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Clarify documentation of singularity/rank-deficiency checks #924

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Merged
merged 8 commits into from
Jul 25, 2024
Merged

Clarify documentation of singularity/rank-deficiency checks #924

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5475251
Add note to *TRTRS and *TBTRS about how only exact singularity is che…
Nov 1, 2023
4afdca2
Add "exact" to *TRTRS and *TBTRS info value descriptions
Nov 1, 2023
6922840
Add notes to *TPTRS about how only exact singularity is checked
Nov 1, 2023
1bf0ea2
Add notes to *GELS about how only exact rank-deficiency is checked
Nov 1, 2023
ba91e7e
Add notes to *GELST about how only exact rank-deficiency is checked
Nov 2, 2023
3ed4768
Add notes to *GETSLS about how only exact rank-deficiency is checked
Nov 22, 2023
b733521
Add notes to *GGLSE about how only exact rank-deficiency is checked
Nov 24, 2023
c3c505b
Add notes to *GGGLM about how only exact rank-deficiency is checked
Nov 26, 2023
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Add note to *TRTRS and *TBTRS about how only exact singularity is che… 
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GYT committed Jul 25, 2024
commit 5475251aba635560a9e006febf29348a574b3b6c
10 changes: 8 additions & 2 deletions SRC/ctbtrs.f
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Expand Up @@ -39,8 +39,14 @@
*>
*> A * X = B, A**T * X = B, or A**H * X = B,
*>
*> where A is a triangular band matrix of order N, and B is an
*> N-by-NRHS matrix. A check is made to verify that A is nonsingular.
*> where A is a triangular band matrix of order N, 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:
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10 changes: 8 additions & 2 deletions SRC/ctrtrs.f
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Original file line number Diff line number Diff line change
Expand Up @@ -39,8 +39,14 @@
*>
*> A * X = B, A**T * X = B, or A**H * X = B,
*>
*> where A is a triangular matrix of order N, 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, 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:
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10 changes: 8 additions & 2 deletions SRC/dtbtrs.f
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Expand Up @@ -39,8 +39,14 @@
*>
*> A * X = B or A**T * X = B,
*>
*> where A is a triangular band matrix of order N, and B is an
*> N-by NRHS matrix. A check is made to verify that A is nonsingular.
*> where A is a triangular band matrix of order N, 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:
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10 changes: 8 additions & 2 deletions SRC/dtrtrs.f
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Original file line number Diff line number Diff line change
Expand Up @@ -39,8 +39,14 @@
*>
*> A * X = B or A**T * X = B,
*>
*> where A is a triangular matrix of order N, 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, 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:
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10 changes: 8 additions & 2 deletions SRC/stbtrs.f
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Expand Up @@ -39,8 +39,14 @@
*>
*> A * X = B or A**T * X = B,
*>
*> where A is a triangular band matrix of order N, and B is an
*> N-by NRHS matrix. A check is made to verify that A is nonsingular.
*> where A is a triangular band matrix of order N, 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:
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10 changes: 8 additions & 2 deletions SRC/strtrs.f
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Original file line number Diff line number Diff line change
Expand Up @@ -39,8 +39,14 @@
*>
*> A * X = B or A**T * X = B,
*>
*> where A is a triangular matrix of order N, 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, 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:
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10 changes: 8 additions & 2 deletions SRC/ztbtrs.f
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Original file line number Diff line number Diff line change
Expand Up @@ -39,8 +39,14 @@
*>
*> A * X = B, A**T * X = B, or A**H * X = B,
*>
*> where A is a triangular band matrix of order N, and B is an
*> N-by-NRHS matrix. A check is made to verify that A is nonsingular.
*> where A is a triangular band matrix of order N, 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:
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10 changes: 8 additions & 2 deletions SRC/ztrtrs.f
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -39,8 +39,14 @@
*>
*> A * X = B, A**T * X = B, or A**H * X = B,
*>
*> where A is a triangular matrix of order N, 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, 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:
Expand Down