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SUBROUTINE MD03BA( N, IPAR, LIPAR, FNORM, J, LDJ, E, JNORMS,
$ GNORM, IPVT, DWORK, LDWORK, INFO )
C
C SLICOT RELEASE 5.0.
C
C Copyright (c) 2002-2009 NICONET e.V.
C
C This program is free software: you can redistribute it and/or
C modify it under the terms of the GNU General Public License as
C published by the Free Software Foundation, either version 2 of
C the License, or (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C
C You should have received a copy of the GNU General Public License
C along with this program. If not, see
C <http://www.gnu.org/licenses/>.
C
C PURPOSE
C
C To compute the QR factorization with column pivoting of an
C m-by-n Jacobian matrix J (m >= n), that is, J*P = Q*R, where Q is
C a matrix with orthogonal columns, P a permutation matrix, and
C R an upper trapezoidal matrix with diagonal elements of
C nonincreasing magnitude, and to apply the transformation Q' on
C the error vector e (in-situ). The 1-norm of the scaled gradient
C is also returned.
C
C This routine is an interface to SLICOT Library routine MD03BX,
C for solving standard nonlinear least squares problems using SLICOT
C routine MD03BD.
C
C ARGUMENTS
C
C Input/Output Parameters
C
C N (input) INTEGER
C The number of columns of the Jacobian matrix J. N >= 0.
C
C IPAR (input) INTEGER array, dimension (LIPAR)
C The integer parameters describing the structure of the
C matrix J, as follows:
C IPAR(1) must contain the number of rows M of the Jacobian
C matrix J. M >= N.
C IPAR is provided for compatibility with SLICOT Library
C routine MD03BD.
C
C LIPAR (input) INTEGER
C The length of the array IPAR. LIPAR >= 1.
C
C FNORM (input) DOUBLE PRECISION
C The Euclidean norm of the vector e. FNORM >= 0.
C
C J (input/output) DOUBLE PRECISION array, dimension (LDJ, N)
C On entry, the leading M-by-N part of this array must
C contain the Jacobian matrix J.
C On exit, the leading N-by-N upper triangular part of this
C array contains the upper triangular factor R of the
C Jacobian matrix. Note that for efficiency of the later
C calculations, the matrix R is delivered with the leading
C dimension MAX(1,N), possibly much smaller than the value
C of LDJ on entry.
C
C LDJ (input/output) INTEGER
C The leading dimension of array J.
C On entry, LDJ >= MAX(1,M).
C On exit, LDJ >= MAX(1,N).
C
C E (input/output) DOUBLE PRECISION array, dimension (M)
C On entry, this array must contain the error vector e.
C On exit, this array contains the updated vector Q'*e.
C
C JNORMS (output) DOUBLE PRECISION array, dimension (N)
C This array contains the Euclidean norms of the columns
C of the Jacobian matrix, considered in the initial order.
C
C GNORM (output) DOUBLE PRECISION
C If FNORM > 0, the 1-norm of the scaled vector
C J'*Q'*e/FNORM, with each element i further divided
C by JNORMS(i) (if JNORMS(i) is nonzero).
C If FNORM = 0, the returned value of GNORM is 0.
C
C IPVT (output) INTEGER array, dimension (N)
C This array defines the permutation matrix P such that
C J*P = Q*R. Column j of P is column IPVT(j) of the identity
C matrix.
C
C Workspace
C
C DWORK DOUBLE PRECISION array, dimension (LDWORK)
C On exit, if INFO = 0, DWORK(1) returns the optimal value
C of LDWORK.
C
C LDWORK INTEGER
C The length of the array DWORK.
C LDWORK >= 1, if N = 0 or M = 1;
C LDWORK >= 4*N+1, if N > 1.
C For optimum performance LDWORK should be larger.
C
C Error Indicator
C
C INFO INTEGER
C = 0: successful exit;
C < 0: if INFO = -i, the i-th argument had an illegal
C value.
C
C METHOD
C
C This routine calls SLICOT Library routine MD03BX to perform the
C calculations.
C
C FURTHER COMMENTS
C
C For efficiency, the arguments are not checked. This is done in
C the routine MD03BX (except for LIPAR).
C
C CONTRIBUTORS
C
C V. Sima, Research Institute for Informatics, Bucharest, Dec. 2001.
C
C REVISIONS
C
C -
C
C KEYWORDS
C
C Elementary matrix operations, Jacobian matrix, matrix algebra,
C matrix operations.
C
C ******************************************************************
C
C .. Scalar Arguments ..
INTEGER INFO, LDJ, LDWORK, LIPAR, N
DOUBLE PRECISION FNORM, GNORM
C .. Array Arguments ..
INTEGER IPAR(*), IPVT(*)
DOUBLE PRECISION DWORK(*), E(*), J(*), JNORMS(*)
C .. External Subroutines ..
EXTERNAL MD03BX
C ..
C .. Executable Statements ..
C
CALL MD03BX( IPAR(1), N, FNORM, J, LDJ, E, JNORMS, GNORM, IPVT,
$ DWORK, LDWORK, INFO )
RETURN
C
C *** Last line of MD03BA ***
END
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