# dlaln2.f man page

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

**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 NA=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:**December 2016

Definition at line 220 of file dlaln2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dlaln2(3) is an alias of dlaln2.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK