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ssysvx (3)
  • >> ssysvx (3) ( Solaris man: Библиотечные вызовы )
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    NAME
         ssysvx - use the diagonal pivoting factorization to  compute
         the solution to a real system of linear equations A * X = B,
    
    SYNOPSIS
         SUBROUTINE SSYSVX( FACT, UPLO, N, NRHS, A,  LDA,  AF,  LDAF,
                   IPIV,  B,  LDB,  X,  LDX, RCOND, FERR, BERR, WORK,
                   LWORK, IWORK, INFO )
    
         CHARACTER FACT, UPLO
    
         INTEGER INFO, LDA, LDAF, LDB, LDX, LWORK, N, NRHS
    
         REAL RCOND
    
         INTEGER IPIV( * ), IWORK( * )
    
         REAL A( LDA, * ), AF( LDAF, * ), B( LDB, *  ),  BERR(  *  ),
                   FERR( * ), WORK( * ), X( LDX, * )
    
    
    
         #include <sunperf.h>
    
         void ssysvx(char fact, char uplo, int  n,  int  nrhs,  float
                   *sa,  int  lda,  float *af, int ldaf, int *ipivot,
                   float *sb, int ldb,  float  *sx,  int  ldx,  float
                   *srcond, float *ferr, float *berr, int *info);
    
    PURPOSE
         SSYSVX 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. 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, steps  3  and  4  are
         skipped.
    
         3. The system of equations is solved for X  using  the  fac-
         tored 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) REAL array, dimension (LDA,N)
                   The symmetric matrix A.  If UPLO = 'U', the  lead-
                   ing 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 refer-
                   enced.  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  tri-
                   angular part of A is not referenced.
    
         LDA       (input) INTEGER
                   The leading dimension of  the  array  A.   LDA  >=
                   max(1,N).
    
         AF        (input or output) REAL 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 SSYTRF.
    
                   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 SSYTRF.
                   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 SSYTRF.
    
         B         (input) REAL 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) REAL array, dimension (LDX,NRHS)
                   If INFO = 0, the N-by-NRHS solution matrix X.
    
         LDX       (input) INTEGER
                   The leading dimension of  the  array  X.   LDX  >=
                   max(1,N).
    
         RCOND     (output) REAL
                   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,  and the solution and error bounds are not com-
                   puted.
    
         FERR      (output) REAL array, dimension (NRHS)
                   The estimated forward error bound for  each  solu-
                   tion  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  ele-
                   ment 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) 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      (workspace/output) REAL 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 SSYTRF.
    
         IWORK     (workspace) INTEGER array, dimension (N)
    
         INFO      (output) INTEGER
                   = 0: successful exit
                   < 0: if INFO = -i, the i-th argument had an  ille-
                   gal value
                   > 0: if INFO = i, and i is
                   <= N: D(i,i) is exactly zero.   The  factorization
                   has  has  been  completed,  but the block diagonal
                   matrix D is exactly singular, so the solution  and
                   error  bounds  could  not be computed.  = N+1: the
                   block diagonal matrix D is nonsingular, but  RCOND
                   is less than machine precision.  The factorization
                   has been completed, but the matrix is singular  to
                   working  precision,  so  the  solution  and  error
                   bounds have not been computed.
    
    
    
    


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