CTRT03(3)

💅 NAME 💅

Okay bestie, welcome to the ctrt03.f(3) page in the Library Functions Manual — manual name folded in right here at the top, as requested. It’s giving test-routine realness, and the file this page is repping is literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ctrt03.f

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine CTRT03 (uplo, trans, diag, n, nrhs, a, lda, scale, cnorm,
    tscal, x, ldx, b, ldb, work, resid)

CTRT03 is the function/subroutine we’re serving on this page. Main character energy, honestly.

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💖 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)

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. In this little situation: A is a triangular matrix, A**T means the transpose of A, A**H means 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) means A, A**T, or A**H, and EPS is the machine epsilon. Math is mathing. ✨

Parameters

• UPLO — CHARACTER*1. This one says whether matrix A is upper or lower triangular. = 'U': upper triangular. = 'L': lower triangular.
• TRANS — CHARACTER*1. This one says which operation gets 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 — CHARACTER*1. This one says whether A is unit triangular or not. = 'N': non-unit triangular. = 'U': unit triangular.
• N — INTEGER. The order of matrix A. Requirement: N >= 0.
• NRHS — INTEGER. The number of right hand sides, aka how many columns X and B have. Requirement: NRHS >= 0.
• A — COMPLEX array, dimension (LDA,N). The triangular matrix A. If UPLO = 'U', the leading n by n upper triangular part of 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 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 — INTEGER. The leading dimension of array A. Requirement: LDA >= max(1,N).
• SCALE — REAL. The scaling factor s used in solving the triangular system.
• CNORM — REAL array, dimension (N). The 1-norms of the columns of A, not counting the diagonal.
• TSCAL — REAL. The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.
• X — COMPLEX array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
• LDX — INTEGER. The leading dimension of array X. Requirement: LDX >= max(1,N).
• B — COMPLEX array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — INTEGER. The leading dimension of array B. Requirement: LDB >= max(1,N).
• WORK — COMPLEX array, dimension (N).
• RESID — 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 ✨

Generated automatically by Doxygen for LAPACK from the source code.

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