is not accessed. C is an input argument if FACT = 'F';
* otherwise, C is an output argument. If FACT = 'F' and
* EQUED = 'C' or 'B', each element of C must be positive.
*
* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
* On entry, the N-by-NRHS right hand side matrix B.
* On exit,
* if EQUED = 'N', B is not modified;
* if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by
* diag(R)*B;
* if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is
* overwritten by diag(C)*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, the N-by-NRHS solution matrix X to the original
* system of equations. Note that A and B are modified on exit
* if EQUED .ne. 'N', and the solution to the equilibrated
* system is inv(diag(C))*X if TRANS = 'N' and EQUED = 'C' or
* 'B', or inv(diag(R))*X if TRANS = 'T' or 'C' and EQUED = 'R'
* or 'B'.
*
* 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 after equilibration (if done). 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, and the solution and
* error bounds are not computed.
*
* FERR (output) DOUBLE PRECISION array, dimension (NRHS)
* The estimated forward error bound for each solution vector
* X(j) (the j-th 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/output) DOUBLE PRECISION array, dimension (4*N)
* On exit, WORK(1) contains the reciprocal pivot growth
* factor norm(A)/norm(U). The "max absolute element" norm is
* used. If WORK(1) is much less than 1, then the stability
* of the LU factorization of the (equilibrated) matrix A
* could be poor. This also means that the solution X, condition
* estimator RCOND, and forward error bound FERR could be
* unreliable. If factorization fails with 0 0: if INFO = i, and i is
* <= N: U(i,i) is exactly zero. The factorization has
* been completed, but the factor U is exactly
* singular, so the solution and error bounds
* could not be computed.
* = N+1: RCOND is less than machine precision. The
* factorization has been completed, but the
* matrix is singular to working precision, and
* the solution and error bounds have not been
* computed.
*
* =====================================================================
*
* .. Parameters ..
-
DGESVX()
-
-
DGESVX(String, String, int, int, double[][], double[][], int[], StringW, double[], double[], double[][], double[][], doubleW, double[], double[], double[], int[], intW)
-
DGESVX
public DGESVX()
DGESVX
public static void DGESVX(String fact,
String trans,
int n,
int nrhs,
double a[][],
double af[][],
int ipiv[],
StringW equed,
double r[],
double c[],
double b[][],
double x[][],
doubleW rcond,
double ferr[],
double berr[],
double work[],
int iwork[],
intW info)
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