larfx(3)

🌸 larfx(3) — larfx: apply Householder reflector, unrolled 🌸

okay bestie, this is a Library Functions Manual page, and it's literally the larfx squad: clarfx, dlarfx, slarfx, zlarfx. four real ones, one job: slap an elementary reflector onto a general rectangular matrix, and do it with loop unrolling when the reflector has order ≤ 10. iconique. 💅

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✨ NAME ✨

larfx — larfx: apply Householder reflector, unrolled

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🎀 SYNOPSIS 🎀

🌈 Functions

subroutine clarfx (side, m, n, v, tau, c, ldc, work)

CLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

subroutine dlarfx (side, m, n, v, tau, c, ldc, work)

DLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

subroutine slarfx (side, m, n, v, tau, c, ldc, work)

SLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

subroutine zlarfx (side, m, n, v, tau, c, ldc, work)

ZLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

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🦋 Detailed Description

💜 Function Documentation

⭐ subroutine clarfx (character side, integer m, integer n, complex, dimension( * ) v, complex tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work)

CLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

🔥 Purpose:

CLARFX applies a complex elementary reflector H to a complex m by n matrix C, from either the left or the right. H is represented in the form

H = I - tau * v * v**H

where tau is a complex scalar and v is a complex vector.

If tau = 0, then H is taken to be the unit matrix 👑

This version uses inline code if H has order < 11.

🫶 Parameters

• SIDE — SIDE is CHARACTER*1
  • = 'L': form H * C
  • = 'R': form C * H
• M — M is INTEGER
  • The number of rows of the matrix C.
• N — N is INTEGER
  • The number of columns of the matrix C.
• V — V is COMPLEX array, dimension (M) if SIDE = 'L' or (N) if SIDE = 'R'
  • The vector v in the representation of H.
• TAU — TAU is COMPLEX
  • The value tau in the representation of H.
• C — C is COMPLEX array, dimension (LDC,N)
  • On entry, the m by n matrix C.
  • On exit, C is overwritten by the matrix H * C if SIDE = 'L', or C * H if SIDE = 'R'. 😭 she's been through it
• LDC — LDC is INTEGER
  • The leading dimension of the array C. LDC >= max(1,M).
• WORK — WORK is COMPLEX array, dimension (N) if SIDE = 'L' or (M) if SIDE = 'R'
  • WORK is not referenced if H has order < 11.

🌸 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🎀 Definition at line 118 of file clarfx.f.

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⭐ subroutine dlarfx (character side, integer m, integer n, double precision, dimension( * ) v, double precision tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work)

DLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

🔥 Purpose:

DLARFX applies a real elementary reflector H to a real m by n matrix C, from either the left or the right. H is represented in the form

H = I - tau * v * v**T

where tau is a real scalar and v is a real vector.

If tau = 0, then H is taken to be the unit matrix 👑

This version uses inline code if H has order < 11.

🫶 Parameters

• SIDE — SIDE is CHARACTER*1
  • = 'L': form H * C
  • = 'R': form C * H
• M — M is INTEGER
  • The number of rows of the matrix C.
• N — N is INTEGER
  • The number of columns of the matrix C.
• V — V is DOUBLE PRECISION array, dimension (M) if SIDE = 'L' or (N) if SIDE = 'R'
  • The vector v in the representation of H.
• TAU — TAU is DOUBLE PRECISION
  • The value tau in the representation of H.
• C — C is DOUBLE PRECISION array, dimension (LDC,N)
  • On entry, the m by n matrix C.
  • On exit, C is overwritten by the matrix H * C if SIDE = 'L', or C * H if SIDE = 'R'.
• LDC — LDC is INTEGER
  • The leading dimension of the array C. LDC >= (1,M). (note: no max here, she's built different — copy it exactly, don't be cute and "fix" it 🙈)
• WORK — WORK is DOUBLE PRECISION array, dimension (N) if SIDE = 'L' or (M) if SIDE = 'R'
  • WORK is not referenced if H has order < 11.

🌸 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🎀 Definition at line 119 of file dlarfx.f.

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⭐ subroutine slarfx (character side, integer m, integer n, real, dimension( * ) v, real tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work)

SLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

🔥 Purpose:

SLARFX applies a real elementary reflector H to a real m by n matrix C, from either the left or the right. H is represented in the form

H = I - tau * v * v**T

where tau is a real scalar and v is a real vector.

If tau = 0, then H is taken to be the unit matrix 👑

This version uses inline code if H has order < 11.

🫶 Parameters

• SIDE — SIDE is CHARACTER*1
  • = 'L': form H * C
  • = 'R': form C * H
• M — M is INTEGER
  • The number of rows of the matrix C.
• N — N is INTEGER
  • The number of columns of the matrix C.
• V — V is REAL array, dimension (M) if SIDE = 'L' or (N) if SIDE = 'R'
  • The vector v in the representation of H.
• TAU — TAU is REAL
  • The value tau in the representation of H.
• C — C is REAL array, dimension (LDC,N)
  • On entry, the m by n matrix C.
  • On exit, C is overwritten by the matrix H * C if SIDE = 'L', or C * H if SIDE = 'R'.
• LDC — LDC is INTEGER
  • The leading dimension of the array C. LDC >= (1,M).
• WORK — WORK is REAL array, dimension (N) if SIDE = 'L' or (M) if SIDE = 'R'
  • WORK is not referenced if H has order < 11.

🌸 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🎀 Definition at line 119 of file slarfx.f.

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⭐ subroutine zlarfx (character side, integer m, integer n, complex*16, dimension( * ) v, complex*16 tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work)

ZLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

🔥 Purpose:

ZLARFX applies a complex elementary reflector H to a complex m by n matrix C, from either the left or the right. H is represented in the form

H = I - tau * v * v**H

where tau is a complex scalar and v is a complex vector.

If tau = 0, then H is taken to be the unit matrix 👑

This version uses inline code if H has order < 11.

🫶 Parameters

• SIDE — SIDE is CHARACTER*1
  • = 'L': form H * C
  • = 'R': form C * H
• M — M is INTEGER
  • The number of rows of the matrix C.
• N — N is INTEGER
  • The number of columns of the matrix C.
• V — V is COMPLEX*16 array, dimension (M) if SIDE = 'L' or (N) if SIDE = 'R'
  • The vector v in the representation of H.
• TAU — TAU is COMPLEX*16
  • The value tau in the representation of H.
• C — C is COMPLEX*16 array, dimension (LDC,N)
  • On entry, the m by n matrix C.
  • On exit, C is overwritten by the matrix H * C if SIDE = 'L', or C * H if SIDE = 'R'.
• LDC — LDC is INTEGER
  • The leading dimension of the array C. LDC >= max(1,M).
• WORK — WORK is COMPLEX*16 array, dimension (N) if SIDE = 'L' or (M) if SIDE = 'R'
  • WORK is not referenced if H has order < 11.

🌸 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🎀 Definition at line 118 of file zlarfx.f.

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👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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<div align="center">💖 ✨ 🎀 🦋 🌸 💅 🫶 </div>

so yeah bestie, that's the whole page — every flag, every dimension, every LDC >= ... variant (yes, they differ, no, don't unify them, I'm watching you 👀). go forth and reflect. periodt. 💜

LAPACK · Version 3.12.0 · larfx(3) — mwah, kisses, see u in the next manpage 🍓🧚‍♀️