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---
:name: dlaln2
:md5sum: 029cdd6fe89ae0077f078ad1c1d1da86
:category: :subroutine
:arguments:
- ltrans:
:type: logical
:intent: input
- na:
:type: integer
:intent: input
- nw:
:type: integer
:intent: input
- smin:
:type: doublereal
:intent: input
- ca:
:type: doublereal
:intent: input
- a:
:type: doublereal
:intent: input
:dims:
- lda
- na
- lda:
:type: integer
:intent: input
- d1:
:type: doublereal
:intent: input
- d2:
:type: doublereal
:intent: input
- b:
:type: doublereal
:intent: input
:dims:
- ldb
- nw
- ldb:
:type: integer
:intent: input
- wr:
:type: doublereal
:intent: input
- wi:
:type: doublereal
:intent: input
- x:
:type: doublereal
:intent: output
:dims:
- ldx
- nw
- ldx:
:type: integer
:intent: input
- scale:
:type: doublereal
:intent: output
- xnorm:
:type: doublereal
:intent: output
- info:
:type: integer
:intent: output
:substitutions:
ldx: na
:fortran_help: " SUBROUTINE DLALN2( LTRANS, NA, NW, SMIN, CA, A, LDA, D1, D2, B, LDB, WR, WI, X, LDX, SCALE, XNORM, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLALN2 solves a system of the form (ca A - w D ) X = s B\n\
* or (ca A' - w D) X = s B with possible scaling (\"s\") and\n\
* perturbation of A. (A' means A-transpose.)\n\
*\n\
* A is an NA x NA real matrix, ca is a real scalar, D is an NA x NA\n\
* real diagonal matrix, w is a real or complex value, and X and B are\n\
* NA x 1 matrices -- real if w is real, complex if w is complex. NA\n\
* may be 1 or 2.\n\
*\n\
* If w is complex, X and B are represented as NA x 2 matrices,\n\
* the first column of each being the real part and the second\n\
* being the imaginary part.\n\
*\n\
* \"s\" is a scaling factor (.LE. 1), computed by DLALN2, which is\n\
* so chosen that X can be computed without overflow. X is further\n\
* scaled if necessary to assure that norm(ca A - w D)*norm(X) is less\n\
* than overflow.\n\
*\n\
* If both singular values of (ca A - w D) are less than SMIN,\n\
* SMIN*identity will be used instead of (ca A - w D). If only one\n\
* singular value is less than SMIN, one element of (ca A - w D) will be\n\
* perturbed enough to make the smallest singular value roughly SMIN.\n\
* If both singular values are at least SMIN, (ca A - w D) will not be\n\
* perturbed. In any case, the perturbation will be at most some small\n\
* multiple of max( SMIN, ulp*norm(ca A - w D) ). The singular values\n\
* are computed by infinity-norm approximations, and thus will only be\n\
* correct to a factor of 2 or so.\n\
*\n\
* Note: all input quantities are assumed to be smaller than overflow\n\
* by a reasonable factor. (See BIGNUM.)\n\
*\n\n\
* Arguments\n\
* ==========\n\
*\n\
* LTRANS (input) LOGICAL\n\
* =.TRUE.: A-transpose will be used.\n\
* =.FALSE.: A will be used (not transposed.)\n\
*\n\
* NA (input) INTEGER\n\
* The size of the matrix A. It may (only) be 1 or 2.\n\
*\n\
* NW (input) INTEGER\n\
* 1 if \"w\" is real, 2 if \"w\" is complex. It may only be 1\n\
* or 2.\n\
*\n\
* SMIN (input) DOUBLE PRECISION\n\
* The desired lower bound on the singular values of A. This\n\
* should be a safe distance away from underflow or overflow,\n\
* say, between (underflow/machine precision) and (machine\n\
* precision * overflow ). (See BIGNUM and ULP.)\n\
*\n\
* CA (input) DOUBLE PRECISION\n\
* The coefficient c, which A is multiplied by.\n\
*\n\
* A (input) DOUBLE PRECISION array, dimension (LDA,NA)\n\
* The NA x NA matrix A.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of A. It must be at least NA.\n\
*\n\
* D1 (input) DOUBLE PRECISION\n\
* The 1,1 element in the diagonal matrix D.\n\
*\n\
* D2 (input) DOUBLE PRECISION\n\
* The 2,2 element in the diagonal matrix D. Not used if NW=1.\n\
*\n\
* B (input) DOUBLE PRECISION array, dimension (LDB,NW)\n\
* The NA x NW matrix B (right-hand side). If NW=2 (\"w\" is\n\
* complex), column 1 contains the real part of B and column 2\n\
* contains the imaginary part.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of B. It must be at least NA.\n\
*\n\
* WR (input) DOUBLE PRECISION\n\
* The real part of the scalar \"w\".\n\
*\n\
* WI (input) DOUBLE PRECISION\n\
* The imaginary part of the scalar \"w\". Not used if NW=1.\n\
*\n\
* X (output) DOUBLE PRECISION array, dimension (LDX,NW)\n\
* The NA x NW matrix X (unknowns), as computed by DLALN2.\n\
* If NW=2 (\"w\" is complex), on exit, column 1 will contain\n\
* the real part of X and column 2 will contain the imaginary\n\
* part.\n\
*\n\
* LDX (input) INTEGER\n\
* The leading dimension of X. It must be at least NA.\n\
*\n\
* SCALE (output) DOUBLE PRECISION\n\
* The scale factor that B must be multiplied by to insure\n\
* that overflow does not occur when computing X. Thus,\n\
* (ca A - w D) X will be SCALE*B, not B (ignoring\n\
* perturbations of A.) It will be at most 1.\n\
*\n\
* XNORM (output) DOUBLE PRECISION\n\
* The infinity-norm of X, when X is regarded as an NA x NW\n\
* real matrix.\n\
*\n\
* INFO (output) INTEGER\n\
* An error flag. It will be set to zero if no error occurs,\n\
* a negative number if an argument is in error, or a positive\n\
* number if ca A - w D had to be perturbed.\n\
* The possible values are:\n\
* = 0: No error occurred, and (ca A - w D) did not have to be\n\
* perturbed.\n\
* = 1: (ca A - w D) had to be perturbed to make its smallest\n\
* (or only) singular value greater than SMIN.\n\
* NOTE: In the interests of speed, this routine does not\n\
* check the inputs for errors.\n\
*\n\n\
* =====================================================================\n\
*\n"
|
