rotmg(3)

💖 rotmg(3) — Library Functions Manual 💖

okay bestie, we're in the Library Functions Manual for rotmg(3), and this page is all about making modified (fast) plane rotations happen. It's giving linear algebra but make it cute. ✨

💖 NAME 💖

rotmg — rotmg: generate modified (fast) plane rotation. Yes, it says rotmg twice, and honestly? she ate. 💅

✨ SYNOPSIS ✨

🌈 Functions 🌈

• subroutine drotmg (dd1, dd2, dx1, dy1, dparam) — DROTMG
• subroutine srotmg (sd1, sd2, sx1, sy1, sparam) — SROTMG

🦋 Detailed Description 🦋

okay so the Detailed Description is literally just the heading before the function docs — no extra lore, no hidden side quest. The real tea is right below. 👇

🌸 Function Documentation 🌸

🎀 subroutine drotmg (double precision dd1, double precision dd2, double precision dx1, double precision dy1, double precision, dimension(5) dparam) 🎀

DROTMG

🔥 Purpose 🔥

bestie, here's the Purpose block exactly as the source serves it, because the matrix forms are the whole moment:

           !>
           !>    CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS
           !>    THE SECOND COMPONENT OF THE 2-VECTOR  (DSQRT(DD1)*DX1,DSQRT(DD2)*>    DY2)**T.
           !>    WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS..
           !>
           !>    DFLAG=-1.D0     DFLAG=0.D0        DFLAG=1.D0     DFLAG=-2.D0
           !>
           !>      (DH11  DH12)    (1.D0  DH12)    (DH11  1.D0)    (1.D0  0.D0)
           !>    H=(          )    (          )    (          )    (          )
           !>      (DH21  DH22),   (DH21  1.D0),   (-1.D0 DH22),   (0.D0  1.D0).
           !>    LOCATIONS 2-4 OF DPARAM CONTAIN DH11, DH21, DH12, AND DH22
           !>    RESPECTIVELY. (VALUES OF 1.D0, -1.D0, OR 0.D0 IMPLIED BY THE
           !>    VALUE OF DPARAM(1) ARE NOT STORED IN DPARAM.)
           !>
           !>    THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE
           !>    INEXACT.  THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE
           !>    OF DD1 AND DD2.  ALL ACTUAL SCALING OF DATA IS DONE USING GAM.
           !>
           !>

Translation for the group chat: it constructs the modified Givens transformation matrix H that zeros the second component of the 2-vector (DSQRT(DD1)*DX1,DSQRT(DD2)*> DY2)**T. — yes, that > is in the original, and we're keeping it exactly. With DPARAM(1)=DFLAG, H has one of the forms above. Locations 2-4 of DPARAM contain DH11, DH21, DH12, and DH22 respectively, and the 1.D0, -1.D0, or 0.D0 values implied by DPARAM(1) are not stored in DPARAM. Also: GAMSQ and RGAMSQ set in the DATA statement may be inexact — that's okay because they're only used for testing the size of DD1 and DD2; all actual scaling of data is done using GAM.

💅 Parameters 💅

• DD1 — yup, DD1 is DOUBLE PRECISION.
• DD2 — DD2 is DOUBLE PRECISION.
• DX1 — DX1 is DOUBLE PRECISION.
• DY1 — DY1 is DOUBLE PRECISION.
• DPARAM — DPARAM is DOUBLE PRECISION array, dimension (5). The slots go:
  • DPARAM(1)=DFLAG
  • DPARAM(2)=DH11
  • DPARAM(3)=DH21
  • DPARAM(4)=DH12
  • DPARAM(5)=DH22

👑 Author 👑

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

Definition: Definition at line 89 of file drotmg.f.

🎀 subroutine srotmg (real sd1, real sd2, real sx1, real sy1, real, dimension(5) sparam) 🎀

SROTMG

🔥 Purpose 🔥

same energy, exact block:

           !>
           !>    CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS
           !>    THE SECOND COMPONENT OF THE 2-VECTOR  (SQRT(SD1)*SX1,SQRT(SD2)*>    SY2)**T.
           !>    WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS..
           !>
           !>    SFLAG=-1.E0     SFLAG=0.E0        SFLAG=1.E0     SFLAG=-2.E0
           !>
           !>      (SH11  SH12)    (1.E0  SH12)    (SH11  1.E0)    (1.E0  0.E0)
           !>    H=(          )    (          )    (          )    (          )
           !>      (SH21  SH22),   (SH21  1.E0),   (-1.E0 SH22),   (0.E0  1.E0).
           !>    LOCATIONS 2-4 OF SPARAM CONTAIN SH11,SH21,SH12, AND SH22
           !>    RESPECTIVELY. (VALUES OF 1.E0, -1.E0, OR 0.E0 IMPLIED BY THE
           !>    VALUE OF SPARAM(1) ARE NOT STORED IN SPARAM.)
           !>
           !>    THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE
           !>    INEXACT.  THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE
           !>    OF SD1 AND SD2.  ALL ACTUAL SCALING OF DATA IS DONE USING GAM.
           !>
           !>

Translation: it constructs the modified Givens transformation matrix H that zeros the second component of the 2-vector (SQRT(SD1)*SX1,SQRT(SD2)*> SY2)**T. — again, that > stays because it's in the original. With SPARAM(1)=SFLAG, H has one of the forms above. Locations 2-4 of SPARAM contain SH11, SH21, SH12, and SH22 respectively, and the 1.E0, -1.E0, or 0.E0 values implied by SPARAM(1) are not stored in SPARAM. Same note as before: GAMSQ and RGAMSQ set in the DATA statement may be inexact, which is fine because they're only used for testing the size of SD1 and SD2; all actual scaling of data is done using GAM.

💅 Parameters 💅

• SD1 — SD1 is REAL.
• SD2 — SD2 is REAL.
• SX1 — SX1 is REAL.
• SY1 — SY1 is REAL.
• SPARAM — SPARAM is REAL array, dimension (5). The slots go:
  • SPARAM(1)=SFLAG
  • SPARAM(2)=SH11
  • SPARAM(3)=SH21
  • SPARAM(4)=SH12
  • SPARAM(5)=SH22

👑 Author 👑

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

Definition: Definition at line 89 of file srotmg.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

---

okay that's the whole page, bestie 🫶 — this one is LAPACK Version 3.12.0, and the page is rotmg(3). There's no date in the footer, just those source/version vibes, and the sign-off is lowkey iconic. periodt. 💅✨