nrm2(3)

📦
version 3.12.1 · 9 versions
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✨ nrm2(3) ✨ — the nrm2 gang, aka || x ||_2 💅

okay bestie, so this page is from the Library Functions Manual and it's literally the whole nrm2 squad — four functions whose entire personality is "give me a vector, I'll give you its euclidean norm." iconic behavior honestly 🎀

🌸 NAME 🌸

nrm2 — nrm2: || x ||_2 💖

🦋 SYNOPSIS 🦋

Functions

  • real(wp) function dnrm2 (n, x, incx) — DNRM2
  • real(wp) function dznrm2 (n, x, incx) — DZNRM2
  • real(wp) function scnrm2 (n, x, incx) — SCNRM2
  • real(wp) function snrm2 (n, x, incx) — SNRM2

👑 Detailed Description 👑

no cap, this is where the actual lore lives. scroll down for the four function glow-ups 💫

🌈 Function Documentation 🌈

💜 real(wp) function dnrm2 (integer n, real(wp), dimension(*) x, integer incx) 💜

DNRM2

Purpose:

!>
!> DNRM2 returns the euclidean norm of a vector via the function
!> name, so that
!>
!>    DNRM2 := sqrt( x'*x )
!>

like, it just hands you the euclidean norm. that's the whole vibe. ✨

Parameters

N

!>          N is INTEGER
!>         number of elements in input vector(s)
!>

X

!>          X is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
!>

INCX

!>          INCX is INTEGER, storage spacing between elements of X
!>          If INCX > 0, X(1+(i-1)*INCX) = x(i) for 1 <= i <= n
!>          If INCX < 0, X(1-(n-i)*INCX) = x(i) for 1 <= i <= n
!>          If INCX = 0, x isn't a vector so there is no need to call
!>          this subroutine.  If you call it anyway, it will count x(1)
!>          in the vector norm N times.
!>
🫶 lowkey important: if INCX = 0, x isn't a vector so there's literally no need to call this subroutine. but if you call it anyway? it'll count x(1) in the vector norm N times. not me warning you twice 💀

Author

Edward Anderson, Lockheed Martin 👑

Date

August 2016 📅

Contributors:

Weslley Pereira, University of Colorado Denver, USA 💖

Further Details:

!>
!>  Anderson E. (2017)
!>  Algorithm 978: Safe Scaling in the Level 1 BLAS
!>  ACM Trans Math Softw 44:1--28
!>  https://doi.org/10.1145/3061665
!>
!>  Blue, James L. (1978)
!>  A Portable Fortran Program to Find the Euclidean Norm of a Vector
!>  ACM Trans Math Softw 4:15--23
!>  https://doi.org/10.1145/355769.355771
!>
!>

Definition at line 88 of file dnrm2.f90. 📍

💙 real(wp) function dznrm2 (integer n, complex(wp), dimension(*) x, integer incx) 💙

DZNRM2

Purpose:

!>
!> DZNRM2 returns the euclidean norm of a vector via the function
!> name, so that
!>
!>    DZNRM2 := sqrt( x**H*x )
!>

note the x**H*x bestie — conjugate transpose energy, we love a complex girlie 🦋

Parameters

N

!>          N is INTEGER
!>         number of elements in input vector(s)
!>

X

!>          X is COMPLEX*16 array, dimension (N)
!>         complex vector with N elements
!>

INCX

!>          INCX is INTEGER, storage spacing between elements of X
!>          If INCX > 0, X(1+(i-1)*INCX) = x(i) for 1 <= i <= n
!>          If INCX < 0, X(1-(n-i)*INCX) = x(i) for 1 <= i <= n
!>          If INCX = 0, x isn't a vector so there is no need to call
!>          this subroutine.  If you call it anyway, it will count x(1)
!>          in the vector norm N times.
!>
🙈 same deal as before: INCX = 0 means x isn't a vector, so there's no need to call this subroutine — and if you do it anyway, it counts x(1) in the vector norm N times.

Author

Edward Anderson, Lockheed Martin 👑

Date

August 2016 📅

Contributors:

Weslley Pereira, University of Colorado Denver, USA 💖

Further Details:

!>
!>  Anderson E. (2017)
!>  Algorithm 978: Safe Scaling in the Level 1 BLAS
!>  ACM Trans Math Softw 44:1--28
!>  https://doi.org/10.1145/3061665
!>
!>  Blue, James L. (1978)
!>  A Portable Fortran Program to Find the Euclidean Norm of a Vector
!>  ACM Trans Math Softw 4:15--23
!>  https://doi.org/10.1145/355769.355771
!>
!>

Definition at line 89 of file dznrm2.f90. 📍

🍓 real(wp) function scnrm2 (integer n, complex(wp), dimension(*) x, integer incx) 🍓

SCNRM2

Purpose:

!>
!> SCNRM2 returns the euclidean norm of a vector via the function
!> name, so that
!>
!>    SCNRM2 := sqrt( x**H*x )
!>

single-precision complex edition, and yes she also ate with that x**H*x 💅

Parameters

N

!>          N is INTEGER
!>         number of elements in input vector(s)
!>

X

!>          X is COMPLEX array, dimension (N)
!>         complex vector with N elements
!>

INCX

!>          INCX is INTEGER, storage spacing between elements of X
!>          If INCX > 0, X(1+(i-1)*INCX) = x(i) for 1 <= i <= n
!>          If INCX < 0, X(1-(n-i)*INCX) = x(i) for 1 <= i <= n
!>          If INCX = 0, x isn't a vector so there is no need to call
!>          this subroutine.  If you call it anyway, it will count x(1)
!>          in the vector norm N times.
!>
💀 third time's the charm: INCX = 0 → x isn't a vector → no need to call this subroutine. call it anyway and x(1) gets counted in the vector norm N times. the math said what it said.

Author

Edward Anderson, Lockheed Martin 👑

Date

August 2016 📅

Contributors:

Weslley Pereira, University of Colorado Denver, USA 💖

Further Details:

!>
!>  Anderson E. (2017)
!>  Algorithm 978: Safe Scaling in the Level 1 BLAS
!>  ACM Trans Math Softw 44:1--28
!>  https://doi.org/10.1145/3061665
!>
!>  Blue, James L. (1978)
!>  A Portable Fortran Program to Find the Euclidean Norm of a Vector
!>  ACM Trans Math Softw 4:15--23
!>  https://doi.org/10.1145/355769.355771
!>
!>

Definition at line 89 of file scnrm2.f90. 📍

🧚 real(wp) function snrm2 (integer n, real(wp), dimension(*) x, integer incx) 🧚

SNRM2

Purpose:

!>
!> SNRM2 returns the euclidean norm of a vector via the function
!> name, so that
!>
!>    SNRM2 := sqrt( x'*x ).
!>

the single-precision real one — tiny period at the end of the formula and everything, she's demure 🎀

Parameters

N

!>          N is INTEGER
!>         number of elements in input vector(s)
!>

X

!>          X is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
!>

INCX

!>          INCX is INTEGER, storage spacing between elements of X
!>          If INCX > 0, X(1+(i-1)*INCX) = x(i) for 1 <= i <= n
!>          If INCX < 0, X(1-(n-i)*INCX) = x(i) for 1 <= i <= n
!>          If INCX = 0, x isn't a vector so there is no need to call
!>          this subroutine.  If you call it anyway, it will count x(1)
!>          in the vector norm N times.
!>
🫶 ok literally final reminder because I care: INCX = 0 means x isn't a vector, so there is no need to call this subroutine — and if you call it anyway, it will count x(1) in the vector norm N times.

Author

Edward Anderson, Lockheed Martin 👑

Date

August 2016 📅

Contributors:

Weslley Pereira, University of Colorado Denver, USA 💖

Further Details:

!>
!>  Anderson E. (2017)
!>  Algorithm 978: Safe Scaling in the Level 1 BLAS
!>  ACM Trans Math Softw 44:1--28
!>  https://doi.org/10.1145/3061665
!>
!>  Blue, James L. (1978)
!>  A Portable Fortran Program to Find the Euclidean Norm of a Vector
!>  ACM Trans Math Softw 4:15--23
!>  https://doi.org/10.1145/355769.355771
!>
!>

Definition at line 88 of file snrm2.f90. 📍

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code. 🤖 (yes the robots wrote this page, and honestly? they ate.)

and that's the whole page bestie 🫶 — this beauty is from LAPACK, Version 3.12.0, dated the LAPACK era of nrm2(3). go compute some norms, you're gonna slay 💖✨👑

📦 where this page comes from