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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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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.
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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.)
[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 NA=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. |
Definition at line 220 of file slaln2.f.