NAME

laqz1 - laqz1: step in ggev3, gges3

SYNOPSIS

Functions

subroutine claqz1 (ilq, ilz, k, istartm, istopm, ihi, a, lda, b, ldb, nq, qstart, q, ldq, nz, zstart, z, ldz)
CLAQZ1 subroutine dlaqz1 (a, lda, b, ldb, sr1, sr2, si, beta1, beta2, v)
DLAQZ1 subroutine slaqz1 (a, lda, b, ldb, sr1, sr2, si, beta1, beta2, v)
SLAQZ1 subroutine zlaqz1 (ilq, ilz, k, istartm, istopm, ihi, a, lda, b, ldb, nq, qstart, q, ldq, nz, zstart, z, ldz)
ZLAQZ1

Detailed Description

Function Documentation

subroutine claqz1 (logical, intent(in) ilq, logical, intent(in) ilz, integer, intent(in) k, integer, intent(in) istartm, integer, intent(in) istopm, integer, intent(in) ihi, complex, dimension( lda, * ) a, integer, intent(in) lda, complex, dimension( ldb, * ) b, integer, intent(in) ldb, integer, intent(in) nq, integer, intent(in) qstart, complex, dimension( ldq, * ) q, integer, intent(in) ldq, integer, intent(in) nz, integer, intent(in) zstart, complex, dimension( ldz, * ) z, integer, intent(in) ldz)

CLAQZ1

Purpose:

      CLAQZ1 chases a 1x1 shift bulge in a matrix pencil down a single position

Parameters

ILQ

          ILQ is LOGICAL
              Determines whether or not to update the matrix Q

ILZ

          ILZ is LOGICAL
              Determines whether or not to update the matrix Z

          K is INTEGER
              Index indicating the position of the bulge.
              On entry, the bulge is located in
              (A(k+1,k),B(k+1,k)).
              On exit, the bulge is located in
              (A(k+2,k+1),B(k+2,k+1)).

ISTARTM

          ISTARTM is INTEGER

ISTOPM

          ISTOPM is INTEGER
              Updates to (A,B) are restricted to
              (istartm:k+2,k:istopm). It is assumed
              without checking that istartm <= k+1 and
              k+2 <= istopm

IHI

          IHI is INTEGER

          A is COMPLEX array, dimension (LDA,N)

LDA

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

          B is COMPLEX array, dimension (LDB,N)

LDB

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

          NQ is INTEGER
              The order of the matrix Q

QSTART

          QSTART is INTEGER
              Start index of the matrix Q. Rotations are applied
              To columns k+2-qStart:k+3-qStart of Q.

          Q is COMPLEX array, dimension (LDQ,NQ)

LDQ

          LDQ is INTEGER
              The leading dimension of Q as declared in
              the calling procedure.

          NZ is INTEGER
              The order of the matrix Z

ZSTART

          ZSTART is INTEGER
              Start index of the matrix Z. Rotations are applied
              To columns k+1-qStart:k+2-qStart of Z.

          Z is COMPLEX array, dimension (LDZ,NZ)

LDZ

          LDZ is INTEGER
              The leading dimension of Q as declared in
              the calling procedure.

Author

Thijs Steel, KU Leuven

Date

May 2020

subroutine dlaqz1 (double precision, dimension( lda, * ), intent(in) a, integer, intent(in) lda, double precision, dimension( ldb, * ), intent(in) b, integer, intent(in) ldb, double precision, intent(in) sr1, double precision, intent(in) sr2, double precision, intent(in) si, double precision, intent(in) beta1, double precision, intent(in) beta2, double precision, dimension( * ), intent(out) v)

DLAQZ1

Purpose:

      Given a 3-by-3 matrix pencil (A,B), DLAQZ1 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 is DOUBLE PRECISION array, dimension (LDA,N)
              The 3-by-3 matrix A in (*).

LDA

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

          B is DOUBLE PRECISION array, dimension (LDB,N)
              The 3-by-3 matrix B in (*).

LDB

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

SR1

          SR1 is DOUBLE PRECISION

SR2

          SR2 is DOUBLE PRECISION

          SI is DOUBLE PRECISION

BETA1

          BETA1 is DOUBLE PRECISION

BETA2

          BETA2 is DOUBLE PRECISION

          V is DOUBLE PRECISION array, dimension (N)
              A scalar multiple of the first column of the
              matrix K in (*).

Author

Thijs Steel, KU Leuven

Date

May 2020

subroutine slaqz1 (real, dimension( lda, * ), intent(in) a, integer, intent(in) lda, real, dimension( ldb, * ), intent(in) b, integer, intent(in) ldb, real, intent(in) sr1, real, intent(in) sr2, real, intent(in) si, real, intent(in) beta1, real, intent(in) beta2, real, dimension( * ), intent(out) v)

SLAQZ1

Purpose:

      Given a 3-by-3 matrix pencil (A,B), SLAQZ1 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 is REAL array, dimension (LDA,N)
              The 3-by-3 matrix A in (*).

LDA

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

          B is REAL array, dimension (LDB,N)
              The 3-by-3 matrix B in (*).

LDB

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

SR1

          SR1 is REAL

SR2

          SR2 is REAL

          SI is REAL

BETA1

          BETA1 is REAL

BETA2

          BETA2 is REAL

          V is REAL array, dimension (N)
              A scalar multiple of the first column of the
              matrix K in (*).

Author

Thijs Steel, KU Leuven

Date

May 2020

subroutine zlaqz1 (logical, intent(in) ilq, logical, intent(in) ilz, integer, intent(in) k, integer, intent(in) istartm, integer, intent(in) istopm, integer, intent(in) ihi, complex16, dimension( lda, ) a, integer, intent(in) lda, complex16, dimension( ldb, ) b, integer, intent(in) ldb, integer, intent(in) nq, integer, intent(in) qstart, complex16, dimension( ldq, ) q, integer, intent(in) ldq, integer, intent(in) nz, integer, intent(in) zstart, complex16, dimension( ldz, ) z, integer, intent(in) ldz)

ZLAQZ1

Purpose:

      ZLAQZ1 chases a 1x1 shift bulge in a matrix pencil down a single position

Parameters

ILQ

          ILQ is LOGICAL
              Determines whether or not to update the matrix Q

ILZ

          ILZ is LOGICAL
              Determines whether or not to update the matrix Z

          K is INTEGER
              Index indicating the position of the bulge.
              On entry, the bulge is located in
              (A(k+1,k),B(k+1,k)).
              On exit, the bulge is located in
              (A(k+2,k+1),B(k+2,k+1)).

ISTARTM

          ISTARTM is INTEGER

ISTOPM

          ISTOPM is INTEGER
              Updates to (A,B) are restricted to
              (istartm:k+2,k:istopm). It is assumed
              without checking that istartm <= k+1 and
              k+2 <= istopm

IHI

          IHI is INTEGER

          A is COMPLEX*16 array, dimension (LDA,N)

LDA

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

          B is COMPLEX*16 array, dimension (LDB,N)

LDB

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

          NQ is INTEGER
              The order of the matrix Q

QSTART

          QSTART is INTEGER
              Start index of the matrix Q. Rotations are applied
              To columns k+2-qStart:k+3-qStart of Q.

          Q is COMPLEX*16 array, dimension (LDQ,NQ)

LDQ

          LDQ is INTEGER
              The leading dimension of Q as declared in
              the calling procedure.

          NZ is INTEGER
              The order of the matrix Z

ZSTART

          ZSTART is INTEGER
              Start index of the matrix Z. Rotations are applied
              To columns k+1-qStart:k+2-qStart of Z.

          Z is COMPLEX*16 array, dimension (LDZ,NZ)

LDZ

          LDZ is INTEGER
              The leading dimension of Q as declared in
              the calling procedure.

Author

Thijs Steel, KU Leuven

Date

May 2020

Author

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