ctbtrs.f

          SUBROUTINE CTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
         $                   LDB, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          DIAG, TRANS, UPLO
          INTEGER            INFO, KD, LDAB, LDB, N, NRHS
    *     ..
    *     .. Array Arguments ..
          COMPLEX            AB( LDAB, * ), B( LDB, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CTBTRS solves a triangular system of the form
    *
    *     A * X = B,  A**T * X = B,  or  A**H * X = B,
    *
    *  where A is a triangular band matrix of order N, and B is an
    *  N-by-NRHS matrix.  A check is made to verify that A is nonsingular.
    *
    *  Arguments
    *  =========
    *
    *  UPLO    (input) CHARACTER*1
    *          = 'U':  A is upper triangular;
    *          = 'L':  A is lower triangular.
    *
    *  TRANS   (input) CHARACTER*1
    *          Specifies the form of the system of equations:
    *          = 'N':  A * X = B     (No transpose)
    *          = 'T':  A**T * X = B  (Transpose)
    *          = 'C':  A**H * X = B  (Conjugate transpose)
    *
    *  DIAG    (input) CHARACTER*1
    *          = 'N':  A is non-unit triangular;
    *          = 'U':  A is unit triangular.
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  KD      (input) INTEGER
    *          The number of superdiagonals or subdiagonals of the
    *          triangular band matrix A.  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) COMPLEX array, dimension (LDAB,N)
    *          The upper or lower triangular band matrix A, stored in the
    *          first kd+1 rows of AB.  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).
    *          If DIAG = 'U', the diagonal elements of A are not referenced
    *          and are assumed to be 1.
    *
    *  LDAB    (input) INTEGER
    *          The leading dimension of the array AB.  LDAB >= KD+1.
    *
    *  B       (input/output) COMPLEX array, dimension (LDB,NRHS)
    *          On entry, the right hand side matrix B.
    *          On exit, if INFO = 0, the 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 i-th diagonal element of A is zero,
    *                indicating that the matrix is singular and the
    *                solutions X have not been computed.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          COMPLEX            ZERO
          PARAMETER          ( ZERO = ( 0.0E+0, 0.0E+0 ) )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            NOUNIT, UPPER
          INTEGER            J
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CTBSV, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          NOUNIT = LSAME( DIAG, 'N' )
          UPPER = LSAME( UPLO, 'U' )
          IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
             INFO = -1
          ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.
         $         LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
             INFO = -2
          ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
             INFO = -3
          ELSE IF( N.LT.0 ) THEN
             INFO = -4
          ELSE IF( KD.LT.0 ) THEN
             INFO = -5
          ELSE IF( NRHS.LT.0 ) THEN
             INFO = -6
          ELSE IF( LDAB.LT.KD+1 ) THEN
             INFO = -8
          ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
             INFO = -10
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'CTBTRS', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
    *     Check for singularity.
    *
          IF( NOUNIT ) THEN
             IF( UPPER ) THEN
                DO 10 INFO = 1, N
                   IF( AB( KD+1, INFO ).EQ.ZERO )
         $            RETURN
       10       CONTINUE
             ELSE
                DO 20 INFO = 1, N
                   IF( AB( 1, INFO ).EQ.ZERO )
         $            RETURN
       20       CONTINUE
             END IF
          END IF
          INFO = 0
    *
    *     Solve A * X = B,  A**T * X = B,  or  A**H * X = B.
    *
          DO 30 J = 1, NRHS
             CALL CTBSV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, B( 1, J ), 1 )
       30 CONTINUE
    *
          RETURN
    *
    *     End of CTBTRS
    *
          END