# cgelss.f - Man Page

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.

## Referenced By

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

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK