zpbsv.f

          SUBROUTINE ZPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INFO, KD, LDAB, LDB, N, NRHS
    *     ..
    *     .. Array Arguments ..
          COMPLEX*16         AB( LDAB, * ), B( LDB, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZPBSV 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*16 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*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, 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.
    *
    *  =====================================================================
    *
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA, ZPBTRF, ZPBTRS
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          ELSE IF( KD.LT.0 ) THEN
             INFO = -3
          ELSE IF( NRHS.LT.0 ) THEN
             INFO = -4
          ELSE IF( LDAB.LT.KD+1 ) THEN
             INFO = -6
          ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
             INFO = -8
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'ZPBSV ', -INFO )
             RETURN
          END IF
    *
    *     Compute the Cholesky factorization A = U'*U or A = L*L'.
    *
          CALL ZPBTRF( UPLO, N, KD, AB, LDAB, INFO )
          IF( INFO.EQ.0 ) THEN
    *
    *        Solve the system A*X = B, overwriting B with X.
    *
             CALL ZPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
    *
          END IF
          RETURN
    *
    *     End of ZPBSV
    *
          END