TESTING/LIN/ctrt03.f(3) | Library Functions Manual | TESTING/LIN/ctrt03.f(3) |
NAME
TESTING/LIN/ctrt03.f
SYNOPSIS
Functions/Subroutines
subroutine ctrt03 (uplo, trans, diag, n, nrhs, a, lda,
scale, cnorm, tscal, x, ldx, b, ldb, work, resid)
CTRT03
Function/Subroutine Documentation
subroutine ctrt03 (character uplo, character trans, character diag, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, real scale, real, dimension( * ) cnorm, real tscal, complex, dimension( ldx, * ) x, integer ldx, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, real resid)
CTRT03
Purpose:
CTRT03 computes the residual for the solution to a scaled triangular system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b. Here A is a triangular matrix, A**T denotes the transpose of A, A**H denotes the conjugate transpose of A, s is a scalar, and x and b are N by NRHS matrices. The test ratio is the maximum over the number of right hand sides of norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), where op(A) denotes A, A**T, or A**H, 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 = s*b (No transpose) = 'T': A**T *x = s*b (Transpose) = 'C': A**H *x = s*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).
SCALE
SCALE is REAL The scaling factor s used in solving the triangular system.
CNORM
CNORM is REAL array, dimension (N) The 1-norms of the columns of A, not counting the diagonal.
TSCAL
TSCAL is REAL The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.
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)
RESID
RESID is REAL The maximum over the number of right hand sides of norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 169 of file ctrt03.f.
Author
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