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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 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.)

 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
          complex), column 1 contains the real part of B and column 2
          contains 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
          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.

