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

Definition at line 106 of file claqr1.f.

  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

Definition at line 120 of file dlaqr1.f.

  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

Definition at line 120 of file slaqr1.f.

  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

Definition at line 106 of file zlaqr1.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.