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 CPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )

           CHARACTER     UPLO

           INTEGER       INFO, KD, LDAB, LDB, N, NRHS

           COMPLEX       AB( LDAB, * ), B( LDB, * )

PURPOSE

       CPBSV computes the solution to a complex system of linear equations
          A * X = B,
        where A is an N-by-N Hermitian positive definite band matrix and X
        and B are N-by-NRHS matrices.
        The Cholesky decomposition is used to factor A as
           A = U**H * U,  if UPLO = 'U', or
           A = L * L**H,  if UPLO = 'L',
        where U is an upper triangular band matrix, and L is a lower
        triangular band matrix, with the same number of superdiagonals or
        subdiagonals as A.  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.

        KD      (input) INTEGER
                The number of superdiagonals of the matrix A if UPLO = 'U',
                or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

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

        AB      (input/output) COMPLEX array, dimension (LDAB,N)
                On entry, the upper or lower triangle of the Hermitian band
                matrix A, stored in the first KD+1 rows of the array.  The
                j-th column of A is stored in the j-th column of the array AB
                as follows:
                if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
                if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(N,j+KD).
                See below for further details.
                On exit, if INFO = 0, the triangular factor U or L from the
                Cholesky factorization A = U**H*U or A = L*L**H of the band
                matrix A, in the same storage format as A.

        LDAB    (input) INTEGER
                The leading dimension of the array AB.  LDAB >= KD+1.

        B       (input/output) COMPLEX 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, the leading minor of order i of A is not
                positive definite, so the factorization could not be
                completed, and the solution has not been computed.

FURTHER DETAILS

        The band storage scheme is illustrated by the following example, when
        N = 6, KD = 2, and UPLO = 'U':
        On entry:                       On exit:
            *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
            *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
           a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
        Similarly, if UPLO = 'L' the format of A is as follows:
        On entry:                       On exit:
           a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
           a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
           a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
        Array elements marked * are not used by the routine.

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