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---
:name: cgglse
:md5sum: 76651864baa26d2d1471eeda133757a5
:category: :subroutine
:arguments:
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- p:
:type: integer
:intent: input
- a:
:type: complex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- b:
:type: complex
:intent: input/output
:dims:
- ldb
- n
- ldb:
:type: integer
:intent: input
- c:
:type: complex
:intent: input/output
:dims:
- m
- d:
:type: complex
:intent: input/output
:dims:
- p
- x:
:type: complex
:intent: output
:dims:
- n
- work:
:type: complex
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: m+n+p
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE CGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CGGLSE solves the linear equality-constrained least squares (LSE)\n\
* problem:\n\
*\n\
* minimize || c - A*x ||_2 subject to B*x = d\n\
*\n\
* where A is an M-by-N matrix, B is a P-by-N matrix, c is a given\n\
* M-vector, and d is a given P-vector. It is assumed that\n\
* P <= N <= M+P, and\n\
*\n\
* rank(B) = P and rank( (A) ) = N.\n\
* ( (B) )\n\
*\n\
* These conditions ensure that the LSE problem has a unique solution,\n\
* which is obtained using a generalized RQ factorization of the\n\
* matrices (B, A) given by\n\
*\n\
* B = (0 R)*Q, A = Z*T*Q.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* M (input) INTEGER\n\
* The number of rows of the matrix A. M >= 0.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the matrices A and B. N >= 0.\n\
*\n\
* P (input) INTEGER\n\
* The number of rows of the matrix B. 0 <= P <= N <= M+P.\n\
*\n\
* A (input/output) COMPLEX array, dimension (LDA,N)\n\
* On entry, the M-by-N matrix A.\n\
* On exit, the elements on and above the diagonal of the array\n\
* contain the min(M,N)-by-N upper trapezoidal matrix T.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,M).\n\
*\n\
* B (input/output) COMPLEX array, dimension (LDB,N)\n\
* On entry, the P-by-N matrix B.\n\
* On exit, the upper triangle of the subarray B(1:P,N-P+1:N)\n\
* contains the P-by-P upper triangular matrix R.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,P).\n\
*\n\
* C (input/output) COMPLEX array, dimension (M)\n\
* On entry, C contains the right hand side vector for the\n\
* least squares part of the LSE problem.\n\
* On exit, the residual sum of squares for the solution\n\
* is given by the sum of squares of elements N-P+1 to M of\n\
* vector C.\n\
*\n\
* D (input/output) COMPLEX array, dimension (P)\n\
* On entry, D contains the right hand side vector for the\n\
* constrained equation.\n\
* On exit, D is destroyed.\n\
*\n\
* X (output) COMPLEX array, dimension (N)\n\
* On exit, X is the solution of the LSE problem.\n\
*\n\
* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))\n\
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
*\n\
* LWORK (input) INTEGER\n\
* The dimension of the array WORK. LWORK >= max(1,M+N+P).\n\
* For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB,\n\
* where NB is an upper bound for the optimal blocksizes for\n\
* CGEQRF, CGERQF, CUNMQR and CUNMRQ.\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates the optimal size of the WORK array, returns\n\
* this value as the first entry of the WORK array, and no error\n\
* message related to LWORK is issued by XERBLA.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit.\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
* = 1: the upper triangular factor R associated with B in the\n\
* generalized RQ factorization of the pair (B, A) is\n\
* singular, so that rank(B) < P; the least squares\n\
* solution could not be computed.\n\
* = 2: the (N-P) by (N-P) part of the upper trapezoidal factor\n\
* T associated with A in the generalized RQ factorization\n\
* of the pair (B, A) is singular, so that\n\
* rank( (A) ) < N; the least squares solution could not\n\
* ( (B) )\n\
* be computed.\n\
*\n\n\
* =====================================================================\n\
*\n"
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