Man page - laqr1(3)

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Manual

laqr1

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine claqr1 (integer n, complex, dimension( ldh, * ) h, integer ldh,complex s1, complex s2, complex, dimension( * ) v)
subroutine dlaqr1 (integer n, double precision, dimension( ldh, * ) h,integer ldh, double precision sr1, double precision si1, doubleprecision sr2, double precision si2, double precision, dimension( * )v)
subroutine slaqr1 (integer n, real, dimension( ldh, * ) h, integer ldh,real sr1, real si1, real sr2, real si2, real, dimension( * ) v)
subroutine zlaqr1 (integer n, complex*16, dimension( ldh, * ) h, integerldh, complex*16 s1, complex*16 s2, complex*16, dimension( * ) v)
Author

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

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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

subroutine dlaqr1 (integer n, double precision, dimension( ldh, * ) h,integer ldh, double precision sr1, double precision si1, doubleprecision 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

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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

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

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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

subroutine zlaqr1 (integer n, complex*16, dimension( ldh, * ) h, integerldh, 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

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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

Author

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