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

NAME
       SRC/zhpsv.f

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

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

       Purpose:


            ZHPSV computes the solution to a complex system of linear equations
               A * X = B,
            where A is an N-by-N Hermitian 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**H,  if UPLO = 'U', or
               A = L * D * L**H,  if UPLO = 'L',
            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, D is Hermitian 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 Hermitian 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**H or A = L*D*L**H as computed by ZHPTRF, 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 ZHPTRF.  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 Hermitian matrix A:

                a11 a12 a13 a14
                    a22 a23 a24
                        a33 a34     (aij = conjg(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 zhpsv.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                  SRC/zhpsv.f(3)