## org.netlib.lapack Class DPBSVX

```java.lang.Object
org.netlib.lapack.DPBSVX
```

`public class DPBSVXextends java.lang.Object`

```DPBSVX is a simplified interface to the JLAPACK routine dpbsvx.
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
*  =======
*
*  DPBSVX 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 N-by-N symmetric positive definite band 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:
*        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 band matrix, and L is a lower
*     triangular band matrix.
*
*  3. If the leading i-by-i 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, AFB contains the factored form of A.
*                  If EQUED = 'Y', the matrix A has been equilibrated
*                  with scaling factors given by S.  AB and AFB will not
*                  be modified.
*          = 'N':  The matrix A will be copied to AFB and factored.
*          = 'E':  The matrix A will be equilibrated if necessary, then

*                  copied to AFB 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.
*
*  KD      (input) INTEGER
*          The number of superdiagonals of the matrix A if UPLO = 'U',
*          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
*
*  NRHS    (input) INTEGER
*          The number of right-hand sides, i.e., the number of columns
*          of the matrices B and X.  NRHS >= 0.
*
*  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
*          On entry, the upper or lower triangle of the symmetric band
*          matrix A, stored in the first KD+1 rows of the array, except

*          if FACT = 'F' and EQUED = 'Y', then A must contain the
*          equilibrated matrix diag(S)*A*diag(S).  The j-th column of A

*          is stored in the j-th column of the array AB as follows:
*          if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(N,j+KD).
*          See below for further details.
*
*          On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by
*          diag(S)*A*diag(S).
*
*  LDAB    (input) INTEGER
*          The leading dimension of the array A.  LDAB >= KD+1.
*
*  AFB     (input or output) DOUBLE PRECISION array, dimension (LDAFB,N)
*          If FACT = 'F', then AFB is an input argument and on entry
*          contains the triangular factor U or L from the Cholesky
*          factorization A = U**T*U or A = L*L**T of the band matrix
*          A, in the same storage format as A (see AB).  If EQUED = 'Y',
*          then AFB is the factored form of the equilibrated matrix A.
*
*          If FACT = 'N', then AFB is an output argument and on exit
*          returns the triangular factor U or L from the Cholesky
*          factorization A = U**T*U or A = L*L**T.
*
*          If FACT = 'E', then AFB is an output argument and on exit
*          returns the triangular factor U or L from the Cholesky
*          factorization A = U**T*U or A = L*L**T of the equilibrated
*          matrix A (see the description of A for the form of the
*          equilibrated matrix).
*
*  LDAFB   (input) INTEGER
*          The leading dimension of the array AFB.  LDAFB >= KD+1.
*
*  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 N-by-NRHS 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 N-by-NRHS 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 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:  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 band storage scheme is illustrated by the following example, when
*  N = 6, KD = 2, and UPLO = 'U':
*
*  Two-dimensional storage of the symmetric matrix A:
*
*     a11  a12  a13
*          a22  a23  a24
*               a33  a34  a35
*                    a44  a45  a46
*                         a55  a56
*     (aij=conjg(aji))         a66
*
*  Band storage of the upper triangle of A:
*
*      *    *   a13  a24  a35  a46
*      *   a12  a23  a34  a45  a56
*     a11  a22  a33  a44  a55  a66
*
*  Similarly, if UPLO = 'L' the format of A is as follows:
*
*     a11  a22  a33  a44  a55  a66
*     a21  a32  a43  a54  a65   *
*     a31  a42  a53  a64   *    *
*
*  Array elements marked * are not used by the routine.
*
*  =====================================================================
*
*     .. Parameters ..
```

Constructor Summary
`DPBSVX()`

Method Summary
`static void` ```DPBSVX(java.lang.String fact, java.lang.String uplo, int n, int kd, int nrhs, double[][] ab, double[][] afb, StringW equed, double[] s, 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`

Constructor Detail

### DPBSVX

`public DPBSVX()`
Method Detail

### DPBSVX

```public static void DPBSVX(java.lang.String fact,
java.lang.String uplo,
int n,
int kd,
int nrhs,
double[][] ab,
double[][] afb,
StringW equed,
double[] s,
double[][] b,
double[][] x,
doubleW rcond,
double[] ferr,
double[] berr,
double[] work,
int[] iwork,
intW info)```