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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 notes to *GGLSE about how only exact rank-deficiency is checked
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GYT committed Jul 25, 2024
commit b7335217c138dce0e01a6ab9b8c9ce51f3299a47
14 changes: 12 additions & 2 deletions SRC/cgglse.f
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Expand Up @@ -52,6 +52,16 @@
*> matrices (B, A) given by
*>
*> B = (0 R)*Q, A = Z*T*Q.
*>
*> Callers of this subroutine should note that the singularity/rank-deficiency checks
*> implemented in this subroutine are rudimentary. The CTRTRS subroutine called by this
*> subroutine only signals a failure due to singularity if the problem is exactly singular.
*>
*> It is conceivable for one (or more) of the factors involved in the generalized RQ
*> factorization of the pair (B, A) to be subnormally close to singularity without this
*> subroutine signalling an error. The solutions computed for such almost-rank-deficient
*> problems may be less accurate due to a loss of numerical precision.
*>
*> \endverbatim
*
* Arguments:
Expand Down Expand Up @@ -153,12 +163,12 @@
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> = 1: the upper triangular factor R associated with B in the
*> generalized RQ factorization of the pair (B, A) is
*> generalized RQ factorization of the pair (B, A) is exactly
*> singular, so that rank(B) < P; the least squares
*> solution could not be computed.
*> = 2: the (N-P) by (N-P) part of the upper trapezoidal factor
*> T associated with A in the generalized RQ factorization
*> of the pair (B, A) is singular, so that
*> of the pair (B, A) is exactly singular, so that
*> rank( (A) ) < N; the least squares solution could not
*> ( (B) )
*> be computed.
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14 changes: 12 additions & 2 deletions SRC/dgglse.f
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Expand Up @@ -52,6 +52,16 @@
*> matrices (B, A) given by
*>
*> B = (0 R)*Q, A = Z*T*Q.
*>
*> Callers of this subroutine should note that the singularity/rank-deficiency checks
*> implemented in this subroutine are rudimentary. The DTRTRS subroutine called by this
*> subroutine only signals a failure due to singularity if the problem is exactly singular.
*>
*> It is conceivable for one (or more) of the factors involved in the generalized RQ
*> factorization of the pair (B, A) to be subnormally close to singularity without this
*> subroutine signalling an error. The solutions computed for such almost-rank-deficient
*> problems may be less accurate due to a loss of numerical precision.
*>
*> \endverbatim
*
* Arguments:
Expand Down Expand Up @@ -153,12 +163,12 @@
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> = 1: the upper triangular factor R associated with B in the
*> generalized RQ factorization of the pair (B, A) is
*> generalized RQ factorization of the pair (B, A) is exactly
*> singular, so that rank(B) < P; the least squares
*> solution could not be computed.
*> = 2: the (N-P) by (N-P) part of the upper trapezoidal factor
*> T associated with A in the generalized RQ factorization
*> of the pair (B, A) is singular, so that
*> of the pair (B, A) is exactly singular, so that
*> rank( (A) ) < N; the least squares solution could not
*> ( (B) )
*> be computed.
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14 changes: 12 additions & 2 deletions SRC/sgglse.f
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Original file line number Diff line number Diff line change
Expand Up @@ -52,6 +52,16 @@
*> matrices (B, A) given by
*>
*> B = (0 R)*Q, A = Z*T*Q.
*>
*> Callers of this subroutine should note that the singularity/rank-deficiency checks
*> implemented in this subroutine are rudimentary. The STRTRS subroutine called by this
*> subroutine only signals a failure due to singularity if the problem is exactly singular.
*>
*> It is conceivable for one (or more) of the factors involved in the generalized RQ
*> factorization of the pair (B, A) to be subnormally close to singularity without this
*> subroutine signalling an error. The solutions computed for such almost-rank-deficient
*> problems may be less accurate due to a loss of numerical precision.
*>
*> \endverbatim
*
* Arguments:
Expand Down Expand Up @@ -153,12 +163,12 @@
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> = 1: the upper triangular factor R associated with B in the
*> generalized RQ factorization of the pair (B, A) is
*> generalized RQ factorization of the pair (B, A) is exactly
*> singular, so that rank(B) < P; the least squares
*> solution could not be computed.
*> = 2: the (N-P) by (N-P) part of the upper trapezoidal factor
*> T associated with A in the generalized RQ factorization
*> of the pair (B, A) is singular, so that
*> of the pair (B, A) is exactly singular, so that
*> rank( (A) ) < N; the least squares solution could not
*> ( (B) )
*> be computed.
Expand Down
14 changes: 12 additions & 2 deletions SRC/zgglse.f
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Original file line number Diff line number Diff line change
Expand Up @@ -52,6 +52,16 @@
*> matrices (B, A) given by
*>
*> B = (0 R)*Q, A = Z*T*Q.
*>
*> Callers of this subroutine should note that the singularity/rank-deficiency checks
*> implemented in this subroutine are rudimentary. The ZTRTRS subroutine called by this
*> subroutine only signals a failure due to singularity if the problem is exactly singular.
*>
*> It is conceivable for one (or more) of the factors involved in the generalized RQ
*> factorization of the pair (B, A) to be subnormally close to singularity without this
*> subroutine signalling an error. The solutions computed for such almost-rank-deficient
*> problems may be less accurate due to a loss of numerical precision.
*>
*> \endverbatim
*
* Arguments:
Expand Down Expand Up @@ -153,12 +163,12 @@
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> = 1: the upper triangular factor R associated with B in the
*> generalized RQ factorization of the pair (B, A) is
*> generalized RQ factorization of the pair (B, A) is exactly
*> singular, so that rank(B) < P; the least squares
*> solution could not be computed.
*> = 2: the (N-P) by (N-P) part of the upper trapezoidal factor
*> T associated with A in the generalized RQ factorization
*> of the pair (B, A) is singular, so that
*> of the pair (B, A) is exactly singular, so that
*> rank( (A) ) < N; the least squares solution could not
*> ( (B) )
*> be computed.
Expand Down