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LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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subroutine zgelsx | ( | integer | m, |
integer | n, | ||
integer | nrhs, | ||
complex*16, dimension( lda, * ) | a, | ||
integer | lda, | ||
complex*16, dimension( ldb, * ) | b, | ||
integer | ldb, | ||
integer, dimension( * ) | jpvt, | ||
double precision | rcond, | ||
integer | rank, | ||
complex*16, dimension( * ) | work, | ||
double precision, dimension( * ) | rwork, | ||
integer | info ) |
ZGELSX solves overdetermined or underdetermined systems for GE matrices
Download ZGELSX + dependencies [TGZ] [ZIP] [TXT]
!> !> This routine is deprecated and has been replaced by routine ZGELSY.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. !>
[in] | M | !> M is INTEGER !> The number of rows of the matrix A. M >= 0. !> |
[in] | N | !> N is INTEGER !> The number of columns of the matrix A. N >= 0. !> |
[in] | NRHS | !> NRHS is INTEGER !> The number of right hand sides, i.e., the number of !> columns of matrices B and X. NRHS >= 0. !> |
[in,out] | 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. !> |
[in] | LDA | !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !> |
[in,out] | 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. !> |
[in] | LDB | !> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,M,N). !> |
[in,out] | 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. !> |
[in] | 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. !> |
[out] | 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. !> |
[out] | WORK | !> WORK is COMPLEX*16 array, dimension !> (min(M,N) + max( N, 2*min(M,N)+NRHS )), !> |
[out] | RWORK | !> RWORK is DOUBLE PRECISION array, dimension (2*N) !> |
[out] | INFO | !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> |
Definition at line 180 of file zgelsx.f.