SGELSY (3)  Linux Manuals
NAME
sgelsy.f 
SYNOPSIS
Functions/Subroutines
subroutine sgelsy (M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, WORK, LWORK, INFO)
SGELSY solves overdetermined or underdetermined systems for GE matrices
Function/Subroutine Documentation
subroutine sgelsy (integerM, integerN, integerNRHS, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, integer, dimension( * )JPVT, realRCOND, integerRANK, real, dimension( * )WORK, integerLWORK, integerINFO)
SGELSY solves overdetermined or underdetermined systems for GE matrices
Purpose:

SGELSY computes the minimumnorm solution to a real 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 orthogonal 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**T [ inv(T11)*Q1**T*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 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. o The permutation of matrix B (the right hand side) is faster and more simple.
Parameters:

M
M is INTEGER The number of rows of the matrix A. M >= 0.
NN is INTEGER The number of columns of the matrix A. N >= 0.
NRHSNRHS is INTEGER The number of right hand sides, i.e., the number of columns of matrices B and X. NRHS >= 0.
AA is REAL array, dimension (LDA,N) On entry, the MbyN matrix A. On exit, A has been overwritten by details of its complete orthogonal factorization.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
BB is REAL array, dimension (LDB,NRHS) On entry, the MbyNRHS right hand side matrix B. On exit, the NbyNRHS solution matrix X.
LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,M,N).
JPVTJPVT 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 AP was the kth column of A.
RCONDRCOND is REAL 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.
RANKRANK 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.
WORKWORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORKLWORK is INTEGER The dimension of the array WORK. The unblocked strategy requires that: LWORK >= MAX( MN+3*N+1, 2*MN+NRHS ), where MN = min( M, N ). The block algorithm requires that: LWORK >= MAX( MN+2*N+NB*(N+1), 2*MN+NB*NRHS ), where NB is an upper bound on the blocksize returned by ILAENV for the routines SGEQP3, STZRZF, STZRQF, SORMQR, and SORMRZ. 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.
INFOINFO is INTEGER = 0: successful exit < 0: If INFO = i, the ith argument had an illegal value.
Author:

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
E. QuintanaOrti, Depto. de Informatica, Universidad Jaime I, Spain
G. QuintanaOrti, Depto. de Informatica, Universidad Jaime I, Spain
Definition at line 204 of file sgelsy.f.
Author
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