DTBTRS (3lapack)

solve a triangular system of the form A * X = B or A**T * X = B,

SYNOPSIS

  SUBROUTINE DTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, INFO )

      CHARACTER      DIAG, TRANS, UPLO

      INTEGER        INFO, KD, LDAB, LDB, N, NRHS

      DOUBLE         PRECISION AB( LDAB, * ), B( LDB, * )

PURPOSE

  DTBTRS solves a triangular system of the form

  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 the system of equations:
          = 'N':  A * X = B  (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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.