ggrqf(3)

NAME
ggrqf - ggrqf: Generalized RQ factor

SYNOPSIS

  Functions

subroutine cggrqf (m, p, n, a, lda, taua, b, ldb, taub, work, lwork, info)
CGGRQF
subroutine dggrqf (m, p, n, a, lda, taua, b, ldb, taub, work, lwork, info)
DGGRQF
subroutine sggrqf (m, p, n, a, lda, taua, b, ldb, taub, work, lwork, info)
SGGRQF
subroutine zggrqf (m, p, n, a, lda, taua, b, ldb, taub, work, lwork, info)
ZGGRQF

Detailed Description

Function Documentation

  subroutine cggrqf (integer m, integer p, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) taua, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) taub, complex, dimension( * ) work, integer lwork, integer info)

CGGRQF

Purpose:

    !>
    !> CGGRQF computes a generalized RQ factorization of an M-by-N matrix A
    !> and a P-by-N matrix B:
    !>
    !>             A = R*Q,        B = Z*T*Q,
    !>
    !> where Q is an N-by-N unitary matrix, Z is a P-by-P unitary
    !> matrix, and R and T assume one of the forms:
    !>
    !> if M <= N,  R = ( 0  R12 ) M,   or if M > N,  R = ( R11 ) M-N,
    !>                  N-M  M                           ( R21 ) N
    !>                                                      N
    !>
    !> where R12 or R21 is upper triangular, and
    !>
    !> if P >= N,  T = ( T11 ) N  ,   or if P < N,  T = ( T11  T12 ) P,
    !>                 (  0  ) P-N                         P   N-P
    !>                    N
    !>
    !> where T11 is upper triangular.
    !>
    !> In particular, if B is square and nonsingular, the GRQ factorization
    !> of A and B implicitly gives the RQ factorization of A*inv(B):
    !>
    !>              A*inv(B) = (R*inv(T))*Z**H
    !>
    !> where inv(B) denotes the inverse of the matrix B, and Z**H denotes the
    !> conjugate transpose of the matrix Z.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    P

    !>          P is INTEGER
    !>          The number of rows of the matrix B.  P >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrices A and B. N >= 0.
    !>

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit, if M <= N, the upper triangle of the subarray
    !>          A(1:M,N-M+1:N) contains the M-by-M upper triangular matrix R;
    !>          if M > N, the elements on and above the (M-N)-th subdiagonal
    !>          contain the M-by-N upper trapezoidal matrix R; the remaining
    !>          elements, with the array TAUA, represent the unitary
    !>          matrix Q as a product of elementary reflectors (see Further
    !>          Details).
    !>

    LDA

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

    TAUA

    !>          TAUA is COMPLEX array, dimension (min(M,N))
    !>          The scalar factors of the elementary reflectors which
    !>          represent the unitary matrix Q (see Further Details).
    !>

    B

    !>          B is COMPLEX array, dimension (LDB,N)
    !>          On entry, the P-by-N matrix B.
    !>          On exit, the elements on and above the diagonal of the array
    !>          contain the min(P,N)-by-N upper trapezoidal matrix T (T is
    !>          upper triangular if P >= N); the elements below the diagonal,
    !>          with the array TAUB, represent the unitary matrix Z as a
    !>          product of elementary reflectors (see Further Details).
    !>

    LDB

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

    TAUB

    !>          TAUB is COMPLEX array, dimension (min(P,N))
    !>          The scalar factors of the elementary reflectors which
    !>          represent the unitary matrix Z (see Further Details).
    !>

    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,M,P).
    !>          For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3),
    !>          where NB1 is the optimal blocksize for the RQ factorization
    !>          of an M-by-N matrix, NB2 is the optimal blocksize for the
    !>          QR factorization of a P-by-N matrix, and NB3 is the optimal
    !>          blocksize for a call of CUNMRQ.
    !>
    !>          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
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The matrix Q is represented as a product of elementary reflectors
    !>
    !>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
    !>
    !>  Each H(i) has the form
    !>
    !>     H(i) = I - taua * v * v**H
    !>
    !>  where taua is a complex scalar, and v is a complex vector with
    !>  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
    !>  A(m-k+i,1:n-k+i-1), and taua in TAUA(i).
    !>  To form Q explicitly, use LAPACK subroutine CUNGRQ.
    !>  To use Q to update another matrix, use LAPACK subroutine CUNMRQ.
    !>
    !>  The matrix Z is represented as a product of elementary reflectors
    !>
    !>     Z = H(1) H(2) . . . H(k), where k = min(p,n).
    !>
    !>  Each H(i) has the form
    !>
    !>     H(i) = I - taub * v * v**H
    !>
    !>  where taub is a complex scalar, and v is a complex vector with
    !>  v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i),
    !>  and taub in TAUB(i).
    !>  To form Z explicitly, use LAPACK subroutine CUNGQR.
    !>  To use Z to update another matrix, use LAPACK subroutine CUNMQR.
    !>

  subroutine dggrqf (integer m, integer p, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) taua, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) taub, double precision, dimension( * ) work, integer lwork, integer info)

DGGRQF

Purpose:

    !>
    !> DGGRQF computes a generalized RQ factorization of an M-by-N matrix A
    !> and a P-by-N matrix B:
    !>
    !>             A = R*Q,        B = Z*T*Q,
    !>
    !> where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal
    !> matrix, and R and T assume one of the forms:
    !>
    !> if M <= N,  R = ( 0  R12 ) M,   or if M > N,  R = ( R11 ) M-N,
    !>                  N-M  M                           ( R21 ) N
    !>                                                      N
    !>
    !> where R12 or R21 is upper triangular, and
    !>
    !> if P >= N,  T = ( T11 ) N  ,   or if P < N,  T = ( T11  T12 ) P,
    !>                 (  0  ) P-N                         P   N-P
    !>                    N
    !>
    !> where T11 is upper triangular.
    !>
    !> In particular, if B is square and nonsingular, the GRQ factorization
    !> of A and B implicitly gives the RQ factorization of A*inv(B):
    !>
    !>              A*inv(B) = (R*inv(T))*Z**T
    !>
    !> where inv(B) denotes the inverse of the matrix B, and Z**T denotes the
    !> transpose of the matrix Z.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    P

    !>          P is INTEGER
    !>          The number of rows of the matrix B.  P >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrices A and B. N >= 0.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit, if M <= N, the upper triangle of the subarray
    !>          A(1:M,N-M+1:N) contains the M-by-M upper triangular matrix R;
    !>          if M > N, the elements on and above the (M-N)-th subdiagonal
    !>          contain the M-by-N upper trapezoidal matrix R; the remaining
    !>          elements, with the array TAUA, represent the orthogonal
    !>          matrix Q as a product of elementary reflectors (see Further
    !>          Details).
    !>

    LDA

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

    TAUA

    !>          TAUA is DOUBLE PRECISION array, dimension (min(M,N))
    !>          The scalar factors of the elementary reflectors which
    !>          represent the orthogonal matrix Q (see Further Details).
    !>

    B

    !>          B is DOUBLE PRECISION array, dimension (LDB,N)
    !>          On entry, the P-by-N matrix B.
    !>          On exit, the elements on and above the diagonal of the array
    !>          contain the min(P,N)-by-N upper trapezoidal matrix T (T is
    !>          upper triangular if P >= N); the elements below the diagonal,
    !>          with the array TAUB, represent the orthogonal matrix Z as a
    !>          product of elementary reflectors (see Further Details).
    !>

    LDB

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

    TAUB

    !>          TAUB is DOUBLE PRECISION array, dimension (min(P,N))
    !>          The scalar factors of the elementary reflectors which
    !>          represent the orthogonal matrix Z (see Further Details).
    !>

    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,M,P).
    !>          For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3),
    !>          where NB1 is the optimal blocksize for the RQ factorization
    !>          of an M-by-N matrix, NB2 is the optimal blocksize for the
    !>          QR factorization of a P-by-N matrix, and NB3 is the optimal
    !>          blocksize for a call of DORMRQ.
    !>
    !>          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 INF0= -i, the i-th argument had an illegal value.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The matrix Q is represented as a product of elementary reflectors
    !>
    !>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
    !>
    !>  Each H(i) has the form
    !>
    !>     H(i) = I - taua * v * v**T
    !>
    !>  where taua is a real scalar, and v is a real vector with
    !>  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
    !>  A(m-k+i,1:n-k+i-1), and taua in TAUA(i).
    !>  To form Q explicitly, use LAPACK subroutine DORGRQ.
    !>  To use Q to update another matrix, use LAPACK subroutine DORMRQ.
    !>
    !>  The matrix Z is represented as a product of elementary reflectors
    !>
    !>     Z = H(1) H(2) . . . H(k), where k = min(p,n).
    !>
    !>  Each H(i) has the form
    !>
    !>     H(i) = I - taub * v * v**T
    !>
    !>  where taub is a real scalar, and v is a real vector with
    !>  v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i),
    !>  and taub in TAUB(i).
    !>  To form Z explicitly, use LAPACK subroutine DORGQR.
    !>  To use Z to update another matrix, use LAPACK subroutine DORMQR.
    !>

  subroutine sggrqf (integer m, integer p, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) taua, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) taub, real, dimension( * ) work, integer lwork, integer info)

SGGRQF

Purpose:

    !>
    !> SGGRQF computes a generalized RQ factorization of an M-by-N matrix A
    !> and a P-by-N matrix B:
    !>
    !>             A = R*Q,        B = Z*T*Q,
    !>
    !> where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal
    !> matrix, and R and T assume one of the forms:
    !>
    !> if M <= N,  R = ( 0  R12 ) M,   or if M > N,  R = ( R11 ) M-N,
    !>                  N-M  M                           ( R21 ) N
    !>                                                      N
    !>
    !> where R12 or R21 is upper triangular, and
    !>
    !> if P >= N,  T = ( T11 ) N  ,   or if P < N,  T = ( T11  T12 ) P,
    !>                 (  0  ) P-N                         P   N-P
    !>                    N
    !>
    !> where T11 is upper triangular.
    !>
    !> In particular, if B is square and nonsingular, the GRQ factorization
    !> of A and B implicitly gives the RQ factorization of A*inv(B):
    !>
    !>              A*inv(B) = (R*inv(T))*Z**T
    !>
    !> where inv(B) denotes the inverse of the matrix B, and Z**T denotes the
    !> transpose of the matrix Z.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    P

    !>          P is INTEGER
    !>          The number of rows of the matrix B.  P >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrices A and B. N >= 0.
    !>

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit, if M <= N, the upper triangle of the subarray
    !>          A(1:M,N-M+1:N) contains the M-by-M upper triangular matrix R;
    !>          if M > N, the elements on and above the (M-N)-th subdiagonal
    !>          contain the M-by-N upper trapezoidal matrix R; the remaining
    !>          elements, with the array TAUA, represent the orthogonal
    !>          matrix Q as a product of elementary reflectors (see Further
    !>          Details).
    !>

    LDA

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

    TAUA

    !>          TAUA is REAL array, dimension (min(M,N))
    !>          The scalar factors of the elementary reflectors which
    !>          represent the orthogonal matrix Q (see Further Details).
    !>

    B

    !>          B is REAL array, dimension (LDB,N)
    !>          On entry, the P-by-N matrix B.
    !>          On exit, the elements on and above the diagonal of the array
    !>          contain the min(P,N)-by-N upper trapezoidal matrix T (T is
    !>          upper triangular if P >= N); the elements below the diagonal,
    !>          with the array TAUB, represent the orthogonal matrix Z as a
    !>          product of elementary reflectors (see Further Details).
    !>

    LDB

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

    TAUB

    !>          TAUB is REAL array, dimension (min(P,N))
    !>          The scalar factors of the elementary reflectors which
    !>          represent the orthogonal matrix Z (see Further Details).
    !>

    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,M,P).
    !>          For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3),
    !>          where NB1 is the optimal blocksize for the RQ factorization
    !>          of an M-by-N matrix, NB2 is the optimal blocksize for the
    !>          QR factorization of a P-by-N matrix, and NB3 is the optimal
    !>          blocksize for a call of SORMRQ.
    !>
    !>          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 INF0= -i, the i-th argument had an illegal value.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The matrix Q is represented as a product of elementary reflectors
    !>
    !>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
    !>
    !>  Each H(i) has the form
    !>
    !>     H(i) = I - taua * v * v**T
    !>
    !>  where taua is a real scalar, and v is a real vector with
    !>  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
    !>  A(m-k+i,1:n-k+i-1), and taua in TAUA(i).
    !>  To form Q explicitly, use LAPACK subroutine SORGRQ.
    !>  To use Q to update another matrix, use LAPACK subroutine SORMRQ.
    !>
    !>  The matrix Z is represented as a product of elementary reflectors
    !>
    !>     Z = H(1) H(2) . . . H(k), where k = min(p,n).
    !>
    !>  Each H(i) has the form
    !>
    !>     H(i) = I - taub * v * v**T
    !>
    !>  where taub is a real scalar, and v is a real vector with
    !>  v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i),
    !>  and taub in TAUB(i).
    !>  To form Z explicitly, use LAPACK subroutine SORGQR.
    !>  To use Z to update another matrix, use LAPACK subroutine SORMQR.
    !>

  subroutine zggrqf (integer m, integer p, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) taua, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) taub, complex*16, dimension( * ) work, integer lwork, integer info)

ZGGRQF

Purpose:

    !>
    !> ZGGRQF computes a generalized RQ factorization of an M-by-N matrix A
    !> and a P-by-N matrix B:
    !>
    !>             A = R*Q,        B = Z*T*Q,
    !>
    !> where Q is an N-by-N unitary matrix, Z is a P-by-P unitary
    !> matrix, and R and T assume one of the forms:
    !>
    !> if M <= N,  R = ( 0  R12 ) M,   or if M > N,  R = ( R11 ) M-N,
    !>                  N-M  M                           ( R21 ) N
    !>                                                      N
    !>
    !> where R12 or R21 is upper triangular, and
    !>
    !> if P >= N,  T = ( T11 ) N  ,   or if P < N,  T = ( T11  T12 ) P,
    !>                 (  0  ) P-N                         P   N-P
    !>                    N
    !>
    !> where T11 is upper triangular.
    !>
    !> In particular, if B is square and nonsingular, the GRQ factorization
    !> of A and B implicitly gives the RQ factorization of A*inv(B):
    !>
    !>              A*inv(B) = (R*inv(T))*Z**H
    !>
    !> where inv(B) denotes the inverse of the matrix B, and Z**H denotes the
    !> conjugate transpose of the matrix Z.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    P

    !>          P is INTEGER
    !>          The number of rows of the matrix B.  P >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrices A and B. N >= 0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit, if M <= N, the upper triangle of the subarray
    !>          A(1:M,N-M+1:N) contains the M-by-M upper triangular matrix R;
    !>          if M > N, the elements on and above the (M-N)-th subdiagonal
    !>          contain the M-by-N upper trapezoidal matrix R; the remaining
    !>          elements, with the array TAUA, represent the unitary
    !>          matrix Q as a product of elementary reflectors (see Further
    !>          Details).
    !>

    LDA

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

    TAUA

    !>          TAUA is COMPLEX*16 array, dimension (min(M,N))
    !>          The scalar factors of the elementary reflectors which
    !>          represent the unitary matrix Q (see Further Details).
    !>

    B

    !>          B is COMPLEX*16 array, dimension (LDB,N)
    !>          On entry, the P-by-N matrix B.
    !>          On exit, the elements on and above the diagonal of the array
    !>          contain the min(P,N)-by-N upper trapezoidal matrix T (T is
    !>          upper triangular if P >= N); the elements below the diagonal,
    !>          with the array TAUB, represent the unitary matrix Z as a
    !>          product of elementary reflectors (see Further Details).
    !>

    LDB

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

    TAUB

    !>          TAUB is COMPLEX*16 array, dimension (min(P,N))
    !>          The scalar factors of the elementary reflectors which
    !>          represent the unitary matrix Z (see Further Details).
    !>

    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,M,P).
    !>          For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3),
    !>          where NB1 is the optimal blocksize for the RQ factorization
    !>          of an M-by-N matrix, NB2 is the optimal blocksize for the
    !>          QR factorization of a P-by-N matrix, and NB3 is the optimal
    !>          blocksize for a call of ZUNMRQ.
    !>
    !>          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
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The matrix Q is represented as a product of elementary reflectors
    !>
    !>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
    !>
    !>  Each H(i) has the form
    !>
    !>     H(i) = I - taua * v * v**H
    !>
    !>  where taua is a complex scalar, and v is a complex vector with
    !>  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
    !>  A(m-k+i,1:n-k+i-1), and taua in TAUA(i).
    !>  To form Q explicitly, use LAPACK subroutine ZUNGRQ.
    !>  To use Q to update another matrix, use LAPACK subroutine ZUNMRQ.
    !>
    !>  The matrix Z is represented as a product of elementary reflectors
    !>
    !>     Z = H(1) H(2) . . . H(k), where k = min(p,n).
    !>
    !>  Each H(i) has the form
    !>
    !>     H(i) = I - taub * v * v**H
    !>
    !>  where taub is a complex scalar, and v is a complex vector with
    !>  v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i),
    !>  and taub in TAUB(i).
    !>  To form Z explicitly, use LAPACK subroutine ZUNGQR.
    !>  To use Z to update another matrix, use LAPACK subroutine ZUNMQR.
    !>

Author

Generated automatically by Doxygen for LAPACK from the source code.