
NAMEzgelss.f SYNOPSISFunctions/Subroutinessubroutine zgelss (M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, RWORK, INFO) Function/Subroutine Documentationsubroutine zgelss (integerM, integerN, integerNRHS, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, double precision, dimension( * )S, double precisionRCOND, integerRANK, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerINFO)ZGELSS solves overdetermined or underdetermined systems for GE matrices Purpose:ZGELSS computes the minimum norm solution to a complex linear least squares problem: Minimize 2norm( b  A*x ). using the singular value decomposition (SVD) of A. A is an MbyN matrix which may be rankdeficient. 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. The effective rank of A is determined by treating as zero those singular values which are less than RCOND times the largest singular value. M
Author:
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. On exit, the first min(m,n) rows of A are overwritten with its right singular vectors, stored rowwise.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 MbyNRHS right hand side matrix B. On exit, B is overwritten by the NbyNRHS solution matrix X. If m >= n and RANK = n, the residual sumofsquares for the solution in the ith column is given by the sum of squares of the modulus of elements n+1:m in that column.LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M,N).S S is DOUBLE PRECISION array, dimension (min(M,N)) The singular values of A in decreasing order. The condition number of A in the 2norm = S(1)/S(min(m,n)).RCOND RCOND is DOUBLE PRECISION RCOND is used to determine the effective rank of A. Singular values S(i) <= RCOND*S(1) are treated as zero. If RCOND < 0, machine precision is used instead.RANK RANK is INTEGER The effective rank of A, i.e., the number of singular values which are greater than RCOND*S(1).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 >= 1, and also: LWORK >= 2*min(M,N) + max(M,N,NRHS) For good performance, LWORK should generally be larger. 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.RWORK RWORK is DOUBLE PRECISION array, dimension (5*min(M,N))INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value. > 0: the algorithm for computing the SVD failed to converge; if INFO = i, i offdiagonal elements of an intermediate bidiagonal form did not converge to zero. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 178 of file zgelss.f.
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