org.netlib.lapack
Class Dppsvx
java.lang.Object
org.netlib.lapack.Dppsvx
public class Dppsvx
 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
* =======
*
* DPPSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to
* compute the solution to a real system of linear equations
* A * X = B,
* where A is an NbyN symmetric positive definite matrix stored in
* packed format 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 = 'E', real scaling factors are computed to equilibrate
* the system:
* diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * 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(S)*A*diag(S) and B by diag(S)*B.
*
* 2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
* factor the matrix A (after equilibration if FACT = 'E') as
* A = U**T* U, if UPLO = 'U', or
* A = L * L**T, if UPLO = 'L',
* where U is an upper triangular matrix and L is a lower triangular
* matrix.
*
* 3. If the leading ibyi principal minor is not positive definite,
* 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.
*
* 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(S) 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, AFP contains the factored form of A.
* If EQUED = 'Y', the matrix A has been equilibrated
* with scaling factors given by S. AP and AFP will not
* be modified.
* = 'N': The matrix A will be copied to AFP and factored.
* = 'E': The matrix A will be equilibrated if necessary, then
* 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/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
* On entry, the upper or lower triangle of the symmetric matrix
* A, packed columnwise in a linear array, except if FACT = 'F'
* and EQUED = 'Y', then A must contain the equilibrated matrix
* diag(S)*A*diag(S). The jth column of A is stored in the
* array AP as follows:
* if UPLO = 'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j;
* if UPLO = 'L', AP(i + (j1)*(2nj)/2) = A(i,j) for j<=i<=n.
* See below for further details. A is not modified if
* FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit.
*
* On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by
* diag(S)*A*diag(S).
*
* 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 triangular factor U or L from the Cholesky
* factorization A = U'*U or A = L*L', in the same storage
* format as A. If EQUED .ne. 'N', then AFP is the factored
* form of the equilibrated matrix A.
*
* If FACT = 'N', then AFP is an output argument and on exit
* returns the triangular factor U or L from the Cholesky
* factorization A = U'*U or A = L*L' of the original matrix A.
*
* If FACT = 'E', then AFP is an output argument and on exit
* returns the triangular factor U or L from the Cholesky
* factorization A = U'*U or A = L*L' of the equilibrated
* matrix A (see the description of AP for the form of the
* equilibrated matrix).
*
* EQUED (input or output) CHARACTER*1
* Specifies the form of equilibration that was done.
* = 'N': No equilibration (always true if FACT = 'N').
* = 'Y': Equilibration was done, i.e., A has been replaced by
* diag(S) * A * diag(S).
* EQUED is an input argument if FACT = 'F'; otherwise, it is an
* output argument.
*
* S (input or output) DOUBLE PRECISION array, dimension (N)
* The scale factors for A; not accessed if EQUED = 'N'. S is
* an input argument if FACT = 'F'; otherwise, S is an output
* argument. If FACT = 'F' and EQUED = 'Y', each element of S
* must be positive.
*
* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
* On entry, the NbyNRHS right hand side matrix B.
* On exit, if EQUED = 'N', B is not modified; if EQUED = 'Y',
* B is overwritten by diag(S) * 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 to
* the original system of equations. Note that if EQUED = 'Y',
* A and B are modified on exit, and the solution to the
* equilibrated system is inv(diag(S))*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 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.
*
* 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: the leading minor of order i of A is
* not positive definite, so the factorization
* could not be completed, and the solution has not
* been 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.
*
* Further Details
* ===============
*
* The packed storage scheme is illustrated by the following example
* when N = 4, UPLO = 'U':
*
* Twodimensional storage of the symmetric matrix A:
*
* a11 a12 a13 a14
* a22 a23 a24
* a33 a34 (aij = conjg(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 
dppsvx(java.lang.String fact,
java.lang.String uplo,
int n,
int nrhs,
double[] ap,
int _ap_offset,
double[] afp,
int _afp_offset,
StringW equed,
double[] s,
int _s_offset,
double[] b,
int _b_offset,
int ldb,
double[] x,
int _x_offset,
int ldx,
doubleW rcond,
double[] ferr,
int _ferr_offset,
double[] berr,
int _berr_offset,
double[] 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 
Dppsvx
public Dppsvx()
dppsvx
public static void dppsvx(java.lang.String fact,
java.lang.String uplo,
int n,
int nrhs,
double[] ap,
int _ap_offset,
double[] afp,
int _afp_offset,
StringW equed,
double[] s,
int _s_offset,
double[] b,
int _b_offset,
int ldb,
double[] x,
int _x_offset,
int ldx,
doubleW rcond,
double[] ferr,
int _ferr_offset,
double[] berr,
int _berr_offset,
double[] work,
int _work_offset,
int[] iwork,
int _iwork_offset,
intW info)