
NAMEzgelsy.f SYNOPSISFunctions/Subroutinessubroutine zgelsy (M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, WORK, LWORK, RWORK, INFO) Function/Subroutine Documentationsubroutine zgelsy (integerM, integerN, integerNRHS, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, integer, dimension( * )JPVT, double precisionRCOND, integerRANK, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerINFO)ZGELSY solves overdetermined or underdetermined systems for GE matrices Purpose:ZGELSY computes the minimumnorm solution to a complex linear least squares problem: minimize  A * X  B  using a complete orthogonal factorization 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 routine first computes a QR factorization with column pivoting: A * P = Q * [ R11 R12 ] [ 0 R22 ] with R11 defined as the largest leading submatrix whose estimated condition number is less than 1/RCOND. The order of R11, RANK, is the effective rank of A. Then, R22 is considered to be negligible, and R12 is annihilated by unitary transformations from the right, arriving at the complete orthogonal factorization: A * P = Q * [ T11 0 ] * Z [ 0 0 ] The minimumnorm solution is then X = P * Z**H [ inv(T11)*Q1**H*B ] [ 0 ] where Q1 consists of the first RANK columns of Q. This routine is basically identical to the original xGELSX except three differences: o The permutation of matrix B (the right hand side) is faster and more simple. o The call to the subroutine xGEQPF has been substituted by the the call to the subroutine xGEQP3. This subroutine is a Blas3 version of the QR factorization with column pivoting. o Matrix B (the right hand side) is updated with Blas3. 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 matrices B and X. NRHS >= 0.A A is COMPLEX*16 array, dimension (LDA,N) On entry, the MbyN matrix A. On exit, A has been overwritten by details of its complete orthogonal factorization.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, the NbyNRHS solution matrix X.LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M,N).JPVT JPVT is INTEGER array, dimension (N) On entry, if JPVT(i) .ne. 0, the ith column of A is permuted to the front of AP, otherwise column i is a free column. On exit, if JPVT(i) = k, then the ith column of A*P was the kth column of A.RCOND RCOND is DOUBLE PRECISION RCOND is used to determine the effective rank of A, which is defined as the order of the largest leading triangular submatrix R11 in the QR factorization with pivoting of A, whose estimated condition number < 1/RCOND.RANK RANK is INTEGER The effective rank of A, i.e., the order of the submatrix R11. This is the same as the order of the submatrix T11 in the complete orthogonal factorization of A.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. The unblocked strategy requires that: LWORK >= MN + MAX( 2*MN, N+1, MN+NRHS ) where MN = min(M,N). The block algorithm requires that: LWORK >= MN + MAX( 2*MN, NB*(N+1), MN+MN*NB, MN+NB*NRHS ) where NB is an upper bound on the blocksize returned by ILAENV for the routines ZGEQP3, ZTZRZF, CTZRQF, ZUNMQR, and ZUNMRZ. 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 (2*N)INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn.,
Knoxville, USA
Definition at line 210 of file zgelsy.f.
E. QuintanaOrti, Depto. de Informatica, Universidad Jaime I, Spain G. QuintanaOrti, Depto. de Informatica, Universidad Jaime I, Spain AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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