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---
:name: zgels
:md5sum: d543f789adef7ad831c7880fbac31097
:category: :subroutine
:arguments:
- trans:
:type: char
:intent: input
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- a:
:type: doublecomplex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- b:
:type: doublecomplex
:intent: input/output
:dims:
- m
- nrhs
:outdims:
- n
- nrhs
- ldb:
:type: integer
:intent: input
- work:
:type: doublecomplex
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: MIN(m,n) + MAX(MIN(m,n),nrhs)
- info:
:type: integer
:intent: output
:substitutions:
m: lda
ldb: MAX(m,n)
:fortran_help: " SUBROUTINE ZGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZGELS solves overdetermined or underdetermined complex linear systems\n\
* involving an M-by-N matrix A, or its conjugate-transpose, using a QR\n\
* or LQ factorization of A. It is assumed that A has full rank.\n\
*\n\
* The following options are provided:\n\
*\n\
* 1. If TRANS = 'N' and m >= n: find the least squares solution of\n\
* an overdetermined system, i.e., solve the least squares problem\n\
* minimize || B - A*X ||.\n\
*\n\
* 2. If TRANS = 'N' and m < n: find the minimum norm solution of\n\
* an underdetermined system A * X = B.\n\
*\n\
* 3. If TRANS = 'C' and m >= n: find the minimum norm solution of\n\
* an undetermined system A**H * X = B.\n\
*\n\
* 4. If TRANS = 'C' and m < n: find the least squares solution of\n\
* an overdetermined system, i.e., solve the least squares problem\n\
* minimize || B - A**H * X ||.\n\
*\n\
* Several right hand side vectors b and solution vectors x can be\n\
* handled in a single call; they are stored as the columns of the\n\
* M-by-NRHS right hand side matrix B and the N-by-NRHS solution\n\
* matrix X.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* TRANS (input) CHARACTER*1\n\
* = 'N': the linear system involves A;\n\
* = 'C': the linear system involves A**H.\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 matrix A. N >= 0.\n\
*\n\
* NRHS (input) INTEGER\n\
* The number of right hand sides, i.e., the number of\n\
* columns of the matrices B and X. NRHS >= 0.\n\
*\n\
* A (input/output) COMPLEX*16 array, dimension (LDA,N)\n\
* On entry, the M-by-N matrix A.\n\
* if M >= N, A is overwritten by details of its QR\n\
* factorization as returned by ZGEQRF;\n\
* if M < N, A is overwritten by details of its LQ\n\
* factorization as returned by ZGELQF.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,M).\n\
*\n\
* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)\n\
* On entry, the matrix B of right hand side vectors, stored\n\
* columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS\n\
* if TRANS = 'C'.\n\
* On exit, if INFO = 0, B is overwritten by the solution\n\
* vectors, stored columnwise:\n\
* if TRANS = 'N' and m >= n, rows 1 to n of B contain the least\n\
* squares solution vectors; the residual sum of squares for the\n\
* solution in each column is given by the sum of squares of the\n\
* modulus of elements N+1 to M in that column;\n\
* if TRANS = 'N' and m < n, rows 1 to N of B contain the\n\
* minimum norm solution vectors;\n\
* if TRANS = 'C' and m >= n, rows 1 to M of B contain the\n\
* minimum norm solution vectors;\n\
* if TRANS = 'C' and m < n, rows 1 to M of B contain the\n\
* least squares solution vectors; the residual sum of squares\n\
* for the solution in each column is given by the sum of\n\
* squares of the modulus of elements M+1 to N in that column.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= MAX(1,M,N).\n\
*\n\
* WORK (workspace/output) COMPLEX*16 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.\n\
* LWORK >= max( 1, MN + max( MN, NRHS ) ).\n\
* For optimal performance,\n\
* LWORK >= max( 1, MN + max( MN, NRHS )*NB ).\n\
* where MN = min(M,N) and NB is the optimum block size.\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\
* > 0: if INFO = i, the i-th diagonal element of the\n\
* triangular factor of A is zero, so that A does not have\n\
* full rank; the least squares solution could not be\n\
* computed.\n\
*\n\n\
* =====================================================================\n\
*\n"
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