.TH "SRC/dlaln2.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/dlaln2.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBdlaln2\fP (ltrans, na, nw, smin, ca, a, lda, d1, d2, b, ldb, wr, wi, x, ldx, scale, xnorm, info)" .br .RI "\fBDLALN2\fP solves a 1-by-1 or 2-by-2 linear system of equations of the specified form\&. " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "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)" .PP \fBDLALN2\fP solves a 1-by-1 or 2-by-2 linear system of equations of the specified form\&. .PP \fBPurpose:\fP .RS 4 .PP .nf 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 (<= 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\&.) .fi .PP .RE .PP \fBParameters\fP .RS 4 \fILTRANS\fP .PP .nf LTRANS is LOGICAL =\&.TRUE\&.: A-transpose will be used\&. =\&.FALSE\&.: A will be used (not transposed\&.) .fi .PP .br \fINA\fP .PP .nf NA is INTEGER The size of the matrix A\&. It may (only) be 1 or 2\&. .fi .PP .br \fINW\fP .PP .nf NW is INTEGER 1 if 'w' is real, 2 if 'w' is complex\&. It may only be 1 or 2\&. .fi .PP .br \fISMIN\fP .PP .nf 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\&.) .fi .PP .br \fICA\fP .PP .nf CA is DOUBLE PRECISION The coefficient c, which A is multiplied by\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension (LDA,NA) The NA x NA matrix A\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of A\&. It must be at least NA\&. .fi .PP .br \fID1\fP .PP .nf D1 is DOUBLE PRECISION The 1,1 element in the diagonal matrix D\&. .fi .PP .br \fID2\fP .PP .nf D2 is DOUBLE PRECISION The 2,2 element in the diagonal matrix D\&. Not used if NA=1\&. .fi .PP .br \fIB\fP .PP .nf 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\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER The leading dimension of B\&. It must be at least NA\&. .fi .PP .br \fIWR\fP .PP .nf WR is DOUBLE PRECISION The real part of the scalar 'w'\&. .fi .PP .br \fIWI\fP .PP .nf WI is DOUBLE PRECISION The imaginary part of the scalar 'w'\&. Not used if NW=1\&. .fi .PP .br \fIX\fP .PP .nf 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\&. .fi .PP .br \fILDX\fP .PP .nf LDX is INTEGER The leading dimension of X\&. It must be at least NA\&. .fi .PP .br \fISCALE\fP .PP .nf 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\&. .fi .PP .br \fIXNORM\fP .PP .nf XNORM is DOUBLE PRECISION The infinity-norm of X, when X is regarded as an NA x NW real matrix\&. .fi .PP .br \fIINFO\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .PP Definition at line \fB216\fP of file \fBdlaln2\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.