.TH "SRC/slaln2.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/slaln2.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBslaln2\fP (ltrans, na, nw, smin, ca, a, lda, d1, d2, b, ldb, wr, wi, x, ldx, scale, xnorm, info)" .br .RI "\fBSLALN2\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 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)" .PP \fBSLALN2\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 !> !> 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 () 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 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\&.) !> .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 is real, 2 if is complex\&. It may only be 1 !> or 2\&. !> .fi .PP .br \fISMIN\fP .PP .nf !> 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\&.) !> .fi .PP .br \fICA\fP .PP .nf !> CA is REAL !> The coefficient c, which A is multiplied by\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is REAL 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 REAL !> The 1,1 element in the diagonal matrix D\&. !> .fi .PP .br \fID2\fP .PP .nf !> D2 is REAL !> The 2,2 element in the diagonal matrix D\&. Not used if NA=1\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is REAL 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\&. !> .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 REAL !> The real part of the scalar \&. !> .fi .PP .br \fIWI\fP .PP .nf !> WI is REAL !> The imaginary part of the scalar \&. Not used if NW=1\&. !> .fi .PP .br \fIX\fP .PP .nf !> X is REAL array, dimension (LDX,NW) !> The NA x NW matrix X (unknowns), as computed by SLALN2\&. !> If NW=2 ( 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 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\&. !> .fi .PP .br \fIXNORM\fP .PP .nf !> XNORM is REAL !> 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 \fBslaln2\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.