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dlaln2 examples
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Man Page Details
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NAME
       DLALN2  - a system of the form (ca A - w D ) X = s B or (ca A' - w D) X
       = s B with possible scaling ("s") and perturbation of A

SYNOPSIS
       SUBROUTINE DLALN2( LTRANS, NA, NW, SMIN, CA, A, LDA, D1,  D2,  B,  LDB,
                          WR, WI, X, LDX, SCALE, XNORM, INFO )

           LOGICAL        LTRANS

           INTEGER        INFO, LDA, LDB, LDX, NA, NW

           DOUBLE         PRECISION CA, D1, D2, SCALE, SMIN, WI, WR, XNORM

           DOUBLE         PRECISION A( LDA, * ), B( LDB, * ), X( LDX, * )

PURPOSE
       DLALN2 solves a system of the form  (ca A - w D ) X = s B or (ca A' - w
       D) X = s B   with possible scaling ("s") and perturbation  of  A.   (A'
       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  cho-
       sen  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  over-
       flow.

       If  both singular values of (ca A - w D) are less than SMIN, SMIN*iden-
       tity 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.)


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

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

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

       SMIN    (input) 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      (input) DOUBLE PRECISION
               The coefficient c, which A is multiplied by.

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

       LDA     (input) INTEGER
               The leading dimension of A.  It must be at least NA.

       D1      (input) DOUBLE PRECISION
               The 1,1 element in the diagonal matrix D.

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

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

       LDB     (input) INTEGER
               The leading dimension of B.  It must be at least NA.

       WR      (input) DOUBLE PRECISION
               The real part of the scalar "w".

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

       X       (output) 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     (input) INTEGER
               The leading dimension of X.  It must be at least NA.

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

       INFO    (output) 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 num-
               ber 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.

