---
name: "cgelss.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/cgelss.f"
---

# cgelss.f(3)

## NAME

SRC/cgelss.f

## SYNOPSIS

### Functions/Subroutines

subroutine **cgelss** (m, n, nrhs, a, lda, b, ldb, s, rcond, rank, work, lwork, rwork, info)\
  **CGELSS solves overdetermined or underdetermined systems for GE matrices**

## Function/Subroutine Documentation

### subroutine cgelss (integer m, integer n, integer nrhs, complex, dimension( lda, \* ) a, integer lda, complex, dimension( ldb, \* ) b, integer ldb, real, dimension( \* ) s, real rcond, integer rank, complex, dimension( \* ) work, integer lwork, real, dimension( \* ) rwork, integer info)

 **CGELSS solves overdetermined or underdetermined systems for GE matrices**

**Purpose:**

```
!>
!> CGELSS computes the minimum norm solution to a complex linear
!> least squares problem:
!>
!> Minimize 2-norm(| b - A*x |).
!>
!> using the singular value decomposition (SVD) of A. A is an M-by-N
!> matrix which may be rank-deficient.
!>
!> 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.
!>
!> The effective rank of A is determined by treating as zero those
!> singular values which are less than RCOND times the largest singular
!> value.
!>
```

**Parameters**

*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, the first min(m,n) rows of A are overwritten with
!>          its right singular vectors, stored rowwise.
!>
```

*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 M-by-NRHS right hand side matrix B.
!>          On exit, B is overwritten by the N-by-NRHS solution matrix X.
!>          If m >= n and RANK = n, the residual sum-of-squares for
!>          the solution in the i-th column is given by the sum of
!>          squares of the modulus of elements n+1:m in that column.
!>
```

*LDB*

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

*S*

```
!>          S is REAL array, dimension (min(M,N))
!>          The singular values of A in decreasing order.
!>          The condition number of A in the 2-norm = S(1)/S(min(m,n)).
!>
```

*RCOND*

```
!>          RCOND is REAL
!>          RCOND is used to determine the effective rank of A.
!>          Singular values S(i) <= RCOND*S(1) are treated as zero.
!>          If RCOND < 0, machine precision is used instead.
!>
```

*RANK*

```
!>          RANK is INTEGER
!>          The effective rank of A, i.e., the number of singular values
!>          which are greater than RCOND*S(1).
!>
```

*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 >= 1, and also:
!>          LWORK >=  2*min(M,N) + max(M,N,NRHS)
!>          For good performance, LWORK should generally be larger.
!>
!>          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.
!>
```

*RWORK*

```
!>          RWORK is REAL array, dimension (5*min(M,N))
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>          > 0:  the algorithm for computing the SVD failed to converge;
!>                if INFO = i, i off-diagonal elements of an intermediate
!>                bidiagonal form did not converge to zero.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **176** of file **cgelss.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.