Functions/Subroutines
subroutine	slaln2 (LTRANS, NA, NW, SMIN, CA, A, LDA, D1, D2, B, LDB, WR, WI, X, LDX, SCALE, XNORM, INFO)
	SLALN2 solves a 1-by-1 or 2-by-2 linear system of equations of the specified form.

Function/Subroutine Documentation

subroutine slaln2	(	logical	LTRANS,
		integer	NA,
		integer	NW,
		real	SMIN,
		real	CA,
		real, dimension( lda, * )	A,
		integer	LDA,
		real	D1,
		real	D2,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real	WR,
		real	WI,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real	SCALE,
		real	XNORM,
		integer	INFO
	)

SLALN2 solves a 1-by-1 or 2-by-2 linear system of equations of the specified form.

Download SLALN2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

 SLALN2 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 SLALN2, 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:

[in]	LTRANS	LTRANS is LOGICAL =.TRUE.: A-transpose will be used. =.FALSE.: A will be used (not transposed.)
[in]	NA	NA is INTEGER The size of the matrix A. It may (only) be 1 or 2.
[in]	NW	NW is INTEGER 1 if "w" is real, 2 if "w" is complex. It may only be 1 or 2.
[in]	SMIN	SMIN is REAL 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.)
[in]	CA	CA is REAL The coefficient c, which A is multiplied by.
[in]	A	A is REAL array, dimension (LDA,NA) The NA x NA matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of A. It must be at least NA.
[in]	D1	D1 is REAL The 1,1 element in the diagonal matrix D.
[in]	D2	D2 is REAL The 2,2 element in the diagonal matrix D. Not used if NW=1.
[in]	B	B is REAL 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.
[in]	LDB	LDB is INTEGER The leading dimension of B. It must be at least NA.
[in]	WR	WR is REAL The real part of the scalar "w".
[in]	WI	WI is REAL The imaginary part of the scalar "w". Not used if NW=1.
[out]	X	X is REAL array, dimension (LDX,NW) The NA x NW matrix X (unknowns), as computed by SLALN2. 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.
[in]	LDX	LDX is INTEGER The leading dimension of X. It must be at least NA.
[out]	SCALE	SCALE is REAL 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.
[out]	XNORM	XNORM is REAL The infinity-norm of X, when X is regarded as an NA x NW real matrix.
[out]	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 slaln2.f.

Here is the call graph for this function:

Here is the caller graph for this function:

Functions/Subroutines

Function/Subroutine Documentation