Man page - laqz1(3)

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Manual

laqz1

NAME
SYNOPSIS
Functions
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)
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)
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)
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, complex*16, dimension( lda, * ) a,integer, intent(in) lda, complex*16, dimension( ldb, * ) b, integer,intent(in) ldb, integer, intent(in) nq, integer, intent(in) qstart,complex*16, dimension( ldq, * ) q, integer, intent(in) ldq, integer,intent(in) nz, integer, intent(in) zstart, complex*16, dimension( ldz,* ) z, integer, intent(in) ldz)
Author

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

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

A is COMPLEX array, dimension (LDA,N)

LDA

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

B

B is COMPLEX array, dimension (LDB,N)

LDB

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

NQ

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

Q is COMPLEX array, dimension (LDQ,NQ)

LDQ

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

NZ

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

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)*BĖ†(-1)*(beta1*A - (sr2 + i*si2)*B)*BĖ†(-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

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

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

SI is DOUBLE PRECISION

BETA1

BETA1 is DOUBLE PRECISION

BETA2

BETA2 is DOUBLE PRECISION

V

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)*BĖ†(-1)*(beta1*A - (sr2 + i*si2)*B)*BĖ†(-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

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

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

SI is REAL

BETA1

BETA1 is REAL

BETA2

BETA2 is REAL

V

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, complex*16, dimension( lda, * ) a,integer, intent(in) lda, complex*16, dimension( ldb, * ) b, integer,intent(in) ldb, integer, intent(in) nq, integer, intent(in) qstart,complex*16, dimension( ldq, * ) q, integer, intent(in) ldq, integer,intent(in) nz, integer, intent(in) zstart, complex*16, 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

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

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

LDA

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

B

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

LDB

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

NQ

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

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

LDQ

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

NZ

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

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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