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

    !>          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, 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

    !>          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, 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

    !>          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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