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

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