laqz1(3)

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)*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

    !>          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)*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

    !>          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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