From 4958a3718bd37740abbf2e831821158b5de935bd Mon Sep 17 00:00:00 2001 From: Christoph Conrads Date: Wed, 21 Sep 2016 16:08:23 +0200 Subject: Revert "Doc: highlight what xPOEQUB actually does" This reverts commit 3c66ad2c7d6e2e73e369dbd919bba259b42e2f6d. --- SRC/cpoequb.f | 14 ++++++++------ SRC/dpoequb.f | 14 +++++++------- SRC/spoequb.f | 14 +++++++------- SRC/zpoequb.f | 12 ++++++------ 4 files changed, 28 insertions(+), 26 deletions(-) (limited to 'SRC') diff --git a/SRC/cpoequb.f b/SRC/cpoequb.f index bf86d1a4..e0f47420 100644 --- a/SRC/cpoequb.f +++ b/SRC/cpoequb.f @@ -37,12 +37,12 @@ *> *> CPOEQUB computes row and column scalings intended to equilibrate a *> symmetric positive definite matrix A and reduce its condition number -*> (with respect to the spectral norm). S contains the scale factors, -*> chosen so that the scaled matrix B with elements -*> B(i,j) = S(i)*A(i,j)*S(j) has diagonal entries close to one. S(i) is -*> a power of b nearest to but not exceeding 1/sqrt(A(i,i)), where b is -*> the basis use for floating point numbers on this machine. This choice -*> of S avoids round-off errors when computing B. +*> (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. *> \endverbatim * * Arguments: @@ -150,6 +150,8 @@ * .. Executable Statements .. * * Test the input parameters. +* +* Positive definite only performs 1 pass of equilibration. * INFO = 0 IF( N.LT.0 ) THEN diff --git a/SRC/dpoequb.f b/SRC/dpoequb.f index d2369141..fcee160e 100644 --- a/SRC/dpoequb.f +++ b/SRC/dpoequb.f @@ -34,14 +34,14 @@ *> *> \verbatim *> -*> DPOEQUB computes row and column scalings intended to equilibrate a +*> DPOEQU computes row and column scalings intended to equilibrate a *> symmetric positive definite matrix A and reduce its condition number -*> (with respect to the spectral norm). S contains the scale factors, -*> chosen so that the scaled matrix B with elements -*> B(i,j) = S(i)*A(i,j)*S(j) has diagonal entries close to one. S(i) is -*> a power of b nearest to but not exceeding 1/sqrt(A(i,i)), where b is -*> the basis use for floating point numbers on this machine. This choice -*> of S avoids round-off errors when computing B. +*> (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. *> \endverbatim * * Arguments: diff --git a/SRC/spoequb.f b/SRC/spoequb.f index 6bdbcda6..523aee04 100644 --- a/SRC/spoequb.f +++ b/SRC/spoequb.f @@ -34,14 +34,14 @@ *> *> \verbatim *> -*> SPOEQUB computes row and column scalings intended to equilibrate a +*> SPOEQU computes row and column scalings intended to equilibrate a *> symmetric positive definite matrix A and reduce its condition number -*> (with respect to the spectral norm). S contains the scale factors, -*> chosen so that the scaled matrix B with elements -*> B(i,j) = S(i)*A(i,j)*S(j) has diagonal entries close to one. S(i) is -*> a power of b nearest to but not exceeding 1/sqrt(A(i,i)), where b is -*> the basis use for floating point numbers on this machine. This choice -*> of S avoids round-off errors when computing B. +*> (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. *> \endverbatim * * Arguments: diff --git a/SRC/zpoequb.f b/SRC/zpoequb.f index bc4ff79b..c0d180c9 100644 --- a/SRC/zpoequb.f +++ b/SRC/zpoequb.f @@ -37,12 +37,12 @@ *> *> ZPOEQUB computes row and column scalings intended to equilibrate a *> symmetric positive definite matrix A and reduce its condition number -*> (with respect to the spectral norm). S contains the scale factors, -*> chosen so that the scaled matrix B with elements -*> B(i,j) = S(i)*A(i,j)*S(j) has diagonal entries close to one. S(i) is -*> a power of b nearest to but not exceeding 1/sqrt(A(i,i)), where b is -*> the basis use for floating point numbers on this machine. This choice -*> of S avoids round-off errors when computing B. +*> (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. *> \endverbatim * * Arguments: -- cgit v1.2.3