LAQZ1 - 5.2 English - 68552

Given a 3-by-3 matrix pencil (A,B), LAQZ1 sets v to a scalar multiple of the first column of the product.

Purpose:

 Given a 3-by-3 matrix pencil (A,B), LAQZ1 sets v to a
   scalar multiple of the first column of the product

   (*)  K = (A - (beta2*sr2 - i*si)*B)*B^(-1)*(beta1*A - (sr2 + i*si2)*B)*B^(-1).

   It is assumed that either

           1) sr1 = sr2
       or
           2) si = 0.

   This is useful for starting double implicit shift bulges
   in the QZ algorithm.

Parameters:

• A – [in]

  A is REAL array, dimension (LDA,N)

  The 3-by-3 matrix A in (*).

• LDA – [in]

  LDA is INTEGER

  The leading dimension of A as declared in the calling procedure.

• B – [in]

  B is REAL array, dimension (LDB,N)

  The 3-by-3 matrix B in (*).

• LDB – [in]

  LDB is INTEGER

  The leading dimension of B as declared in the calling procedure.

• SR1 – [in] SR1 is REAL

• SR2 – [in] SR2 is REAL

• SI – [in] SI is REAL

• BETA1 – [in] BETA1 is REAL

• BETA2 – [in] BETA2 is REAL

• V – [out]

  V is REAL array, dimension (N)

  A scalar multiple of the first column of the matrix K in (*).