Skip to content

New algorithms for computing Givens rotations #631

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
merged 10 commits into from
Nov 9, 2022
Merged

New algorithms for computing Givens rotations #631

Show file tree
Hide file tree
Changes from 1 commit
Commits
Show all changes
10 commits
Select commit Hold shift + click to select a range
2495f1c
Solves a precision bug in clartg
weslleyspereira Oct 15, 2021
b89b15b
Removes one line from clartg
weslleyspereira Oct 18, 2021
ac11f62
Several changes to reduce the computation error
weslleyspereira Oct 26, 2021
4320882
Starting to modify zlartg
weslleyspereira Oct 28, 2021
37a1a1e
Fix all other Givens rotation routines
weslleyspereira Nov 3, 2021
a49a659
Merge branch 'fix-precision-in-clartgf90-2' of github.com:weslleysper…
weslleyspereira Nov 3, 2021
2904d87
Algorithm precise and with no bias in the error
weslleyspereira Nov 23, 2021
95b6e84
Updates Givens rotations with preciser algorithms
weslleyspereira Dec 10, 2021
cdc8f33
Fix documentation thanks to @vladimir-ch
weslleyspereira Dec 13, 2021
c362fff
Minor changes
weslleyspereira Dec 13, 2021
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
Prev Previous commit
Minor changes
  • Loading branch information
@weslleyspereira
weslleyspereira committed Dec 13, 2021
commit c362fff1eee80fdd88b6fd60be3fb9d045cb08bb
44 changes: 29 additions & 15 deletions BLAS/SRC/crotg.f90
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -69,7 +69,7 @@
!
!> \date December 2021
!
!> \ingroup OTHERauxiliary
!> \ingroup single_blas_level1
!
!> \par Further Details:
! =====================
Expand Down Expand Up @@ -136,24 +136,38 @@ subroutine CROTG( a, b, c, s )
r = f
else if( f == czero ) then
c = zero
g1 = max( abs(real(g)), abs(aimag(g)) )
rtmax = sqrt( safmax/2 )
if( g1 > rtmin .and. g1 < rtmax ) then
if( real(g) == zero ) then
r = abs(aimag(g))
s = conjg( g ) / r
elseif( aimag(g) == zero ) then
r = abs(real(g))
s = conjg( g ) / r
else
g1 = max( abs(real(g)), abs(aimag(g)) )
rtmax = sqrt( safmax/2 )
if( g1 > rtmin .and. g1 < rtmax ) then
!
! Use unscaled algorithm
!
d = abs( g )
s = conjg( g ) / d
r = d
else
! The following two lines can be replaced by `d = abs( g )`.
! This algorithm do not use the intrinsic complex abs.
g2 = ABSSQ( g )
d = sqrt( g2 )
s = conjg( g ) / d
r = d
else
!
! Use scaled algorithm
!
u = min( safmax, max( safmin, g1 ) )
gs = g / u
d = abs( gs )
s = conjg( gs ) / d
r = d*u
u = min( safmax, max( safmin, g1 ) )
gs = g / u
! The following two lines can be replaced by `d = abs( gs )`.
! This algorithm do not use the intrinsic complex abs.
g2 = ABSSQ( gs )
d = sqrt( g2 )
s = conjg( gs ) / d
r = d*u
end if
end if
else
f1 = max( abs(real(f)), abs(aimag(f)) )
Expand Down Expand Up @@ -192,7 +206,7 @@ subroutine CROTG( a, b, c, s )
r = f / c
else
! f2 / sqrt(f2 * h2) < safmin, then
! h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
! sqrt(safmin) <= f2 * sqrt(safmax) <= h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
r = f * ( h2 / d )
end if
s = conjg( g ) * ( f / d )
Expand Down Expand Up @@ -248,7 +262,7 @@ subroutine CROTG( a, b, c, s )
r = fs / c
else
! f2 / sqrt(f2 * h2) < safmin, then
! h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
! sqrt(safmin) <= f2 * sqrt(safmax) <= h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
r = fs * ( h2 / d )
end if
s = conjg( gs ) * ( fs / d )
Expand Down
44 changes: 29 additions & 15 deletions BLAS/SRC/zrotg.f90
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -69,7 +69,7 @@
!
!> \date December 2021
!
!> \ingroup OTHERauxiliary
!> \ingroup single_blas_level1
!
!> \par Further Details:
! =====================
Expand Down Expand Up @@ -136,24 +136,38 @@ subroutine ZROTG( a, b, c, s )
r = f
else if( f == czero ) then
c = zero
g1 = max( abs(real(g)), abs(aimag(g)) )
rtmax = sqrt( safmax/2 )
if( g1 > rtmin .and. g1 < rtmax ) then
if( real(g) == zero ) then
r = abs(aimag(g))
s = conjg( g ) / r
elseif( aimag(g) == zero ) then
r = abs(real(g))
s = conjg( g ) / r
else
g1 = max( abs(real(g)), abs(aimag(g)) )
rtmax = sqrt( safmax/2 )
if( g1 > rtmin .and. g1 < rtmax ) then
!
! Use unscaled algorithm
!
d = abs( g )
s = conjg( g ) / d
r = d
else
! The following two lines can be replaced by `d = abs( g )`.
! This algorithm do not use the intrinsic complex abs.
g2 = ABSSQ( g )
d = sqrt( g2 )
s = conjg( g ) / d
r = d
else
!
! Use scaled algorithm
!
u = min( safmax, max( safmin, g1 ) )
gs = g / u
d = abs( gs )
s = conjg( gs ) / d
r = d*u
u = min( safmax, max( safmin, g1 ) )
gs = g / u
! The following two lines can be replaced by `d = abs( gs )`.
! This algorithm do not use the intrinsic complex abs.
g2 = ABSSQ( gs )
d = sqrt( g2 )
s = conjg( gs ) / d
r = d*u
end if
end if
else
f1 = max( abs(real(f)), abs(aimag(f)) )
Expand Down Expand Up @@ -192,7 +206,7 @@ subroutine ZROTG( a, b, c, s )
r = f / c
else
! f2 / sqrt(f2 * h2) < safmin, then
! h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
! sqrt(safmin) <= f2 * sqrt(safmax) <= h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
r = f * ( h2 / d )
end if
s = conjg( g ) * ( f / d )
Expand Down Expand Up @@ -248,7 +262,7 @@ subroutine ZROTG( a, b, c, s )
r = fs / c
else
! f2 / sqrt(f2 * h2) < safmin, then
! h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
! sqrt(safmin) <= f2 * sqrt(safmax) <= h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
r = fs * ( h2 / d )
end if
s = conjg( gs ) * ( fs / d )
Expand Down
42 changes: 28 additions & 14 deletions SRC/clartg.f90
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -150,24 +150,38 @@ subroutine CLARTG( f, g, c, s, r )
r = f
else if( f == czero ) then
c = zero
g1 = max( abs(real(g)), abs(aimag(g)) )
rtmax = sqrt( safmax/2 )
if( g1 > rtmin .and. g1 < rtmax ) then
if( real(g) == zero ) then
r = abs(aimag(g))
s = conjg( g ) / r
elseif( aimag(g) == zero ) then
r = abs(real(g))
s = conjg( g ) / r
else
g1 = max( abs(real(g)), abs(aimag(g)) )
rtmax = sqrt( safmax/2 )
if( g1 > rtmin .and. g1 < rtmax ) then
!
! Use unscaled algorithm
!
d = abs( g )
s = conjg( g ) / d
r = d
else
! The following two lines can be replaced by `d = abs( g )`.
! This algorithm do not use the intrinsic complex abs.
g2 = ABSSQ( g )
d = sqrt( g2 )
s = conjg( g ) / d
r = d
else
!
! Use scaled algorithm
!
u = min( safmax, max( safmin, g1 ) )
gs = g / u
d = abs( gs )
s = conjg( gs ) / d
r = d*u
u = min( safmax, max( safmin, g1 ) )
gs = g / u
! The following two lines can be replaced by `d = abs( gs )`.
! This algorithm do not use the intrinsic complex abs.
g2 = ABSSQ( gs )
d = sqrt( g2 )
s = conjg( gs ) / d
r = d*u
end if
end if
else
f1 = max( abs(real(f)), abs(aimag(f)) )
Expand Down Expand Up @@ -206,7 +220,7 @@ subroutine CLARTG( f, g, c, s, r )
r = f / c
else
! f2 / sqrt(f2 * h2) < safmin, then
! h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
! sqrt(safmin) <= f2 * sqrt(safmax) <= h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
r = f * ( h2 / d )
end if
s = conjg( g ) * ( f / d )
Expand Down Expand Up @@ -262,7 +276,7 @@ subroutine CLARTG( f, g, c, s, r )
r = fs / c
else
! f2 / sqrt(f2 * h2) < safmin, then
! h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
! sqrt(safmin) <= f2 * sqrt(safmax) <= h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
r = fs * ( h2 / d )
end if
s = conjg( gs ) * ( fs / d )
Expand Down
42 changes: 28 additions & 14 deletions SRC/zlartg.f90
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -150,24 +150,38 @@ subroutine ZLARTG( f, g, c, s, r )
r = f
else if( f == czero ) then
c = zero
g1 = max( abs(real(g)), abs(aimag(g)) )
rtmax = sqrt( safmax/2 )
if( g1 > rtmin .and. g1 < rtmax ) then
if( real(g) == zero ) then
r = abs(aimag(g))
s = conjg( g ) / r
elseif( aimag(g) == zero ) then
r = abs(real(g))
s = conjg( g ) / r
else
g1 = max( abs(real(g)), abs(aimag(g)) )
rtmax = sqrt( safmax/2 )
if( g1 > rtmin .and. g1 < rtmax ) then
!
! Use unscaled algorithm
!
d = abs( g )
s = conjg( g ) / d
r = d
else
! The following two lines can be replaced by `d = abs( g )`.
! This algorithm do not use the intrinsic complex abs.
g2 = ABSSQ( g )
d = sqrt( g2 )
s = conjg( g ) / d
r = d
else
!
! Use scaled algorithm
!
u = min( safmax, max( safmin, g1 ) )
gs = g / u
d = abs( gs )
s = conjg( gs ) / d
r = d*u
u = min( safmax, max( safmin, g1 ) )
gs = g / u
! The following two lines can be replaced by `d = abs( gs )`.
! This algorithm do not use the intrinsic complex abs.
g2 = ABSSQ( gs )
d = sqrt( g2 )
s = conjg( gs ) / d
r = d*u
end if
end if
else
f1 = max( abs(real(f)), abs(aimag(f)) )
Expand Down Expand Up @@ -206,7 +220,7 @@ subroutine ZLARTG( f, g, c, s, r )
r = f / c
else
! f2 / sqrt(f2 * h2) < safmin, then
! h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
! sqrt(safmin) <= f2 * sqrt(safmax) <= h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
r = f * ( h2 / d )
end if
s = conjg( g ) * ( f / d )
Expand Down Expand Up @@ -262,7 +276,7 @@ subroutine ZLARTG( f, g, c, s, r )
r = fs / c
else
! f2 / sqrt(f2 * h2) < safmin, then
! h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
! sqrt(safmin) <= f2 * sqrt(safmax) <= h2 / sqrt(f2 * h2) <= h2 * (safmin / f2) <= h2 <= safmax
r = fs * ( h2 / d )
end if
s = conjg( gs ) * ( fs / d )
Expand Down