diff options
Diffstat (limited to 'SRC')
| -rw-r--r-- | SRC/cpoequb.f | 14 | ||||
| -rw-r--r-- | SRC/dpoequb.f | 14 | ||||
| -rw-r--r-- | SRC/spoequb.f | 14 | ||||
| -rw-r--r-- | SRC/zpoequb.f | 12 |
4 files changed, 28 insertions, 26 deletions
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: @@ -151,6 +151,8 @@ * * Test the input parameters. * +* Positive definite only performs 1 pass of equilibration. +* INFO = 0 IF( N.LT.0 ) THEN INFO = -1 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: |