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2
Commits
| Author | SHA1 | Date | |
|---|---|---|---|
 thijssteel
|
5ceb107887 | ||
|
thijssteel
|
6c7e38b850 |
@@ -82,15 +82,15 @@ set(ZBLAS2 zgemv.f zgbmv.f zhemv.f zhbmv.f zhpmv.f
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#---------------------------------------------------------
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# Level 3 BLAS
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#---------------------------------------------------------
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set(SBLAS3 sgemm.f ssymm.f ssyrk.f ssyr2k.f strmm.f strsm.f sgemmtr.f)
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set(SBLAS3 sgemm.f ssymm.f ssyrk.f ssyr2k.f strmm.f strsm.f sgemmtr.f srotc.f90)
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set(CBLAS3 cgemm.f csymm.f csyrk.f csyr2k.f ctrmm.f ctrsm.f
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chemm.f cherk.f cher2k.f cgemmtr.f)
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chemm.f cherk.f cher2k.f cgemmtr.f crotc.f90 scrotc.f90)
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set(DBLAS3 dgemm.f dsymm.f dsyrk.f dsyr2k.f dtrmm.f dtrsm.f dgemmtr.f)
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set(DBLAS3 dgemm.f dsymm.f dsyrk.f dsyr2k.f dtrmm.f dtrsm.f dgemmtr.f drotc.f90)
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set(ZBLAS3 zgemm.f zsymm.f zsyrk.f zsyr2k.f ztrmm.f ztrsm.f
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zhemm.f zherk.f zher2k.f zgemmtr.f)
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zhemm.f zherk.f zher2k.f zgemmtr.f zrotc.f90 dzrotc.f90)
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set(SOURCES)
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@@ -0,0 +1,256 @@
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!> \brief \b CROTC applies a chain of rotation sequences to a matrix.
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!
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! =========== DOCUMENTATION ===========
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!
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! Online html documentation available at
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! http://www.netlib.org/lapack/explore-html/
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!
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! Definition:
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! ===========
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!
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! subroutine crotc(side, dir, startup, shutdown, m, n, k,&
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! A, lda, C, ldc, S, lds)
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! .. Scalar Arguments ..
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! integer, intent(in) :: m, n, k
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! ...
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!
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!> \par Purpose:
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! =============
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!>
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!> \verbatim
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!>
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!> CROTC applies a chain of k rotation sequences of length n to a matrix A.
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!>
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!> Each rotation is specified by a cosine and a sine, stored in the
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!> matrices C and S respectively. Rotation G(i,j) is formed by
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!> C(i,j) and S(i,j).
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!>
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!> If side = 'L', rotation G(i,j) is applied to rows i and i+1 of A.
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!> [ A(i,j) ] = [ C(i,j) S(i,j) ] [ A(i,j) ]
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!> [ A(i+1,j) ] [ -conjg(S(i,j)) C(i,j) ] [ A(i+1,j) ]
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!> If side = 'R', rotation G(i,j) is applied to columns j and j+1 of A.
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!> [ A(i,j) A(i,j+1) ] = [ A(i,j) A(i,j+1) ] [ C(i,j) -conjg(S(i,j)) ]
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!> [ A(i+1,j) A(i+1,j+1) ] [ A(i+1,j) A(i+1,j+1) ] [ S(i,j) C(i,j) ]
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!>
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!> \endverbatim
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!
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! Arguments:
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! ==========
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!
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!> \param[in] side
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!> \verbatim
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!> side is CHARACTER*1
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!> If side = 'L', the rotations are applied to A from the left.
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!> If side = 'R', the rotations are applied to A from the right.
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!> \endverbatim
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!>
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!> \param[in] dir
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!> \verbatim
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!> dir is CHARACTER*1
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!> If dir = 'F', the rotations are applied in sequence from the
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!> first column/row to the last column/row.
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!> If dir = 'B', the rotations are applied in sequence from the
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!> last column/row to the first column/row.
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!> \endverbatim
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!>
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!> \param[in] startup
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!> \verbatim
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!> startup is LOGICAL
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!> If startup = .FALSE., the first (k-1) x (k-1) triangle
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!> of rotations is not applied.
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!> \endverbatim
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!>
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!> \param[in] shutdown
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!> \verbatim
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!> shutdown is LOGICAL
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!> If shutdown = .FALSE., the last (k-1) x (k-1) triangle
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!> of rotations is not applied.
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!> \endverbatim
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!>
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!> \param[in] m
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!> \verbatim
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!> m is INTEGER
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!> If side = 'L', m is the number of columns of A.
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!> If side = 'R', m is the number of rows of A.
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!> \endverbatim
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!>
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!> \param[in] n
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!> \verbatim
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!> n is INTEGER
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!> The number of rotations in one sequence.
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!> \endverbatim
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!>
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!> \param[in] k
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!> \verbatim
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!> k is INTEGER
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!> The number of sequences of rotations.
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!> \endverbatim
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!>
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!> \param[in,out] A
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!> \verbatim
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!> A is COMPLEX array
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!> If side = 'L', A has dimension (n+1,m).
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!> If side = 'R', A has dimension (m,n+1).
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!> The matrix to which the rotations are applied.
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!> \endverbatim
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!>
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!> \param[in] lda
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!> \verbatim
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!> lda is INTEGER
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!> The leading dimension of A.
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!> If side = 'L', lda >= n+1.
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!> If side = 'R', lda >= m.
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!> \endverbatim
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!>
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!> \param[in,out] C
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!> \verbatim
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!> C is REAL array, dimension (ldc,k)
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!> The matrix containing the cosines of the rotations.
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!> \endverbatim
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!>
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!> \param[in] ldc
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!> \verbatim
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!> ldc is INTEGER
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!> The leading dimension of C.
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!> ldc >= n.
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!> \endverbatim
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!>
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!> \param[in,out] S
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!> \verbatim
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!> S is COMPLEX array, dimension (lds,k)
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!> The matrix containing the sines of the rotations.
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!> \endverbatim
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!>
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!> \param[in] lds
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!> \verbatim
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!> lds is INTEGER
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!> The leading dimension of S.
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!> lds >= n.
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!> \endverbatim
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!
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! Authors:
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! ========
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!
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!> \author Thijs Steel, KU Leuven, Belgium
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!
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!> \date October 2024
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!
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!> \ingroup rotc
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!
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subroutine crotc(side, dir, startup, shutdown, m, n, k,&
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A, lda, C, ldc, S, lds)
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! .. Scalar Arguments ..
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integer, intent(in) :: m, n, k, lda, ldc, lds
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character, intent(in) :: dir, side
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logical, intent(in) :: startup, shutdown
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! .. Array Arguments ..
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complex, intent(inout) :: A(lda,*)
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complex, intent(in) :: S(lds,*)
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real, intent(in) :: C(ldc,*)
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! .. Local Scalars ..
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integer i, j, l, j1, j2, incj, incj1, incj2, info
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complex temp, sn
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real cs
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! .. Executable Statements ..
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! Test the input parameters
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info = 0
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if(.not. (side .eq. 'L' .or. side .eq. 'R')) then
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info = 1
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end if
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if(.not. (dir .eq. 'F' .or. dir .eq. 'B')) then
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info = 2
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end if
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if(m .lt. 0) then
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info = 5
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end if
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if(n .lt. 0) then
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info = 6
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end if
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if(k .lt. 0) then
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info = 7
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end if
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if(side .eq. 'L') then
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if(lda .lt. n+1) then
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info = 9
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end if
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else
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if(lda .lt. m) then
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info = 9
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end if
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end if
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if(ldc .lt. n) then
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info = 11
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end if
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if(lds .lt. n) then
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info = 13
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end if
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if(info .ne. 0) then
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call xerbla('CROTC ', info)
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return
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end if
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! Determine ranges for loops around C and S
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! The range for sequence l is:
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! j1+(l-1)*incj1:incj:j2+(l-1)*incj2
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if( dir .eq. 'F') then
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incj = 1
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if(startup) then
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j1 = 1
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incj1 = 0
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else
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j1 = k
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incj1 = -1
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end if
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j2 = n
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if(shutdown) then
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incj2 = 0
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else
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incj2 = -1
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end if
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else
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incj = -1
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j1 = 1
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if(startup) then
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incj1 = 1
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else
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incj1 = 0
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end if
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if(shutdown) then
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j2 = 0
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incj2 = 0
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else
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j2 = n-k+1
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incj2 = 1
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end if
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end if
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! Apply the rotations
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if(side .eq. 'L') then
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do l = 1, k
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do j = j1+(l-1)*incj1, j2+(l-1)*incj2, incj
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cs = C(j,l)
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sn = S(j,l)
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do i = 1, m
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temp = cs*A(i,j) + sn*A(i,j+1)
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A(i,j+1) = -conjg(sn*A(i,j)) + cs*A(i,j+1)
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A(i,j) = temp
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end do
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end do
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end do
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else
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do l = 1, k
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do j = j1+(l-1)*incj1, j2+(l-1)*incj2, incj
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cs = C(l,j)
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sn = S(l,j)
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do i = 1, m
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temp = cs*A(j,i) + sn*A(j+1,i)
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A(j+1,i) = -conjg(sn*A(j,i)) + cs*A(j+1,i)
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A(j,i) = temp
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end do
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end do
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end do
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end if
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end subroutine crotc
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@@ -0,0 +1,254 @@
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!> \brief \b DROTC applies a chain of rotation sequences to a matrix.
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!
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! =========== DOCUMENTATION ===========
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!
|
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! Online html documentation available at
|
||||
! http://www.netlib.org/lapack/explore-html/
|
||||
!
|
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! Definition:
|
||||
! ===========
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!
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! subroutine drotc(side, dir, startup, shutdown, m, n, k,&
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! A, lda, C, ldc, S, lds)
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! .. Scalar Arguments ..
|
||||
! integer, intent(in) :: m, n, k
|
||||
! ...
|
||||
!
|
||||
!> \par Purpose:
|
||||
! =============
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> DROTC applies a chain of k rotation sequences of length n to a matrix A.
|
||||
!>
|
||||
!> Each rotation is specified by a cosine and a sine, stored in the
|
||||
!> matrices C and S respectively. Rotation G(i,j) is formed by
|
||||
!> C(i,j) and S(i,j).
|
||||
!>
|
||||
!> If side = 'L', rotation G(i,j) is applied to rows i and i+1 of A.
|
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!> [ A(i,j) ] = [ C(i,j) S(i,j) ] [ A(i,j) ]
|
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!> [ A(i+1,j) ] [ -S(i,j) C(i,j) ] [ A(i+1,j) ]
|
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!> If side = 'R', rotation G(i,j) is applied to columns j and j+1 of A.
|
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!> [ A(i,j) A(i,j+1) ] = [ A(i,j) A(i,j+1) ] [ C(i,j) -S(i,j) ]
|
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!> [ A(i+1,j) A(i+1,j+1) ] [ A(i+1,j) A(i+1,j+1) ] [ S(i,j) C(i,j) ]
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!>
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!> \endverbatim
|
||||
!
|
||||
! Arguments:
|
||||
! ==========
|
||||
!
|
||||
!> \param[in] side
|
||||
!> \verbatim
|
||||
!> side is CHARACTER*1
|
||||
!> If side = 'L', the rotations are applied to A from the left.
|
||||
!> If side = 'R', the rotations are applied to A from the right.
|
||||
!> \endverbatim
|
||||
!>
|
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!> \param[in] dir
|
||||
!> \verbatim
|
||||
!> dir is CHARACTER*1
|
||||
!> If dir = 'F', the rotations are applied in sequence from the
|
||||
!> first column/row to the last column/row.
|
||||
!> If dir = 'B', the rotations are applied in sequence from the
|
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!> last column/row to the first column/row.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] startup
|
||||
!> \verbatim
|
||||
!> startup is LOGICAL
|
||||
!> If startup = .FALSE., the first (k-1) x (k-1) triangle
|
||||
!> of rotations is not applied.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] shutdown
|
||||
!> \verbatim
|
||||
!> shutdown is LOGICAL
|
||||
!> If shutdown = .FALSE., the last (k-1) x (k-1) triangle
|
||||
!> of rotations is not applied.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] m
|
||||
!> \verbatim
|
||||
!> m is INTEGER
|
||||
!> If side = 'L', m is the number of columns of A.
|
||||
!> If side = 'R', m is the number of rows of A.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] n
|
||||
!> \verbatim
|
||||
!> n is INTEGER
|
||||
!> The number of rotations in one sequence.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] k
|
||||
!> \verbatim
|
||||
!> k is INTEGER
|
||||
!> The number of sequences of rotations.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] A
|
||||
!> \verbatim
|
||||
!> A is DOUBLE PRECISION array
|
||||
!> If side = 'L', A has dimension (n+1,m).
|
||||
!> If side = 'R', A has dimension (m,n+1).
|
||||
!> The matrix to which the rotations are applied.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] lda
|
||||
!> \verbatim
|
||||
!> lda is INTEGER
|
||||
!> The leading dimension of A.
|
||||
!> If side = 'L', lda >= n+1.
|
||||
!> If side = 'R', lda >= m.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] C
|
||||
!> \verbatim
|
||||
!> C is DOUBLE PRECISION array, dimension (ldc,k)
|
||||
!> The matrix containing the cosines of the rotations.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] ldc
|
||||
!> \verbatim
|
||||
!> ldc is INTEGER
|
||||
!> The leading dimension of C.
|
||||
!> ldc >= n.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] S
|
||||
!> \verbatim
|
||||
!> S is DOUBLE PRECISION array, dimension (lds,k)
|
||||
!> The matrix containing the sines of the rotations.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] lds
|
||||
!> \verbatim
|
||||
!> lds is INTEGER
|
||||
!> The leading dimension of S.
|
||||
!> lds >= n.
|
||||
!> \endverbatim
|
||||
!
|
||||
! Authors:
|
||||
! ========
|
||||
!
|
||||
!> \author Thijs Steel, KU Leuven, Belgium
|
||||
!
|
||||
!> \date October 2024
|
||||
!
|
||||
!> \ingroup rotc
|
||||
!
|
||||
subroutine drotc(side, dir, startup, shutdown, m, n, k,&
|
||||
A, lda, C, ldc, S, lds)
|
||||
! .. Scalar Arguments ..
|
||||
integer, intent(in) :: m, n, k, lda, ldc, lds
|
||||
character, intent(in) :: dir, side
|
||||
logical, intent(in) :: startup, shutdown
|
||||
! .. Array Arguments ..
|
||||
double precision, intent(inout) :: A(lda,*)
|
||||
double precision, intent(in) :: C(ldc,*), S(lds,*)
|
||||
! .. Local Scalars ..
|
||||
integer i, j, l, j1, j2, incj, incj1, incj2, info
|
||||
double precision temp, cs, sn
|
||||
! .. Executable Statements ..
|
||||
|
||||
! Test the input parameters
|
||||
info = 0
|
||||
if(.not. (side .eq. 'L' .or. side .eq. 'R')) then
|
||||
info = 1
|
||||
end if
|
||||
if(.not. (dir .eq. 'F' .or. dir .eq. 'B')) then
|
||||
info = 2
|
||||
end if
|
||||
if(m .lt. 0) then
|
||||
info = 5
|
||||
end if
|
||||
if(n .lt. 0) then
|
||||
info = 6
|
||||
end if
|
||||
if(k .lt. 0) then
|
||||
info = 7
|
||||
end if
|
||||
if(side .eq. 'L') then
|
||||
if(lda .lt. n+1) then
|
||||
info = 9
|
||||
end if
|
||||
else
|
||||
if(lda .lt. m) then
|
||||
info = 9
|
||||
end if
|
||||
end if
|
||||
if(ldc .lt. n) then
|
||||
info = 11
|
||||
end if
|
||||
if(lds .lt. n) then
|
||||
info = 13
|
||||
end if
|
||||
|
||||
if(info .ne. 0) then
|
||||
call xerbla('DROTC ', info)
|
||||
return
|
||||
end if
|
||||
|
||||
! Determine ranges for loops around C and S
|
||||
! The range for sequence l is:
|
||||
! j1+(l-1)*incj1:incj:j2+(l-1)*incj2
|
||||
if( dir .eq. 'F') then
|
||||
incj = 1
|
||||
if(startup) then
|
||||
j1 = 1
|
||||
incj1 = 0
|
||||
else
|
||||
j1 = k
|
||||
incj1 = -1
|
||||
end if
|
||||
j2 = n
|
||||
if(shutdown) then
|
||||
incj2 = 0
|
||||
else
|
||||
incj2 = -1
|
||||
end if
|
||||
else
|
||||
incj = -1
|
||||
j1 = 1
|
||||
if(startup) then
|
||||
incj1 = 1
|
||||
else
|
||||
incj1 = 0
|
||||
end if
|
||||
if(shutdown) then
|
||||
j2 = 0
|
||||
incj2 = 0
|
||||
else
|
||||
j2 = n-k+1
|
||||
incj2 = 1
|
||||
end if
|
||||
end if
|
||||
|
||||
! Apply the rotations
|
||||
if(side .eq. 'L') then
|
||||
do l = 1, k
|
||||
do j = j1+(l-1)*incj1, j2+(l-1)*incj2, incj
|
||||
cs = C(j,l)
|
||||
sn = S(j,l)
|
||||
do i = 1, m
|
||||
temp = cs*A(i,j) + sn*A(i,j+1)
|
||||
A(i,j+1) = -sn*A(i,j) + cs*A(i,j+1)
|
||||
A(i,j) = temp
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
else
|
||||
do l = 1, k
|
||||
do j = j1+(l-1)*incj1, j2+(l-1)*incj2, incj
|
||||
cs = C(l,j)
|
||||
sn = S(l,j)
|
||||
do i = 1, m
|
||||
temp = cs*A(j,i) + sn*A(j+1,i)
|
||||
A(j+1,i) = -sn*A(j,i) + cs*A(j+1,i)
|
||||
A(j,i) = temp
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
end if
|
||||
|
||||
end subroutine drotc
|
||||
@@ -0,0 +1,255 @@
|
||||
!> \brief \b DZROTC applies a chain of rotation sequences to a matrix.
|
||||
!
|
||||
! =========== DOCUMENTATION ===========
|
||||
!
|
||||
! Online html documentation available at
|
||||
! http://www.netlib.org/lapack/explore-html/
|
||||
!
|
||||
! Definition:
|
||||
! ===========
|
||||
!
|
||||
! subroutine dzrotc(side, dir, startup, shutdown, m, n, k,&
|
||||
! A, lda, C, ldc, S, lds)
|
||||
! .. Scalar Arguments ..
|
||||
! integer, intent(in) :: m, n, k
|
||||
! ...
|
||||
!
|
||||
!> \par Purpose:
|
||||
! =============
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> DZROTC applies a chain of k rotation sequences of length n to a matrix A.
|
||||
!>
|
||||
!> Each rotation is specified by a cosine and a sine, stored in the
|
||||
!> matrices C and S respectively. Rotation G(i,j) is formed by
|
||||
!> C(i,j) and S(i,j).
|
||||
!>
|
||||
!> If side = 'L', rotation G(i,j) is applied to rows i and i+1 of A.
|
||||
!> [ A(i,j) ] = [ C(i,j) S(i,j) ] [ A(i,j) ]
|
||||
!> [ A(i+1,j) ] [ -S(i,j) C(i,j) ] [ A(i+1,j) ]
|
||||
!> If side = 'R', rotation G(i,j) is applied to columns j and j+1 of A.
|
||||
!> [ A(i,j) A(i,j+1) ] = [ A(i,j) A(i,j+1) ] [ C(i,j) -S(i,j) ]
|
||||
!> [ A(i+1,j) A(i+1,j+1) ] [ A(i+1,j) A(i+1,j+1) ] [ S(i,j) C(i,j) ]
|
||||
!>
|
||||
!> \endverbatim
|
||||
!
|
||||
! Arguments:
|
||||
! ==========
|
||||
!
|
||||
!> \param[in] side
|
||||
!> \verbatim
|
||||
!> side is CHARACTER*1
|
||||
!> If side = 'L', the rotations are applied to A from the left.
|
||||
!> If side = 'R', the rotations are applied to A from the right.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] dir
|
||||
!> \verbatim
|
||||
!> dir is CHARACTER*1
|
||||
!> If dir = 'F', the rotations are applied in sequence from the
|
||||
!> first column/row to the last column/row.
|
||||
!> If dir = 'B', the rotations are applied in sequence from the
|
||||
!> last column/row to the first column/row.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] startup
|
||||
!> \verbatim
|
||||
!> startup is LOGICAL
|
||||
!> If startup = .FALSE., the first (k-1) x (k-1) triangle
|
||||
!> of rotations is not applied.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] shutdown
|
||||
!> \verbatim
|
||||
!> shutdown is LOGICAL
|
||||
!> If shutdown = .FALSE., the last (k-1) x (k-1) triangle
|
||||
!> of rotations is not applied.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] m
|
||||
!> \verbatim
|
||||
!> m is INTEGER
|
||||
!> If side = 'L', m is the number of columns of A.
|
||||
!> If side = 'R', m is the number of rows of A.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] n
|
||||
!> \verbatim
|
||||
!> n is INTEGER
|
||||
!> The number of rotations in one sequence.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] k
|
||||
!> \verbatim
|
||||
!> k is INTEGER
|
||||
!> The number of sequences of rotations.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] A
|
||||
!> \verbatim
|
||||
!> A is DOUBLE COMPLEX array
|
||||
!> If side = 'L', A has dimension (n+1,m).
|
||||
!> If side = 'R', A has dimension (m,n+1).
|
||||
!> The matrix to which the rotations are applied.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] lda
|
||||
!> \verbatim
|
||||
!> lda is INTEGER
|
||||
!> The leading dimension of A.
|
||||
!> If side = 'L', lda >= n+1.
|
||||
!> If side = 'R', lda >= m.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] C
|
||||
!> \verbatim
|
||||
!> C is DOUBLE PRECISION array, dimension (ldc,k)
|
||||
!> The matrix containing the cosines of the rotations.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] ldc
|
||||
!> \verbatim
|
||||
!> ldc is INTEGER
|
||||
!> The leading dimension of C.
|
||||
!> ldc >= n.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] S
|
||||
!> \verbatim
|
||||
!> S is DOUBLE PRECISION array, dimension (lds,k)
|
||||
!> The matrix containing the sines of the rotations.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] lds
|
||||
!> \verbatim
|
||||
!> lds is INTEGER
|
||||
!> The leading dimension of S.
|
||||
!> lds >= n.
|
||||
!> \endverbatim
|
||||
!
|
||||
! Authors:
|
||||
! ========
|
||||
!
|
||||
!> \author Thijs Steel, KU Leuven, Belgium
|
||||
!
|
||||
!> \date October 2024
|
||||
!
|
||||
!> \ingroup rotc
|
||||
!
|
||||
subroutine dzrotc(side, dir, startup, shutdown, m, n, k,&
|
||||
A, lda, C, ldc, S, lds)
|
||||
! .. Scalar Arguments ..
|
||||
integer, intent(in) :: m, n, k, lda, ldc, lds
|
||||
character, intent(in) :: dir, side
|
||||
logical, intent(in) :: startup, shutdown
|
||||
! .. Array Arguments ..
|
||||
double complex, intent(inout) :: A(lda,*)
|
||||
double precision, intent(in) :: C(ldc,*), S(lds,*)
|
||||
! .. Local Scalars ..
|
||||
integer i, j, l, j1, j2, incj, incj1, incj2, info
|
||||
double complex temp
|
||||
double precision cs, sn
|
||||
! .. Executable Statements ..
|
||||
|
||||
! Test the input parameters
|
||||
info = 0
|
||||
if(.not. (side .eq. 'L' .or. side .eq. 'R')) then
|
||||
info = 1
|
||||
end if
|
||||
if(.not. (dir .eq. 'F' .or. dir .eq. 'B')) then
|
||||
info = 2
|
||||
end if
|
||||
if(m .lt. 0) then
|
||||
info = 5
|
||||
end if
|
||||
if(n .lt. 0) then
|
||||
info = 6
|
||||
end if
|
||||
if(k .lt. 0) then
|
||||
info = 7
|
||||
end if
|
||||
if(side .eq. 'L') then
|
||||
if(lda .lt. n+1) then
|
||||
info = 9
|
||||
end if
|
||||
else
|
||||
if(lda .lt. m) then
|
||||
info = 9
|
||||
end if
|
||||
end if
|
||||
if(ldc .lt. n) then
|
||||
info = 11
|
||||
end if
|
||||
if(lds .lt. n) then
|
||||
info = 13
|
||||
end if
|
||||
|
||||
if(info .ne. 0) then
|
||||
call xerbla('DZROTC ', info)
|
||||
return
|
||||
end if
|
||||
|
||||
! Determine ranges for loops around C and S
|
||||
! The range for sequence l is:
|
||||
! j1+(l-1)*incj1:incj:j2+(l-1)*incj2
|
||||
if( dir .eq. 'F') then
|
||||
incj = 1
|
||||
if(startup) then
|
||||
j1 = 1
|
||||
incj1 = 0
|
||||
else
|
||||
j1 = k
|
||||
incj1 = -1
|
||||
end if
|
||||
j2 = n
|
||||
if(shutdown) then
|
||||
incj2 = 0
|
||||
else
|
||||
incj2 = -1
|
||||
end if
|
||||
else
|
||||
incj = -1
|
||||
j1 = 1
|
||||
if(startup) then
|
||||
incj1 = 1
|
||||
else
|
||||
incj1 = 0
|
||||
end if
|
||||
if(shutdown) then
|
||||
j2 = 0
|
||||
incj2 = 0
|
||||
else
|
||||
j2 = n-k+1
|
||||
incj2 = 1
|
||||
end if
|
||||
end if
|
||||
|
||||
! Apply the rotations
|
||||
if(side .eq. 'L') then
|
||||
do l = 1, k
|
||||
do j = j1+(l-1)*incj1, j2+(l-1)*incj2, incj
|
||||
cs = C(j,l)
|
||||
sn = S(j,l)
|
||||
do i = 1, m
|
||||
temp = cs*A(i,j) + sn*A(i,j+1)
|
||||
A(i,j+1) = -sn*A(i,j) + cs*A(i,j+1)
|
||||
A(i,j) = temp
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
else
|
||||
do l = 1, k
|
||||
do j = j1+(l-1)*incj1, j2+(l-1)*incj2, incj
|
||||
cs = C(l,j)
|
||||
sn = S(l,j)
|
||||
do i = 1, m
|
||||
temp = cs*A(j,i) + sn*A(j+1,i)
|
||||
A(j+1,i) = -sn*A(j,i) + cs*A(j+1,i)
|
||||
A(j,i) = temp
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
end if
|
||||
|
||||
end subroutine dzrotc
|
||||
@@ -0,0 +1,255 @@
|
||||
!> \brief \b SCROTC applies a chain of rotation sequences to a matrix.
|
||||
!
|
||||
! =========== DOCUMENTATION ===========
|
||||
!
|
||||
! Online html documentation available at
|
||||
! http://www.netlib.org/lapack/explore-html/
|
||||
!
|
||||
! Definition:
|
||||
! ===========
|
||||
!
|
||||
! subroutine scrotc(side, dir, startup, shutdown, m, n, k,&
|
||||
! A, lda, C, ldc, S, lds)
|
||||
! .. Scalar Arguments ..
|
||||
! integer, intent(in) :: m, n, k
|
||||
! ...
|
||||
!
|
||||
!> \par Purpose:
|
||||
! =============
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> SCROTC applies a chain of k rotation sequences of length n to a matrix A.
|
||||
!>
|
||||
!> Each rotation is specified by a cosine and a sine, stored in the
|
||||
!> matrices C and S respectively. Rotation G(i,j) is formed by
|
||||
!> C(i,j) and S(i,j).
|
||||
!>
|
||||
!> If side = 'L', rotation G(i,j) is applied to rows i and i+1 of A.
|
||||
!> [ A(i,j) ] = [ C(i,j) S(i,j) ] [ A(i,j) ]
|
||||
!> [ A(i+1,j) ] [ -S(i,j) C(i,j) ] [ A(i+1,j) ]
|
||||
!> If side = 'R', rotation G(i,j) is applied to columns j and j+1 of A.
|
||||
!> [ A(i,j) A(i,j+1) ] = [ A(i,j) A(i,j+1) ] [ C(i,j) -S(i,j) ]
|
||||
!> [ A(i+1,j) A(i+1,j+1) ] [ A(i+1,j) A(i+1,j+1) ] [ S(i,j) C(i,j) ]
|
||||
!>
|
||||
!> \endverbatim
|
||||
!
|
||||
! Arguments:
|
||||
! ==========
|
||||
!
|
||||
!> \param[in] side
|
||||
!> \verbatim
|
||||
!> side is CHARACTER*1
|
||||
!> If side = 'L', the rotations are applied to A from the left.
|
||||
!> If side = 'R', the rotations are applied to A from the right.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] dir
|
||||
!> \verbatim
|
||||
!> dir is CHARACTER*1
|
||||
!> If dir = 'F', the rotations are applied in sequence from the
|
||||
!> first column/row to the last column/row.
|
||||
!> If dir = 'B', the rotations are applied in sequence from the
|
||||
!> last column/row to the first column/row.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] startup
|
||||
!> \verbatim
|
||||
!> startup is LOGICAL
|
||||
!> If startup = .FALSE., the first (k-1) x (k-1) triangle
|
||||
!> of rotations is not applied.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] shutdown
|
||||
!> \verbatim
|
||||
!> shutdown is LOGICAL
|
||||
!> If shutdown = .FALSE., the last (k-1) x (k-1) triangle
|
||||
!> of rotations is not applied.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] m
|
||||
!> \verbatim
|
||||
!> m is INTEGER
|
||||
!> If side = 'L', m is the number of columns of A.
|
||||
!> If side = 'R', m is the number of rows of A.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] n
|
||||
!> \verbatim
|
||||
!> n is INTEGER
|
||||
!> The number of rotations in one sequence.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] k
|
||||
!> \verbatim
|
||||
!> k is INTEGER
|
||||
!> The number of sequences of rotations.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] A
|
||||
!> \verbatim
|
||||
!> A is COMPLEX array
|
||||
!> If side = 'L', A has dimension (n+1,m).
|
||||
!> If side = 'R', A has dimension (m,n+1).
|
||||
!> The matrix to which the rotations are applied.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] lda
|
||||
!> \verbatim
|
||||
!> lda is INTEGER
|
||||
!> The leading dimension of A.
|
||||
!> If side = 'L', lda >= n+1.
|
||||
!> If side = 'R', lda >= m.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] C
|
||||
!> \verbatim
|
||||
!> C is REAL array, dimension (ldc,k)
|
||||
!> The matrix containing the cosines of the rotations.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] ldc
|
||||
!> \verbatim
|
||||
!> ldc is INTEGER
|
||||
!> The leading dimension of C.
|
||||
!> ldc >= n.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] S
|
||||
!> \verbatim
|
||||
!> S is REAL array, dimension (lds,k)
|
||||
!> The matrix containing the sines of the rotations.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] lds
|
||||
!> \verbatim
|
||||
!> lds is INTEGER
|
||||
!> The leading dimension of S.
|
||||
!> lds >= n.
|
||||
!> \endverbatim
|
||||
!
|
||||
! Authors:
|
||||
! ========
|
||||
!
|
||||
!> \author Thijs Steel, KU Leuven, Belgium
|
||||
!
|
||||
!> \date October 2024
|
||||
!
|
||||
!> \ingroup rotc
|
||||
!
|
||||
subroutine scrotc(side, dir, startup, shutdown, m, n, k,&
|
||||
A, lda, C, ldc, S, lds)
|
||||
! .. Scalar Arguments ..
|
||||
integer, intent(in) :: m, n, k, lda, ldc, lds
|
||||
character, intent(in) :: dir, side
|
||||
logical, intent(in) :: startup, shutdown
|
||||
! .. Array Arguments ..
|
||||
complex, intent(inout) :: A(lda,*)
|
||||
real, intent(in) :: C(ldc,*), S(lds,*)
|
||||
! .. Local Scalars ..
|
||||
integer i, j, l, j1, j2, incj, incj1, incj2, info
|
||||
complex temp
|
||||
real cs, sn
|
||||
! .. Executable Statements ..
|
||||
|
||||
! Test the input parameters
|
||||
info = 0
|
||||
if(.not. (side .eq. 'L' .or. side .eq. 'R')) then
|
||||
info = 1
|
||||
end if
|
||||
if(.not. (dir .eq. 'F' .or. dir .eq. 'B')) then
|
||||
info = 2
|
||||
end if
|
||||
if(m .lt. 0) then
|
||||
info = 5
|
||||
end if
|
||||
if(n .lt. 0) then
|
||||
info = 6
|
||||
end if
|
||||
if(k .lt. 0) then
|
||||
info = 7
|
||||
end if
|
||||
if(side .eq. 'L') then
|
||||
if(lda .lt. n+1) then
|
||||
info = 9
|
||||
end if
|
||||
else
|
||||
if(lda .lt. m) then
|
||||
info = 9
|
||||
end if
|
||||
end if
|
||||
if(ldc .lt. n) then
|
||||
info = 11
|
||||
end if
|
||||
if(lds .lt. n) then
|
||||
info = 13
|
||||
end if
|
||||
|
||||
if(info .ne. 0) then
|
||||
call xerbla('SCROTC ', info)
|
||||
return
|
||||
end if
|
||||
|
||||
! Determine ranges for loops around C and S
|
||||
! The range for sequence l is:
|
||||
! j1+(l-1)*incj1:incj:j2+(l-1)*incj2
|
||||
if( dir .eq. 'F') then
|
||||
incj = 1
|
||||
if(startup) then
|
||||
j1 = 1
|
||||
incj1 = 0
|
||||
else
|
||||
j1 = k
|
||||
incj1 = -1
|
||||
end if
|
||||
j2 = n
|
||||
if(shutdown) then
|
||||
incj2 = 0
|
||||
else
|
||||
incj2 = -1
|
||||
end if
|
||||
else
|
||||
incj = -1
|
||||
j1 = 1
|
||||
if(startup) then
|
||||
incj1 = 1
|
||||
else
|
||||
incj1 = 0
|
||||
end if
|
||||
if(shutdown) then
|
||||
j2 = 0
|
||||
incj2 = 0
|
||||
else
|
||||
j2 = n-k+1
|
||||
incj2 = 1
|
||||
end if
|
||||
end if
|
||||
|
||||
! Apply the rotations
|
||||
if(side .eq. 'L') then
|
||||
do l = 1, k
|
||||
do j = j1+(l-1)*incj1, j2+(l-1)*incj2, incj
|
||||
cs = C(j,l)
|
||||
sn = S(j,l)
|
||||
do i = 1, m
|
||||
temp = cs*A(i,j) + sn*A(i,j+1)
|
||||
A(i,j+1) = -sn*A(i,j) + cs*A(i,j+1)
|
||||
A(i,j) = temp
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
else
|
||||
do l = 1, k
|
||||
do j = j1+(l-1)*incj1, j2+(l-1)*incj2, incj
|
||||
cs = C(l,j)
|
||||
sn = S(l,j)
|
||||
do i = 1, m
|
||||
temp = cs*A(j,i) + sn*A(j+1,i)
|
||||
A(j+1,i) = -sn*A(j,i) + cs*A(j+1,i)
|
||||
A(j,i) = temp
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
end if
|
||||
|
||||
end subroutine scrotc
|
||||
@@ -0,0 +1,254 @@
|
||||
!> \brief \b SROTC applies a chain of rotation sequences to a matrix.
|
||||
!
|
||||
! =========== DOCUMENTATION ===========
|
||||
!
|
||||
! Online html documentation available at
|
||||
! http://www.netlib.org/lapack/explore-html/
|
||||
!
|
||||
! Definition:
|
||||
! ===========
|
||||
!
|
||||
! subroutine srotc(side, dir, startup, shutdown, m, n, k,&
|
||||
! A, lda, C, ldc, S, lds)
|
||||
! .. Scalar Arguments ..
|
||||
! integer, intent(in) :: m, n, k
|
||||
! ...
|
||||
!
|
||||
!> \par Purpose:
|
||||
! =============
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> SROTC applies a chain of k rotation sequences of length n to a matrix A.
|
||||
!>
|
||||
!> Each rotation is specified by a cosine and a sine, stored in the
|
||||
!> matrices C and S respectively. Rotation G(i,j) is formed by
|
||||
!> C(i,j) and S(i,j).
|
||||
!>
|
||||
!> If side = 'L', rotation G(i,j) is applied to rows i and i+1 of A.
|
||||
!> [ A(i,j) ] = [ C(i,j) S(i,j) ] [ A(i,j) ]
|
||||
!> [ A(i+1,j) ] [ -S(i,j) C(i,j) ] [ A(i+1,j) ]
|
||||
!> If side = 'R', rotation G(i,j) is applied to columns j and j+1 of A.
|
||||
!> [ A(i,j) A(i,j+1) ] = [ A(i,j) A(i,j+1) ] [ C(i,j) -S(i,j) ]
|
||||
!> [ A(i+1,j) A(i+1,j+1) ] [ A(i+1,j) A(i+1,j+1) ] [ S(i,j) C(i,j) ]
|
||||
!>
|
||||
!> \endverbatim
|
||||
!
|
||||
! Arguments:
|
||||
! ==========
|
||||
!
|
||||
!> \param[in] side
|
||||
!> \verbatim
|
||||
!> side is CHARACTER*1
|
||||
!> If side = 'L', the rotations are applied to A from the left.
|
||||
!> If side = 'R', the rotations are applied to A from the right.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] dir
|
||||
!> \verbatim
|
||||
!> dir is CHARACTER*1
|
||||
!> If dir = 'F', the rotations are applied in sequence from the
|
||||
!> first column/row to the last column/row.
|
||||
!> If dir = 'B', the rotations are applied in sequence from the
|
||||
!> last column/row to the first column/row.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] startup
|
||||
!> \verbatim
|
||||
!> startup is LOGICAL
|
||||
!> If startup = .FALSE., the first (k-1) x (k-1) triangle
|
||||
!> of rotations is not applied.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] shutdown
|
||||
!> \verbatim
|
||||
!> shutdown is LOGICAL
|
||||
!> If shutdown = .FALSE., the last (k-1) x (k-1) triangle
|
||||
!> of rotations is not applied.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] m
|
||||
!> \verbatim
|
||||
!> m is INTEGER
|
||||
!> If side = 'L', m is the number of columns of A.
|
||||
!> If side = 'R', m is the number of rows of A.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] n
|
||||
!> \verbatim
|
||||
!> n is INTEGER
|
||||
!> The number of rotations in one sequence.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] k
|
||||
!> \verbatim
|
||||
!> k is INTEGER
|
||||
!> The number of sequences of rotations.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] A
|
||||
!> \verbatim
|
||||
!> A is REAL array
|
||||
!> If side = 'L', A has dimension (n+1,m).
|
||||
!> If side = 'R', A has dimension (m,n+1).
|
||||
!> The matrix to which the rotations are applied.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] lda
|
||||
!> \verbatim
|
||||
!> lda is INTEGER
|
||||
!> The leading dimension of A.
|
||||
!> If side = 'L', lda >= n+1.
|
||||
!> If side = 'R', lda >= m.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] C
|
||||
!> \verbatim
|
||||
!> C is REAL array, dimension (ldc,k)
|
||||
!> The matrix containing the cosines of the rotations.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] ldc
|
||||
!> \verbatim
|
||||
!> ldc is INTEGER
|
||||
!> The leading dimension of C.
|
||||
!> ldc >= n.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] S
|
||||
!> \verbatim
|
||||
!> S is REAL array, dimension (lds,k)
|
||||
!> The matrix containing the sines of the rotations.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] lds
|
||||
!> \verbatim
|
||||
!> lds is INTEGER
|
||||
!> The leading dimension of S.
|
||||
!> lds >= n.
|
||||
!> \endverbatim
|
||||
!
|
||||
! Authors:
|
||||
! ========
|
||||
!
|
||||
!> \author Thijs Steel, KU Leuven, Belgium
|
||||
!
|
||||
!> \date October 2024
|
||||
!
|
||||
!> \ingroup rotc
|
||||
!
|
||||
subroutine srotc(side, dir, startup, shutdown, m, n, k,&
|
||||
A, lda, C, ldc, S, lds)
|
||||
! .. Scalar Arguments ..
|
||||
integer, intent(in) :: m, n, k, lda, ldc, lds
|
||||
character, intent(in) :: dir, side
|
||||
logical, intent(in) :: startup, shutdown
|
||||
! .. Array Arguments ..
|
||||
real, intent(inout) :: A(lda,*)
|
||||
real, intent(in) :: C(ldc,*), S(lds,*)
|
||||
! .. Local Scalars ..
|
||||
integer i, j, l, j1, j2, incj, incj1, incj2, info
|
||||
real temp, cs, sn
|
||||
! .. Executable Statements ..
|
||||
|
||||
! Test the input parameters
|
||||
info = 0
|
||||
if(.not. (side .eq. 'L' .or. side .eq. 'R')) then
|
||||
info = 1
|
||||
end if
|
||||
if(.not. (dir .eq. 'F' .or. dir .eq. 'B')) then
|
||||
info = 2
|
||||
end if
|
||||
if(m .lt. 0) then
|
||||
info = 5
|
||||
end if
|
||||
if(n .lt. 0) then
|
||||
info = 6
|
||||
end if
|
||||
if(k .lt. 0) then
|
||||
info = 7
|
||||
end if
|
||||
if(side .eq. 'L') then
|
||||
if(lda .lt. n+1) then
|
||||
info = 9
|
||||
end if
|
||||
else
|
||||
if(lda .lt. m) then
|
||||
info = 9
|
||||
end if
|
||||
end if
|
||||
if(ldc .lt. n) then
|
||||
info = 11
|
||||
end if
|
||||
if(lds .lt. n) then
|
||||
info = 13
|
||||
end if
|
||||
|
||||
if(info .ne. 0) then
|
||||
call xerbla('SROTC ', info)
|
||||
return
|
||||
end if
|
||||
|
||||
! Determine ranges for loops around C and S
|
||||
! The range for sequence l is:
|
||||
! j1+(l-1)*incj1:incj:j2+(l-1)*incj2
|
||||
if( dir .eq. 'F') then
|
||||
incj = 1
|
||||
if(startup) then
|
||||
j1 = 1
|
||||
incj1 = 0
|
||||
else
|
||||
j1 = k
|
||||
incj1 = -1
|
||||
end if
|
||||
j2 = n
|
||||
if(shutdown) then
|
||||
incj2 = 0
|
||||
else
|
||||
incj2 = -1
|
||||
end if
|
||||
else
|
||||
incj = -1
|
||||
j1 = 1
|
||||
if(startup) then
|
||||
incj1 = 1
|
||||
else
|
||||
incj1 = 0
|
||||
end if
|
||||
if(shutdown) then
|
||||
j2 = 0
|
||||
incj2 = 0
|
||||
else
|
||||
j2 = n-k+1
|
||||
incj2 = 1
|
||||
end if
|
||||
end if
|
||||
|
||||
! Apply the rotations
|
||||
if(side .eq. 'L') then
|
||||
do l = 1, k
|
||||
do j = j1+(l-1)*incj1, j2+(l-1)*incj2, incj
|
||||
cs = C(j,l)
|
||||
sn = S(j,l)
|
||||
do i = 1, m
|
||||
temp = cs*A(i,j) + sn*A(i,j+1)
|
||||
A(i,j+1) = -sn*A(i,j) + cs*A(i,j+1)
|
||||
A(i,j) = temp
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
else
|
||||
do l = 1, k
|
||||
do j = j1+(l-1)*incj1, j2+(l-1)*incj2, incj
|
||||
cs = C(l,j)
|
||||
sn = S(l,j)
|
||||
do i = 1, m
|
||||
temp = cs*A(j,i) + sn*A(j+1,i)
|
||||
A(j+1,i) = -sn*A(j,i) + cs*A(j+1,i)
|
||||
A(j,i) = temp
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
end if
|
||||
|
||||
end subroutine srotc
|
||||
@@ -0,0 +1,256 @@
|
||||
!> \brief \b ZROTC applies a chain of rotation sequences to a matrix.
|
||||
!
|
||||
! =========== DOCUMENTATION ===========
|
||||
!
|
||||
! Online html documentation available at
|
||||
! http://www.netlib.org/lapack/explore-html/
|
||||
!
|
||||
! Definition:
|
||||
! ===========
|
||||
!
|
||||
! subroutine zrotc(side, dir, startup, shutdown, m, n, k,&
|
||||
! A, lda, C, ldc, S, lds)
|
||||
! .. Scalar Arguments ..
|
||||
! integer, intent(in) :: m, n, k
|
||||
! ...
|
||||
!
|
||||
!> \par Purpose:
|
||||
! =============
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> ZROTC applies a chain of k rotation sequences of length n to a matrix A.
|
||||
!>
|
||||
!> Each rotation is specified by a cosine and a sine, stored in the
|
||||
!> matrices C and S respectively. Rotation G(i,j) is formed by
|
||||
!> C(i,j) and S(i,j).
|
||||
!>
|
||||
!> If side = 'L', rotation G(i,j) is applied to rows i and i+1 of A.
|
||||
!> [ A(i,j) ] = [ C(i,j) S(i,j) ] [ A(i,j) ]
|
||||
!> [ A(i+1,j) ] [ -conjg(S(i,j)) C(i,j) ] [ A(i+1,j) ]
|
||||
!> If side = 'R', rotation G(i,j) is applied to columns j and j+1 of A.
|
||||
!> [ A(i,j) A(i,j+1) ] = [ A(i,j) A(i,j+1) ] [ C(i,j) -conjg(S(i,j)) ]
|
||||
!> [ A(i+1,j) A(i+1,j+1) ] [ A(i+1,j) A(i+1,j+1) ] [ S(i,j) C(i,j) ]
|
||||
!>
|
||||
!> \endverbatim
|
||||
!
|
||||
! Arguments:
|
||||
! ==========
|
||||
!
|
||||
!> \param[in] side
|
||||
!> \verbatim
|
||||
!> side is CHARACTER*1
|
||||
!> If side = 'L', the rotations are applied to A from the left.
|
||||
!> If side = 'R', the rotations are applied to A from the right.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] dir
|
||||
!> \verbatim
|
||||
!> dir is CHARACTER*1
|
||||
!> If dir = 'F', the rotations are applied in sequence from the
|
||||
!> first column/row to the last column/row.
|
||||
!> If dir = 'B', the rotations are applied in sequence from the
|
||||
!> last column/row to the first column/row.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] startup
|
||||
!> \verbatim
|
||||
!> startup is LOGICAL
|
||||
!> If startup = .FALSE., the first (k-1) x (k-1) triangle
|
||||
!> of rotations is not applied.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] shutdown
|
||||
!> \verbatim
|
||||
!> shutdown is LOGICAL
|
||||
!> If shutdown = .FALSE., the last (k-1) x (k-1) triangle
|
||||
!> of rotations is not applied.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] m
|
||||
!> \verbatim
|
||||
!> m is INTEGER
|
||||
!> If side = 'L', m is the number of columns of A.
|
||||
!> If side = 'R', m is the number of rows of A.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] n
|
||||
!> \verbatim
|
||||
!> n is INTEGER
|
||||
!> The number of rotations in one sequence.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] k
|
||||
!> \verbatim
|
||||
!> k is INTEGER
|
||||
!> The number of sequences of rotations.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] A
|
||||
!> \verbatim
|
||||
!> A is DOUBLE COMPLEX array
|
||||
!> If side = 'L', A has dimension (n+1,m).
|
||||
!> If side = 'R', A has dimension (m,n+1).
|
||||
!> The matrix to which the rotations are applied.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] lda
|
||||
!> \verbatim
|
||||
!> lda is INTEGER
|
||||
!> The leading dimension of A.
|
||||
!> If side = 'L', lda >= n+1.
|
||||
!> If side = 'R', lda >= m.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] C
|
||||
!> \verbatim
|
||||
!> C is DOUBLE PRECISION array, dimension (ldc,k)
|
||||
!> The matrix containing the cosines of the rotations.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] ldc
|
||||
!> \verbatim
|
||||
!> ldc is INTEGER
|
||||
!> The leading dimension of C.
|
||||
!> ldc >= n.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] S
|
||||
!> \verbatim
|
||||
!> S is DOUBLE COMPLEX array, dimension (lds,k)
|
||||
!> The matrix containing the sines of the rotations.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] lds
|
||||
!> \verbatim
|
||||
!> lds is INTEGER
|
||||
!> The leading dimension of S.
|
||||
!> lds >= n.
|
||||
!> \endverbatim
|
||||
!
|
||||
! Authors:
|
||||
! ========
|
||||
!
|
||||
!> \author Thijs Steel, KU Leuven, Belgium
|
||||
!
|
||||
!> \date October 2024
|
||||
!
|
||||
!> \ingroup rotc
|
||||
!
|
||||
subroutine zrotc(side, dir, startup, shutdown, m, n, k,&
|
||||
A, lda, C, ldc, S, lds)
|
||||
! .. Scalar Arguments ..
|
||||
integer, intent(in) :: m, n, k, lda, ldc, lds
|
||||
character, intent(in) :: dir, side
|
||||
logical, intent(in) :: startup, shutdown
|
||||
! .. Array Arguments ..
|
||||
double complex, intent(inout) :: A(lda,*)
|
||||
double complex, intent(in) :: S(lds,*)
|
||||
double precision, intent(in) :: C(ldc,*)
|
||||
! .. Local Scalars ..
|
||||
integer i, j, l, j1, j2, incj, incj1, incj2, info
|
||||
double complex temp, sn
|
||||
double precision cs
|
||||
! .. Executable Statements ..
|
||||
|
||||
! Test the input parameters
|
||||
info = 0
|
||||
if(.not. (side .eq. 'L' .or. side .eq. 'R')) then
|
||||
info = 1
|
||||
end if
|
||||
if(.not. (dir .eq. 'F' .or. dir .eq. 'B')) then
|
||||
info = 2
|
||||
end if
|
||||
if(m .lt. 0) then
|
||||
info = 5
|
||||
end if
|
||||
if(n .lt. 0) then
|
||||
info = 6
|
||||
end if
|
||||
if(k .lt. 0) then
|
||||
info = 7
|
||||
end if
|
||||
if(side .eq. 'L') then
|
||||
if(lda .lt. n+1) then
|
||||
info = 9
|
||||
end if
|
||||
else
|
||||
if(lda .lt. m) then
|
||||
info = 9
|
||||
end if
|
||||
end if
|
||||
if(ldc .lt. n) then
|
||||
info = 11
|
||||
end if
|
||||
if(lds .lt. n) then
|
||||
info = 13
|
||||
end if
|
||||
|
||||
if(info .ne. 0) then
|
||||
call xerbla('ZROTC ', info)
|
||||
return
|
||||
end if
|
||||
|
||||
! Determine ranges for loops around C and S
|
||||
! The range for sequence l is:
|
||||
! j1+(l-1)*incj1:incj:j2+(l-1)*incj2
|
||||
if( dir .eq. 'F') then
|
||||
incj = 1
|
||||
if(startup) then
|
||||
j1 = 1
|
||||
incj1 = 0
|
||||
else
|
||||
j1 = k
|
||||
incj1 = -1
|
||||
end if
|
||||
j2 = n
|
||||
if(shutdown) then
|
||||
incj2 = 0
|
||||
else
|
||||
incj2 = -1
|
||||
end if
|
||||
else
|
||||
incj = -1
|
||||
j1 = 1
|
||||
if(startup) then
|
||||
incj1 = 1
|
||||
else
|
||||
incj1 = 0
|
||||
end if
|
||||
if(shutdown) then
|
||||
j2 = 0
|
||||
incj2 = 0
|
||||
else
|
||||
j2 = n-k+1
|
||||
incj2 = 1
|
||||
end if
|
||||
end if
|
||||
|
||||
! Apply the rotations
|
||||
if(side .eq. 'L') then
|
||||
do l = 1, k
|
||||
do j = j1+(l-1)*incj1, j2+(l-1)*incj2, incj
|
||||
cs = C(j,l)
|
||||
sn = S(j,l)
|
||||
do i = 1, m
|
||||
temp = cs*A(i,j) + sn*A(i,j+1)
|
||||
A(i,j+1) = -conjg(sn*A(i,j)) + cs*A(i,j+1)
|
||||
A(i,j) = temp
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
else
|
||||
do l = 1, k
|
||||
do j = j1+(l-1)*incj1, j2+(l-1)*incj2, incj
|
||||
cs = C(l,j)
|
||||
sn = S(l,j)
|
||||
do i = 1, m
|
||||
temp = cs*A(j,i) + sn*A(j+1,i)
|
||||
A(j+1,i) = -conjg(sn*A(j,i)) + cs*A(j+1,i)
|
||||
A(j,i) = temp
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
end if
|
||||
|
||||
end subroutine zrotc
|
||||
Reference in New Issue
Block a user