table of contents
| laqr1(3) | LAPACK | laqr1(3) |
NAME¶
laqr1 - laqr1: step in hseqr
SYNOPSIS¶
Functions¶
subroutine claqr1 (n, h, ldh, s1, s2, v)
CLAQR1 sets a scalar multiple of the first column of the product of
2-by-2 or 3-by-3 matrix H and specified shifts. subroutine dlaqr1 (n,
h, ldh, sr1, si1, sr2, si2, v)
DLAQR1 sets a scalar multiple of the first column of the product of
2-by-2 or 3-by-3 matrix H and specified shifts. subroutine slaqr1 (n,
h, ldh, sr1, si1, sr2, si2, v)
SLAQR1 sets a scalar multiple of the first column of the product of
2-by-2 or 3-by-3 matrix H and specified shifts. subroutine zlaqr1 (n,
h, ldh, s1, s2, v)
ZLAQR1 sets a scalar multiple of the first column of the product of
2-by-2 or 3-by-3 matrix H and specified shifts.
Detailed Description¶
Function Documentation¶
subroutine claqr1 (integer n, complex, dimension( ldh, * ) h, integer ldh, complex s1, complex s2, complex, dimension( * ) v)¶
CLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.
Purpose:
!> !> Given a 2-by-2 or 3-by-3 matrix H, CLAQR1 sets v to a !> scalar multiple of the first column of the product !> !> (*) K = (H - s1*I)*(H - s2*I) !> !> scaling to avoid overflows and most underflows. !> !> This is useful for starting double implicit shift bulges !> in the QR algorithm. !>
Parameters
!> N is INTEGER !> Order of the matrix H. N must be either 2 or 3. !>
H
!> H is COMPLEX array, dimension (LDH,N) !> The 2-by-2 or 3-by-3 matrix H in (*). !>
LDH
!> LDH is INTEGER !> The leading dimension of H as declared in !> the calling procedure. LDH >= N !>
S1
!> S1 is COMPLEX !>
S2
!> S2 is COMPLEX !> !> S1 and S2 are the shifts defining K in (*) above. !>
V
!> V is COMPLEX array, dimension (N) !> A scalar multiple of the first column of the !> matrix K in (*). !>
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
subroutine dlaqr1 (integer n, double precision, dimension( ldh, * ) h, integer ldh, double precision sr1, double precision si1, double precision sr2, double precision si2, double precision, dimension( * ) v)¶
DLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.
Purpose:
!> !> Given a 2-by-2 or 3-by-3 matrix H, DLAQR1 sets v to a !> scalar multiple of the first column of the product !> !> (*) K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I) !> !> scaling to avoid overflows and most underflows. It !> is assumed that either !> !> 1) sr1 = sr2 and si1 = -si2 !> or !> 2) si1 = si2 = 0. !> !> This is useful for starting double implicit shift bulges !> in the QR algorithm. !>
Parameters
!> N is INTEGER !> Order of the matrix H. N must be either 2 or 3. !>
H
!> H is DOUBLE PRECISION array, dimension (LDH,N) !> The 2-by-2 or 3-by-3 matrix H in (*). !>
LDH
!> LDH is INTEGER !> The leading dimension of H as declared in !> the calling procedure. LDH >= N !>
SR1
!> SR1 is DOUBLE PRECISION !>
SI1
!> SI1 is DOUBLE PRECISION !>
SR2
!> SR2 is DOUBLE PRECISION !>
SI2
!> SI2 is DOUBLE PRECISION !> The shifts in (*). !>
V
!> V is DOUBLE PRECISION array, dimension (N) !> A scalar multiple of the first column of the !> matrix K in (*). !>
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
subroutine slaqr1 (integer n, real, dimension( ldh, * ) h, integer ldh, real sr1, real si1, real sr2, real si2, real, dimension( * ) v)¶
SLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.
Purpose:
!> !> Given a 2-by-2 or 3-by-3 matrix H, SLAQR1 sets v to a !> scalar multiple of the first column of the product !> !> (*) K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I) !> !> scaling to avoid overflows and most underflows. It !> is assumed that either !> !> 1) sr1 = sr2 and si1 = -si2 !> or !> 2) si1 = si2 = 0. !> !> This is useful for starting double implicit shift bulges !> in the QR algorithm. !>
Parameters
!> N is INTEGER !> Order of the matrix H. N must be either 2 or 3. !>
H
!> H is REAL array, dimension (LDH,N) !> The 2-by-2 or 3-by-3 matrix H in (*). !>
LDH
!> LDH is INTEGER !> The leading dimension of H as declared in !> the calling procedure. LDH >= N !>
SR1
!> SR1 is REAL !>
SI1
!> SI1 is REAL !>
SR2
!> SR2 is REAL !>
SI2
!> SI2 is REAL !> The shifts in (*). !>
V
!> V is REAL array, dimension (N) !> A scalar multiple of the first column of the !> matrix K in (*). !>
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
subroutine zlaqr1 (integer n, complex*16, dimension( ldh, * ) h, integer ldh, complex*16 s1, complex*16 s2, complex*16, dimension( * ) v)¶
ZLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.
Purpose:
!> !> Given a 2-by-2 or 3-by-3 matrix H, ZLAQR1 sets v to a !> scalar multiple of the first column of the product !> !> (*) K = (H - s1*I)*(H - s2*I) !> !> scaling to avoid overflows and most underflows. !> !> This is useful for starting double implicit shift bulges !> in the QR algorithm. !>
Parameters
!> N is INTEGER !> Order of the matrix H. N must be either 2 or 3. !>
H
!> H is COMPLEX*16 array, dimension (LDH,N) !> The 2-by-2 or 3-by-3 matrix H in (*). !>
LDH
!> LDH is INTEGER !> The leading dimension of H as declared in !> the calling procedure. LDH >= N !>
S1
!> S1 is COMPLEX*16 !>
S2
!> S2 is COMPLEX*16 !> !> S1 and S2 are the shifts defining K in (*) above. !>
V
!> V is COMPLEX*16 array, dimension (N) !> A scalar multiple of the first column of the !> matrix K in (*). !>
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Author¶
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| Tue Jun 30 2026 04:57:07 | Version 3.12.0 |