TESTING/LIN/stpt02.f(3)

💅 TESTING/LIN/stpt02.f(3) 💅

okay bestie, welcome to the Library Functions Manual page for TESTING/LIN/stpt02.f(3). yes we are deep in the Fortran testing docs and it's giving main character energy. 💖

🦋 NAME 🦋

TESTING/LIN/stpt02.f — that's the file, periodt. 🫶

✨ SYNOPSIS ✨

💫 Functions/Subroutines 💫

subroutine stpt02 (uplo, trans, diag, n, nrhs, ap, x, ldx, b, ldb, work,
     resid)

STPT02 — iconic, no cap. 🌈

💖 Function/Subroutine Documentation 💖

subroutine stpt02 (character uplo, character trans, character diag, integer
     n, integer nrhs, real, dimension( * ) ap, real, dimension( ldx, * ) x,
     integer ldx, real, dimension( ldb, * ) b, integer ldb, real, dimension(
     * ) work, real resid)

STPT02 💅

🌸 Purpose 🌸

okay so here's the tea, bestie: STPT02 computes the residual for the computed solution to a triangular system of linear equations op(A)*X = B, when the triangular matrix A is stored in packed format. The test ratio is the maximum over

norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS )

where op(A) = A or A**T, b is the column of B, x is the solution vector, and EPS is the machine epsilon.

The norm used is the 1-norm. ⭐

🎀 Parameters 🎀

• UPLO — CHARACTER*1. Specifies whether the matrix A is upper or lower triangular. The values are:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — CHARACTER*1. Specifies the operation applied to A. The values are:
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose = Transpose)
• DIAG — CHARACTER*1. Specifies whether or not the matrix A is unit triangular. The values are:
  • = '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. 🫶
• AP — 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.

• 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 - B) / ( norm(op(A)) * norm(X) * EPS ). 🔥

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 140 of file stpt02.f.

👑 Author 👑

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