COMPLEX routines for (complex) unitary matrix

cung2l :
cung2r :
cungbr : Generates the unitary transformation matrices froma reduction to bidiagonal form determined by CGEBRD.
cunghr : Generates the unitary transformation matrix froma reduction to Hessenberg form determined by CGEHRD.
cungl2 :
cunglq : Generates all or part of the unitary matrix Q froman LQ factorization determined by CGELQF.
cungql : Generates all or part of the unitary matrix Q froma QL factorization determined by CGEQLF.
cungqr : Generates all or part of the unitary matrix Q froma QR factorization determined by CGEQRF.
cungr2 :
cungrq : Generates all or part of the unitary matrix Q froman RQ factorization determined by CGERQF.
cungtr : Generates the unitary transformation matrix froma reduction to tridiagonal form determined by CHETRD.
cunm2l :
cunm2r :
cunmbr : Multiplies a general matrix by one of the unitarytransformation matrices from a reduction to bidiagonal formdetermined by CGEBRD.
cunmhr : Multiplies a general matrix by the unitary transformationmatrix from a reduction to Hessenberg form determined by CGEHRD.
cunml2 :
cunmlq : Multiplies a general matrix by the unitary matrixfrom an LQ factorization determined by CGELQF.
cunmql : Multiplies a general matrix by the unitary matrixfrom a QL factorization determined by CGEQLF.
cunmqr : Multiplies a general matrix by the unitary matrixfrom a QR factorization determined by CGEQRF.
cunmr2 :
cunmr3 : Multiples a general matrix by the unitary matrixfrom an RZ factorization determined by CTZRZF.
cunmrq : Multiplies a general matrix by the unitary matrixfrom an RQ factorization determined by CGERQF.
cunmrz : Multiples a general matrix by the unitary matrixfrom an RZ factorization determined by CTZRZF.
cunmtr : Multiplies a general matrix by the unitarytransformation matrix from a reduction to tridiagonal formdetermined by CHETRD.

cung2l

USAGE:
  info, a = NumRu::Lapack.cung2l( m, a, tau)
    or
  NumRu::Lapack.cung2l  # print help


FORTRAN MANUAL
      SUBROUTINE CUNG2L( M, N, K, A, LDA, TAU, WORK, INFO )

*  Purpose
*  =======
*
*  CUNG2L generates an m by n complex matrix Q with orthonormal columns,
*  which is defined as the last n columns of a product of k elementary
*  reflectors of order m
*
*        Q  =  H(k) . . . H(2) H(1)
*
*  as returned by CGEQLF.
*

*  Arguments
*  =========
*
*  M       (input) INTEGER
*          The number of rows of the matrix Q. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix Q. M >= N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q. N >= K >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the (n-k+i)-th column must contain the vector which
*          defines the elementary reflector H(i), for i = 1,2,...,k, as
*          returned by CGEQLF in the last k columns of its array
*          argument A.
*          On exit, the m-by-n matrix Q.
*
*  LDA     (input) INTEGER
*          The first dimension of the array A. LDA >= max(1,M).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGEQLF.
*
*  WORK    (workspace) COMPLEX array, dimension (N)
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument has an illegal value
*

*  =====================================================================
*

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cung2r

USAGE:
  info, a = NumRu::Lapack.cung2r( m, a, tau)
    or
  NumRu::Lapack.cung2r  # print help


FORTRAN MANUAL
      SUBROUTINE CUNG2R( M, N, K, A, LDA, TAU, WORK, INFO )

*  Purpose
*  =======
*
*  CUNG2R generates an m by n complex matrix Q with orthonormal columns,
*  which is defined as the first n columns of a product of k elementary
*  reflectors of order m
*
*        Q  =  H(1) H(2) . . . H(k)
*
*  as returned by CGEQRF.
*

*  Arguments
*  =========
*
*  M       (input) INTEGER
*          The number of rows of the matrix Q. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix Q. M >= N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q. N >= K >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the i-th column must contain the vector which
*          defines the elementary reflector H(i), for i = 1,2,...,k, as
*          returned by CGEQRF in the first k columns of its array
*          argument A.
*          On exit, the m by n matrix Q.
*
*  LDA     (input) INTEGER
*          The first dimension of the array A. LDA >= max(1,M).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGEQRF.
*
*  WORK    (workspace) COMPLEX array, dimension (N)
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument has an illegal value
*

*  =====================================================================
*

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cungbr

Generates the unitary transformation matrices froma reduction to bidiagonal form determined by CGEBRD.

USAGE:
  work, info, a = NumRu::Lapack.cungbr( vect, m, k, a, tau, lwork)
    or
  NumRu::Lapack.cungbr  # print help


FORTRAN MANUAL
      SUBROUTINE CUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )

*  Purpose
*  =======
*
*  CUNGBR generates one of the complex unitary matrices Q or P**H
*  determined by CGEBRD when reducing a complex matrix A to bidiagonal
*  form: A = Q * B * P**H.  Q and P**H are defined as products of
*  elementary reflectors H(i) or G(i) respectively.
*
*  If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
*  is of order M:
*  if m >= k, Q = H(1) H(2) . . . H(k) and CUNGBR returns the first n
*  columns of Q, where m >= n >= k;
*  if m < k, Q = H(1) H(2) . . . H(m-1) and CUNGBR returns Q as an
*  M-by-M matrix.
*
*  If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H
*  is of order N:
*  if k < n, P**H = G(k) . . . G(2) G(1) and CUNGBR returns the first m
*  rows of P**H, where n >= m >= k;
*  if k >= n, P**H = G(n-1) . . . G(2) G(1) and CUNGBR returns P**H as
*  an N-by-N matrix.
*

*  Arguments
*  =========
*
*  VECT    (input) CHARACTER*1
*          Specifies whether the matrix Q or the matrix P**H is
*          required, as defined in the transformation applied by CGEBRD:
*          = 'Q':  generate Q;
*          = 'P':  generate P**H.
*
*  M       (input) INTEGER
*          The number of rows of the matrix Q or P**H to be returned.
*          M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix Q or P**H to be returned.
*          N >= 0.
*          If VECT = 'Q', M >= N >= min(M,K);
*          if VECT = 'P', N >= M >= min(N,K).
*
*  K       (input) INTEGER
*          If VECT = 'Q', the number of columns in the original M-by-K
*          matrix reduced by CGEBRD.
*          If VECT = 'P', the number of rows in the original K-by-N
*          matrix reduced by CGEBRD.
*          K >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the vectors which define the elementary reflectors,
*          as returned by CGEBRD.
*          On exit, the M-by-N matrix Q or P**H.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A. LDA >= M.
*
*  TAU     (input) COMPLEX array, dimension
*                                (min(M,K)) if VECT = 'Q'
*                                (min(N,K)) if VECT = 'P'
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i) or G(i), which determines Q or P**H, as
*          returned by CGEBRD in its array argument TAUQ or TAUP.
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= max(1,min(M,N)).
*          For optimum performance LWORK >= min(M,N)*NB, where NB
*          is the optimal blocksize.
*
*          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    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*

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cunghr

Generates the unitary transformation matrix froma reduction to Hessenberg form determined by CGEHRD.

USAGE:
  work, info, a = NumRu::Lapack.cunghr( ilo, ihi, a, tau, lwork)
    or
  NumRu::Lapack.cunghr  # print help


FORTRAN MANUAL
      SUBROUTINE CUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )

*  Purpose
*  =======
*
*  CUNGHR generates a complex unitary matrix Q which is defined as the
*  product of IHI-ILO elementary reflectors of order N, as returned by
*  CGEHRD:
*
*  Q = H(ilo) H(ilo+1) . . . H(ihi-1).
*

*  Arguments
*  =========
*
*  N       (input) INTEGER
*          The order of the matrix Q. N >= 0.
*
*  ILO     (input) INTEGER
*  IHI     (input) INTEGER
*          ILO and IHI must have the same values as in the previous call
*          of CGEHRD. Q is equal to the unit matrix except in the
*          submatrix Q(ilo+1:ihi,ilo+1:ihi).
*          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the vectors which define the elementary reflectors,
*          as returned by CGEHRD.
*          On exit, the N-by-N unitary matrix Q.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A. LDA >= max(1,N).
*
*  TAU     (input) COMPLEX array, dimension (N-1)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGEHRD.
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= IHI-ILO.
*          For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
*          the optimal blocksize.
*
*          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    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*

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cungl2

USAGE:
  info, a = NumRu::Lapack.cungl2( a, tau)
    or
  NumRu::Lapack.cungl2  # print help


FORTRAN MANUAL
      SUBROUTINE CUNGL2( M, N, K, A, LDA, TAU, WORK, INFO )

*  Purpose
*  =======
*
*  CUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
*  which is defined as the first m rows of a product of k elementary
*  reflectors of order n
*
*        Q  =  H(k)' . . . H(2)' H(1)'
*
*  as returned by CGELQF.
*

*  Arguments
*  =========
*
*  M       (input) INTEGER
*          The number of rows of the matrix Q. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix Q. N >= M.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q. M >= K >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the i-th row must contain the vector which defines
*          the elementary reflector H(i), for i = 1,2,...,k, as returned
*          by CGELQF in the first k rows of its array argument A.
*          On exit, the m by n matrix Q.
*
*  LDA     (input) INTEGER
*          The first dimension of the array A. LDA >= max(1,M).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGELQF.
*
*  WORK    (workspace) COMPLEX array, dimension (M)
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument has an illegal value
*

*  =====================================================================
*

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cunglq

Generates all or part of the unitary matrix Q froman LQ factorization determined by CGELQF.

USAGE:
  work, info, a = NumRu::Lapack.cunglq( m, a, tau, lwork)
    or
  NumRu::Lapack.cunglq  # print help


FORTRAN MANUAL
      SUBROUTINE CUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )

*  Purpose
*  =======
*
*  CUNGLQ generates an M-by-N complex matrix Q with orthonormal rows,
*  which is defined as the first M rows of a product of K elementary
*  reflectors of order N
*
*        Q  =  H(k)' . . . H(2)' H(1)'
*
*  as returned by CGELQF.
*

*  Arguments
*  =========
*
*  M       (input) INTEGER
*          The number of rows of the matrix Q. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix Q. N >= M.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q. M >= K >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the i-th row must contain the vector which defines
*          the elementary reflector H(i), for i = 1,2,...,k, as returned
*          by CGELQF in the first k rows of its array argument A.
*          On exit, the M-by-N matrix Q.
*
*  LDA     (input) INTEGER
*          The first dimension of the array A. LDA >= max(1,M).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGELQF.
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= max(1,M).
*          For optimum performance LWORK >= M*NB, where NB is
*          the optimal blocksize.
*
*          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    (output) INTEGER
*          = 0:  successful exit;
*          < 0:  if INFO = -i, the i-th argument has an illegal value
*

*  =====================================================================
*

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cungql

Generates all or part of the unitary matrix Q froma QL factorization determined by CGEQLF.

USAGE:
  work, info, a = NumRu::Lapack.cungql( m, a, tau, lwork)
    or
  NumRu::Lapack.cungql  # print help


FORTRAN MANUAL
      SUBROUTINE CUNGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )

*  Purpose
*  =======
*
*  CUNGQL generates an M-by-N complex matrix Q with orthonormal columns,
*  which is defined as the last N columns of a product of K elementary
*  reflectors of order M
*
*        Q  =  H(k) . . . H(2) H(1)
*
*  as returned by CGEQLF.
*

*  Arguments
*  =========
*
*  M       (input) INTEGER
*          The number of rows of the matrix Q. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix Q. M >= N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q. N >= K >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the (n-k+i)-th column must contain the vector which
*          defines the elementary reflector H(i), for i = 1,2,...,k, as
*          returned by CGEQLF in the last k columns of its array
*          argument A.
*          On exit, the M-by-N matrix Q.
*
*  LDA     (input) INTEGER
*          The first dimension of the array A. LDA >= max(1,M).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGEQLF.
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= max(1,N).
*          For optimum performance LWORK >= N*NB, where NB is the
*          optimal blocksize.
*
*          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    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument has an illegal value
*

*  =====================================================================
*

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cungqr

Generates all or part of the unitary matrix Q froma QR factorization determined by CGEQRF.

USAGE:
  work, info, a = NumRu::Lapack.cungqr( m, a, tau, lwork)
    or
  NumRu::Lapack.cungqr  # print help


FORTRAN MANUAL
      SUBROUTINE CUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )

*  Purpose
*  =======
*
*  CUNGQR generates an M-by-N complex matrix Q with orthonormal columns,
*  which is defined as the first N columns of a product of K elementary
*  reflectors of order M
*
*        Q  =  H(1) H(2) . . . H(k)
*
*  as returned by CGEQRF.
*

*  Arguments
*  =========
*
*  M       (input) INTEGER
*          The number of rows of the matrix Q. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix Q. M >= N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q. N >= K >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the i-th column must contain the vector which
*          defines the elementary reflector H(i), for i = 1,2,...,k, as
*          returned by CGEQRF in the first k columns of its array
*          argument A.
*          On exit, the M-by-N matrix Q.
*
*  LDA     (input) INTEGER
*          The first dimension of the array A. LDA >= max(1,M).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGEQRF.
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= max(1,N).
*          For optimum performance LWORK >= N*NB, where NB is the
*          optimal blocksize.
*
*          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    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument has an illegal value
*

*  =====================================================================
*

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cungr2

USAGE:
  info, a = NumRu::Lapack.cungr2( a, tau)
    or
  NumRu::Lapack.cungr2  # print help


FORTRAN MANUAL
      SUBROUTINE CUNGR2( M, N, K, A, LDA, TAU, WORK, INFO )

*  Purpose
*  =======
*
*  CUNGR2 generates an m by n complex matrix Q with orthonormal rows,
*  which is defined as the last m rows of a product of k elementary
*  reflectors of order n
*
*        Q  =  H(1)' H(2)' . . . H(k)'
*
*  as returned by CGERQF.
*

*  Arguments
*  =========
*
*  M       (input) INTEGER
*          The number of rows of the matrix Q. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix Q. N >= M.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q. M >= K >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the (m-k+i)-th row must contain the vector which
*          defines the elementary reflector H(i), for i = 1,2,...,k, as
*          returned by CGERQF in the last k rows of its array argument
*          A.
*          On exit, the m-by-n matrix Q.
*
*  LDA     (input) INTEGER
*          The first dimension of the array A. LDA >= max(1,M).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGERQF.
*
*  WORK    (workspace) COMPLEX array, dimension (M)
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument has an illegal value
*

*  =====================================================================
*

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cungrq

Generates all or part of the unitary matrix Q froman RQ factorization determined by CGERQF.

USAGE:
  work, info, a = NumRu::Lapack.cungrq( m, a, tau, lwork)
    or
  NumRu::Lapack.cungrq  # print help


FORTRAN MANUAL
      SUBROUTINE CUNGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )

*  Purpose
*  =======
*
*  CUNGRQ generates an M-by-N complex matrix Q with orthonormal rows,
*  which is defined as the last M rows of a product of K elementary
*  reflectors of order N
*
*        Q  =  H(1)' H(2)' . . . H(k)'
*
*  as returned by CGERQF.
*

*  Arguments
*  =========
*
*  M       (input) INTEGER
*          The number of rows of the matrix Q. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix Q. N >= M.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q. M >= K >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the (m-k+i)-th row must contain the vector which
*          defines the elementary reflector H(i), for i = 1,2,...,k, as
*          returned by CGERQF in the last k rows of its array argument
*          A.
*          On exit, the M-by-N matrix Q.
*
*  LDA     (input) INTEGER
*          The first dimension of the array A. LDA >= max(1,M).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGERQF.
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= max(1,M).
*          For optimum performance LWORK >= M*NB, where NB is the
*          optimal blocksize.
*
*          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    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument has an illegal value
*

*  =====================================================================
*

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cungtr

Generates the unitary transformation matrix froma reduction to tridiagonal form determined by CHETRD.

USAGE:
  work, info, a = NumRu::Lapack.cungtr( uplo, a, tau, lwork)
    or
  NumRu::Lapack.cungtr  # print help


FORTRAN MANUAL
      SUBROUTINE CUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )

*  Purpose
*  =======
*
*  CUNGTR generates a complex unitary matrix Q which is defined as the
*  product of n-1 elementary reflectors of order N, as returned by
*  CHETRD:
*
*  if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
*
*  if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
*

*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U': Upper triangle of A contains elementary reflectors
*                 from CHETRD;
*          = 'L': Lower triangle of A contains elementary reflectors
*                 from CHETRD.
*
*  N       (input) INTEGER
*          The order of the matrix Q. N >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the vectors which define the elementary reflectors,
*          as returned by CHETRD.
*          On exit, the N-by-N unitary matrix Q.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A. LDA >= N.
*
*  TAU     (input) COMPLEX array, dimension (N-1)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CHETRD.
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= N-1.
*          For optimum performance LWORK >= (N-1)*NB, where NB is
*          the optimal blocksize.
*
*          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    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*

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cunm2l

USAGE:
  info, c = NumRu::Lapack.cunm2l( side, trans, m, a, tau, c)
    or
  NumRu::Lapack.cunm2l  # print help


FORTRAN MANUAL
      SUBROUTINE CUNM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO )

*  Purpose
*  =======
*
*  CUNM2L overwrites the general complex m-by-n matrix C with
*
*        Q * C  if SIDE = 'L' and TRANS = 'N', or
*
*        Q'* C  if SIDE = 'L' and TRANS = 'C', or
*
*        C * Q  if SIDE = 'R' and TRANS = 'N', or
*
*        C * Q' if SIDE = 'R' and TRANS = 'C',
*
*  where Q is a complex unitary matrix defined as the product of k
*  elementary reflectors
*
*        Q = H(k) . . . H(2) H(1)
*
*  as returned by CGEQLF. Q is of order m if SIDE = 'L' and of order n
*  if SIDE = 'R'.
*

*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply Q or Q' from the Left
*          = 'R': apply Q or Q' from the Right
*
*  TRANS   (input) CHARACTER*1
*          = 'N': apply Q  (No transpose)
*          = 'C': apply Q' (Conjugate transpose)
*
*  M       (input) INTEGER
*          The number of rows of the matrix C. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C. N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines
*          the matrix Q.
*          If SIDE = 'L', M >= K >= 0;
*          if SIDE = 'R', N >= K >= 0.
*
*  A       (input) COMPLEX array, dimension (LDA,K)
*          The i-th column must contain the vector which defines the
*          elementary reflector H(i), for i = 1,2,...,k, as returned by
*          CGEQLF in the last k columns of its array argument A.
*          A is modified by the routine but restored on exit.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.
*          If SIDE = 'L', LDA >= max(1,M);
*          if SIDE = 'R', LDA >= max(1,N).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGEQLF.
*
*  C       (input/output) COMPLEX array, dimension (LDC,N)
*          On entry, the m-by-n matrix C.
*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace) COMPLEX array, dimension
*                                   (N) if SIDE = 'L',
*                                   (M) if SIDE = 'R'
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*

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cunm2r

USAGE:
  info, c = NumRu::Lapack.cunm2r( side, trans, m, a, tau, c)
    or
  NumRu::Lapack.cunm2r  # print help


FORTRAN MANUAL
      SUBROUTINE CUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO )

*  Purpose
*  =======
*
*  CUNM2R overwrites the general complex m-by-n matrix C with
*
*        Q * C  if SIDE = 'L' and TRANS = 'N', or
*
*        Q'* C  if SIDE = 'L' and TRANS = 'C', or
*
*        C * Q  if SIDE = 'R' and TRANS = 'N', or
*
*        C * Q' if SIDE = 'R' and TRANS = 'C',
*
*  where Q is a complex unitary matrix defined as the product of k
*  elementary reflectors
*
*        Q = H(1) H(2) . . . H(k)
*
*  as returned by CGEQRF. Q is of order m if SIDE = 'L' and of order n
*  if SIDE = 'R'.
*

*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply Q or Q' from the Left
*          = 'R': apply Q or Q' from the Right
*
*  TRANS   (input) CHARACTER*1
*          = 'N': apply Q  (No transpose)
*          = 'C': apply Q' (Conjugate transpose)
*
*  M       (input) INTEGER
*          The number of rows of the matrix C. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C. N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines
*          the matrix Q.
*          If SIDE = 'L', M >= K >= 0;
*          if SIDE = 'R', N >= K >= 0.
*
*  A       (input) COMPLEX array, dimension (LDA,K)
*          The i-th column must contain the vector which defines the
*          elementary reflector H(i), for i = 1,2,...,k, as returned by
*          CGEQRF in the first k columns of its array argument A.
*          A is modified by the routine but restored on exit.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.
*          If SIDE = 'L', LDA >= max(1,M);
*          if SIDE = 'R', LDA >= max(1,N).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGEQRF.
*
*  C       (input/output) COMPLEX array, dimension (LDC,N)
*          On entry, the m-by-n matrix C.
*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace) COMPLEX array, dimension
*                                   (N) if SIDE = 'L',
*                                   (M) if SIDE = 'R'
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*

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cunmbr

Multiplies a general matrix by one of the unitarytransformation matrices from a reduction to bidiagonal formdetermined by CGEBRD.

USAGE:
  work, info, c = NumRu::Lapack.cunmbr( vect, side, trans, m, k, a, tau, c, lwork)
    or
  NumRu::Lapack.cunmbr  # print help


FORTRAN MANUAL
      SUBROUTINE CUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

*  Purpose
*  =======
*
*  If VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C
*  with
*                  SIDE = 'L'     SIDE = 'R'
*  TRANS = 'N':      Q * C          C * Q
*  TRANS = 'C':      Q**H * C       C * Q**H
*
*  If VECT = 'P', CUNMBR overwrites the general complex M-by-N matrix C
*  with
*                  SIDE = 'L'     SIDE = 'R'
*  TRANS = 'N':      P * C          C * P
*  TRANS = 'C':      P**H * C       C * P**H
*
*  Here Q and P**H are the unitary matrices determined by CGEBRD when
*  reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
*  and P**H are defined as products of elementary reflectors H(i) and
*  G(i) respectively.
*
*  Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
*  order of the unitary matrix Q or P**H that is applied.
*
*  If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
*  if nq >= k, Q = H(1) H(2) . . . H(k);
*  if nq < k, Q = H(1) H(2) . . . H(nq-1).
*
*  If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
*  if k < nq, P = G(1) G(2) . . . G(k);
*  if k >= nq, P = G(1) G(2) . . . G(nq-1).
*

*  Arguments
*  =========
*
*  VECT    (input) CHARACTER*1
*          = 'Q': apply Q or Q**H;
*          = 'P': apply P or P**H.
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply Q, Q**H, P or P**H from the Left;
*          = 'R': apply Q, Q**H, P or P**H from the Right.
*
*  TRANS   (input) CHARACTER*1
*          = 'N':  No transpose, apply Q or P;
*          = 'C':  Conjugate transpose, apply Q**H or P**H.
*
*  M       (input) INTEGER
*          The number of rows of the matrix C. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C. N >= 0.
*
*  K       (input) INTEGER
*          If VECT = 'Q', the number of columns in the original
*          matrix reduced by CGEBRD.
*          If VECT = 'P', the number of rows in the original
*          matrix reduced by CGEBRD.
*          K >= 0.
*
*  A       (input) COMPLEX array, dimension
*                                (LDA,min(nq,K)) if VECT = 'Q'
*                                (LDA,nq)        if VECT = 'P'
*          The vectors which define the elementary reflectors H(i) and
*          G(i), whose products determine the matrices Q and P, as
*          returned by CGEBRD.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.
*          If VECT = 'Q', LDA >= max(1,nq);
*          if VECT = 'P', LDA >= max(1,min(nq,K)).
*
*  TAU     (input) COMPLEX array, dimension (min(nq,K))
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i) or G(i) which determines Q or P, as returned
*          by CGEBRD in the array argument TAUQ or TAUP.
*
*  C       (input/output) COMPLEX array, dimension (LDC,N)
*          On entry, the M-by-N matrix C.
*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
*          or P*C or P**H*C or C*P or C*P**H.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.
*          If SIDE = 'L', LWORK >= max(1,N);
*          if SIDE = 'R', LWORK >= max(1,M);
*          if N = 0 or M = 0, LWORK >= 1.
*          For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
*          and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
*          optimal blocksize. (NB = 0 if M = 0 or N = 0.)
*
*          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    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            APPLYQ, LEFT, LQUERY, NOTRAN
      CHARACTER          TRANST
      INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           ILAENV, LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           CUNMLQ, CUNMQR, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..

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cunmhr

Multiplies a general matrix by the unitary transformationmatrix from a reduction to Hessenberg form determined by CGEHRD.

USAGE:
  work, info, c = NumRu::Lapack.cunmhr( side, trans, ilo, ihi, a, tau, c, lwork)
    or
  NumRu::Lapack.cunmhr  # print help


FORTRAN MANUAL
      SUBROUTINE CUNMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

*  Purpose
*  =======
*
*  CUNMHR overwrites the general complex M-by-N matrix C with
*
*                  SIDE = 'L'     SIDE = 'R'
*  TRANS = 'N':      Q * C          C * Q
*  TRANS = 'C':      Q**H * C       C * Q**H
*
*  where Q is a complex unitary matrix of order nq, with nq = m if
*  SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
*  IHI-ILO elementary reflectors, as returned by CGEHRD:
*
*  Q = H(ilo) H(ilo+1) . . . H(ihi-1).
*

*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply Q or Q**H from the Left;
*          = 'R': apply Q or Q**H from the Right.
*
*  TRANS   (input) CHARACTER*1
*          = 'N': apply Q  (No transpose)
*          = 'C': apply Q**H (Conjugate transpose)
*
*  M       (input) INTEGER
*          The number of rows of the matrix C. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C. N >= 0.
*
*  ILO     (input) INTEGER
*  IHI     (input) INTEGER
*          ILO and IHI must have the same values as in the previous call
*          of CGEHRD. Q is equal to the unit matrix except in the
*          submatrix Q(ilo+1:ihi,ilo+1:ihi).
*          If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
*          ILO = 1 and IHI = 0, if M = 0;
*          if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
*          ILO = 1 and IHI = 0, if N = 0.
*
*  A       (input) COMPLEX array, dimension
*                               (LDA,M) if SIDE = 'L'
*                               (LDA,N) if SIDE = 'R'
*          The vectors which define the elementary reflectors, as
*          returned by CGEHRD.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.
*          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
*
*  TAU     (input) COMPLEX array, dimension
*                               (M-1) if SIDE = 'L'
*                               (N-1) if SIDE = 'R'
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGEHRD.
*
*  C       (input/output) COMPLEX array, dimension (LDC,N)
*          On entry, the M-by-N matrix C.
*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.
*          If SIDE = 'L', LWORK >= max(1,N);
*          if SIDE = 'R', LWORK >= max(1,M).
*          For optimum performance LWORK >= N*NB if SIDE = 'L', and
*          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
*          blocksize.
*
*          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    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            LEFT, LQUERY
      INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NH, NI, NQ, NW
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           ILAENV, LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           CUNMQR, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..

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cunml2

USAGE:
  info, c = NumRu::Lapack.cunml2( side, trans, a, tau, c)
    or
  NumRu::Lapack.cunml2  # print help


FORTRAN MANUAL
      SUBROUTINE CUNML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO )

*  Purpose
*  =======
*
*  CUNML2 overwrites the general complex m-by-n matrix C with
*
*        Q * C  if SIDE = 'L' and TRANS = 'N', or
*
*        Q'* C  if SIDE = 'L' and TRANS = 'C', or
*
*        C * Q  if SIDE = 'R' and TRANS = 'N', or
*
*        C * Q' if SIDE = 'R' and TRANS = 'C',
*
*  where Q is a complex unitary matrix defined as the product of k
*  elementary reflectors
*
*        Q = H(k)' . . . H(2)' H(1)'
*
*  as returned by CGELQF. Q is of order m if SIDE = 'L' and of order n
*  if SIDE = 'R'.
*

*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply Q or Q' from the Left
*          = 'R': apply Q or Q' from the Right
*
*  TRANS   (input) CHARACTER*1
*          = 'N': apply Q  (No transpose)
*          = 'C': apply Q' (Conjugate transpose)
*
*  M       (input) INTEGER
*          The number of rows of the matrix C. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C. N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines
*          the matrix Q.
*          If SIDE = 'L', M >= K >= 0;
*          if SIDE = 'R', N >= K >= 0.
*
*  A       (input) COMPLEX array, dimension
*                               (LDA,M) if SIDE = 'L',
*                               (LDA,N) if SIDE = 'R'
*          The i-th row must contain the vector which defines the
*          elementary reflector H(i), for i = 1,2,...,k, as returned by
*          CGELQF in the first k rows of its array argument A.
*          A is modified by the routine but restored on exit.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A. LDA >= max(1,K).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGELQF.
*
*  C       (input/output) COMPLEX array, dimension (LDC,N)
*          On entry, the m-by-n matrix C.
*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace) COMPLEX array, dimension
*                                   (N) if SIDE = 'L',
*                                   (M) if SIDE = 'R'
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*

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cunmlq

Multiplies a general matrix by the unitary matrixfrom an LQ factorization determined by CGELQF.

USAGE:
  work, info, c = NumRu::Lapack.cunmlq( side, trans, a, tau, c, lwork)
    or
  NumRu::Lapack.cunmlq  # print help


FORTRAN MANUAL
      SUBROUTINE CUNMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

*  Purpose
*  =======
*
*  CUNMLQ overwrites the general complex M-by-N matrix C with
*
*                  SIDE = 'L'     SIDE = 'R'
*  TRANS = 'N':      Q * C          C * Q
*  TRANS = 'C':      Q**H * C       C * Q**H
*
*  where Q is a complex unitary matrix defined as the product of k
*  elementary reflectors
*
*        Q = H(k)' . . . H(2)' H(1)'
*
*  as returned by CGELQF. Q is of order M if SIDE = 'L' and of order N
*  if SIDE = 'R'.
*

*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply Q or Q**H from the Left;
*          = 'R': apply Q or Q**H from the Right.
*
*  TRANS   (input) CHARACTER*1
*          = 'N':  No transpose, apply Q;
*          = 'C':  Conjugate transpose, apply Q**H.
*
*  M       (input) INTEGER
*          The number of rows of the matrix C. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C. N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines
*          the matrix Q.
*          If SIDE = 'L', M >= K >= 0;
*          if SIDE = 'R', N >= K >= 0.
*
*  A       (input) COMPLEX array, dimension
*                               (LDA,M) if SIDE = 'L',
*                               (LDA,N) if SIDE = 'R'
*          The i-th row must contain the vector which defines the
*          elementary reflector H(i), for i = 1,2,...,k, as returned by
*          CGELQF in the first k rows of its array argument A.
*          A is modified by the routine but restored on exit.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A. LDA >= max(1,K).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGELQF.
*
*  C       (input/output) COMPLEX array, dimension (LDC,N)
*          On entry, the M-by-N matrix C.
*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.
*          If SIDE = 'L', LWORK >= max(1,N);
*          if SIDE = 'R', LWORK >= max(1,M).
*          For optimum performance LWORK >= N*NB if SIDE 'L', and
*          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
*          blocksize.
*
*          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    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*

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cunmql

Multiplies a general matrix by the unitary matrixfrom a QL factorization determined by CGEQLF.

USAGE:
  work, info, c = NumRu::Lapack.cunmql( side, trans, m, a, tau, c, lwork)
    or
  NumRu::Lapack.cunmql  # print help


FORTRAN MANUAL
      SUBROUTINE CUNMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

*  Purpose
*  =======
*
*  CUNMQL overwrites the general complex M-by-N matrix C with
*
*                  SIDE = 'L'     SIDE = 'R'
*  TRANS = 'N':      Q * C          C * Q
*  TRANS = 'C':      Q**H * C       C * Q**H
*
*  where Q is a complex unitary matrix defined as the product of k
*  elementary reflectors
*
*        Q = H(k) . . . H(2) H(1)
*
*  as returned by CGEQLF. Q is of order M if SIDE = 'L' and of order N
*  if SIDE = 'R'.
*

*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply Q or Q**H from the Left;
*          = 'R': apply Q or Q**H from the Right.
*
*  TRANS   (input) CHARACTER*1
*          = 'N':  No transpose, apply Q;
*          = 'C':  Transpose, apply Q**H.
*
*  M       (input) INTEGER
*          The number of rows of the matrix C. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C. N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines
*          the matrix Q.
*          If SIDE = 'L', M >= K >= 0;
*          if SIDE = 'R', N >= K >= 0.
*
*  A       (input) COMPLEX array, dimension (LDA,K)
*          The i-th column must contain the vector which defines the
*          elementary reflector H(i), for i = 1,2,...,k, as returned by
*          CGEQLF in the last k columns of its array argument A.
*          A is modified by the routine but restored on exit.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.
*          If SIDE = 'L', LDA >= max(1,M);
*          if SIDE = 'R', LDA >= max(1,N).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGEQLF.
*
*  C       (input/output) COMPLEX array, dimension (LDC,N)
*          On entry, the M-by-N matrix C.
*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.
*          If SIDE = 'L', LWORK >= max(1,N);
*          if SIDE = 'R', LWORK >= max(1,M).
*          For optimum performance LWORK >= N*NB if SIDE = 'L', and
*          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
*          blocksize.
*
*          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    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*

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cunmqr

Multiplies a general matrix by the unitary matrixfrom a QR factorization determined by CGEQRF.

USAGE:
  work, info, c = NumRu::Lapack.cunmqr( side, trans, m, a, tau, c, lwork)
    or
  NumRu::Lapack.cunmqr  # print help


FORTRAN MANUAL
      SUBROUTINE CUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

*  Purpose
*  =======
*
*  CUNMQR overwrites the general complex M-by-N matrix C with
*
*                  SIDE = 'L'     SIDE = 'R'
*  TRANS = 'N':      Q * C          C * Q
*  TRANS = 'C':      Q**H * C       C * Q**H
*
*  where Q is a complex unitary matrix defined as the product of k
*  elementary reflectors
*
*        Q = H(1) H(2) . . . H(k)
*
*  as returned by CGEQRF. Q is of order M if SIDE = 'L' and of order N
*  if SIDE = 'R'.
*

*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply Q or Q**H from the Left;
*          = 'R': apply Q or Q**H from the Right.
*
*  TRANS   (input) CHARACTER*1
*          = 'N':  No transpose, apply Q;
*          = 'C':  Conjugate transpose, apply Q**H.
*
*  M       (input) INTEGER
*          The number of rows of the matrix C. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C. N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines
*          the matrix Q.
*          If SIDE = 'L', M >= K >= 0;
*          if SIDE = 'R', N >= K >= 0.
*
*  A       (input) COMPLEX array, dimension (LDA,K)
*          The i-th column must contain the vector which defines the
*          elementary reflector H(i), for i = 1,2,...,k, as returned by
*          CGEQRF in the first k columns of its array argument A.
*          A is modified by the routine but restored on exit.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.
*          If SIDE = 'L', LDA >= max(1,M);
*          if SIDE = 'R', LDA >= max(1,N).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGEQRF.
*
*  C       (input/output) COMPLEX array, dimension (LDC,N)
*          On entry, the M-by-N matrix C.
*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.
*          If SIDE = 'L', LWORK >= max(1,N);
*          if SIDE = 'R', LWORK >= max(1,M).
*          For optimum performance LWORK >= N*NB if SIDE = 'L', and
*          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
*          blocksize.
*
*          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    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*

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cunmr2

USAGE:
  info, c = NumRu::Lapack.cunmr2( side, trans, a, tau, c)
    or
  NumRu::Lapack.cunmr2  # print help


FORTRAN MANUAL
      SUBROUTINE CUNMR2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO )

*  Purpose
*  =======
*
*  CUNMR2 overwrites the general complex m-by-n matrix C with
*
*        Q * C  if SIDE = 'L' and TRANS = 'N', or
*
*        Q'* C  if SIDE = 'L' and TRANS = 'C', or
*
*        C * Q  if SIDE = 'R' and TRANS = 'N', or
*
*        C * Q' if SIDE = 'R' and TRANS = 'C',
*
*  where Q is a complex unitary matrix defined as the product of k
*  elementary reflectors
*
*        Q = H(1)' H(2)' . . . H(k)'
*
*  as returned by CGERQF. Q is of order m if SIDE = 'L' and of order n
*  if SIDE = 'R'.
*

*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply Q or Q' from the Left
*          = 'R': apply Q or Q' from the Right
*
*  TRANS   (input) CHARACTER*1
*          = 'N': apply Q  (No transpose)
*          = 'C': apply Q' (Conjugate transpose)
*
*  M       (input) INTEGER
*          The number of rows of the matrix C. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C. N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines
*          the matrix Q.
*          If SIDE = 'L', M >= K >= 0;
*          if SIDE = 'R', N >= K >= 0.
*
*  A       (input) COMPLEX array, dimension
*                               (LDA,M) if SIDE = 'L',
*                               (LDA,N) if SIDE = 'R'
*          The i-th row must contain the vector which defines the
*          elementary reflector H(i), for i = 1,2,...,k, as returned by
*          CGERQF in the last k rows of its array argument A.
*          A is modified by the routine but restored on exit.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A. LDA >= max(1,K).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGERQF.
*
*  C       (input/output) COMPLEX array, dimension (LDC,N)
*          On entry, the m-by-n matrix C.
*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace) COMPLEX array, dimension
*                                   (N) if SIDE = 'L',
*                                   (M) if SIDE = 'R'
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*

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cunmr3

Multiples a general matrix by the unitary matrixfrom an RZ factorization determined by CTZRZF.

USAGE:
  info, c = NumRu::Lapack.cunmr3( side, trans, l, a, tau, c)
    or
  NumRu::Lapack.cunmr3  # print help


FORTRAN MANUAL
      SUBROUTINE CUNMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO )

*  Purpose
*  =======
*
*  CUNMR3 overwrites the general complex m by n matrix C with
*
*        Q * C  if SIDE = 'L' and TRANS = 'N', or
*
*        Q'* C  if SIDE = 'L' and TRANS = 'C', or
*
*        C * Q  if SIDE = 'R' and TRANS = 'N', or
*
*        C * Q' if SIDE = 'R' and TRANS = 'C',
*
*  where Q is a complex unitary matrix defined as the product of k
*  elementary reflectors
*
*        Q = H(1) H(2) . . . H(k)
*
*  as returned by CTZRZF. Q is of order m if SIDE = 'L' and of order n
*  if SIDE = 'R'.
*

*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply Q or Q' from the Left
*          = 'R': apply Q or Q' from the Right
*
*  TRANS   (input) CHARACTER*1
*          = 'N': apply Q  (No transpose)
*          = 'C': apply Q' (Conjugate transpose)
*
*  M       (input) INTEGER
*          The number of rows of the matrix C. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C. N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines
*          the matrix Q.
*          If SIDE = 'L', M >= K >= 0;
*          if SIDE = 'R', N >= K >= 0.
*
*  L       (input) INTEGER
*          The number of columns of the matrix A containing
*          the meaningful part of the Householder reflectors.
*          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
*
*  A       (input) COMPLEX array, dimension
*                               (LDA,M) if SIDE = 'L',
*                               (LDA,N) if SIDE = 'R'
*          The i-th row must contain the vector which defines the
*          elementary reflector H(i), for i = 1,2,...,k, as returned by
*          CTZRZF in the last k rows of its array argument A.
*          A is modified by the routine but restored on exit.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A. LDA >= max(1,K).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CTZRZF.
*
*  C       (input/output) COMPLEX array, dimension (LDC,N)
*          On entry, the m-by-n matrix C.
*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace) COMPLEX array, dimension
*                                   (N) if SIDE = 'L',
*                                   (M) if SIDE = 'R'
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument had an illegal value
*

*  Further Details
*  ===============
*
*  Based on contributions by
*    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            LEFT, NOTRAN
      INTEGER            I, I1, I2, I3, IC, JA, JC, MI, NI, NQ
      COMPLEX            TAUI
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           CLARZ, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          CONJG, MAX
*     ..

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cunmrq

Multiplies a general matrix by the unitary matrixfrom an RQ factorization determined by CGERQF.

USAGE:
  work, info, c = NumRu::Lapack.cunmrq( side, trans, a, tau, c, lwork)
    or
  NumRu::Lapack.cunmrq  # print help


FORTRAN MANUAL
      SUBROUTINE CUNMRQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

*  Purpose
*  =======
*
*  CUNMRQ overwrites the general complex M-by-N matrix C with
*
*                  SIDE = 'L'     SIDE = 'R'
*  TRANS = 'N':      Q * C          C * Q
*  TRANS = 'C':      Q**H * C       C * Q**H
*
*  where Q is a complex unitary matrix defined as the product of k
*  elementary reflectors
*
*        Q = H(1)' H(2)' . . . H(k)'
*
*  as returned by CGERQF. Q is of order M if SIDE = 'L' and of order N
*  if SIDE = 'R'.
*

*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply Q or Q**H from the Left;
*          = 'R': apply Q or Q**H from the Right.
*
*  TRANS   (input) CHARACTER*1
*          = 'N':  No transpose, apply Q;
*          = 'C':  Transpose, apply Q**H.
*
*  M       (input) INTEGER
*          The number of rows of the matrix C. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C. N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines
*          the matrix Q.
*          If SIDE = 'L', M >= K >= 0;
*          if SIDE = 'R', N >= K >= 0.
*
*  A       (input) COMPLEX array, dimension
*                               (LDA,M) if SIDE = 'L',
*                               (LDA,N) if SIDE = 'R'
*          The i-th row must contain the vector which defines the
*          elementary reflector H(i), for i = 1,2,...,k, as returned by
*          CGERQF in the last k rows of its array argument A.
*          A is modified by the routine but restored on exit.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A. LDA >= max(1,K).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CGERQF.
*
*  C       (input/output) COMPLEX array, dimension (LDC,N)
*          On entry, the M-by-N matrix C.
*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.
*          If SIDE = 'L', LWORK >= max(1,N);
*          if SIDE = 'R', LWORK >= max(1,M).
*          For optimum performance LWORK >= N*NB if SIDE = 'L', and
*          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
*          blocksize.
*
*          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    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*

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cunmrz

Multiples a general matrix by the unitary matrixfrom an RZ factorization determined by CTZRZF.

USAGE:
  work, info, c = NumRu::Lapack.cunmrz( side, trans, l, a, tau, c, lwork)
    or
  NumRu::Lapack.cunmrz  # print help


FORTRAN MANUAL
      SUBROUTINE CUNMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

*  Purpose
*  =======
*
*  CUNMRZ overwrites the general complex M-by-N matrix C with
*
*                  SIDE = 'L'     SIDE = 'R'
*  TRANS = 'N':      Q * C          C * Q
*  TRANS = 'C':      Q**H * C       C * Q**H
*
*  where Q is a complex unitary matrix defined as the product of k
*  elementary reflectors
*
*        Q = H(1) H(2) . . . H(k)
*
*  as returned by CTZRZF. Q is of order M if SIDE = 'L' and of order N
*  if SIDE = 'R'.
*

*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply Q or Q**H from the Left;
*          = 'R': apply Q or Q**H from the Right.
*
*  TRANS   (input) CHARACTER*1
*          = 'N':  No transpose, apply Q;
*          = 'C':  Conjugate transpose, apply Q**H.
*
*  M       (input) INTEGER
*          The number of rows of the matrix C. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C. N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines
*          the matrix Q.
*          If SIDE = 'L', M >= K >= 0;
*          if SIDE = 'R', N >= K >= 0.
*
*  L       (input) INTEGER
*          The number of columns of the matrix A containing
*          the meaningful part of the Householder reflectors.
*          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
*
*  A       (input) COMPLEX array, dimension
*                               (LDA,M) if SIDE = 'L',
*                               (LDA,N) if SIDE = 'R'
*          The i-th row must contain the vector which defines the
*          elementary reflector H(i), for i = 1,2,...,k, as returned by
*          CTZRZF in the last k rows of its array argument A.
*          A is modified by the routine but restored on exit.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A. LDA >= max(1,K).
*
*  TAU     (input) COMPLEX array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CTZRZF.
*
*  C       (input/output) COMPLEX array, dimension (LDC,N)
*          On entry, the M-by-N matrix C.
*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.
*          If SIDE = 'L', LWORK >= max(1,N);
*          if SIDE = 'R', LWORK >= max(1,M).
*          For optimum performance LWORK >= N*NB if SIDE = 'L', and
*          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
*          blocksize.
*
*          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    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*

*  Further Details
*  ===============
*
*  Based on contributions by
*    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
*
*  =====================================================================
*

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cunmtr

Multiplies a general matrix by the unitarytransformation matrix from a reduction to tridiagonal formdetermined by CHETRD.

USAGE:
  work, info, c = NumRu::Lapack.cunmtr( side, uplo, trans, a, tau, c, lwork)
    or
  NumRu::Lapack.cunmtr  # print help


FORTRAN MANUAL
      SUBROUTINE CUNMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

*  Purpose
*  =======
*
*  CUNMTR overwrites the general complex M-by-N matrix C with
*
*                  SIDE = 'L'     SIDE = 'R'
*  TRANS = 'N':      Q * C          C * Q
*  TRANS = 'C':      Q**H * C       C * Q**H
*
*  where Q is a complex unitary matrix of order nq, with nq = m if
*  SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
*  nq-1 elementary reflectors, as returned by CHETRD:
*
*  if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
*
*  if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
*

*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply Q or Q**H from the Left;
*          = 'R': apply Q or Q**H from the Right.
*
*  UPLO    (input) CHARACTER*1
*          = 'U': Upper triangle of A contains elementary reflectors
*                 from CHETRD;
*          = 'L': Lower triangle of A contains elementary reflectors
*                 from CHETRD.
*
*  TRANS   (input) CHARACTER*1
*          = 'N':  No transpose, apply Q;
*          = 'C':  Conjugate transpose, apply Q**H.
*
*  M       (input) INTEGER
*          The number of rows of the matrix C. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C. N >= 0.
*
*  A       (input) COMPLEX array, dimension
*                               (LDA,M) if SIDE = 'L'
*                               (LDA,N) if SIDE = 'R'
*          The vectors which define the elementary reflectors, as
*          returned by CHETRD.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.
*          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
*
*  TAU     (input) COMPLEX array, dimension
*                               (M-1) if SIDE = 'L'
*                               (N-1) if SIDE = 'R'
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by CHETRD.
*
*  C       (input/output) COMPLEX array, dimension (LDC,N)
*          On entry, the M-by-N matrix C.
*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.
*          If SIDE = 'L', LWORK >= max(1,N);
*          if SIDE = 'R', LWORK >= max(1,M).
*          For optimum performance LWORK >= N*NB if SIDE = 'L', and
*          LWORK >=M*NB if SIDE = 'R', where NB is the optimal
*          blocksize.
*
*          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    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            LEFT, LQUERY, UPPER
      INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           ILAENV, LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           CUNMQL, CUNMQR, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..

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