Add notes to *TPTRS about how only exact singularity is checked

Author: GYT

SRC/ctptrs.f

@@ -38,9 +38,14 @@
 *>
 *>    A * X = B,  A**T * X = B,  or  A**H * X = B,
 *>
-*> where A is a triangular matrix of order N stored in packed format,
-*> and B is an N-by-NRHS matrix.  A check is made to verify that A is
-*> nonsingular.
+*> where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix.
+*>
+*> This subroutine verifies that A is nonsingular, but callers should note that only exact
+*> singularity is detected. It is conceivable for one or more diagonal elements of A to be
+*> subnormally tiny numbers without this subroutine signalling an error.
+*>
+*> If a possible loss of numerical precision due to near-singular matrices is a concern, the
+*> caller should verify that A is nonsingular within some tolerance before calling this subroutine.
 *> \endverbatim
 *
 *  Arguments:
@@ -110,7 +115,7 @@
 *>          INFO is INTEGER
 *>          = 0:  successful exit
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
-*>          > 0:  if INFO = i, the i-th diagonal element of A is zero,
+*>          > 0:  if INFO = i, the i-th diagonal element of A is exactly zero,
 *>                indicating that the matrix is singular and the
 *>                solutions X have not been computed.
 *> \endverbatim

SRC/dtptrs.f

@@ -38,9 +38,14 @@
 *>
 *>    A * X = B  or  A**T * X = B,
 *>
-*> where A is a triangular matrix of order N stored in packed format,
-*> and B is an N-by-NRHS matrix.  A check is made to verify that A is
-*> nonsingular.
+*> where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix.
+*>
+*> This subroutine verifies that A is nonsingular, but callers should note that only exact
+*> singularity is detected. It is conceivable for one or more diagonal elements of A to be
+*> subnormally tiny numbers without this subroutine signalling an error.
+*>
+*> If a possible loss of numerical precision due to near-singular matrices is a concern, the
+*> caller should verify that A is nonsingular within some tolerance before calling this subroutine.
 *> \endverbatim
 *
 *  Arguments:
@@ -110,7 +115,7 @@
 *>          INFO is INTEGER
 *>          = 0:  successful exit
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
-*>          > 0:  if INFO = i, the i-th diagonal element of A is zero,
+*>          > 0:  if INFO = i, the i-th diagonal element of A is exactly zero,
 *>                indicating that the matrix is singular and the
 *>                solutions X have not been computed.
 *> \endverbatim

SRC/stptrs.f

@@ -38,9 +38,14 @@
 *>
 *>    A * X = B  or  A**T * X = B,
 *>
-*> where A is a triangular matrix of order N stored in packed format,
-*> and B is an N-by-NRHS matrix.  A check is made to verify that A is
-*> nonsingular.
+*> where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix.
+*>
+*> This subroutine verifies that A is nonsingular, but callers should note that only exact
+*> singularity is detected. It is conceivable for one or more diagonal elements of A to be
+*> subnormally tiny numbers without this subroutine signalling an error.
+*>
+*> If a possible loss of numerical precision due to near-singular matrices is a concern, the
+*> caller should verify that A is nonsingular within some tolerance before calling this subroutine.
 *> \endverbatim
 *
 *  Arguments:
@@ -110,7 +115,7 @@
 *>          INFO is INTEGER
 *>          = 0:  successful exit
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
-*>          > 0:  if INFO = i, the i-th diagonal element of A is zero,
+*>          > 0:  if INFO = i, the i-th diagonal element of A is exactly zero,
 *>                indicating that the matrix is singular and the
 *>                solutions X have not been computed.
 *> \endverbatim

SRC/ztptrs.f

@@ -38,9 +38,14 @@
 *>
 *>    A * X = B,  A**T * X = B,  or  A**H * X = B,
 *>
-*> where A is a triangular matrix of order N stored in packed format,
-*> and B is an N-by-NRHS matrix.  A check is made to verify that A is
-*> nonsingular.
+*> where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix.
+*>
+*> This subroutine verifies that A is nonsingular, but callers should note that only exact
+*> singularity is detected. It is conceivable for one or more diagonal elements of A to be
+*> subnormally tiny numbers without this subroutine signalling an error.
+*>
+*> If a possible loss of numerical precision due to near-singular matrices is a concern, the
+*> caller should verify that A is nonsingular within some tolerance before calling this subroutine.
 *> \endverbatim
 *
 *  Arguments:
@@ -110,7 +115,7 @@
 *>          INFO is INTEGER
 *>          = 0:  successful exit
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
-*>          > 0:  if INFO = i, the i-th diagonal element of A is zero,
+*>          > 0:  if INFO = i, the i-th diagonal element of A is exactly zero,
 *>                indicating that the matrix is singular and the
 *>                solutions X have not been computed.
 *> \endverbatim