SRC/zgelsd.f(3) Library Functions Manual SRC/zgelsd.f(3) NAME SRC/zgelsd.f SYNOPSIS Functions/Subroutines subroutine zgelsd (m, n, nrhs, a, lda, b, ldb, s, rcond, rank, work, lwork, rwork, iwork, info) ZGELSD computes the minimum-norm solution to a linear least squares problem for GE matrices Function/Subroutine Documentation subroutine zgelsd (integer m, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) s, double precision rcond, integer rank, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer, dimension( * ) iwork, integer info) ZGELSD computes the minimum-norm solution to a linear least squares problem for GE matrices Purpose: !> !> ZGELSD computes the minimum-norm solution to a real linear least !> squares problem: !> minimize 2-norm(| b - A*x |) !> using the singular value decomposition (SVD) of A. A is an M-by-N !> matrix which may be rank-deficient. !> !> 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 !> M-by-NRHS right hand side matrix B and the N-by-NRHS solution !> matrix X. !> !> The problem is solved in three steps: !> (1) Reduce the coefficient matrix A to bidiagonal form with !> Householder transformations, reducing the original problem !> into a (BLS) !> (2) Solve the BLS using a divide and conquer approach. !> (3) Apply back all the Householder transformations to solve !> the original least squares problem. !> !> The effective rank of A is determined by treating as zero those !> singular values which are less than RCOND times the largest singular !> value. !> !> Parameters 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 M-by-N matrix A. !> On exit, A has been destroyed. !> 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 M-by-NRHS right hand side matrix B. !> On exit, B is overwritten by the N-by-NRHS solution matrix X. !> If m >= n and RANK = n, the residual sum-of-squares for !> the solution in the i-th 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 2-norm = 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 must be at least 1. !> The exact minimum amount of workspace needed depends on M, !> N and NRHS. As long as LWORK is at least !> 2*N + N*NRHS !> if M is greater than or equal to N or !> 2*M + M*NRHS !> if M is less than N, the code will execute correctly. !> 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 array WORK and the !> minimum sizes of the arrays RWORK and IWORK, and returns !> these values as the first entries of the WORK, RWORK and !> IWORK arrays, and no error message related to LWORK is issued !> by XERBLA. !> RWORK !> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) !> LRWORK >= !> 10*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS + !> MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS ) !> if M is greater than or equal to N or !> 10*M + 2*M*SMLSIZ + 8*M*NLVL + 3*SMLSIZ*NRHS + !> MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS ) !> if M is less than N, the code will execute correctly. !> SMLSIZ is returned by ILAENV and is equal to the maximum !> size of the subproblems at the bottom of the computation !> tree (usually about 25), and !> NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 ) !> On exit, if INFO = 0, RWORK(1) returns the minimum LRWORK. !> IWORK !> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) !> LIWORK >= max(1, 3*MINMN*NLVL + 11*MINMN), !> where MINMN = MIN( M,N ). !> On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK. !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value. !> > 0: the algorithm for computing the SVD failed to converge; !> if INFO = i, i off-diagonal elements of an intermediate !> bidiagonal form did not converge to zero. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: Ming Gu and Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA Osni Marques, LBNL/NERSC, USA Definition at line 217 of file zgelsd.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 SRC/zgelsd.f(3)