CQRT17(3)

✨ NAME ✨

okay bestie, you're looking at CQRT17(3) from the Library Functions Manual 💅 — and the source file for this whole thing is literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/cqrt17.f

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

       real function CQRT17 (trans, iresid, m, n, nrhs, a, lda, x, ldx, b, ldb,
           c, work, lwork)
           CQRT17

💅 Function/Subroutine Documentation 💅

   real function CQRT17 (character trans, integer iresid, integer m, integer n,
       integer nrhs, complex, dimension( lda, * ) a, integer lda, complex,
       dimension( ldx, * ) x, integer ldx, complex, dimension( ldb, * ) b,
       integer ldb, complex, dimension( ldb, * ) c, complex, dimension( lwork )
       work, integer lwork)
       CQRT17

🎀 Purpose 🎀

okay so what does CQRT17 actually compute? It's this ratio, no cap:

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

where R = B - op(A)*X, op(A) is A or A**H, depending on TRANS, and EPS is the machine epsilon. Then the alpha tea is:

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

And the norm used is the 1-norm. periodt 💅

🦋 Parameters 🦋

🦋 TRANS

TRANS is CHARACTER*1 and it decides whether the transpose of A is used. The values are:

• 'N': no transpose, so op(A) = A.
• 'C': conjugate transpose, so op(A) = A**H.

🦋 IRESID

IRESID is INTEGER. The tea is:

• IRESID = 1 means zero-residual problem.
• IRESID = 2 means non-zero residual.

🦋 M

M is INTEGER.

It's the number of rows of the matrix A.

If TRANS = 'N', it's the number of rows of the matrix B.

If TRANS = 'C', it's the number of rows of the matrix X.

🦋 N

N is INTEGER.

It's the number of columns of the matrix A.

If TRANS = 'N', it's the number of rows of the matrix X.

If TRANS = 'C', it's the number of rows of the matrix B.

🦋 NRHS

NRHS is INTEGER.

It's the number of columns of the matrices X and B.

🦋 A

A is COMPLEX array, dimension (LDA,N).

It's the m-by-n matrix A.

🦋 LDA

LDA is INTEGER.

It's the leading dimension of the array A. LDA >= M.

🦋 X

X is COMPLEX array, dimension (LDX,NRHS).

If TRANS = 'N', it's the n-by-nrhs matrix X.

If TRANS = 'C', it's the m-by-nrhs matrix X.

🦋 LDX

LDX is INTEGER.

It's the leading dimension of the array X.

If TRANS = 'N', LDX >= N.

If TRANS = 'C', LDX >= M.

🦋 B

B is COMPLEX array, dimension (LDB,NRHS).

If TRANS = 'N', it's the m-by-nrhs matrix B.

If TRANS = 'C', it's the n-by-nrhs matrix B.

🦋 LDB

LDB is INTEGER.

It's the leading dimension of the array B.

If TRANS = 'N', LDB >= M.

If TRANS = 'C', LDB >= N.

🦋 C

C is COMPLEX array, dimension (LDB,NRHS).

That's the whole note in the source, bestie — no extra description here.

🦋 WORK

WORK is COMPLEX array, dimension (LWORK).

🦋 LWORK

LWORK is INTEGER.

It's 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 cqrt17.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo 💖 — footer tea: source/version is LAPACK Version 3.12.0, and the page path is /home/abui...IN/cqrt17.f(3). date? not printed in this footer, bestie — no fake dates here. 🫶✨