LATBS - 5.2 English - 68552

LATBS solves a triangular banded system of equations.

Purpose:

   LATBS solves one of the triangular systems

      A *x = s*b  or  A**T*x = s*b

   with scaling to prevent overflow, where A is an upper or lower
   triangular band matrix.  Here A**T denotes the transpose of A, x and b
   are n-element vectors, and s is a scaling factor, usually less than
   or equal to 1, chosen so that the components of x will be less than
   the overflow threshold.  If the unscaled problem will not cause
   overflow, the Level 2 BLAS routine STBSV is called.  If the matrix A
   is singular (A(j,j) = 0 for some j), then s is set to 0 and a
   non-trivial solution to A*x = 0 is   returned.

Parameters:

• UPLO – [in]

  UPLO is CHARACTER*1

  Specifies whether the matrix A is upper or lower triangular.

  = ‘U’: Upper triangular

  = ‘L’: Lower triangular

• TRANS – [in]

  TRANS is CHARACTER*1

  Specifies the operation applied to A.

  = ‘N’: Solve A * x = s*b (No transpose)

  = ‘T’: Solve A**T* x = s*b (Transpose)

  = ‘C’: Solve A**T* x = s*b (Conjugate transpose = Transpose)

• DIAG – [in]

  DIAG is CHARACTER*1

  Specifies whether or not the matrix A is unit triangular.

  = ‘N’: Non-unit triangular

  = ‘U’: Unit triangular

• NORMIN – [in]

  NORMIN is CHARACTER*1

  Specifies whether CNORM has been set or not.

  = ‘Y’: CNORM contains the column norms on entry

  = ‘N’: CNORM is not set on entry. On exit, the norms will be computed and stored in CNORM.

• N – [in]

  N is INTEGER

  The order of the matrix A. N >= 0.

• KD – [in]

  KD is INTEGER

  The number of subdiagonals or superdiagonals in the triangular matrix A. KD >= 0.

• AB – [in]

  AB is REAL array, dimension (LDAB,N)

  The upper or lower triangular 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 fla_max(1,j-kd)<=i<=j;

  if UPLO = ‘L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

• LDAB – [in]

  LDAB is INTEGER

  The leading dimension of the array AB. LDAB >= KD+1.

• X – [inout]

  X is REAL array, dimension (N)

  On entry, the right hand side b of the triangular system. On exit, X is overwritten by the solution vector x.

• SCALE – [out]

  SCALE is REAL

  The scaling factor s for the triangular system

  A * x = s*b or A**T* x = s*b.

  If SCALE = 0, the matrix A is singular or badly scaled, and the vector x is an exact or approximate solution to A*x = 0.

• CNORM – [inout]

  CNORM is REAL array, dimension (N)

  If NORMIN = ‘Y’, CNORM is an input argument and CNORM(j) contains the norm of the off-diagonal part of the j-th column of A. If TRANS = ‘N’, CNORM(j) must be greater than or equal to the infinity-norm, and if TRANS = ‘T’ or ‘C’, CNORM(j) must be greater than or equal to the 1-norm.

  If NORMIN = ‘N’, CNORM is an output argument and CNORM(j) returns the 1-norm of the offdiagonal part of the j-th column of A.

• INFO – [out]

  INFO is INTEGER

  = 0: successful exit

  < 0: if INFO = -k, the k-th argument had an illegal value