LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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spbrfs.f File Reference

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Function/Subroutine Documentation

subroutine spbrfs ( character  UPLO,
integer  N,
integer  KD,
integer  NRHS,
real, dimension( ldab, * )  AB,
integer  LDAB,
real, dimension( ldafb, * )  AFB,
integer  LDAFB,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( ldx, * )  X,
integer  LDX,
real, dimension( * )  FERR,
real, dimension( * )  BERR,
real, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  INFO 


Download SPBRFS + dependencies [TGZ] [ZIP] [TXT]
 SPBRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is symmetric positive definite
 and banded, and provides error bounds and backward error estimates
 for the solution.
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.
          N is INTEGER
          The order of the matrix A.  N >= 0.
          KD is INTEGER
          The number of superdiagonals of the matrix A if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.
          AB is REAL array, dimension (LDAB,N)
          The upper or lower triangle of the symmetric band matrix A,
          stored in the first KD+1 rows of the array.  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).
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
          AFB is REAL array, dimension (LDAFB,N)
          The triangular factor U or L from the Cholesky factorization
          A = U**T*U or A = L*L**T of the band matrix A as computed by
          SPBTRF, in the same storage format as A (see AB).
          LDAFB is INTEGER
          The leading dimension of the array AFB.  LDAFB >= KD+1.
          B is REAL array, dimension (LDB,NRHS)
          The right hand side matrix B.
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
          X is REAL array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by SPBTRS.
          On exit, the improved solution matrix X.
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
          FERR is REAL 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 is REAL 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 is REAL array, dimension (3*N)
          IWORK is INTEGER array, dimension (N)
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Internal Parameters:
  ITMAX is the maximum number of steps of iterative refinement.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
November 2011

Definition at line 189 of file spbrfs.f.

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