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dlaln2.f(3)				      LAPACK				      dlaln2.f(3)

NAME
       dlaln2.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dlaln2 (LTRANS, NA, NW, SMIN, CA, A, LDA, D1, D2, B, LDB, WR, WI, X, LDX,
	   SCALE, XNORM, INFO)
	   DLALN2 solves a 1-by-1 or 2-by-2 linear system of equations of the specified form.

Function/Subroutine Documentation
   subroutine dlaln2 (logicalLTRANS, integerNA, integerNW, double precisionSMIN, double
       precisionCA, double precision, dimension( lda, * )A, integerLDA, double precisionD1,
       double precisionD2, double precision, dimension( ldb, * )B, integerLDB, double
       precisionWR, double precisionWI, double precision, dimension( ldx, * )X, integerLDX,
       double precisionSCALE, double precisionXNORM, integerINFO)
       DLALN2 solves a 1-by-1 or 2-by-2 linear system of equations of the specified form.

       Purpose:

	    DLALN2 solves a system of the form	(ca A - w D ) X = s B
	    or (ca A**T - w D) X = s B	 with possible scaling ("s") and
	    perturbation of A.	(A**T means A-transpose.)

	    A is an NA x NA real matrix, ca is a real scalar, D is an NA x NA
	    real diagonal matrix, w is a real or complex value, and X and B are
	    NA x 1 matrices -- real if w is real, complex if w is complex.  NA
	    may be 1 or 2.

	    If w is complex, X and B are represented as NA x 2 matrices,
	    the first column of each being the real part and the second
	    being the imaginary part.

	    "s" is a scaling factor (.LE. 1), computed by DLALN2, which is
	    so chosen that X can be computed without overflow.	X is further
	    scaled if necessary to assure that norm(ca A - w D)*norm(X) is less
	    than overflow.

	    If both singular values of (ca A - w D) are less than SMIN,
	    SMIN*identity will be used instead of (ca A - w D).  If only one
	    singular value is less than SMIN, one element of (ca A - w D) will be
	    perturbed enough to make the smallest singular value roughly SMIN.
	    If both singular values are at least SMIN, (ca A - w D) will not be
	    perturbed.	In any case, the perturbation will be at most some small
	    multiple of max( SMIN, ulp*norm(ca A - w D) ).  The singular values
	    are computed by infinity-norm approximations, and thus will only be
	    correct to a factor of 2 or so.

	    Note: all input quantities are assumed to be smaller than overflow
	    by a reasonable factor.  (See BIGNUM.)

       Parameters:
	   LTRANS

		     LTRANS is LOGICAL
		     =.TRUE.:  A-transpose will be used.
		     =.FALSE.: A will be used (not transposed.)

	   NA

		     NA is INTEGER
		     The size of the matrix A.	It may (only) be 1 or 2.

	   NW

		     NW is INTEGER
		     1 if "w" is real, 2 if "w" is complex.  It may only be 1
		     or 2.

	   SMIN

		     SMIN is DOUBLE PRECISION
		     The desired lower bound on the singular values of A.  This
		     should be a safe distance away from underflow or overflow,
		     say, between (underflow/machine precision) and  (machine
		     precision * overflow ).  (See BIGNUM and ULP.)

	   CA

		     CA is DOUBLE PRECISION
		     The coefficient c, which A is multiplied by.

	   A

		     A is DOUBLE PRECISION array, dimension (LDA,NA)
		     The NA x NA matrix A.

	   LDA

		     LDA is INTEGER
		     The leading dimension of A.  It must be at least NA.

	   D1

		     D1 is DOUBLE PRECISION
		     The 1,1 element in the diagonal matrix D.

	   D2

		     D2 is DOUBLE PRECISION
		     The 2,2 element in the diagonal matrix D.	Not used if NW=1.

	   B

		     B is DOUBLE PRECISION array, dimension (LDB,NW)
		     The NA x NW matrix B (right-hand side).  If NW=2 ("w" is
		     complex), column 1 contains the real part of B and column 2
		     contains the imaginary part.

	   LDB

		     LDB is INTEGER
		     The leading dimension of B.  It must be at least NA.

	   WR

		     WR is DOUBLE PRECISION
		     The real part of the scalar "w".

	   WI

		     WI is DOUBLE PRECISION
		     The imaginary part of the scalar "w".  Not used if NW=1.

	   X

		     X is DOUBLE PRECISION array, dimension (LDX,NW)
		     The NA x NW matrix X (unknowns), as computed by DLALN2.
		     If NW=2 ("w" is complex), on exit, column 1 will contain
		     the real part of X and column 2 will contain the imaginary
		     part.

	   LDX

		     LDX is INTEGER
		     The leading dimension of X.  It must be at least NA.

	   SCALE

		     SCALE is DOUBLE PRECISION
		     The scale factor that B must be multiplied by to insure
		     that overflow does not occur when computing X.  Thus,
		     (ca A - w D) X  will be SCALE*B, not B (ignoring
		     perturbations of A.)  It will be at most 1.

	   XNORM

		     XNORM is DOUBLE PRECISION
		     The infinity-norm of X, when X is regarded as an NA x NW
		     real matrix.

	   INFO

		     INFO is INTEGER
		     An error flag.  It will be set to zero if no error occurs,
		     a negative number if an argument is in error, or a positive
		     number if	ca A - w D  had to be perturbed.
		     The possible values are:
		     = 0: No error occurred, and (ca A - w D) did not have to be
			    perturbed.
		     = 1: (ca A - w D) had to be perturbed to make its smallest
			  (or only) singular value greater than SMIN.
		     NOTE: In the interests of speed, this routine does not
			   check the inputs for errors.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Definition at line 218 of file dlaln2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      dlaln2.f(3)
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