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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