--- 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