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zgelsx.f(3) LAPACK zgelsx.f(3)

zgelsx.f -


subroutine zgelsx (M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, WORK, RWORK, INFO)
 
ZGELSX solves overdetermined or underdetermined systems for GE matrices

ZGELSX solves overdetermined or underdetermined systems for GE matrices
Purpose:
 This routine is deprecated and has been replaced by routine ZGELSY.
ZGELSX computes the minimum-norm solution to a complex linear least squares problem: minimize || A * X - B || using a complete orthogonal factorization 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 routine first computes a QR factorization with column pivoting: A * P = Q * [ R11 R12 ] [ 0 R22 ] with R11 defined as the largest leading submatrix whose estimated condition number is less than 1/RCOND. The order of R11, RANK, is the effective rank of A.
Then, R22 is considered to be negligible, and R12 is annihilated by unitary transformations from the right, arriving at the complete orthogonal factorization: A * P = Q * [ T11 0 ] * Z [ 0 0 ] The minimum-norm solution is then X = P * Z**H [ inv(T11)*Q1**H*B ] [ 0 ] where Q1 consists of the first RANK columns of Q.
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 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, A has been overwritten by details of its
          complete orthogonal factorization.
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, 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,M,N).
JPVT
          JPVT is INTEGER array, dimension (N)
          On entry, if JPVT(i) .ne. 0, the i-th column of A is an
          initial column, otherwise it is a free column.  Before
          the QR factorization of A, all initial columns are
          permuted to the leading positions; only the remaining
          free columns are moved as a result of column pivoting
          during the factorization.
          On exit, if JPVT(i) = k, then the i-th column of A*P
          was the k-th column of A.
RCOND
          RCOND is DOUBLE PRECISION
          RCOND is used to determine the effective rank of A, which
          is defined as the order of the largest leading triangular
          submatrix R11 in the QR factorization with pivoting of A,
          whose estimated condition number < 1/RCOND.
RANK
          RANK is INTEGER
          The effective rank of A, i.e., the order of the submatrix
          R11.  This is the same as the order of the submatrix T11
          in the complete orthogonal factorization of A.
WORK
          WORK is COMPLEX*16 array, dimension
                      (min(M,N) + max( N, 2*min(M,N)+NRHS )),
RWORK
          RWORK is DOUBLE PRECISION array, dimension (2*N)
INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 184 of file zgelsx.f.

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