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    1:       SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
    2: *
    3: *  -- LAPACK routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       CHARACTER          UPLO
   10:       INTEGER            INFO, KD, LDAB, LDB, N, NRHS
   11: *     ..
   12: *     .. Array Arguments ..
   13:       DOUBLE PRECISION   AB( LDAB, * ), B( LDB, * )
   14: *     ..
   15: *
   16: *  Purpose
   17: *  =======
   18: *
   19: *  DPBTRS solves a system of linear equations A*X = B with a symmetric
   20: *  positive definite band matrix A using the Cholesky factorization
   21: *  A = U**T*U or A = L*L**T computed by DPBTRF.
   22: *
   23: *  Arguments
   24: *  =========
   25: *
   26: *  UPLO    (input) CHARACTER*1
   27: *          = 'U':  Upper triangular factor stored in AB;
   28: *          = 'L':  Lower triangular factor stored in AB.
   29: *
   30: *  N       (input) INTEGER
   31: *          The order of the matrix A.  N >= 0.
   32: *
   33: *  KD      (input) INTEGER
   34: *          The number of superdiagonals of the matrix A if UPLO = 'U',
   35: *          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
   36: *
   37: *  NRHS    (input) INTEGER
   38: *          The number of right hand sides, i.e., the number of columns
   39: *          of the matrix B.  NRHS >= 0.
   40: *
   41: *  AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
   42: *          The triangular factor U or L from the Cholesky factorization
   43: *          A = U**T*U or A = L*L**T of the band matrix A, stored in the
   44: *          first KD+1 rows of the array.  The j-th column of U or L is
   45: *          stored in the j-th column of the array AB as follows:
   46: *          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
   47: *          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
   48: *
   49: *  LDAB    (input) INTEGER
   50: *          The leading dimension of the array AB.  LDAB >= KD+1.
   51: *
   52: *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
   53: *          On entry, the right hand side matrix B.
   54: *          On exit, the solution matrix X.
   55: *
   56: *  LDB     (input) INTEGER
   57: *          The leading dimension of the array B.  LDB >= max(1,N).
   58: *
   59: *  INFO    (output) INTEGER
   60: *          = 0:  successful exit
   61: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   62: *
   63: *  =====================================================================
   64: *
   65: *     .. Local Scalars ..
   66:       LOGICAL            UPPER
   67:       INTEGER            J
   68: *     ..
   69: *     .. External Functions ..
   70:       LOGICAL            LSAME
   71:       EXTERNAL           LSAME
   72: *     ..
   73: *     .. External Subroutines ..
   74:       EXTERNAL           DTBSV, XERBLA
   75: *     ..
   76: *     .. Intrinsic Functions ..
   77:       INTRINSIC          MAX
   78: *     ..
   79: *     .. Executable Statements ..
   80: *
   81: *     Test the input parameters.
   82: *
   83:       INFO = 0
   84:       UPPER = LSAME( UPLO, 'U' )
   85:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
   86:          INFO = -1
   87:       ELSE IF( N.LT.0 ) THEN
   88:          INFO = -2
   89:       ELSE IF( KD.LT.0 ) THEN
   90:          INFO = -3
   91:       ELSE IF( NRHS.LT.0 ) THEN
   92:          INFO = -4
   93:       ELSE IF( LDAB.LT.KD+1 ) THEN
   94:          INFO = -6
   95:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
   96:          INFO = -8
   97:       END IF
   98:       IF( INFO.NE.0 ) THEN
   99:          CALL XERBLA( 'DPBTRS', -INFO )
  100:          RETURN
  101:       END IF
  102: *
  103: *     Quick return if possible
  104: *
  105:       IF( N.EQ.0 .OR. NRHS.EQ.0 )
  106:      $   RETURN
  107: *
  108:       IF( UPPER ) THEN
  109: *
  110: *        Solve A*X = B where A = U'*U.
  111: *
  112:          DO 10 J = 1, NRHS
  113: *
  114: *           Solve U'*X = B, overwriting B with X.
  115: *
  116:             CALL DTBSV( 'Upper', 'Transpose', 'Non-unit', N, KD, AB,
  117:      $                  LDAB, B( 1, J ), 1 )
  118: *
  119: *           Solve U*X = B, overwriting B with X.
  120: *
  121:             CALL DTBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
  122:      $                  LDAB, B( 1, J ), 1 )
  123:    10    CONTINUE
  124:       ELSE
  125: *
  126: *        Solve A*X = B where A = L*L'.
  127: *
  128:          DO 20 J = 1, NRHS
  129: *
  130: *           Solve L*X = B, overwriting B with X.
  131: *
  132:             CALL DTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
  133:      $                  LDAB, B( 1, J ), 1 )
  134: *
  135: *           Solve L'*X = B, overwriting B with X.
  136: *
  137:             CALL DTBSV( 'Lower', 'Transpose', 'Non-unit', N, KD, AB,
  138:      $                  LDAB, B( 1, J ), 1 )
  139:    20    CONTINUE
  140:       END IF
  141: *
  142:       RETURN
  143: *
  144: *     End of DPBTRS
  145: *
  146:       END