ZTRT03(3)

okay so bestie, this page comes from the Library Functions Manual, and it is literally all about the ZTRT03 subroutine in ztrt03.f. It is giving LAPACK testing energy, and we are obsessed. 💅✨

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ztrt03.f — that is the file path, and that is the whole NAME section. periodt. 🫶

🌸 SYNOPSIS 🌸

🦋 Functions/Subroutines 🦋

subroutine ZTRT03 (uplo, trans, diag, n, nrhs, a, lda, scale, cnorm,
    tscal, x, ldx, b, ldb, work, resid)
    ZTRT03

🫶 Function/Subroutine Documentation 🫶

subroutine ZTRT03 (character uplo, character trans, character diag, integer
    n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, double
    precision scale, double precision, dimension( * ) cnorm, double
    precision tscal, complex*16, dimension( ldx, * ) x, integer ldx,
    complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( *
    ) work, double precision resid)
    ZTRT03

💖 Purpose 💖

okay so ZTRT03 computes the residual for the solution to a scaled triangular system of equations. The systems in question are 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. That's the whole purpose, and it ate. 🔥

🌈 Parameters 🌈

• UPLO — CHARACTER*1. Specifies whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — 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 — CHARACTER*1. Specifies whether or not the matrix A is unit triangular.
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular
• N — INTEGER. The order of the matrix A. N >= 0.
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
• A — COMPLEX*16 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• SCALE — DOUBLE PRECISION. The scaling factor s used in solving the triangular system.
• CNORM — DOUBLE PRECISION array, dimension (N). The 1-norms of the columns of A, not counting the diagonal.
• TSCAL — DOUBLE PRECISION. The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.
• X — COMPLEX*16 array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• B — COMPLEX*16 array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• WORK — COMPLEX*16 array, dimension (N). That's it — array time. 🫶
• RESID — DOUBLE PRECISION. 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 ztrt03.f 📌

Definition at line 169 of file ztrt03.f.

🤖 Author (Doxygen’s autogenerated note) 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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footer tea: this page is from LAPACK, Version 3.12.0, and the footer path is /home/abui...IN/ztrt03.f(3). That's a wrap, bestie — slay, periodt, and go compute that residual 💖✨🎀