cpbtf2.f

          SUBROUTINE CPBTF2( UPLO, N, KD, AB, LDAB, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INFO, KD, LDAB, N
    *     ..
    *     .. Array Arguments ..
          COMPLEX            AB( LDAB, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CPBTF2 computes the Cholesky factorization of a complex Hermitian
    *  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 conjugate 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
    *          Hermitian 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) 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).
    *
    *          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 ..
          REAL               ONE, ZERO
          PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            UPPER
          INTEGER            J, KLD, KN
          REAL               AJJ
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CHER, CLACGV, CSSCAL, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, MIN, REAL, 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( 'CPBTF2', -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 = REAL( AB( KD+1, J ) )
                IF( AJJ.LE.ZERO ) THEN
                   AB( KD+1, J ) = AJJ
                   GO TO 30
                END IF
                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 CSSCAL( KN, ONE / AJJ, AB( KD, J+1 ), KLD )
                   CALL CLACGV( KN, AB( KD, J+1 ), KLD )
                   CALL CHER( 'Upper', KN, -ONE, AB( KD, J+1 ), KLD,
         $                    AB( KD+1, J+1 ), KLD )
                   CALL CLACGV( KN, AB( KD, 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 = REAL( AB( 1, J ) )
                IF( AJJ.LE.ZERO ) THEN
                   AB( 1, J ) = AJJ
                   GO TO 30
                END IF
                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 CSSCAL( KN, ONE / AJJ, AB( 2, J ), 1 )
                   CALL CHER( '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 CPBTF2
    *
          END