# ctrt02.f - Man Page

TESTING/LIN/ctrt02.f

## Synopsis

### Functions/Subroutines

subroutine **ctrt02** (uplo, trans, diag, n, nrhs, a, lda, x, ldx, b, ldb, work, rwork, resid)**CTRT02**

## Function/Subroutine Documentation

### subroutine ctrt02 (character uplo, character trans, character diag, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldx, * ) x, integer ldx, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, real, dimension( * ) rwork, real resid)

**CTRT02**

**Purpose:**

CTRT02 computes the residual for the computed solution to a triangular system of linear equations op(A)*X = B, where A is a triangular matrix. The test ratio is the maximum over norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ), where op(A) = A, A**T, or A**H, b is the column of B, x is the solution vector, and EPS is the machine epsilon.

**Parameters***UPLO*UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular

*TRANS*TRANS is CHARACTER*1 Specifies the operation applied to A. = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose)

*DIAG*DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular

*N*N is INTEGER The order of the matrix A. N >= 0.

*NRHS*NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.

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

*X*X is COMPLEX array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.

*LDX*LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).

*B*B is COMPLEX array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.

*LDB*LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).

*WORK*WORK is COMPLEX array, dimension (N)

*RWORK*RWORK is REAL array, dimension (N)

*RESID*RESID is REAL The maximum over the number of right hand sides of norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **153** of file **ctrt02.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page ctrt02(3) is an alias of ctrt02.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK