---
name: "ctbtrs"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/ctbtrs/3lapack"
---

# ctbtrs(3lapack)

solves a triangular system of the form A \* X = B, A\*\*T \* X = B, or A\*\*H \* X = B,

## NAME

CTBTRS - solves a triangular system of the form   A \* X = B, A\*\*T \* X = B, or A\*\*H \* X = B,

## SYNOPSIS

- SUBROUTINE CTBTRS(

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

- CHARACTER

  DIAG, TRANS, UPLO

- INTEGER

  INFO, KD, LDAB, LDB, N, NRHS

- COMPLEX

  AB( LDAB, \* ), B( LDB, \* )

## PURPOSE

CTBTRS 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 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.