dgelss.f3

!>
!> DGELSS computes the minimum norm solution to a real 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.
!> 

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, 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 DOUBLE PRECISION 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 elements n+1:m in that column.
!> 

LDB

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

S

!>          S is DOUBLE PRECISION 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 DOUBLE PRECISION
!>          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 DOUBLE PRECISION 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 >= 3*min(M,N) + max( 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.
!> 

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.
!> 

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