Doc: improve xPOEQUB description

- highlight difference to xPOEQU
- replace "symmetric" with "Hermitian" for {c,z}POEQUB

diff --git a/SRC/cpoequb.f b/SRC/cpoequb.f
index e0f4742..53320ee 100644 (file)
--- a/SRC/cpoequb.f
+++ b/SRC/cpoequb.f
@@ -36,13 +36,19 @@
 *> \verbatim
 *>
 *> CPOEQUB 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 CPOEQU 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 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

diff --git a/SRC/dpoequb.f b/SRC/dpoequb.f
index fcee160..1220f8f 100644 (file)
--- a/SRC/dpoequb.f
+++ b/SRC/dpoequb.f
@@ -34,7 +34,7 @@
 *>
 *> \verbatim
 *>
-*> DPOEQU computes row and column scalings intended to equilibrate a
+*> DPOEQUB computes row and column scalings intended to equilibrate a
 *> symmetric 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
@@ -42,6 +42,12 @@
 *> 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 DPOEQU 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:

diff --git a/SRC/spoequb.f b/SRC/spoequb.f
index 523aee0..2242770 100644 (file)
--- a/SRC/spoequb.f
+++ b/SRC/spoequb.f
@@ -34,7 +34,7 @@
 *>
 *> \verbatim
 *>
-*> SPOEQU computes row and column scalings intended to equilibrate a
+*> SPOEQUB computes row and column scalings intended to equilibrate a
 *> symmetric 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
@@ -42,6 +42,12 @@
 *> 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 SPOEQU 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:

diff --git a/SRC/zpoequb.f b/SRC/zpoequb.f
index c0d180c..b78470f 100644 (file)
--- a/SRC/zpoequb.f
+++ b/SRC/zpoequb.f
@@ -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