TESTING/LIN/dqrt17.f(3)

okay so welcome to the TESTING/LIN/dqrt17.f(3) page in the Library Functions Manual, bestie 💖 — this is the DQRT17 documentation and we’re keeping every lil detail, no cap.

🎀 NAME

TESTING/LIN/dqrt17.f — yep, that’s the page, bestie. It’s the DQRT17 function/subroutine documentation, and it’s giving very “linear algebra tester” energy. ✨

✨ SYNOPSIS

🧚 Functions/Subroutines

double precision function dqrt17 (trans, iresid, m, n, nrhs, a, lda, x,
    ldx, b, ldb, c, work, lwork)
    DQRT17

DQRT17 is the main character here. 👑

💅 Function/Subroutine Documentation

   double precision function dqrt17 (character trans, integer iresid, integer
       m, integer n, integer nrhs, double precision, dimension( lda, * ) a,
       integer lda, double precision, dimension( ldx, * ) x, integer ldx,
       double precision, dimension( ldb, * ) b, integer ldb, double precision,
       dimension( ldb, * ) c, double precision, dimension( lwork ) work,
       integer lwork)

DQRT17 ✨

Purpose

Okay so DQRT17 computes the ratio — brace yourself, it’s a whole formula:

norm(R**T * op(A)) / ( norm(A) * alpha * max(M,N,NRHS) * EPS ),

where R = B - op(A)*X, op(A) is A or A**T, depending on TRANS, EPS is the machine epsilon, and

alpha = norm(B) if IRESID = 1 (zero-residual problem)
alpha = norm(R) if IRESID = 2 (otherwise).

The norm used is the 1-norm. Periodt. 💅

Parameters

TRANS

TRANS is CHARACTER*1 — it specifies whether or not the transpose of A is used. 🦋

• = 'N' — No transpose, op(A) = A.
• = 'T' — Transpose, op(A) = A**T.

IRESID

IRESID is INTEGER — the residual situation, lowkey important:

• IRESID = 1 — indicates zero-residual problem.
• IRESID = 2 — indicates non-zero residual.

M

M is INTEGER — the number of rows of the matrix A.

• If TRANS = 'N', the number of rows of the matrix B.
• If TRANS = 'T', the number of rows of the matrix X.

N

N is INTEGER — the number of columns of the matrix A.

• If TRANS = 'N', the number of rows of the matrix X.
• If TRANS = 'T', the number of rows of the matrix B.

NRHS

NRHS is INTEGER — the number of columns of the matrices X and B. 🌸

A

A is DOUBLE PRECISION array, dimension (LDA,N) — the m-by-n matrix A. 🫶

LDA

LDA is INTEGER — the leading dimension of the array A. LDA >= M.

X

X is DOUBLE PRECISION array, dimension (LDX,NRHS).

• If TRANS = 'N', the n-by-nrhs matrix X.
• If TRANS = 'T', the m-by-nrhs matrix X.

LDX

LDX is INTEGER — the leading dimension of the array X.

• If TRANS = 'N', LDX >= N.
• If TRANS = 'T', LDX >= M.

B

B is DOUBLE PRECISION array, dimension (LDB,NRHS).

• If TRANS = 'N', the m-by-nrhs matrix B.
• If TRANS = 'T', the n-by-nrhs matrix B.

LDB

LDB is INTEGER — the leading dimension of the array B.

• If TRANS = 'N', LDB >= M.
• If TRANS = 'T', LDB >= N.

C

C is DOUBLE PRECISION array, dimension (LDB,NRHS). 💜

WORK

WORK is DOUBLE PRECISION array, dimension (LWORK). 🧚

LWORK

LWORK is INTEGER — the length of the array WORK. LWORK >= NRHS*(M+N).

Author

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

Definition at line 151 of file dqrt17.f.

🌈 Author

Generated automatically by Doxygen for LAPACK from the source code.

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