dgelsx (l)  Linux Man Pages
dgelsx: routine i deprecated and has been replaced by routine DGELSY
NAME
DGELSX  routine i deprecated and has been replaced by routine DGELSYSYNOPSIS
 SUBROUTINE DGELSX(
 M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, WORK, INFO )
 INTEGER INFO, LDA, LDB, M, N, NRHS, RANK
 DOUBLE PRECISION RCOND
 INTEGER JPVT( * )
 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
PURPOSE
This routine is deprecated and has been replaced by routine DGELSY. DGELSX computes the minimumnorm solution to a real linear least squares problem:using a complete orthogonal factorization 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 routine first computes a QR factorization with column pivoting:
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 orthogonal transformations from the right, arriving at the complete orthogonal factorization:
A
The minimumnorm solution is then
X
where Q1 consists of the first RANK columns of Q.
ARGUMENTS
 M (input) INTEGER
 The number of rows of the matrix A. M >= 0.
 N (input) INTEGER
 The number of columns of the matrix A. N >= 0.
 NRHS (input) INTEGER
 The number of right hand sides, i.e., the number of columns of matrices B and X. NRHS >= 0.
 A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
 On entry, the MbyN matrix A. On exit, A has been overwritten by details of its complete orthogonal factorization.
 LDA (input) INTEGER
 The leading dimension of the array A. LDA >= max(1,M).
 B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
 On entry, the MbyNRHS right hand side matrix B. On exit, 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 (input) INTEGER
 The leading dimension of the array B. LDB >= max(1,M,N).
 JPVT (input/output) INTEGER array, dimension (N)
 On entry, if JPVT(i) .ne. 0, the ith 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 ith column of A*P was the kth column of A.
 RCOND (input) 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 (output) 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 (workspace) DOUBLE PRECISION array, dimension
 (max( min(M,N)+3*N, 2*min(M,N)+NRHS )),
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value