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

# ctrtrs(3lapack)

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

## NAME

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

## SYNOPSIS

- SUBROUTINE CTRTRS(

  UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, INFO )

- CHARACTER

  DIAG, TRANS, UPLO

- INTEGER

  INFO, LDA, LDB, N, NRHS

- COMPLEX

  A( LDA, \* ), B( LDB, \* )

## PURPOSE

CTRTRS solves a triangular system of the form where A is a triangular 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.

- NRHS (input) INTEGER

  The number of right hand sides, i.e., the number of columns of the matrix B.  NRHS \>= 0.

- A (input) COMPLEX array, dimension (LDA,N)

  The triangular matrix A.  If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced.  If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced.  If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.

- LDA (input) INTEGER

  The leading dimension of the array A.  LDA \>= max(1,N).

- 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.