# ctpt02.f - Man Page

TESTING/LIN/ctpt02.f

## Synopsis

### Functions/Subroutines

subroutine **ctpt02** (uplo, trans, diag, n, nrhs, ap, x, ldx, b, ldb, work, rwork, resid)**CTPT02**

## Function/Subroutine Documentation

### subroutine ctpt02 (character uplo, character trans, character diag, integer n, integer nrhs, complex, dimension( * ) ap, complex, dimension( ldx, * ) x, integer ldx, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, real, dimension( * ) rwork, real resid)

**CTPT02**

**Purpose:**

CTPT02 computes the residual for the computed solution to a triangular system of linear equations op(A)*X = B, when the triangular matrix A is stored in packed format. 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.

*AP*AP is COMPLEX array, dimension (N*(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=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)*B - B) / ( norm(op(A)) * norm(X) * EPS ).

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **145** of file **ctpt02.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page ctpt02(3) is an alias of ctpt02.f(3).

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