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zgelss.f(3) LAPACK zgelss.f(3)

zgelss.f -


subroutine zgelss (M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, RWORK, INFO)
 
ZGELSS solves overdetermined or underdetermined systems for GE matrices

ZGELSS solves overdetermined or underdetermined systems for GE matrices
Purpose:
 ZGELSS 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*16 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*16 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 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 COMPLEX*16 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 DOUBLE PRECISION 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.
Date:
November 2011
Definition at line 178 of file zgelss.f.

Generated automatically by Doxygen for LAPACK from the source code.
Sat Nov 16 2013 Version 3.4.2

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