
sgelsd.f(3) LAPACK sgelsd.f(3)
NAME
sgelsd.f 
SYNOPSIS
Functions/Subroutines
subroutine sgelsd (M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, IWORK, INFO)
SGELSD computes the minimumnorm solution to a linear least squares problem for GE
matrices
Function/Subroutine Documentation
subroutine sgelsd (integerM, integerN, integerNRHS, real, dimension( lda, * )A, integerLDA,
real, dimension( ldb, * )B, integerLDB, real, dimension( * )S, realRCOND, integerRANK,
real, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerINFO)
SGELSD computes the minimumnorm solution to a linear least squares problem for GE
matrices
Purpose:
SGELSD computes the minimumnorm solution to a real linear least
squares problem:
minimize 2norm( b  A*x )
using the singular value decomposition (SVD) of A. A is an MbyN
matrix which may be rankdeficient.
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
MbyNRHS right hand side matrix B and the NbyNRHS solution
matrix X.
The problem is solved in three steps:
(1) Reduce the coefficient matrix A to bidiagonal form with
Householder transformations, reducing the original problem
into a "bidiagonal least squares problem" (BLS)
(2) Solve the BLS using a divide and conquer approach.
(3) Apply back all the Householder tranformations to solve
the original least squares problem.
The effective rank of A is determined by treating as zero those
singular values which are less than RCOND times the largest singular
value.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray XMP, Cray YMP, Cray C90, or
Cray2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Parameters:
M
M is INTEGER
The number of rows of A. M >= 0.
N
N is INTEGER
The number of columns of 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 MbyN matrix A.
On exit, A has been destroyed.
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 MbyNRHS right hand side matrix B.
On exit, B is overwritten by the NbyNRHS solution
matrix X. If m >= n and RANK = n, the residual
sumofsquares for the solution in the ith 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 REAL array, dimension (min(M,N))
The singular values of A in decreasing order.
The condition number of A in the 2norm = 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 REAL 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 must be at least 1.
The exact minimum amount of workspace needed depends on M,
N and NRHS. As long as LWORK is at least
12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2,
if M is greater than or equal to N or
12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2,
if M is less than N, the code will execute correctly.
SMLSIZ is returned by ILAENV and is equal to the maximum
size of the subproblems at the bottom of the computation
tree (usually about 25), and
NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
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 array WORK and the
minimum size of the array IWORK, and returns these values as
the first entries of the WORK and IWORK arrays, and no error
message related to LWORK is issued by XERBLA.
IWORK
IWORK is INTEGER array, dimension (MAX(1,LIWORK))
LIWORK >= max(1, 3*MINMN*NLVL + 11*MINMN),
where MINMN = MIN( M,N ).
On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value.
> 0: the algorithm for computing the SVD failed to converge;
if INFO = i, i offdiagonal 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.
Date:
November 2011
Contributors:
Ming Gu and RenCang Li, Computer Science Division, University of California at
Berkeley, USA
Osni Marques, LBNL/NERSC, USA
Definition at line 210 of file sgelsd.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 sgelsd.f(3) 
