table of contents
| laqz1(3) | Library Functions Manual | laqz1(3) |
NAME¶
laqz1 - laqz1: step in ggev3, gges3
SYNOPSIS¶
Functions¶
subroutine CLAQZ1 (ilq, ilz, k, istartm, istopm, ihi, a,
lda, b, ldb, nq, qstart, q, ldq, nz, zstart, z, ldz)
CLAQZ1 subroutine DLAQZ1 (a, lda, b, ldb, sr1, sr2, si, beta1,
beta2, v)
DLAQZ1 subroutine SLAQZ1 (a, lda, b, ldb, sr1, sr2, si, beta1,
beta2, v)
SLAQZ1 subroutine ZLAQZ1 (ilq, ilz, k, istartm, istopm, ihi, a,
lda, b, ldb, nq, qstart, q, ldq, nz, zstart, z, ldz)
ZLAQZ1
Detailed Description¶
Function Documentation¶
subroutine CLAQZ1 (logical, intent(in) ilq, logical, intent(in) ilz, integer, intent(in) k, integer, intent(in) istartm, integer, intent(in) istopm, integer, intent(in) ihi, complex, dimension( lda, * ) a, integer, intent(in) lda, complex, dimension( ldb, * ) b, integer, intent(in) ldb, integer, intent(in) nq, integer, intent(in) qstart, complex, dimension( ldq, * ) q, integer, intent(in) ldq, integer, intent(in) nz, integer, intent(in) zstart, complex, dimension( ldz, * ) z, integer, intent(in) ldz)¶
CLAQZ1
Purpose:
!> !> CLAQZ1 chases a 1x1 shift bulge in a matrix pencil down a single position !>
Parameters
ILQ
!> ILQ is LOGICAL !> Determines whether or not to update the matrix Q !>
ILZ
!> ILZ is LOGICAL !> Determines whether or not to update the matrix Z !>
K
!> K is INTEGER !> Index indicating the position of the bulge. !> On entry, the bulge is located in !> (A(k+1,k),B(k+1,k)). !> On exit, the bulge is located in !> (A(k+2,k+1),B(k+2,k+1)). !>
ISTARTM
!> ISTARTM is INTEGER !>
ISTOPM
!> ISTOPM is INTEGER !> Updates to (A,B) are restricted to !> (istartm:k+2,k:istopm). It is assumed !> without checking that istartm <= k+1 and !> k+2 <= istopm !>
IHI
!> IHI is INTEGER !>
A
!> A is COMPLEX array, dimension (LDA,N) !>
LDA
!> LDA is INTEGER !> The leading dimension of A as declared in !> the calling procedure. !>
B
!> B is COMPLEX array, dimension (LDB,N) !>
LDB
!> LDB is INTEGER !> The leading dimension of B as declared in !> the calling procedure. !>
NQ
!> NQ is INTEGER !> The order of the matrix Q !>
QSTART
!> QSTART is INTEGER !> Start index of the matrix Q. Rotations are applied !> To columns k+2-qStart:k+3-qStart of Q. !>
Q
!> Q is COMPLEX array, dimension (LDQ,NQ) !>
LDQ
!> LDQ is INTEGER !> The leading dimension of Q as declared in !> the calling procedure. !>
NZ
!> NZ is INTEGER !> The order of the matrix Z !>
ZSTART
!> ZSTART is INTEGER !> Start index of the matrix Z. Rotations are applied !> To columns k+1-qStart:k+2-qStart of Z. !>
Z
!> Z is COMPLEX array, dimension (LDZ,NZ) !>
LDZ
!> LDZ is INTEGER !> The leading dimension of Q as declared in !> the calling procedure. !>
Author
Thijs Steel, KU Leuven
Date
May 2020
Definition at line 171 of file claqz1.f.
subroutine DLAQZ1 (double precision, dimension( lda, * ), intent(in) a, integer, intent(in) lda, double precision, dimension( ldb, * ), intent(in) b, integer, intent(in) ldb, double precision, intent(in) sr1, double precision, intent(in) sr2, double precision, intent(in) si, double precision, intent(in) beta1, double precision, intent(in) beta2, double precision, dimension( * ), intent(out) v)¶
DLAQZ1
Purpose:
!> !> Given a 3-by-3 matrix pencil (A,B), DLAQZ1 sets v to a !> scalar multiple of the first column of the product !> !> (*) K = (A - (beta2*sr2 - i*si)*B)*B^(-1)*(beta1*A - (sr2 + i*si2)*B)*B^(-1). !> !> It is assumed that either !> !> 1) sr1 = sr2 !> or !> 2) si = 0. !> !> This is useful for starting double implicit shift bulges !> in the QZ algorithm. !>
Parameters
A
!> A is DOUBLE PRECISION array, dimension (LDA,N) !> The 3-by-3 matrix A in (*). !>
LDA
!> LDA is INTEGER !> The leading dimension of A as declared in !> the calling procedure. !>
B
!> B is DOUBLE PRECISION array, dimension (LDB,N) !> The 3-by-3 matrix B in (*). !>
LDB
!> LDB is INTEGER !> The leading dimension of B as declared in !> the calling procedure. !>
SR1
!> SR1 is DOUBLE PRECISION !>
SR2
!> SR2 is DOUBLE PRECISION !>
SI
!> SI is DOUBLE PRECISION !>
BETA1
!> BETA1 is DOUBLE PRECISION !>
BETA2
!> BETA2 is DOUBLE PRECISION !>
V
!> V is DOUBLE PRECISION array, dimension (N) !> A scalar multiple of the first column of the !> matrix K in (*). !>
Author
Thijs Steel, KU Leuven
Date
May 2020
Definition at line 125 of file dlaqz1.f.
subroutine SLAQZ1 (real, dimension( lda, * ), intent(in) a, integer, intent(in) lda, real, dimension( ldb, * ), intent(in) b, integer, intent(in) ldb, real, intent(in) sr1, real, intent(in) sr2, real, intent(in) si, real, intent(in) beta1, real, intent(in) beta2, real, dimension( * ), intent(out) v)¶
SLAQZ1
Purpose:
!> !> Given a 3-by-3 matrix pencil (A,B), SLAQZ1 sets v to a !> scalar multiple of the first column of the product !> !> (*) K = (A - (beta2*sr2 - i*si)*B)*B^(-1)*(beta1*A - (sr2 + i*si2)*B)*B^(-1). !> !> It is assumed that either !> !> 1) sr1 = sr2 !> or !> 2) si = 0. !> !> This is useful for starting double implicit shift bulges !> in the QZ algorithm. !>
Parameters
A
!> A is REAL array, dimension (LDA,N) !> The 3-by-3 matrix A in (*). !>
LDA
!> LDA is INTEGER !> The leading dimension of A as declared in !> the calling procedure. !>
B
!> B is REAL array, dimension (LDB,N) !> The 3-by-3 matrix B in (*). !>
LDB
!> LDB is INTEGER !> The leading dimension of B as declared in !> the calling procedure. !>
SR1
!> SR1 is REAL !>
SR2
!> SR2 is REAL !>
SI
!> SI is REAL !>
BETA1
!> BETA1 is REAL !>
BETA2
!> BETA2 is REAL !>
V
!> V is REAL array, dimension (N) !> A scalar multiple of the first column of the !> matrix K in (*). !>
Author
Thijs Steel, KU Leuven
Date
May 2020
Definition at line 125 of file slaqz1.f.
subroutine ZLAQZ1 (logical, intent(in) ilq, logical, intent(in) ilz, integer, intent(in) k, integer, intent(in) istartm, integer, intent(in) istopm, integer, intent(in) ihi, complex*16, dimension( lda, * ) a, integer, intent(in) lda, complex*16, dimension( ldb, * ) b, integer, intent(in) ldb, integer, intent(in) nq, integer, intent(in) qstart, complex*16, dimension( ldq, * ) q, integer, intent(in) ldq, integer, intent(in) nz, integer, intent(in) zstart, complex*16, dimension( ldz, * ) z, integer, intent(in) ldz)¶
ZLAQZ1
Purpose:
!> !> ZLAQZ1 chases a 1x1 shift bulge in a matrix pencil down a single position !>
Parameters
ILQ
!> ILQ is LOGICAL !> Determines whether or not to update the matrix Q !>
ILZ
!> ILZ is LOGICAL !> Determines whether or not to update the matrix Z !>
K
!> K is INTEGER !> Index indicating the position of the bulge. !> On entry, the bulge is located in !> (A(k+1,k),B(k+1,k)). !> On exit, the bulge is located in !> (A(k+2,k+1),B(k+2,k+1)). !>
ISTARTM
!> ISTARTM is INTEGER !>
ISTOPM
!> ISTOPM is INTEGER !> Updates to (A,B) are restricted to !> (istartm:k+2,k:istopm). It is assumed !> without checking that istartm <= k+1 and !> k+2 <= istopm !>
IHI
!> IHI is INTEGER !>
A
!> A is COMPLEX*16 array, dimension (LDA,N) !>
LDA
!> LDA is INTEGER !> The leading dimension of A as declared in !> the calling procedure. !>
B
!> B is COMPLEX*16 array, dimension (LDB,N) !>
LDB
!> LDB is INTEGER !> The leading dimension of B as declared in !> the calling procedure. !>
NQ
!> NQ is INTEGER !> The order of the matrix Q !>
QSTART
!> QSTART is INTEGER !> Start index of the matrix Q. Rotations are applied !> To columns k+2-qStart:k+3-qStart of Q. !>
Q
!> Q is COMPLEX*16 array, dimension (LDQ,NQ) !>
LDQ
!> LDQ is INTEGER !> The leading dimension of Q as declared in !> the calling procedure. !>
NZ
!> NZ is INTEGER !> The order of the matrix Z !>
ZSTART
!> ZSTART is INTEGER !> Start index of the matrix Z. Rotations are applied !> To columns k+1-qStart:k+2-qStart of Z. !>
Z
!> Z is COMPLEX*16 array, dimension (LDZ,NZ) !>
LDZ
!> LDZ is INTEGER !> The leading dimension of Q as declared in !> the calling procedure. !>
Author
Thijs Steel, KU Leuven
Date
May 2020
Definition at line 171 of file zlaqz1.f.
Author¶
Generated automatically by Doxygen for LAPACK from the source code.
| Version 3.12.0 | LAPACK |