# zgelst.f - Man Page

SRC/zgelst.f

## Synopsis

### Functions/Subroutines

subroutine zgelst (trans, m, n, nrhs, a, lda, b, ldb, work, lwork, info)
ZGELST solves overdetermined or underdetermined systems for GE matrices using QR or LQ factorization with compact WY representation of Q.

## Function/Subroutine Documentation

### subroutine zgelst (character trans, integer m, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info)

ZGELST solves overdetermined or underdetermined systems for GE matrices using QR or LQ factorization with compact WY representation of Q.

Purpose:

``` 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.```
Parameters

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.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Contributors:

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

Definition at line 192 of file zgelst.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zgelst(3) is an alias of zgelst.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK