TESTING/LIN/stpt03.f(3)

🎀 TESTING/LIN/stpt03.f(3) 🎀

okay so this page is from the Library Functions Manual, and the main character is TESTING/LIN/stpt03.f — a Fortran subroutine page that’s lowkey serving linear-algebra realness. 💅✨

✨ NAME ✨

TESTING/LIN/stpt03.f — that’s the file, bestie. 🫶

🌸 SYNOPSIS 🌸

Functions/Subroutines

       subroutine stpt03 (uplo, trans, diag, n, nrhs, ap, scale, cnorm, tscal,
           x, ldx, b, ldb, work, resid)
           STPT03

🦋 Function/Subroutine Documentation 🦋

   subroutine stpt03 (character uplo, character trans, character diag, integer
       n, integer nrhs, real, dimension( * ) ap, real scale, real, dimension( *
       ) cnorm, real tscal, real, dimension( ldx, * ) x, integer ldx, real,
       dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, real
       resid)
       STPT03

💖 Purpose 💖

STPT03 computes the residual for the solution to a scaled triangular system of equations A*x = s*b or A'*x = s*b when the triangular matrix A is stored in packed format. Here 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. 🧚✨

🎀 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'*x = s*b (Transpose)
  • = 'C': A'*x = s*b (Conjugate transpose = 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.
• AP — AP is REAL array, dimension (N*(N+1)/2). The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:

if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
if UPLO = 'L',
   AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=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 REAL 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 REAL 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 REAL 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 159 of file stpt03.f.

💜 Author 💜

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That’s the whole page, bestie. The footer says source/version LAPACK Version 3.12.0, and the date slot is blank in this copy — so no date to spill. Byeee 🫶✨