lacon(3)

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💖 lacon(3) 💖

okay so bestie, welcome to lacon(3) from the Library Functions Manual — she's giving vintage LAPACK energy and I'm obsessed 💅. This page is all about four routines that estimate a 1-norm using reverse communication, and every parameter, author, reference, and definition line is staying right here, no cap ✨.

🌸 NAME 🌸

lacon — lacon: 1-norm estimate, e.g., || A^{-1} ||_1 in gecon, old

✨ SYNOPSIS ✨

🌟 Functions 🌟

subroutine clacon (n, v, x, est, kase) — CLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
subroutine dlacon (n, v, x, isgn, est, kase) — DLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
subroutine slacon (n, v, x, isgn, est, kase) — SLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
subroutine zlacon (n, v, x, est, kase) — ZLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

🦋 Detailed Description 🦋

This section is lowkey a landing pad in the original — the full tea is in Function Documentation below. Every routine here is about estimating a 1-norm with reverse communication, and each one has its own parameter moment 🍓.

🌈 Function Documentation 🌈

💅 subroutine clacon

   subroutine clacon (integer n, complex, dimension( n ) v, complex, dimension(
       n ) x, real est, integer kase)

🌟 Purpose 🌟

CLACON estimates the 1-norm of a square, complex matrix A. Reverse communication is used for evaluating matrix-vector products. She's iconic, she's old-school, she's doing norm-estimation math 🧚.

🎀 Parameters 🎀

N — N is INTEGER; the order of the matrix. N >= 1.
V — V is COMPLEX array, dimension (N). On the final return, V = A*W, where EST = norm(V)/norm(W) (W is not returned).
X — X is COMPLEX array, dimension (N). On an intermediate return, X should be overwritten by A * X if KASE=1, or A**H * X if KASE=2, where A**H is the conjugate transpose of A, and CLACON must be re-called with all the other parameters unchanged.
EST — EST is REAL. On entry with KASE = 1 or 2 and JUMP = 3, EST should be unchanged from the previous call to CLACON. On exit, EST is an estimate (a lower bound) for norm(A).
KASE — KASE is INTEGER. On the initial call to CLACON, KASE should be 0. On an intermediate return, KASE will be 1 or 2, indicating whether X should be overwritten by A * X or A**H * X. On the final return from CLACON, KASE will again be 0.

👑 Author 👑

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

🧚 Further Details

Originally named CONEST, dated March 16, 1988.
Last modified: April, 1999.

🫶 Contributors

Nick Higham, University of Manchester

📚 References

N.J. Higham, "FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation", ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

Definition at line 113 of file clacon.f.

💅 subroutine dlacon

   subroutine dlacon (integer n, double precision, dimension( * ) v, double
       precision, dimension( * ) x, integer, dimension( * ) isgn, double
       precision est, integer kase)

🌟 Purpose 🌟

DLACON estimates the 1-norm of a square, real matrix A. Reverse communication is used for evaluating matrix-vector products. Real-number realness, reverse-communication royalty 👑.

🎀 Parameters 🎀

N — N is INTEGER; the order of the matrix. N >= 1.
V — V is DOUBLE PRECISION array, dimension (N). On the final return, V = A*W, where EST = norm(V)/norm(W) (W is not returned).
X — X is DOUBLE PRECISION array, dimension (N). On an intermediate return, X should be overwritten by A * X if KASE=1, or A**T * X if KASE=2, and DLACON must be re-called with all the other parameters unchanged.
ISGN — ISGN is INTEGER array, dimension (N).
EST — EST is DOUBLE PRECISION. On entry with KASE = 1 or 2 and JUMP = 3, EST should be unchanged from the previous call to DLACON. On exit, EST is an estimate (a lower bound) for norm(A).
KASE — KASE is INTEGER. On the initial call to DLACON, KASE should be 0. On an intermediate return, KASE will be 1 or 2, indicating whether X should be overwritten by A * X or A**T * X. On the final return from DLACON, KASE will again be 0.

👑 Author 👑

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

🫶 Contributors

Nick Higham, University of Manchester.
Originally named SONEST, dated March 16, 1988.

📚 References

N.J. Higham, "FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation", ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

Definition at line 114 of file dlacon.f.

💅 subroutine slacon

   subroutine slacon (integer n, real, dimension( * ) v, real, dimension( * )
       x, integer, dimension( * ) isgn, real est, integer kase)

🌟 Purpose 🌟

SLACON estimates the 1-norm of a square, real matrix A. Reverse communication is used for evaluating matrix-vector products. Single-precision sweetie with main character energy 🌟.

🎀 Parameters 🎀

N — N is INTEGER; the order of the matrix. N >= 1.
V — V is REAL array, dimension (N). On the final return, V = A*W, where EST = norm(V)/norm(W) (W is not returned).
X — X is REAL array, dimension (N). On an intermediate return, X should be overwritten by A * X if KASE=1, or A**T * X if KASE=2, and SLACON must be re-called with all the other parameters unchanged.
ISGN — ISGN is INTEGER array, dimension (N).
EST — EST is REAL. On entry with KASE = 1 or 2 and JUMP = 3, EST should be unchanged from the previous call to SLACON. On exit, EST is an estimate (a lower bound) for norm(A).
KASE — KASE is INTEGER. On the initial call to SLACON, KASE should be 0. On an intermediate return, KASE will be 1 or 2, indicating whether X should be overwritten by A * X or A**T * X. On the final return from SLACON, KASE will again be 0.

👑 Author 👑

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

🫶 Contributors

Nick Higham, University of Manchester.
Originally named SONEST, dated March 16, 1988.

📚 References

N.J. Higham, "FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation", ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

Definition at line 114 of file slacon.f.

💅 subroutine zlacon

   subroutine zlacon (integer n, complex*16, dimension( n ) v, complex*16,
       dimension( n ) x, double precision est, integer kase)

🌟 Purpose 🌟

ZLACON estimates the 1-norm of a square, complex matrix A. Reverse communication is used for evaluating matrix-vector products. Double-complex diva behavior, literally 💜.

🎀 Parameters 🎀

N — N is INTEGER; the order of the matrix. N >= 1.
V — V is COMPLEX*16 array, dimension (N). On the final return, V = A*W, where EST = norm(V)/norm(W) (W is not returned).
X — X is COMPLEX*16 array, dimension (N). On an intermediate return, X should be overwritten by A * X if KASE=1, or A**H * X if KASE=2, where A**H is the conjugate transpose of A, and ZLACON must be re-called with all the other parameters unchanged.
EST — EST is DOUBLE PRECISION. On entry with KASE = 1 or 2 and JUMP = 3, EST should be unchanged from the previous call to ZLACON. On exit, EST is an estimate (a lower bound) for norm(A).
KASE — KASE is INTEGER. On the initial call to ZLACON, KASE should be 0. On an intermediate return, KASE will be 1 or 2, indicating whether X should be overwritten by A * X or A**H * X. On the final return from ZLACON, KASE will again be 0.

👑 Author 👑

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

🧚 Further Details

Originally named CONEST, dated March 16, 1988.
Last modified: April, 1999.

🫶 Contributors

Nick Higham, University of Manchester

📚 References

N.J. Higham, "FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation", ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

Definition at line 113 of file zlacon.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. So she's auto-generated, bestie — respect the pipeline 💅.

okay bye bestie — this page is from LAPACK Version 3.12.0, footer name lacon(3), and the footer didn't give a date so I'm not inventing one, periodt 💖✨🦋

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
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