NAME

laqz3 - laqz3: step in ggev3, gges3

SYNOPSIS

Functions

subroutine claqz3 (ilschur, ilq, ilz, n, ilo, ihi, nshifts, nblock_desired, alpha, beta, a, lda, b, ldb, q, ldq, z, ldz, qc, ldqc, zc, ldzc, work, lwork, info)
CLAQZ3 recursive subroutine dlaqz3 (ilschur, ilq, ilz, n, ilo, ihi, nw, a, lda, b, ldb, q, ldq, z, ldz, ns, nd, alphar, alphai, beta, qc, ldqc, zc, ldzc, work, lwork, rec, info)
DLAQZ3 recursive subroutine slaqz3 (ilschur, ilq, ilz, n, ilo, ihi, nw, a, lda, b, ldb, q, ldq, z, ldz, ns, nd, alphar, alphai, beta, qc, ldqc, zc, ldzc, work, lwork, rec, info)
SLAQZ3 subroutine zlaqz3 (ilschur, ilq, ilz, n, ilo, ihi, nshifts, nblock_desired, alpha, beta, a, lda, b, ldb, q, ldq, z, ldz, qc, ldqc, zc, ldzc, work, lwork, info)
ZLAQZ3

Detailed Description

Function Documentation

subroutine claqz3 (logical, intent(in) ilschur, logical, intent(in) ilq, logical, intent(in) ilz, integer, intent(in) n, integer, intent(in) ilo, integer, intent(in) ihi, integer, intent(in) nshifts, integer, intent(in) nblock_desired, complex, dimension( * ), intent(inout) alpha, complex, dimension( * ), intent(inout) beta, complex, dimension( lda, * ), intent(inout) a, integer, intent(in) lda, complex, dimension( ldb, * ), intent(inout) b, integer, intent(in) ldb, complex, dimension( ldq, * ), intent(inout) q, integer, intent(in) ldq, complex, dimension( ldz, * ), intent(inout) z, integer, intent(in) ldz, complex, dimension( ldqc, * ), intent(inout) qc, integer, intent(in) ldqc, complex, dimension( ldzc, * ), intent(inout) zc, integer, intent(in) ldzc, complex, dimension( * ), intent(inout) work, integer, intent(in) lwork, integer, intent(out) info)

CLAQZ3

Purpose:

 CLAQZ3 Executes a single multishift QZ sweep

Parameters

ILSCHUR

          ILSCHUR is LOGICAL
              Determines whether or not to update the full Schur form

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

          N is INTEGER
          The order of the matrices A, B, Q, and Z.  N >= 0.

ILO

          ILO is INTEGER

IHI

          IHI is INTEGER

NSHIFTS

          NSHIFTS is INTEGER
          The desired number of shifts to use

NBLOCK_DESIRED

          NBLOCK_DESIRED is INTEGER
          The desired size of the computational windows

ALPHA

          ALPHA is COMPLEX array. SR contains
          the alpha parts of the shifts to use.

BETA

          BETA is COMPLEX array. SS contains
          the scale of the shifts to use.

          A is COMPLEX array, dimension (LDA, N)

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max( 1, N ).

          B is COMPLEX array, dimension (LDB, N)

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max( 1, N ).

          Q is COMPLEX array, dimension (LDQ, N)

LDQ

          LDQ is INTEGER

          Z is COMPLEX array, dimension (LDZ, N)

LDZ

          LDZ is INTEGER

          QC is COMPLEX array, dimension (LDQC, NBLOCK_DESIRED)

LDQC

          LDQC is INTEGER

          ZC is COMPLEX array, dimension (LDZC, NBLOCK_DESIRED)

LDZC

          LDZ is INTEGER

WORK

          WORK is COMPLEX array, dimension (MAX(1,LWORK))
          On exit, if INFO >= 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= max(1,N).
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value

Author

Thijs Steel, KU Leuven

Date

May 2020

recursive subroutine dlaqz3 (logical, intent(in) ilschur, logical, intent(in) ilq, logical, intent(in) ilz, integer, intent(in) n, integer, intent(in) ilo, integer, intent(in) ihi, integer, intent(in) nw, double precision, dimension( lda, * ), intent(inout) a, integer, intent(in) lda, double precision, dimension( ldb, * ), intent(inout) b, integer, intent(in) ldb, double precision, dimension( ldq, * ), intent(inout) q, integer, intent(in) ldq, double precision, dimension( ldz, * ), intent(inout) z, integer, intent(in) ldz, integer, intent(out) ns, integer, intent(out) nd, double precision, dimension( * ), intent(inout) alphar, double precision, dimension( * ), intent(inout) alphai, double precision, dimension( * ), intent(inout) beta, double precision, dimension( ldqc, * ) qc, integer, intent(in) ldqc, double precision, dimension( ldzc, * ) zc, integer, intent(in) ldzc, double precision, dimension( * ) work, integer, intent(in) lwork, integer, intent(in) rec, integer, intent(out) info)

DLAQZ3

Purpose:

 DLAQZ3 performs AED

Parameters

ILSCHUR

          ILSCHUR is LOGICAL
              Determines whether or not to update the full Schur form

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

          N is INTEGER
          The order of the matrices A, B, Q, and Z.  N >= 0.

ILO

          ILO is INTEGER

IHI

          IHI is INTEGER
          ILO and IHI mark the rows and columns of (A,B) which
          are to be normalized

          NW is INTEGER
          The desired size of the deflation window.

          A is DOUBLE PRECISION array, dimension (LDA, N)

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max( 1, N ).

          B is DOUBLE PRECISION array, dimension (LDB, N)

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max( 1, N ).

          Q is DOUBLE PRECISION array, dimension (LDQ, N)

LDQ

          LDQ is INTEGER

          Z is DOUBLE PRECISION array, dimension (LDZ, N)

LDZ

          LDZ is INTEGER

          NS is INTEGER
          The number of unconverged eigenvalues available to
          use as shifts.

          ND is INTEGER
          The number of converged eigenvalues found.

ALPHAR

          ALPHAR is DOUBLE PRECISION array, dimension (N)
          The real parts of each scalar alpha defining an eigenvalue
          of GNEP.

ALPHAI

          ALPHAI is DOUBLE PRECISION array, dimension (N)
          The imaginary parts of each scalar alpha defining an
          eigenvalue of GNEP.
          If ALPHAI(j) is zero, then the j-th eigenvalue is real; if
          positive, then the j-th and (j+1)-st eigenvalues are a
          complex conjugate pair, with ALPHAI(j+1) = -ALPHAI(j).

BETA

          BETA is DOUBLE PRECISION array, dimension (N)
          The scalars beta that define the eigenvalues of GNEP.
          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
          beta = BETA(j) represent the j-th eigenvalue of the matrix
          pair (A,B), in one of the forms lambda = alpha/beta or
          mu = beta/alpha.  Since either lambda or mu may overflow,
          they should not, in general, be computed.

          QC is DOUBLE PRECISION array, dimension (LDQC, NW)

LDQC

          LDQC is INTEGER

          ZC is DOUBLE PRECISION array, dimension (LDZC, NW)

LDZC

          LDZ is INTEGER

WORK

          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO >= 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= max(1,N).
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

REC

          REC is INTEGER
             REC indicates the current recursion level. Should be set
             to 0 on first call.

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value

Author

Thijs Steel, KU Leuven

Date

May 2020

recursive subroutine slaqz3 (logical, intent(in) ilschur, logical, intent(in) ilq, logical, intent(in) ilz, integer, intent(in) n, integer, intent(in) ilo, integer, intent(in) ihi, integer, intent(in) nw, real, dimension( lda, * ), intent(inout) a, integer, intent(in) lda, real, dimension( ldb, * ), intent(inout) b, integer, intent(in) ldb, real, dimension( ldq, * ), intent(inout) q, integer, intent(in) ldq, real, dimension( ldz, * ), intent(inout) z, integer, intent(in) ldz, integer, intent(out) ns, integer, intent(out) nd, real, dimension( * ), intent(inout) alphar, real, dimension( * ), intent(inout) alphai, real, dimension( * ), intent(inout) beta, real, dimension( ldqc, * ) qc, integer, intent(in) ldqc, real, dimension( ldzc, * ) zc, integer, intent(in) ldzc, real, dimension( * ) work, integer, intent(in) lwork, integer, intent(in) rec, integer, intent(out) info)

SLAQZ3

Purpose:

 SLAQZ3 performs AED

Parameters

ILSCHUR

          ILSCHUR is LOGICAL
              Determines whether or not to update the full Schur form

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

          N is INTEGER
          The order of the matrices A, B, Q, and Z.  N >= 0.

ILO

          ILO is INTEGER

IHI

          IHI is INTEGER
          ILO and IHI mark the rows and columns of (A,B) which
          are to be normalized

          NW is INTEGER
          The desired size of the deflation window.

          A is REAL array, dimension (LDA, N)

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max( 1, N ).

          B is REAL array, dimension (LDB, N)

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max( 1, N ).

          Q is REAL array, dimension (LDQ, N)

LDQ

          LDQ is INTEGER

          Z is REAL array, dimension (LDZ, N)

LDZ

          LDZ is INTEGER

          NS is INTEGER
          The number of unconverged eigenvalues available to
          use as shifts.

          ND is INTEGER
          The number of converged eigenvalues found.

ALPHAR

          ALPHAR is REAL array, dimension (N)
          The real parts of each scalar alpha defining an eigenvalue
          of GNEP.

ALPHAI

          ALPHAI is REAL array, dimension (N)
          The imaginary parts of each scalar alpha defining an
          eigenvalue of GNEP.
          If ALPHAI(j) is zero, then the j-th eigenvalue is real; if
          positive, then the j-th and (j+1)-st eigenvalues are a
          complex conjugate pair, with ALPHAI(j+1) = -ALPHAI(j).

BETA

          BETA is REAL array, dimension (N)
          The scalars beta that define the eigenvalues of GNEP.
          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
          beta = BETA(j) represent the j-th eigenvalue of the matrix
          pair (A,B), in one of the forms lambda = alpha/beta or
          mu = beta/alpha.  Since either lambda or mu may overflow,
          they should not, in general, be computed.

          QC is REAL array, dimension (LDQC, NW)

LDQC

          LDQC is INTEGER

          ZC is REAL array, dimension (LDZC, NW)

LDZC

          LDZ is INTEGER

WORK

          WORK is REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO >= 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= max(1,N).
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

REC

          REC is INTEGER
             REC indicates the current recursion level. Should be set
             to 0 on first call.

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value

Author

Thijs Steel, KU Leuven

Date

May 2020

subroutine zlaqz3 (logical, intent(in) ilschur, logical, intent(in) ilq, logical, intent(in) ilz, integer, intent(in) n, integer, intent(in) ilo, integer, intent(in) ihi, integer, intent(in) nshifts, integer, intent(in) nblock_desired, complex16, dimension( ), intent(inout) alpha, complex16, dimension( ), intent(inout) beta, complex16, dimension( lda, ), intent(inout) a, integer, intent(in) lda, complex16, dimension( ldb, ), intent(inout) b, integer, intent(in) ldb, complex16, dimension( ldq, ), intent(inout) q, integer, intent(in) ldq, complex16, dimension( ldz, ), intent(inout) z, integer, intent(in) ldz, complex16, dimension( ldqc, ), intent(inout) qc, integer, intent(in) ldqc, complex16, dimension( ldzc, ), intent(inout) zc, integer, intent(in) ldzc, complex16, dimension( ), intent(inout) work, integer, intent(in) lwork, integer, intent(out) info)

ZLAQZ3

Purpose:

 ZLAQZ3 Executes a single multishift QZ sweep

Parameters

ILSCHUR

          ILSCHUR is LOGICAL
              Determines whether or not to update the full Schur form

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

          N is INTEGER
          The order of the matrices A, B, Q, and Z.  N >= 0.

ILO

          ILO is INTEGER

IHI

          IHI is INTEGER

NSHIFTS

          NSHIFTS is INTEGER
          The desired number of shifts to use

NBLOCK_DESIRED

          NBLOCK_DESIRED is INTEGER
          The desired size of the computational windows

ALPHA

          ALPHA is COMPLEX*16 array. SR contains
          the alpha parts of the shifts to use.

BETA

          BETA is COMPLEX*16 array. SS contains
          the scale of the shifts to use.

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

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max( 1, N ).

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

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max( 1, N ).

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

LDQ

          LDQ is INTEGER

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

LDZ

          LDZ is INTEGER

          QC is COMPLEX*16 array, dimension (LDQC, NBLOCK_DESIRED)

LDQC

          LDQC is INTEGER

          ZC is COMPLEX*16 array, dimension (LDZC, NBLOCK_DESIRED)

LDZC

          LDZ is INTEGER

WORK

          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO >= 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= max(1,N).
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value

Author

Thijs Steel, KU Leuven

Date

May 2020

Author

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