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---
:name: dggglm
:md5sum: b132b24d18eb3c974ddf79f3c310f812
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- m:
:type: integer
:intent: input
- p:
:type: integer
:intent: input
- a:
:type: doublereal
:intent: input/output
:dims:
- lda
- m
- lda:
:type: integer
:intent: input
- b:
:type: doublereal
:intent: input/output
:dims:
- ldb
- p
- ldb:
:type: integer
:intent: input
- d:
:type: doublereal
:intent: input/output
:dims:
- n
- x:
:type: doublereal
:intent: output
:dims:
- m
- y:
:type: doublereal
:intent: output
:dims:
- p
- work:
:type: doublereal
: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 DGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DGGGLM solves a general Gauss-Markov linear model (GLM) problem:\n\
*\n\
* minimize || y ||_2 subject to d = A*x + B*y\n\
* x\n\
*\n\
* where A is an N-by-M matrix, B is an N-by-P matrix, and d is a\n\
* given N-vector. It is assumed that M <= N <= M+P, and\n\
*\n\
* rank(A) = M and rank( A B ) = N.\n\
*\n\
* Under these assumptions, the constrained equation is always\n\
* consistent, and there is a unique solution x and a minimal 2-norm\n\
* solution y, which is obtained using a generalized QR factorization\n\
* of the matrices (A, B) given by\n\
*\n\
* A = Q*(R), B = Q*T*Z.\n\
* (0)\n\
*\n\
* In particular, if matrix B is square nonsingular, then the problem\n\
* GLM is equivalent to the following weighted linear least squares\n\
* problem\n\
*\n\
* minimize || inv(B)*(d-A*x) ||_2\n\
* x\n\
*\n\
* where inv(B) denotes the inverse of B.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The number of rows of the matrices A and B. N >= 0.\n\
*\n\
* M (input) INTEGER\n\
* The number of columns of the matrix A. 0 <= M <= N.\n\
*\n\
* P (input) INTEGER\n\
* The number of columns of the matrix B. P >= N-M.\n\
*\n\
* A (input/output) DOUBLE PRECISION array, dimension (LDA,M)\n\
* On entry, the N-by-M matrix A.\n\
* On exit, the upper triangular part of the array A contains\n\
* the M-by-M upper triangular matrix R.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* B (input/output) DOUBLE PRECISION array, dimension (LDB,P)\n\
* On entry, the N-by-P matrix B.\n\
* On exit, if N <= P, the upper triangle of the subarray\n\
* B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;\n\
* if N > P, the elements on and above the (N-P)th subdiagonal\n\
* contain the N-by-P upper trapezoidal matrix T.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,N).\n\
*\n\
* D (input/output) DOUBLE PRECISION array, dimension (N)\n\
* On entry, D is the left hand side of the GLM equation.\n\
* On exit, D is destroyed.\n\
*\n\
* X (output) DOUBLE PRECISION array, dimension (M)\n\
* Y (output) DOUBLE PRECISION array, dimension (P)\n\
* On exit, X and Y are the solutions of the GLM problem.\n\
*\n\
* WORK (workspace/output) DOUBLE PRECISION 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,N+M+P).\n\
* For optimum performance, LWORK >= M+min(N,P)+max(N,P)*NB,\n\
* where NB is an upper bound for the optimal blocksizes for\n\
* DGEQRF, SGERQF, DORMQR and SORMRQ.\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 A in the\n\
* generalized QR factorization of the pair (A, B) is\n\
* singular, so that rank(A) < M; the least squares\n\
* solution could not be computed.\n\
* = 2: the bottom (N-M) by (N-M) part of the upper trapezoidal\n\
* factor T associated with B in the generalized QR\n\
* factorization of the pair (A, B) is singular, so that\n\
* rank( A B ) < N; the least squares solution could not\n\
* be computed.\n\
*\n\n\
* ===================================================================\n\
*\n"
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