larf(3)

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version 3.12.1 · 9 versions
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💅 larf(3) — apply Householder reflector 💅

Library Functions Manual energy, bestie. The manual name is larf(3), and this page is the whole friend group for applying a Householder reflector. No cap, it’s giving linear-algebra main character energy. ✨

🎀 NAME 🎀

larf - larf: apply Householder reflector

🌸 SYNOPSIS 🌸

✨ Functions ✨

Here’s the whole squad — every subroutine signature exactly as the original lists it. No renaming, no merging, no invented options. 💅

  • subroutine clarf (character side, integer m, integer n, complex, dimension( * ) v, integer incv, complex tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work) — CLARF applies an elementary reflector to a general rectangular matrix.
  • subroutine dlarf (character side, integer m, integer n, double precision, dimension( * ) v, integer incv, double precision tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work) — DLARF applies an elementary reflector to a general rectangular matrix.
  • subroutine dlarf1f (character side, integer m, integer n, double precision, dimension( * ) v, integer incv, double precision tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work) — DLARF1F applies an elementary reflector to a general rectangular
  • subroutine dlarf1l (character side, integer m, integer n, double precision, dimension( * ) v, integer incv, double precision tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work) — DLARF1L applies an elementary reflector to a general rectangular
  • subroutine slarf (character side, integer m, integer n, real, dimension( * ) v, integer incv, real tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work) — SLARF applies an elementary reflector to a general rectangular matrix.
  • subroutine zlarf (character side, integer m, integer n, complex*16, dimension( * ) v, integer incv, complex*16 tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work) — ZLARF applies an elementary reflector to a general rectangular matrix.
  • subroutine zlarf1f (character side, integer m, integer n, complex*16, dimension( * ) v, integer incv, complex*16 tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work) — ZLARF1F applies an elementary reflector to a general rectangular

🦋 Detailed Description 🦋

Okay bestie, real talk: the original page leaves this heading with no extra body text. So no invented lore here — the actual tea is under Function Documentation below. 💅

🌈 Function Documentation 🌈

💖 subroutine clarf 💖

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

CLARF applies an elementary reflector to a general rectangular matrix.

💖 Purpose 💖

CLARF 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.

To apply H**H (the conjugate transpose of H), supply conjg(tau) instead of tau.

🍓 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 (1 + (M-1)*abs(INCV)) if SIDE = 'L', or (1 + (N-1)*abs(INCV)) if SIDE = 'R'. The vector v in the representation of H. V is not used if TAU = 0.
  • INCV — INCV is INTEGER — the increment between elements of v. INCV <> 0.
  • 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'.
  • 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'.

👑 Author 👑

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

🧚 Definition 🧚

Definition: at line 127 of file clarf.f.

💖 subroutine dlarf 💖

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

DLARF applies an elementary reflector to a general rectangular matrix.

💖 Purpose 💖

DLARF 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.

🍓 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 (1 + (M-1)*abs(INCV)) if SIDE = 'L', or (1 + (N-1)*abs(INCV)) if SIDE = 'R'. The vector v in the representation of H. V is not used if TAU = 0.
  • INCV — INCV is INTEGER — the increment between elements of v. INCV <> 0.
  • 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 >= max(1,M).
  • WORK — WORK is DOUBLE PRECISION array, dimension (N) if SIDE = 'L', or (M) if SIDE = 'R'.

👑 Author 👑

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

🧚 Definition 🧚

Definition: at line 123 of file dlarf.f.

💖 subroutine dlarf1f 💖

subroutine dlarf1f (character side, integer m, integer n, double precision, dimension( * ) v, integer incv, double precision tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work)

DLARF1F applies an elementary reflector to a general rectangular

💖 Purpose 💖

DLARF1F 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.

🍓 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 (1 + (M-1)*abs(INCV)) if SIDE = 'L', or (1 + (N-1)*abs(INCV)) if SIDE = 'R'. The vector v in the representation of H. V is not used if TAU = 0. V(1) is not referenced or modified.
  • INCV — INCV is INTEGER — the increment between elements of v. INCV <> 0.
  • 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 >= max(1,M).
  • WORK — WORK is DOUBLE PRECISION array, dimension (N) if SIDE = 'L', or (M) if SIDE = 'R'.

👑 Author 👑

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

🧚 Definition 🧚

Definition: at line 158 of file dlarf1f.f.

💖 subroutine dlarf1l 💖

subroutine dlarf1l (character side, integer m, integer n, double precision, dimension( * ) v, integer incv, double precision tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work)

DLARF1L applies an elementary reflector to a general rectangular

💖 Purpose 💖

DLARF1L 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.

🍓 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 (1 + (M-1)*abs(INCV)) if SIDE = 'L', or (1 + (N-1)*abs(INCV)) if SIDE = 'R'. The vector v in the representation of H. V is not used if TAU = 0.
  • INCV — INCV is INTEGER — the increment between elements of v. INCV <> 0.
  • 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 >= max(1,M).
  • WORK — WORK is DOUBLE PRECISION array, dimension (N) if SIDE = 'L', or (M) if SIDE = 'R'.

👑 Author 👑

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

🧚 Definition 🧚

Definition: at line 125 of file dlarf1l.f.

🫶 slarf — the real elementary reflector moment

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

Quick vibe: SLARF applies an elementary reflector to a general rectangular matrix.

Purpose:

SLARF 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. Periodt.

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 (1 + (M-1)*abs(INCV)) if SIDE = 'L', or (1 + (N-1)*abs(INCV)) if SIDE = 'R'. The vector v in the representation of H. V is not used if TAU = 0.
  • INCV — INCV is INTEGER. The increment between elements of v. INCV <> 0.
  • 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 >= max(1,M).
  • WORK — WORK is REAL array, dimension (N) if SIDE = 'L' or (M) if SIDE = 'R'.

Author:

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

Definition: at line 123 of file slarf.f.

🦋 zlarf — same reflector energy, but complex

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

Quick vibe: ZLARF applies an elementary reflector to a general rectangular matrix.

Purpose:

ZLARF 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.

To apply H**H, supply conjg(tau) instead tau. iykyk 💅

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 (1 + (M-1)*abs(INCV)) if SIDE = 'L', or (1 + (N-1)*abs(INCV)) if SIDE = 'R'. The vector v in the representation of H. V is not used if TAU = 0.
  • INCV — INCV is INTEGER. The increment between elements of v. INCV <> 0.
  • 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'.

Author:

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

Definition: at line 127 of file zlarf.f.

🎀 zlarf1f — the fancy complex reflector variant

subroutine zlarf1f (character side, integer m, integer n, complex*16,
    dimension( * ) v, integer incv, complex*16 tau, complex*16, dimension(
    ldc, * ) c, integer ldc, complex*16, dimension( * ) work)

Quick vibe: ZLARF1F applies an elementary reflector to a general rectangular

Purpose:

ZLARF1F applies a complex 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**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.

To apply H**H, supply conjg(tau) instead tau. literally the same energy, just saying it again ✨

Parameters:

  • SIDE — SIDE is CHARACTER*1
    • = 'L': form H * C
  • 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 (1 + (M-1)*abs(INCV)) if SIDE = 'L', or (1 + (N-1)*abs(INCV)) if SIDE = 'R'. The vector v in the representation of H. V is not used if TAU = 0. V(1) is not referenced or modified.
  • INCV — INCV is INTEGER. The increment between elements of v. INCV <> 0.
  • 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'.

Author:

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

Definition: at line 158 of file zlarf1f.f.

🌈 Author

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