# getsls - Man Page

getsls: least squares using tall-skinny QR/LQ

## Synopsis

### Functions

subroutine cgetsls (trans, m, n, nrhs, a, lda, b, ldb, work, lwork, info)
CGETSLS
subroutine dgetsls (trans, m, n, nrhs, a, lda, b, ldb, work, lwork, info)
DGETSLS
subroutine sgetsls (trans, m, n, nrhs, a, lda, b, ldb, work, lwork, info)
SGETSLS
subroutine zgetsls (trans, m, n, nrhs, a, lda, b, ldb, work, lwork, info)
ZGETSLS

## Function Documentation

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

CGETSLS

Purpose:

CGETSLS solves overdetermined or underdetermined complex 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 = 'C' and m >= n:  find the minimum norm solution of
an undetermined 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 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 CGEQR or CGELQ.

LDA

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

B

B is COMPLEX 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.
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.

LDB

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

WORK

(workspace) COMPLEX 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

NAG Ltd.

Definition at line 160 of file cgetsls.f.

### 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)

DGETSLS

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

NAG Ltd.

Definition at line 160 of file dgetsls.f.

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

SGETSLS

Purpose:

SGETSLS 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 REAL 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 SGEQR or SGELQ.

LDA

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

B

B is REAL 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) REAL 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

NAG Ltd.

Definition at line 160 of file sgetsls.f.

### subroutine zgetsls (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)

ZGETSLS

Purpose:

ZGETSLS solves overdetermined or underdetermined complex 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 = 'C' and m >= n:  find the minimum norm solution of
an undetermined 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,
A is overwritten by details of its QR or LQ
factorization as returned by ZGEQR or ZGELQ.

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.
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.

LDB

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

WORK

(workspace) COMPLEX*16 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