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psblas3/base/modules/serial/psb_serial_mod.f90

361 lines
11 KiB
Fortran

!
! Parallel Sparse BLAS version 3.5
! (C) Copyright 2006-2018
! Salvatore Filippone
! Alfredo Buttari
!
! Redistribution and use in source and binary forms, with or without
! modification, are permitted provided that the following conditions
! are met:
! 1. Redistributions of source code must retain the above copyright
! notice, this list of conditions and the following disclaimer.
! 2. Redistributions in binary form must reproduce the above copyright
! notice, this list of conditions, and the following disclaimer in the
! documentation and/or other materials provided with the distribution.
! 3. The name of the PSBLAS group or the names of its contributors may
! not be used to endorse or promote products derived from this
! software without specific written permission.
!
! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
! ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
! TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
! PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS
! BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
! CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
! SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
! INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
! CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
! POSSIBILITY OF SUCH DAMAGE.
!
!
module psb_serial_mod
use psb_const_mod
use psb_error_mod
use psb_realloc_mod
use psb_string_mod
use psb_sort_mod
use psi_serial_mod, &
& psb_gth => psi_gth,&
& psb_sct => psi_sct
use psb_s_serial_mod
use psb_d_serial_mod
use psb_c_serial_mod
use psb_z_serial_mod
interface psb_nrm1
module procedure psb_snrm1, psb_dnrm1, psb_cnrm1, psb_znrm1
end interface psb_nrm1
interface psb_minreal
module procedure psb_sminreal, psb_dminreal, psb_cminreal, psb_zminreal
end interface psb_minreal
interface psb_nspaxpby
subroutine psb_d_nspaxpby(nz,iz,z,alpha, nx, ix, x, beta, ny,iy,y,info)
use psb_const_mod, only : psb_ipk_, psb_spk_, psb_dpk_
integer(psb_ipk_), intent(out) :: nz
integer(psb_ipk_), intent(out) :: iz(:)
real(psb_dpk_), intent (out) :: z(:)
integer(psb_ipk_), intent(in) :: nx, ny
integer(psb_ipk_), intent(in) :: ix(:), iy(:)
real(psb_dpk_), intent (in) :: x(:), y(:)
real(psb_dpk_), intent (in) :: alpha, beta
integer(psb_ipk_), intent(out) :: info
end subroutine psb_d_nspaxpby
end interface psb_nspaxpby
contains
elemental function psb_snrm1(x) result(res)
real(psb_spk_), intent(in) :: x
real(psb_spk_) :: res
res = abs( x )
end function psb_snrm1
elemental function psb_dnrm1(x) result(res)
real(psb_dpk_), intent(in) :: x
real(psb_dpk_) :: res
res = abs( x )
end function psb_dnrm1
elemental function psb_cnrm1(x) result(res)
complex(psb_spk_), intent(in) :: x
real(psb_spk_) :: res
res = abs( real( x ) ) + abs( aimag( x ) )
end function psb_cnrm1
elemental function psb_znrm1(x) result(res)
complex(psb_dpk_), intent(in) :: x
real(psb_dpk_) :: res
res = abs( real( x ) ) + abs( aimag( x ) )
end function psb_znrm1
elemental function psb_sminreal(x) result(res)
real(psb_spk_), intent(in) :: x
real(psb_spk_) :: res
res = ( x )
end function psb_sminreal
elemental function psb_dminreal(x) result(res)
real(psb_dpk_), intent(in) :: x
real(psb_dpk_) :: res
res = ( x )
end function psb_dminreal
elemental function psb_cminreal(x) result(res)
complex(psb_spk_), intent(in) :: x
real(psb_spk_) :: res
res = min( real( x ) , aimag( x ) )
end function psb_cminreal
elemental function psb_zminreal(x) result(res)
complex(psb_dpk_), intent(in) :: x
real(psb_dpk_) :: res
res = min( real( x ) , aimag( x ) )
end function psb_zminreal
subroutine crot( n, cx, incx, cy, incy, c, s )
!
! -- lapack auxiliary routine (version 3.0) --
! univ. of tennessee, univ. of california berkeley, nag ltd.,
! courant institute, argonne national lab, and rice university
! october 31, 1992
!
! .. scalar arguments ..
integer(psb_mpik_) :: incx, incy, n
real(psb_spk_) c
complex(psb_spk_) s
! ..
! .. array arguments ..
complex(psb_spk_) cx( * ), cy( * )
! ..
!
! purpose
! == = ====
!
! zrot applies a plane rotation, where the cos (c) is real and the
! sin (s) is complex, and the vectors cx and cy are complex.
!
! arguments
! == = ======
!
! n (input) integer
! the number of elements in the vectors cx and cy.
!
! cx (input/output) complex*16 array, dimension (n)
! on input, the vector x.
! on output, cx is overwritten with c*x + s*y.
!
! incx (input) integer
! the increment between successive values of cy. incx <> 0.
!
! cy (input/output) complex*16 array, dimension (n)
! on input, the vector y.
! on output, cy is overwritten with -conjg(s)*x + c*y.
!
! incy (input) integer
! the increment between successive values of cy. incx <> 0.
!
! c (input) double precision
! s (input) complex*16
! c and s define a rotation
! [ c s ]
! [ -conjg(s) c ]
! where c*c + s*conjg(s) = 1.0.
!
! == = ==================================================================
!
! .. local scalars ..
integer(psb_mpik_) :: i, ix, iy
complex(psb_spk_) stemp
! ..
! .. intrinsic functions ..
! ..
! .. executable statements ..
!
if( n <= 0 ) return
if( incx == 1 .and. incy == 1 ) then
!
! code for both increments equal to 1
!
do i = 1, n
stemp = c*cx(i) + s*cy(i)
cy(i) = c*cy(i) - conjg(s)*cx(i)
cx(i) = stemp
end do
else
!
! code for unequal increments or equal increments not equal to 1
!
ix = 1
iy = 1
if( incx < 0 )ix = ( -n+1 )*incx + 1
if( incy < 0 )iy = ( -n+1 )*incy + 1
do i = 1, n
stemp = c*cx(ix) + s*cy(iy)
cy(iy) = c*cy(iy) - conjg(s)*cx(ix)
cx(ix) = stemp
ix = ix + incx
iy = iy + incy
end do
end if
return
end subroutine crot
!
!
subroutine crotg(ca,cb,c,s)
complex(psb_spk_) ca,cb,s
real(psb_spk_) c
real(psb_spk_) norm,scale
complex(psb_spk_) alpha
!
if (cabs(ca) == 0.0) then
!
c = 0.0d0
s = (1.0,0.0)
ca = cb
return
end if
!
scale = cabs(ca) + cabs(cb)
norm = scale*sqrt((cabs(ca/cmplx(scale,0.0)))**2 +&
& (cabs(cb/cmplx(scale,0.0)))**2)
alpha = ca /cabs(ca)
c = cabs(ca) / norm
s = alpha * conjg(cb) / norm
ca = alpha * norm
!
return
end subroutine crotg
subroutine zrot( n, cx, incx, cy, incy, c, s )
!
! -- lapack auxiliary routine (version 3.0) --
! univ. of tennessee, univ. of california berkeley, nag ltd.,
! courant institute, argonne national lab, and rice university
! october 31, 1992
!
! .. scalar arguments ..
integer(psb_mpik_) :: incx, incy, n
real(psb_dpk_) c
complex(psb_dpk_) s
! ..
! .. array arguments ..
complex(psb_dpk_) cx( * ), cy( * )
! ..
!
! purpose
! == = ====
!
! zrot applies a plane rotation, where the cos (c) is real and the
! sin (s) is complex, and the vectors cx and cy are complex.
!
! arguments
! == = ======
!
! n (input) integer
! the number of elements in the vectors cx and cy.
!
! cx (input/output) complex*16 array, dimension (n)
! on input, the vector x.
! on output, cx is overwritten with c*x + s*y.
!
! incx (input) integer
! the increment between successive values of cy. incx <> 0.
!
! cy (input/output) complex*16 array, dimension (n)
! on input, the vector y.
! on output, cy is overwritten with -conjg(s)*x + c*y.
!
! incy (input) integer
! the increment between successive values of cy. incx <> 0.
!
! c (input) double precision
! s (input) complex*16
! c and s define a rotation
! [ c s ]
! [ -conjg(s) c ]
! where c*c + s*conjg(s) = 1.0.
!
! == = ==================================================================
!
! .. local scalars ..
integer(psb_mpik_) :: i, ix, iy
complex(psb_dpk_) stemp
! ..
! .. intrinsic functions ..
intrinsic dconjg
! ..
! .. executable statements ..
!
if( n <= 0 ) return
if( incx == 1 .and. incy == 1 ) then
!
! code for both increments equal to 1
!
do i = 1, n
stemp = c*cx(i) + s*cy(i)
cy(i) = c*cy(i) - dconjg(s)*cx(i)
cx(i) = stemp
end do
else
!
! code for unequal increments or equal increments not equal to 1
!
ix = 1
iy = 1
if( incx < 0 )ix = ( -n+1 )*incx + 1
if( incy < 0 )iy = ( -n+1 )*incy + 1
do i = 1, n
stemp = c*cx(ix) + s*cy(iy)
cy(iy) = c*cy(iy) - dconjg(s)*cx(ix)
cx(ix) = stemp
ix = ix + incx
iy = iy + incy
end do
end if
return
end subroutine zrot
!
!
subroutine zrotg(ca,cb,c,s)
complex(psb_dpk_) ca,cb,s
real(psb_dpk_) c
real(psb_dpk_) norm,scale
complex(psb_dpk_) alpha
!
if (cdabs(ca) == 0.0d0) then
!
c = 0.0d0
s = (1.0d0,0.0d0)
ca = cb
return
end if
!
scale = cdabs(ca) + cdabs(cb)
norm = scale*dsqrt((cdabs(ca/cmplx(scale,0.0d0,kind=psb_dpk_)))**2 +&
& (cdabs(cb/cmplx(scale,0.0d0,kind=psb_dpk_)))**2)
alpha = ca /cdabs(ca)
c = cdabs(ca) / norm
s = alpha * conjg(cb) / norm
ca = alpha * norm
!
return
end subroutine zrotg
end module psb_serial_mod