laqr1(3) LAPACK laqr1(3)

laqr1 - laqr1: step in hseqr


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.

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

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

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

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

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