Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - computes the solution to a complex system of linear equations  A * X = B,

SYNOPSIS

       SUBROUTINE ZHPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )

           CHARACTER     UPLO

           INTEGER       INFO, LDB, N, NRHS

           INTEGER       IPIV( * )

           COMPLEX*16    AP( * ), B( LDB, * )

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.

ARGUMENTS

        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 matrix B.  NRHS >= 0.

        AP      (input/output) 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    (output) 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       (input/output) 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     (input) INTEGER
                The leading dimension of the array B.  LDB >= max(1,N).

        INFO    (output) 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.

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 ]

 LAPACK driver routine (version 3.3.1)      April 2011                             ZHPSV(3lapack)