STRT03(3)

STRT03(3) 💖✨

okay so welcome to STRT03(3), bestie. This one lives in the Library Functions Manual, and the header path is /home/abui...IN/strt03.f(3). The full file path is literally down there in NAME, and the whole page is obsessed with one tiny subroutine. We are reading all of it. No skipping, no cap. 🫶

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💖 NAME 💖

This page documents this exact file path:

/home/abuild/rpmbuild/BUILD/lapack-
       static-3.12.0-build/lapack-3.12.0/TESTING/LIN/strt03.f

And the routine itself is STRT03. The page is literally named after it. iconic. 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine STRT03 (uplo, trans, diag, n, nrhs, a, lda, scale, cnorm,
           tscal, x, ldx, b, ldb, work, resid)
           STRT03

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🦋 Function/Subroutine Documentation 🦋

subroutine STRT03 (character uplo, character trans, character diag, integer
       n, integer nrhs, real, dimension( lda, * ) a, integer lda, real scale,
       real, dimension( * ) cnorm, real tscal, real, dimension( ldx, * ) x,
       integer ldx, real, dimension( ldb, * ) b, integer ldb, real, dimension(
       * ) work, real resid)
       STRT03

🌸 Purpose 🌸

STRT03 computes the residual for the solution to a scaled triangular system of equations:

A*x = s*b  or  A'*x = s*b

Here A is a triangular matrix, A' is the 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 or A' and EPS is the machine epsilon. lowkey important, highkey elegant. ✨

🎀 Parameters 🎀

• UPLO — CHARACTER*1. It specifies whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — CHARACTER*1. It specifies the operation applied to A.
  • = 'N': A *x = s*b (No transpose)
  • = 'T': A'*x = s*b (Transpose)
  • = 'C': A'*x = s*b (Conjugate transpose = Transpose)
• DIAG — CHARACTER*1. It 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 — REAL 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 — 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 — REAL 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 — REAL 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 — REAL 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 ⭐

Definition at line 167 of file strt03.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 that's the whole page, bestie. This one came from LAPACK Version 3.12.0, and the footer path was /home/abui...IN/strt03.f(3). There's no date in the footer, so I'm not inventing one — just serving the version and the path with main character energy. 👑💖