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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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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 | ||
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CTRT03
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.
[in] | UPLO | UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular |
[in] | 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) |
[in] | DIAG | DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular |
[in] | N | N is INTEGER The order of the matrix A. N >= 0. |
[in] | NRHS | NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0. |
[in] | 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. |
[in] | LDA | LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[in] | SCALE | SCALE is REAL The scaling factor s used in solving the triangular system. |
[in] | CNORM | CNORM is REAL array, dimension (N) The 1-norms of the columns of A, not counting the diagonal. |
[in] | TSCAL | TSCAL is REAL The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A. |
[in] | X | X is COMPLEX array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations. |
[in] | LDX | LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N). |
[in] | B | B is COMPLEX array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations. |
[in] | LDB | LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). |
[out] | WORK | WORK is COMPLEX array, dimension (N) |
[out] | 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 ). |
Definition at line 169 of file ctrt03.f.