org.netlib.lapack
Class DSYSVX
java.lang.Object
org.netlib.lapack.DSYSVX
public class DSYSVX
- extends java.lang.Object
DSYSVX is a simplified interface to the JLAPACK routine dsysvx.
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
* =======
*
* DSYSVX uses the diagonal pivoting factorization to compute the
* solution to a real system of linear equations A * X = B,
* where A is an N-by-N symmetric 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 = 'N', the diagonal pivoting method is used to factor A.
* The form of the factorization is
* A = U * D * U**T, if UPLO = 'U', or
* A = L * D * L**T, if UPLO = 'L',
* where U (or L) is a product of permutation and unit upper (lower)
* triangular matrices, and D is symmetric and block diagonal with
* 1-by-1 and 2-by-2 diagonal blocks.
*
* 2. If some D(i,i)=0, so that D 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': On entry, AF and IPIV contain the factored form of
* A. AF and IPIV will not be modified.
* = 'N': The matrix A will be copied to AF and factored.
*
* UPLO (input) CHARACTER*1
* = 'U': Upper triangle of A is stored;
* = 'L': Lower triangle of A is stored.
*
* 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) DOUBLE PRECISION array, dimension (LDA,N)
* The symmetric matrix A. If UPLO = 'U', the leading N-by-N
* upper triangular part of A contains the upper triangular part
* of the matrix A, and the strictly lower triangular part of A
* is not referenced. If UPLO = 'L', the leading N-by-N lower
* triangular part of A contains the lower triangular part of
* the matrix A, and the strictly upper triangular part of A is
* not referenced.
*
* 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 block diagonal matrix D and the multipliers used
* to obtain the factor U or L from the factorization
* A = U*D*U**T or A = L*D*L**T as computed by DSYTRF.
*
* If FACT = 'N', then AF is an output argument and on exit
* returns the block diagonal matrix D and the multipliers used
* to obtain the factor U or L from the factorization
* A = U*D*U**T or A = L*D*L**T.
*
* 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 details of the interchanges and the block structure
* of D, as determined by DSYTRF.
* If IPIV(k) > 0, then rows and columns k and IPIV(k) were
* interchanged and D(k,k) is a 1-by-1 diagonal block.
* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) =
* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
*
* If FACT = 'N', then IPIV is an output argument and on exit
* contains details of the interchanges and the block structure
* of D, as determined by DSYTRF.
*
* B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
* The N-by-NRHS 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 N-by-NRHS 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 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 (LWORK)
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
* LWORK (input) INTEGER
* The length of WORK. LWORK >= 3*N, and for best performance
* LWORK >= N*NB, where NB is the optimal blocksize for
* DSYTRF.
*
* If LWORK = -1, then a workspace query is assumed; the routine
* only calculates the optimal size of the WORK array, returns
* this value as the first entry of the WORK array, and no error
* message related to LWORK is issued by XERBLA.
*
* IWORK (workspace) INTEGER array, dimension (N)
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
* > 0: if INFO = i, and i is
* <= N: D(i,i) is exactly zero. The factorization
* has been completed but the factor D is exactly
* singular, so the solution and error bounds could
* not be computed. RCOND = 0 is returned.
* = N+1: D 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 |
DSYSVX(java.lang.String fact,
java.lang.String uplo,
int n,
int nrhs,
double[][] a,
double[][] af,
int[] ipiv,
double[][] b,
double[][] x,
doubleW rcond,
double[] ferr,
double[] berr,
double[] work,
int lwork,
int[] iwork,
intW info)
|
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
DSYSVX
public DSYSVX()
DSYSVX
public static void DSYSVX(java.lang.String fact,
java.lang.String uplo,
int n,
int nrhs,
double[][] a,
double[][] af,
int[] ipiv,
double[][] b,
double[][] x,
doubleW rcond,
double[] ferr,
double[] berr,
double[] work,
int lwork,
int[] iwork,
intW info)