TESTING/LIN/ctpt03.f(3)

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version 3.12.1 · 3 versions
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🌸 NAME 🌸

TESTING/LIN/ctpt03.f — okay bestie, this is the page for that file, and it lives in the Library Functions Manual. 💖

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine ctpt03 (uplo, trans, diag, n, nrhs, ap, scale, cnorm, tscal,
    x, ldx, b, ldb, work, resid)
    CTPT03

✨ Function/Subroutine Documentation ✨

CTPT03

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

🎀 Purpose 🎀

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 means the transpose of A, A**H means 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 tells you whether matrix A is upper or lower triangular, bestie.

  • '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 says whether or not matrix A is unit triangular.

  • 'N': Non-unit triangular
  • 'U': Unit triangular

N

N is INTEGER — the order of matrix A. N >= 0. ✨

NRHS

NRHS is INTEGER — the number of right hand sides, i.e., the number of columns of 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 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 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 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 📍

Definition at line 160 of file ctpt03.f.

💜 Author 💜

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