
NAMEzgels.f SYNOPSISFunctions/Subroutinessubroutine zgels (TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, INFO) Function/Subroutine Documentationsubroutine zgels (characterTRANS, integerM, integerN, integerNRHS, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( * )WORK, integerLWORK, integerINFO)ZGELS solves overdetermined or underdetermined systems for GE matrices Purpose:ZGELS solves overdetermined or underdetermined complex linear systems involving an MbyN matrix A, or its conjugatetranspose, using a QR or LQ factorization of A. It is assumed that A has full rank. The following options are provided: 1. If TRANS = 'N' and m >= n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize  B  A*X . 2. If TRANS = 'N' and m < n: find the minimum norm solution of an underdetermined system A * X = B. 3. If TRANS = 'C' and m >= n: find the minimum norm solution of an undetermined system A**H * X = B. 4. If TRANS = 'C' and m < n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize  B  A**H * X . 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. TRANS
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TRANS is CHARACTER*1 = 'N': the linear system involves A; = 'C': the linear system involves A**H.M M is INTEGER The number of rows of the matrix A. M >= 0.N N is INTEGER The number of columns of the matrix A. N >= 0.NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.A A is COMPLEX*16 array, dimension (LDA,N) On entry, the MbyN matrix A. if M >= N, A is overwritten by details of its QR factorization as returned by ZGEQRF; if M < N, A is overwritten by details of its LQ factorization as returned by ZGELQF.LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).B B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the matrix B of right hand side vectors, stored columnwise; B is MbyNRHS if TRANS = 'N', or NbyNRHS if TRANS = 'C'. On exit, if INFO = 0, B is overwritten by the solution vectors, stored columnwise: if TRANS = 'N' and m >= n, rows 1 to n of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of the modulus of elements N+1 to M in that column; if TRANS = 'N' and m < n, rows 1 to N of B contain the minimum norm solution vectors; if TRANS = 'C' and m >= n, rows 1 to M of B contain the minimum norm solution vectors; if TRANS = 'C' and m < n, rows 1 to M of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of the modulus of elements M+1 to N in that column.LDB LDB is INTEGER The leading dimension of the array B. LDB >= MAX(1,M,N).WORK WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.LWORK LWORK is INTEGER The dimension of the array WORK. LWORK >= max( 1, MN + max( MN, NRHS ) ). For optimal performance, LWORK >= max( 1, MN + max( MN, NRHS )*NB ). where MN = min(M,N) and NB is the optimum block size. If LWORK = 1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value > 0: if INFO = i, the ith diagonal element of the triangular factor of A is zero, so that A does not have full rank; the least squares solution could not be computed. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 182 of file zgels.f.
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