SRC/zspsv.f(3)             Library Functions Manual             SRC/zspsv.f(3)

NAME
       SRC/zspsv.f

SYNOPSIS
   Functions/Subroutines
       subroutine zspsv (uplo, n, nrhs, ap, ipiv, b, ldb, info)
            ZSPSV computes the solution to system of linear equations A * X =
           B for OTHER matrices

Function/Subroutine Documentation
   subroutine zspsv (character uplo, integer n, integer nrhs, complex*16,
       dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension(
       ldb, * ) b, integer ldb, integer info)
        ZSPSV computes the solution to system of linear equations A * X = B
       for OTHER matrices

       Purpose:


           !>
           !> ZSPSV computes the solution to a complex 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 COMPLEX*16 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 ZSPTRF, 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 ZSPTRF.  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 COMPLEX*16 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.

       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 161 of file zspsv.f.

Author
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LAPACK                          Version 3.12.0                  SRC/zspsv.f(3)