--- rpl/lapack/lapack/zpoequb.f 2016/08/27 15:35:04 1.11 +++ rpl/lapack/lapack/zpoequb.f 2017/06/17 10:54:25 1.12 @@ -2,24 +2,24 @@ * * =========== DOCUMENTATION =========== * -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * *> \htmlonly -*> Download ZPOEQUB + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> +*> Download ZPOEQUB + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> *> [TXT] -*> \endhtmlonly +*> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO ) -* +* * .. Scalar Arguments .. * INTEGER INFO, LDA, N * DOUBLE PRECISION AMAX, SCOND @@ -28,7 +28,7 @@ * COMPLEX*16 A( LDA, * ) * DOUBLE PRECISION S( * ) * .. -* +* * *> \par Purpose: * ============= @@ -36,13 +36,19 @@ *> \verbatim *> *> ZPOEQUB computes row and column scalings intended to equilibrate a -*> symmetric positive definite matrix A and reduce its condition number +*> Hermitian positive definite matrix A and reduce its condition number *> (with respect to the two-norm). S contains the scale factors, *> S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with *> elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This *> choice of S puts the condition number of B within a factor N of the *> smallest possible condition number over all possible diagonal *> scalings. +*> +*> This routine differs from ZPOEQU by restricting the scaling factors +*> to a power of the radix. Barring over- and underflow, scaling by +*> these factors introduces no additional rounding errors. However, the +*> scaled diagonal entries are no longer approximately 1 but lie +*> between sqrt(radix) and 1/sqrt(radix). *> \endverbatim * * Arguments: @@ -57,7 +63,7 @@ *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) -*> The N-by-N symmetric positive definite matrix whose scaling +*> The N-by-N Hermitian positive definite matrix whose scaling *> factors are to be computed. Only the diagonal elements of A *> are referenced. *> \endverbatim @@ -101,22 +107,22 @@ * Authors: * ======== * -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -*> \date November 2011 +*> \date December 2016 * *> \ingroup complex16POcomputational * * ===================================================================== SUBROUTINE ZPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO ) * -* -- LAPACK computational routine (version 3.4.0) -- +* -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2011 +* December 2016 * * .. Scalar Arguments .. INTEGER INFO, LDA, N