org.netlib.lapack
Class DSPSVX
java.lang.Object
org.netlib.lapack.DSPSVX
public class DSPSVX
- extends java.lang.Object
DSPSVX is a simplified interface to the JLAPACK routine dspsvx.
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
* =======
*
* DSPSVX uses the diagonal pivoting factorization A = U*D*U**T or
* A = L*D*L**T to compute the solution to a real system of linear
* equations A * X = B, where A is an N-by-N symmetric matrix stored
* in packed format 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 as
* 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, AFP and IPIV contain the factored form of
* A. AP, AFP and IPIV will not be modified.
* = 'N': The matrix A will be copied to AFP 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.
*
* AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
* The upper or lower triangle of the symmetric matrix A, packed
* columnwise in a linear array. The j-th column of A is stored
* in the array AP as follows:
* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
* See below for further details.
*
* AFP (input or output) DOUBLE PRECISION array, dimension
* (N*(N+1)/2)
* If FACT = 'F', then AFP 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 DSPTRF, stored as
* a packed triangular matrix in the same storage format as A.
*
* If FACT = 'N', then AFP is an output argument and on exit
* 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 DSPTRF, stored as
* a packed triangular matrix in the same storage format as A.
*
* 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 DSPTRF.
* 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 DSPTRF.
*
* 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) DOUBLE PRECISION array, dimension (3*N)
*
* 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.
*
* Further Details
* ===============
*
* The packed storage scheme is illustrated by the following example
* when N = 4, UPLO = 'U':
*
* Two-dimensional storage of the symmetric matrix A:
*
* a11 a12 a13 a14
* a22 a23 a24
* a33 a34 (aij = aji)
* a44
*
* Packed storage of the upper triangle of A:
*
* AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
*
* =====================================================================
*
* .. Parameters ..
|
Method Summary |
static void |
DSPSVX(java.lang.String fact,
java.lang.String uplo,
int n,
int nrhs,
double[] ap,
double[] afp,
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 |
DSPSVX
public DSPSVX()
DSPSVX
public static void DSPSVX(java.lang.String fact,
java.lang.String uplo,
int n,
int nrhs,
double[] ap,
double[] afp,
int[] ipiv,
double[][] b,
double[][] x,
doubleW rcond,
double[] ferr,
double[] berr,
double[] work,
int[] iwork,
intW info)