CTPT03(3)

💖 CTPT03(3) — the LAPACK residual-testing bestie 💖

Welcome to CTPT03(3), bestie — this is a page from the Library Functions Manual, and it's all about a LAPACK test routine that checks the residual for scaled triangular solves. No cap, it's niche but iconic. ✨

🌸 NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ctpt03.f

That's the file path this page is documenting — yes, the whole NAME section is literally just the path, and honestly? Main character energy. 🫶

🦋 SYNOPSIS

Functions/Subroutines

subroutine CTPT03 (uplo, trans, diag, n, nrhs, ap, scale, cnorm, tscal,
    x, ldx, b, ldb, work, resid)

• CTPT03 — the subroutine we're hyping up on this page.

✨ Function/Subroutine Documentation ✨

subroutine CTPT03 (character uplo, character trans, character diag, integer
       n, integer nrhs, complex, dimension( * ) ap, real scale, real,
       dimension( * ) cnorm, real tscal, complex, dimension( ldx, * ) x,
       integer ldx, complex, dimension( ldb, * ) b, integer ldb, complex,
       dimension( * ) work, real resid)

CTPT03 — okay so this is the full signature, and every argument is about to get its moment. 💅

🎀 Purpose

Okay so CTPT03 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, when the triangular matrix A is stored in packed format. Here 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.

🌸 Parameters

UPLO

UPLO is CHARACTER*1. It specifies whether the matrix A is upper or lower triangular.

• = 'U': Upper triangular
• = 'L': Lower triangular

TRANS

TRANS is CHARACTER*1. It 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

DIAG is CHARACTER*1. It 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 160 of file ctpt03.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that's the whole page 💖. Footer check: LAPACK Version 3.12.0, page path /home/abui...IN/ctpt03.f(3) — that's the source/version vibe, with no extra date listed on the page. Slay. 💅✨