dspsv.f(3)

NAME
dspsv.f -

SYNOPSIS

  Functions/Subroutines

subroutine dspsv (UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
DSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Function/Subroutine Documentation

  subroutine dspsv (characterUPLO, integerN, integerNRHS, double precision, dimension( * )AP, integer, dimension( * )IPIV, double precision, dimension( ldb, * )B, integerLDB, integerINFO)

DSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

     DSPSV computes 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.

     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, D is symmetric and block diagonal with 1-by-1
     and 2-by-2 diagonal blocks.  The factored form of A is then used to
     solve the system of equations A * X = B.

Parameters:
    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
              The number of linear equations, i.e., the order of the
              matrix A.  N >= 0.

    NRHS

              NRHS is INTEGER
              The number of right hand sides, i.e., the number of columns
              of the matrix B.  NRHS >= 0.

    AP

              AP is 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.  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)*(2n-j)/2) = A(i,j) for j<=i<=n.
              See below for further details.

              On exit, 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

              IPIV is INTEGER array, dimension (N)
              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.

    B

              B is DOUBLE PRECISION array, dimension (LDB,NRHS)
              On entry, the N-by-NRHS right hand side matrix B.
              On exit, if INFO = 0, the N-by-NRHS solution matrix X.

    LDB

              LDB is INTEGER
              The leading dimension of the array B.  LDB >= max(1,N).

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value
              > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
                    has been completed, but the block diagonal matrix D is
                    exactly singular, so the solution could not be
                    computed.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

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 ]

Definition at line 163 of file dspsv.f.

Author

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