dpbtf2.f

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      SUBROUTINE dpbtf2( UPLO, N, KD, AB, LDAB, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     February 29, 1992
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, KD, LDAB, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AB( LDAB, * )
*     ..
*
*  Purpose
*  =======
*
*  DPBTF2 computes the Cholesky factorization of a real symmetric
*  positive definite band matrix A.
*
*  The factorization has the form
*     A = U' * U ,  if UPLO = 'U', or
*     A = L  * L',  if UPLO = 'L',
*  where U is an upper triangular matrix, U' is the transpose of U, and
*  L is lower triangular.
*
*  This is the unblocked version of the algorithm, calling Level 2 BLAS.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the upper or lower triangular part of the
*          symmetric matrix A is stored:
*          = 'U':  Upper triangular
*          = 'L':  Lower triangular
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  KD      (input) INTEGER
*          The number of super-diagonals of the matrix A if UPLO = 'U',
*          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
*
*  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
*          On entry, the upper or lower triangle of the symmetric 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).
*
*          On exit, if INFO = 0, the triangular factor U or L from the
*          Cholesky factorization A = U'*U or A = L*L' 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.
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -k, the k-th argument had an illegal value
*          > 0: if INFO = k, the leading minor of order k is not
*               positive definite, and the factorization could not be
*               completed.
*
*  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.
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      parameter( one = 1.0d+0, zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            J, KLD, KN
      DOUBLE PRECISION   AJJ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           dscal, dsyr, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min, sqrt
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      upper = lsame( uplo, 'U' )
      IF( .NOT.upper .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( ldab.LT.kd+1 ) THEN
         info = -5
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DPBTF2', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
      kld = max( 1, ldab-1 )
*
      IF( upper ) THEN
*
*        Compute the Cholesky factorization A = U'*U.
*
         DO 10 j = 1, n
*
*           Compute U(J,J) and test for non-positive-definiteness.
*
            ajj = ab( kd+1, j )
            IF( ajj.LE.zero )
     $         GO TO 30
            ajj = sqrt( ajj )
            ab( kd+1, j ) = ajj
*
*           Compute elements J+1:J+KN of row J and update the
*           trailing submatrix within the band.
*
            kn = min( kd, n-j )
            IF( kn.GT.0 ) THEN
               CALL dscal( kn, one / ajj, ab( kd, j+1 ), kld )
               CALL dsyr( 'Upper', kn, -one, ab( kd, j+1 ), kld,
     $                    ab( kd+1, j+1 ), kld )
            END IF
   10    CONTINUE
      ELSE
*
*        Compute the Cholesky factorization A = L*L'.
*
         DO 20 j = 1, n
*
*           Compute L(J,J) and test for non-positive-definiteness.
*
            ajj = ab( 1, j )
            IF( ajj.LE.zero )
     $         GO TO 30
            ajj = sqrt( ajj )
            ab( 1, j ) = ajj
*
*           Compute elements J+1:J+KN of column J and update the
*           trailing submatrix within the band.
*
            kn = min( kd, n-j )
            IF( kn.GT.0 ) THEN
               CALL dscal( kn, one / ajj, ab( 2, j ), 1 )
               CALL dsyr( 'Lower', kn, -one, ab( 2, j ), 1,
     $                    ab( 1, j+1 ), kld )
            END IF
   20    CONTINUE
      END IF
      RETURN
*
   30 CONTINUE
      info = j
      RETURN
*
*     End of DPBTF2
*
      END