!>
!> ZGELST solves overdetermined or underdetermined real linear systems
!> involving an M-by-N matrix A, or its conjugate-transpose, using a QR
!> or LQ factorization of A with compact WY representation of Q.
!> It is assumed that A has full rank.
!>
!> The following options are provided:
!>
!> 1. If TRANS = 'N' and m >= n:  find the least squares solution of
!>    an overdetermined system, i.e., solve the least squares problem
!>                 minimize || B - A*X ||.
!>
!> 2. If TRANS = 'N' and m < n:  find the minimum norm solution of
!>    an underdetermined system A * X = B.
!>
!> 3. If TRANS = 'C' and m >= n:  find the minimum norm solution of
!>    an underdetermined system A**T * X = B.
!>
!> 4. If TRANS = 'C' and m < n:  find the least squares solution of
!>    an overdetermined system, i.e., solve the least squares problem
!>                 minimize || B - A**T * X ||.
!>
!> Several right hand side vectors b and solution vectors x can be
!> handled in a single call; they are stored as the columns of the
!> M-by-NRHS right hand side matrix B and the N-by-NRHS solution
!> matrix X.
!> 

TRANS

!>          TRANS is CHARACTER*1
!>          = 'N': the linear system involves A;
!>          = 'C': the linear system involves A**H.
!> 

M

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

N

!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!> 

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of
!>          columns of the matrices B and X. NRHS >=0.
!> 

A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the M-by-N matrix A.
!>          On exit,
!>            if M >= N, A is overwritten by details of its QR
!>                       factorization as returned by ZGEQRT;
!>            if M <  N, A is overwritten by details of its LQ
!>                       factorization as returned by ZGELQT.
!> 

LDA

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

B

!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the matrix B of right hand side vectors, stored
!>          columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS
!>          if TRANS = 'C'.
!>          On exit, if INFO = 0, B is overwritten by the solution
!>          vectors, stored columnwise:
!>          if TRANS = 'N' and m >= n, rows 1 to n of B contain the least
!>          squares solution vectors; the residual sum of squares for the
!>          solution in each column is given by the sum of squares of
!>          modulus of elements N+1 to M in that column;
!>          if TRANS = 'N' and m < n, rows 1 to N of B contain the
!>          minimum norm solution vectors;
!>          if TRANS = 'C' and m >= n, rows 1 to M of B contain the
!>          minimum norm solution vectors;
!>          if TRANS = 'C' and m < n, rows 1 to M of B contain the
!>          least squares solution vectors; the residual sum of squares
!>          for the solution in each column is given by the sum of
!>          squares of the modulus of elements M+1 to N in that column.
!> 

LDB

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

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, MN + max( MN, NRHS ) ).
!>          For optimal performance,
!>          LWORK >= max( 1, (MN + max( MN, NRHS ))*NB ).
!>          where MN = min(M,N) and NB is the optimum block size.
!>
!>          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
!>          > 0:  if INFO =  i, the i-th diagonal element of the
!>                triangular factor of A is zero, so that A does not have
!>                full rank; the least squares solution could not be
!>                computed.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!>  November 2022,  Igor Kozachenko,
!>                  Computer Science Division,
!>                  University of California, Berkeley
!>