# dgetsls.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
Page Index

dgetsls.f

## SYNOPSIS

### Functions/Subroutines

subroutine dgetsls (TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, INFO)

## Function/Subroutine Documentation

### subroutine dgetsls (character TRANS, integer M, integer N, integer NRHS, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) WORK, integer LWORK, integer INFO)

Purpose:

DGETSLS solves overdetermined or underdetermined real linear systems involving an M-by-N matrix A, using a tall skinny QR or short wide LQ factorization of A. 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 = 'T' and m >= n: find the minimum norm solution of an undetermined system A**T * X = B.
4.
If TRANS = 'T' 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;
= 'T': the linear system involves A**T.
```

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 DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit,
A is overwritten by details of its QR or LQ
factorization as returned by DGEQR or DGELQ.
```

LDA

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

B

```          B is DOUBLE PRECISION 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 = 'T'.
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.
if TRANS = 'N' and m < n, rows 1 to N of B contain the
minimum norm solution vectors;
if TRANS = 'T' and m >= n, rows 1 to M of B contain the
minimum norm solution vectors;
if TRANS = 'T' and m < n, rows 1 to M of B contain the
least squares solution vectors.
```

LDB

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

WORK

```          (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
or optimal, if query was assumed) LWORK.
See LWORK for details.
```

LWORK

```          LWORK is INTEGER
The dimension of the array WORK.
If LWORK = -1 or -2, then a workspace query is assumed.
If LWORK = -1, the routine calculates optimal size of WORK for the
optimal performance and returns this value in WORK(1).
If LWORK = -2, the routine calculates minimal size of WORK and
returns this value in WORK(1).
```

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