lapll(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💅 lapll(3) — the manual page, but make it a group chat 💅

okay so bestie, you know how sometimes you have two vectors and you're like "are these two lowkey the same vibe or what?" That's literally what lapll is for. It's the linear dependence detection bestie of LAPACK, and it's about to slay your whole numerical linear algebra situation. Periodt. 💖

✨ NAME ✨

lapll — figuring out if two vectors are besties or if they're lowkey copying each other's whole personality 💅✨

🦋 SYNOPSIS 🦋

Functions (yes, there's a whole squad of them, one for every precision, iykyk)

subroutine clapll (n, x, incx, y, incy, ssmin)
    CLAPLL measures the linear dependence of two vectors.

subroutine dlapll (n, x, incx, y, incy, ssmin)
    DLAPLL measures the linear dependence of two vectors.

subroutine slapll (n, x, incx, y, incy, ssmin)
    SLAPLL measures the linear dependence of two vectors.

subroutine zlapll (n, x, incx, y, incy, ssmin)
    ZLAPLL measures the linear dependence of two vectors.

🌸 DETAILED DESCRIPTION 🌸

Okay so real talk, this is the page for the whole lapll family. We got single precision, double precision, complex, and complex*16 all showing up to the same party, each with their own vibe but all doing the exact same iconic thing. 🎀

💅 FUNCTION DOCUMENTATION 💅

🫶 subroutine clapll (integer n, complex, dimension( * ) x, integer incx, complex, dimension( * ) y, integer incy, real ssmin) 🫶

CLAPLL measures the linear dependence of two vectors. Single precision complex, slaying as always. 💖

🔥 Purpose: 🔥

bestie, listen. Given two column vectors X and Y, let

A = ( X Y ).

So the subroutine is out here doing the most (in a good way) by first computing the QR factorization of A = Q*R, and then it computes the SVD of the 2-by-2 upper triangular matrix R. The smaller singular value of R is returned in SSMIN, which is used as the measurement of the linear dependency of the vectors X and Y. No cap, that's the whole plot. 📖✨

🎀 Parameters 🎀

  • N — it's an INTEGER, bestie. The length of the vectors X and Y. How many elements we're working with, you know? No skipping. 💅
  • X — it's a COMPLEX array, dimension (1+(N-1)*INCX). On entry, X contains the N-vector X. On exit, X is overwritten. It gets a whole glow-up (or glow-down depending on what the subroutine decides). 🙈
  • INCX — it's an INTEGER. The increment between successive elements of X. INCX > 0. If you're out here with INCX = 0 or negative, that's not the vibe. Don't do it. Real ones know. 🔥
  • Y — it's a COMPLEX array, dimension (1+(N-1)*INCY). On entry, Y contains the N-vector Y. On exit, Y is overwritten. Same energy as X, just the other half of the duo. 🦋
  • INCY — it's an INTEGER. The increment between successive elements of Y. INCY > 0. Again, positive only. We don't do anything else here. 💀
  • SSMIN — it's a REAL. The smallest singular value of the N-by-2 matrix A = ( X Y ). This is the main character of the return values, honestly. It's the final answer to "are these vectors lowkey the same?" 👑

⭐ Author ⭐

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📍 Definition at line 99 of file clapll.f. 📍

🫶 subroutine dlapll (integer n, double precision, dimension( * ) x, integer incx, double precision, dimension( * ) y, integer incy, double precision ssmin) 🫶

DLAPLL measures the linear dependence of two vectors. Double precision, double the slay, double the precision. 💅💖

🔥 Purpose: 🔥

bestie, listen. Given two column vectors X and Y, let

A = ( X Y ).

So the subroutine is out here doing the most (in a good way) by first computing the QR factorization of A = Q*R, and then it computes the SVD of the 2-by-2 upper triangular matrix R. The smaller singular value of R is returned in SSMIN, which is used as the measurement of the linear dependency of the vectors X and Y. No cap, that's the whole plot. 📖✨

🎀 Parameters 🎀

  • N — it's an INTEGER, bestie. The length of the vectors X and Y. How many elements we're working with, you know? No skipping. 💅
  • X — it's a DOUBLE PRECISION array, dimension (1+(N-1)*INCX). On entry, X contains the N-vector X. On exit, X is overwritten. It gets a whole glow-up (or glow-down depending on what the subroutine decides). 🙈
  • INCX — it's an INTEGER. The increment between successive elements of X. INCX > 0. If you're out here with INCX = 0 or negative, that's not the vibe. Don't do it. Real ones know. 🔥
  • Y — it's a DOUBLE PRECISION array, dimension (1+(N-1)*INCY). On entry, Y contains the N-vector Y. On exit, Y is overwritten. Same energy as X, just the other half of the duo. 🦋
  • INCY — it's an INTEGER. The increment between successive elements of Y. INCY > 0. Again, positive only. We don't do anything else here. 💀
  • SSMIN — it's a DOUBLE PRECISION. The smallest singular value of the N-by-2 matrix A = ( X Y ). This is the main character of the return values, honestly. It's the final answer to "are these vectors lowkey the same?" 👑

⭐ Author ⭐

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📍 Definition at line 101 of file dlapll.f. 📍

🫶 subroutine slapll (integer n, real, dimension( * ) x, integer incx, real, dimension( * ) y, integer incy, real ssmin) 🫶

SLAPLL measures the linear dependence of two vectors. Single precision real, keeping it simple but still iconic. 🎀✨

🔥 Purpose: 🔥

bestie, listen. Given two column vectors X and Y, let

A = ( X Y ).

So the subroutine is out here doing the most (in a good way) by first computing the QR factorization of A = Q*R, and then it computes the SVD of the 2-by-2 upper triangular matrix R. The smaller singular value of R is returned in SSMIN, which is used as the measurement of the linear dependency of the vectors X and Y. No cap, that's the whole plot. 📖✨

🎀 Parameters 🎀

  • N — it's an INTEGER, bestie. The length of the vectors X and Y. How many elements we're working with, you know? No skipping. 💅
  • X — it's a REAL array, dimension (1+(N-1)*INCX). On entry, X contains the N-vector X. On exit, X is overwritten. It gets a whole glow-up (or glow-down depending on what the subroutine decides). 🙈
  • INCX — it's an INTEGER. The increment between successive elements of X. INCX > 0. If you're out here with INCX = 0 or negative, that's not the vibe. Don't do it. Real ones know. 🔥
  • Y — it's a REAL array, dimension (1+(N-1)*INCY). On entry, Y contains the N-vector Y. On exit, Y is overwritten. Same energy as X, just the other half of the duo. 🦋
  • INCY — it's an INTEGER. The increment between successive elements of Y. INCY > 0. Again, positive only. We don't do anything else here. 💀
  • SSMIN — it's a REAL. The smallest singular value of the N-by-2 matrix A = ( X Y ). This is the main character of the return values, honestly. It's the final answer to "are these vectors lowkey the same?" 👑

⭐ Author ⭐

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📍 Definition at line 101 of file slapll.f. 📍

🫶 subroutine zlapll (integer n, complex*16, dimension( * ) x, integer incx, complex*16, dimension( * ) y, integer incy, double precision ssmin) 🫶

ZLAPLL measures the linear dependence of two vectors. Double complex, the most extra of them all, and we love that for her. 💅👑

🔥 Purpose: 🔥

bestie, listen. Given two column vectors X and Y, let

A = ( X Y ).

So the subroutine is out here doing the most (in a good way) by first computing the QR factorization of A = Q*R, and then it computes the SVD of the 2-by-2 upper triangular matrix R. The smaller singular value of R is returned in SSMIN, which is used as the measurement of the linear dependency of the vectors X and Y. No cap, that's the whole plot. 📖✨

🎀 Parameters 🎀

  • N — it's an INTEGER, bestie. The length of the vectors X and Y. How many elements we're working with, you know? No skipping. 💅
  • X — it's a COMPLEX*16 array, dimension (1+(N-1)*INCX). On entry, X contains the N-vector X. On exit, X is overwritten. It gets a whole glow-up (or glow-down depending on what the subroutine decides). 🙈
  • INCX — it's an INTEGER. The increment between successive elements of X. INCX > 0. If you're out here with INCX = 0 or negative, that's not the vibe. Don't do it. Real ones know. 🔥
  • Y — it's a COMPLEX*16 array, dimension (1+(N-1)*INCY). On entry, Y contains the N-vector Y. On exit, Y is overwritten. Same energy as X, just the other half of the duo. 🦋
  • INCY — it's an INTEGER. The increment between successive elements of Y. INCY > 0. Again, positive only. We don't do anything else here. 💀
  • SSMIN — it's a DOUBLE PRECISION. The smallest singular value of the N-by-2 matrix A = ( X Y ). This is the main character of the return values, honestly. It's the final answer to "are these vectors lowkey the same?" 👑

⭐ Author ⭐

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📍 Definition at line 99 of file zlapll.f. 📍

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. (So you know it's legit, bestie. The robots wrote this one but we made it cute. 🤖💖)

okay so that's the whole page! You're now fully caught up on lapll and all her friends. Go measure some linear dependence, bestie. You got this. 💅✨🦋

sending you all the good vibes from LAPACK Version 3.12.0, date-stamped at the very bottom of the original page but we're mentioning it here because we're cute like that 💖

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