lacn2(3)

📦

version 3.12.1 · 9 versions

3.12.1 · arch rolling (latest)
3.12.0 · opensuse-leap 16.0
3.12.1 · ubuntu stonking
3.12.1 · ubuntu questing
3.12.0 · ubuntu noble
3.12.0 · ubuntu noble
3.12.0 · centos-stream 10, fedora 43, fedora 44
3.12.1 · ubuntu resolute
3.12.1 · debian trixie

💅 bestie's guide to `lacn2(3)` 💅

Okay so this is lacn2(3) from the Library Functions Manual, and ngl it's a whole family situation — four subroutines, all doing the same iconic thing in different precisions. Let's get into it 🫶

✨ NAME ✨

lacn2 — it's the lacn2: a 1-norm estimate, e.g., || A^{-1} ||_1 in gecon. Periodt. 💅

🌸 SYNOPSIS 🌸

💖 Functions

subroutine clacn2 (n, v, x, est, kase, isave) — CLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
subroutine dlacn2 (n, v, x, isgn, est, kase, isave) — DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
subroutine slacn2 (n, v, x, isgn, est, kase, isave) — SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
subroutine zlacn2 (n, v, x, est, kase, isave) — ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

🦋 Detailed Description 🦋

Not me checking this section three times — bestie there is literally nothing here. It's a heading with no body. The actual tea is all in Function Documentation below, so keep scrolling 👑

🔥 Function Documentation 🔥

💜 `clacn2`

subroutine clacn2 (integer n, complex, dimension( * ) v, complex, dimension( * ) x, real est, integer kase, integer, dimension( 3 ) isave)

CLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

⭐ Purpose

CLACN2 estimates the 1-norm of a square, complex matrix A. Reverse communication is used for evaluating matrix-vector products.

🎀 Parameters

N — N is INTEGER. The order of the matrix. N >= 1. No zero-sized matrices bestie, the math said so.
V — V is COMPLEX array, dimension (N). On the final return, V = A*W, where EST = norm(V)/norm(W) (W is not returned). Yeah she's not giving you W back, don't ask 😭
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 CLACN2 must be re-called with all the other parameters unchanged. All of them. Don't touch. 🙈
EST — EST is REAL. On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be unchanged from the previous call to CLACN2. On exit, EST is an estimate (a lower bound) for norm(A).
KASE — KASE is INTEGER. On the initial call to CLACN2, 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 CLACN2, KASE will again be 0. It's giving ✨full circle✨
ISAVE — ISAVE is INTEGER array, dimension (3). ISAVE is used to save variables between calls to SLACN2.

Yeah bestie, that last line says SLACN2 on the CLACN2 page 💀 that's just how the doc is written, I'm reporting it exactly as it lives.

👑 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
This is a thread safe version of CLACON, which uses the array ISAVE in place of a SAVE statement, as follows:

 CLACON     CLACN2
  JUMP     ISAVE(1)
  J        ISAVE(2)
  ITER     ISAVE(3)

🫶 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 132 of file clacn2.f.

🧚 `dlacn2`

subroutine dlacn2 (integer n, double precision, dimension( * ) v, double precision, dimension( * ) x, integer, dimension( * ) isgn, double precision est, integer kase, integer, dimension( 3 ) isave)

DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

⭐ Purpose

DLACN2 estimates the 1-norm of a square, real matrix A. Reverse communication is used for evaluating matrix-vector products.

🎀 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 DLACN2 must be re-called with all the other parameters unchanged.
ISGN — ISGN is INTEGER array, dimension (N). That's it. That's the whole description. Iconic minimalism 💅
EST — EST is DOUBLE PRECISION. On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be unchanged from the previous call to DLACN2. On exit, EST is an estimate (a lower bound) for norm(A).
KASE — KASE is INTEGER. On the initial call to DLACN2, 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 DLACN2, KASE will again be 0.
ISAVE — ISAVE is INTEGER array, dimension (3). ISAVE is used to save variables between calls to DLACN2.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

💀 Further Details:

Originally named SONEST, dated March 16, 1988.
This is a thread safe version of DLACON, which uses the array ISAVE in place of a SAVE statement, as follows:

 DLACON     DLACN2
  JUMP     ISAVE(1)
  J        ISAVE(2)
  ITER     ISAVE(3)

🫶 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 135 of file dlacn2.f.

🌈 `slacn2`

subroutine slacn2 (integer n, real, dimension( * ) v, real, dimension( * ) x, integer, dimension( * ) isgn, real est, integer kase, integer, dimension( 3 ) isave)

SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

⭐ Purpose

SLACN2 estimates the 1-norm of a square, real matrix A. Reverse communication is used for evaluating matrix-vector products.

🎀 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 SLACN2 must be re-called with all the other parameters unchanged.
ISGN — ISGN is INTEGER array, dimension (N). Again, that's the whole thing. She said "no notes" 🙈
EST — EST is REAL. On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be unchanged from the previous call to SLACN2. On exit, EST is an estimate (a lower bound) for norm(A).
KASE — KASE is INTEGER. On the initial call to SLACN2, 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 SLACN2, KASE will again be 0.
ISAVE — ISAVE is INTEGER array, dimension (3). ISAVE is used to save variables between calls to SLACN2.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

💀 Further Details:

Originally named SONEST, dated March 16, 1988.
This is a thread safe version of SLACON, which uses the array ISAVE in place of a SAVE statement, as follows:

 SLACON     SLACN2
  JUMP     ISAVE(1)
  J        ISAVE(2)
  ITER     ISAVE(3)

🫶 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 135 of file slacn2.f.

🦄 `zlacn2`

subroutine zlacn2 (integer n, complex*16, dimension( * ) v, complex*16, dimension( * ) x, double precision est, integer kase, integer, dimension( 3 ) isave)

ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

⭐ Purpose

ZLACN2 estimates the 1-norm of a square, complex matrix A. Reverse communication is used for evaluating matrix-vector products.

🎀 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 ZLACN2 must be re-called with all the other parameters unchanged.
EST — EST is DOUBLE PRECISION. On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be unchanged from the previous call to ZLACN2. On exit, EST is an estimate (a lower bound) for norm(A).
KASE — 🎀 okay bestie this is exactly where part 1 cuts off — KASE, plus the rest of zlacn2's details, roll right into part 2. Don't move, we're mid-sentence on purpose 🎀
KASE — okay so KASE is INTEGER 💅. On the initial call to ZLACN2, 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 ZLACN2, KASE will again be 0. 🫶
ISAVE — ISAVE is INTEGER array, dimension (3) ✨. ISAVE is used to save variables between calls to ZLACN2. Lowkey the memory keeper of the whole situation. 🎀

🌸 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 🕰️

This is a thread safe version of ZLACON, which uses the array ISAVE in place of a SAVE statement, as follows:

     ZLACON     ZLACN2
      JUMP     ISAVE(1)
      J        ISAVE(2)
      ITER     ISAVE(3)

🌈 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 132 of file zlacn2.f. 🫶

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code. 🤖💖

Cute sign-off: this is LAPACK Version 3.12.0, page lacn2(3) — and the footer didn’t give us a date, so that’s the whole story, bestie. 💅✨

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

lacn2(3)

💅 bestie's guide to lacn2(3) 💅

✨ NAME ✨

🌸 SYNOPSIS 🌸

💖 Functions

🦋 Detailed Description 🦋

🔥 Function Documentation 🔥

💜 clacn2

⭐ Purpose

🎀 Parameters

👑 Author

💀 Further Details:

🫶 Contributors:

📚 References:

🧚 dlacn2

⭐ Purpose

🎀 Parameters

👑 Author

💀 Further Details:

🫶 Contributors:

📚 References:

🌈 slacn2

⭐ Purpose

🎀 Parameters

👑 Author

💀 Further Details:

🫶 Contributors:

📚 References:

🦄 zlacn2

⭐ Purpose

🎀 Parameters

🌸 Author 🌸

🧚 Further Details:

🌈 Contributors:

💜 References:

🎀 Author 🎀

💅 bestie's guide to `lacn2(3)` 💅

💜 `clacn2`

🧚 `dlacn2`

🌈 `slacn2`

🦄 `zlacn2`