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 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 is COMPLEX



          S2 is COMPLEX


          S1 and S2 are the shifts defining K in (*) above.



          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 is INTEGER


              Order of the matrix H. N must be either 2 or 3.



          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 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 is INTEGER


              Order of the matrix H. N must be either 2 or 3.



          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 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, complex16, dimension( ldh, ) h, integer ldh, complex16 s1, complex16 s2, complex16, 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 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 is COMPLEX*16



          S2 is COMPLEX*16


          S1 and S2 are the shifts defining K in (*) above.



          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

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