dlaln2.f3

!>
!> 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 () 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.
!>
!>  is a scaling factor (<= 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.)
!> 

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  is real, 2 if  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 NA=1.
!> 

B

!>          B is DOUBLE PRECISION array, dimension (LDB,NW)
!>          The NA x NW matrix B (right-hand side).  If NW=2 ( 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 .
!> 

WI

!>          WI is DOUBLE PRECISION
!>          The imaginary part of the scalar .  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 ( 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.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.