From 9d3154701ca0391d1e3dedd7b79739bef7dbe65d Mon Sep 17 00:00:00 2001 From: Martin Kroeker Date: Thu, 22 Jun 2023 16:09:14 +0200 Subject: [PATCH 1/6] Fix confusing use of "minor" in inline documentation (Reference-LAPACK PR849) --- lapack-netlib/SRC/VARIANTS/cholesky/RL/cpotrf.f | 4 ++-- lapack-netlib/SRC/VARIANTS/cholesky/RL/dpotrf.f | 4 ++-- lapack-netlib/SRC/VARIANTS/cholesky/RL/spotrf.f | 4 ++-- lapack-netlib/SRC/VARIANTS/cholesky/RL/zpotrf.f | 4 ++-- 4 files changed, 8 insertions(+), 8 deletions(-) diff --git a/lapack-netlib/SRC/VARIANTS/cholesky/RL/cpotrf.f b/lapack-netlib/SRC/VARIANTS/cholesky/RL/cpotrf.f index f9384b416..1b8e53cc2 100644 --- a/lapack-netlib/SRC/VARIANTS/cholesky/RL/cpotrf.f +++ b/lapack-netlib/SRC/VARIANTS/cholesky/RL/cpotrf.f @@ -79,8 +79,8 @@ C> \verbatim C> INFO is INTEGER C> = 0: successful exit C> < 0: if INFO = -i, the i-th argument had an illegal value -C> > 0: if INFO = i, the leading minor of order i is not -C> positive definite, and the factorization could not be +C> > 0: if INFO = i, the leading principal minor of order i +C> is not positive, and the factorization could not be C> completed. C> \endverbatim C> diff --git a/lapack-netlib/SRC/VARIANTS/cholesky/RL/dpotrf.f b/lapack-netlib/SRC/VARIANTS/cholesky/RL/dpotrf.f index 1575bd95c..e0a621b2e 100644 --- a/lapack-netlib/SRC/VARIANTS/cholesky/RL/dpotrf.f +++ b/lapack-netlib/SRC/VARIANTS/cholesky/RL/dpotrf.f @@ -79,8 +79,8 @@ C> \verbatim C> INFO is INTEGER C> = 0: successful exit C> < 0: if INFO = -i, the i-th argument had an illegal value -C> > 0: if INFO = i, the leading minor of order i is not -C> positive definite, and the factorization could not be +C> > 0: if INFO = i, the leading principal minor of order i +C> is not positive, and the factorization could not be C> completed. C> \endverbatim C> diff --git a/lapack-netlib/SRC/VARIANTS/cholesky/RL/spotrf.f b/lapack-netlib/SRC/VARIANTS/cholesky/RL/spotrf.f index 67ebae335..f3b66a9e3 100644 --- a/lapack-netlib/SRC/VARIANTS/cholesky/RL/spotrf.f +++ b/lapack-netlib/SRC/VARIANTS/cholesky/RL/spotrf.f @@ -79,8 +79,8 @@ C> \verbatim C> INFO is INTEGER C> = 0: successful exit C> < 0: if INFO = -i, the i-th argument had an illegal value -C> > 0: if INFO = i, the leading minor of order i is not -C> positive definite, and the factorization could not be +C> > 0: if INFO = i, the leading principal minor of order i +C> is not positive, and the factorization could not be C> completed. C> \endverbatim C> diff --git a/lapack-netlib/SRC/VARIANTS/cholesky/RL/zpotrf.f b/lapack-netlib/SRC/VARIANTS/cholesky/RL/zpotrf.f index bef27afa7..dda42faf9 100644 --- a/lapack-netlib/SRC/VARIANTS/cholesky/RL/zpotrf.f +++ b/lapack-netlib/SRC/VARIANTS/cholesky/RL/zpotrf.f @@ -79,8 +79,8 @@ C> \verbatim C> INFO is INTEGER C> = 0: successful exit C> < 0: if INFO = -i, the i-th argument had an illegal value -C> > 0: if INFO = i, the leading minor of order i is not -C> positive definite, and the factorization could not be +C> > 0: if INFO = i, the leading principal minor of order i +C> is not positive, and the factorization could not be C> completed. C> \endverbatim C> From f12b1c7b08c3f6aa00a0133bcf056be91adc7bfd Mon Sep 17 00:00:00 2001 From: Martin Kroeker Date: Thu, 22 Jun 2023 16:10:27 +0200 Subject: [PATCH 2/6] Fix confusing use of "minor" in inline documentation (Reference-LAPACK PR849) --- lapack-netlib/SRC/VARIANTS/cholesky/TOP/cpotrf.f | 4 ++-- lapack-netlib/SRC/VARIANTS/cholesky/TOP/dpotrf.f | 4 ++-- lapack-netlib/SRC/VARIANTS/cholesky/TOP/spotrf.f | 4 ++-- lapack-netlib/SRC/VARIANTS/cholesky/TOP/zpotrf.f | 4 ++-- 4 files changed, 8 insertions(+), 8 deletions(-) diff --git a/lapack-netlib/SRC/VARIANTS/cholesky/TOP/cpotrf.f b/lapack-netlib/SRC/VARIANTS/cholesky/TOP/cpotrf.f index c810a1533..b9dffa4ec 100644 --- a/lapack-netlib/SRC/VARIANTS/cholesky/TOP/cpotrf.f +++ b/lapack-netlib/SRC/VARIANTS/cholesky/TOP/cpotrf.f @@ -79,8 +79,8 @@ C> \verbatim C> INFO is INTEGER C> = 0: successful exit C> < 0: if INFO = -i, the i-th argument had an illegal value -C> > 0: if INFO = i, the leading minor of order i is not -C> positive definite, and the factorization could not be +C> > 0: if INFO = i, the leading principal minor of order i +C> is not positive, and the factorization could not be C> completed. C> \endverbatim C> diff --git a/lapack-netlib/SRC/VARIANTS/cholesky/TOP/dpotrf.f b/lapack-netlib/SRC/VARIANTS/cholesky/TOP/dpotrf.f index e49200ea5..e68a559ba 100644 --- a/lapack-netlib/SRC/VARIANTS/cholesky/TOP/dpotrf.f +++ b/lapack-netlib/SRC/VARIANTS/cholesky/TOP/dpotrf.f @@ -79,8 +79,8 @@ C> \verbatim C> INFO is INTEGER C> = 0: successful exit C> < 0: if INFO = -i, the i-th argument had an illegal value -C> > 0: if INFO = i, the leading minor of order i is not -C> positive definite, and the factorization could not be +C> > 0: if INFO = i, the leading principal minor of order i +C> is not positive, and the factorization could not be C> completed. C> \endverbatim C> diff --git a/lapack-netlib/SRC/VARIANTS/cholesky/TOP/spotrf.f b/lapack-netlib/SRC/VARIANTS/cholesky/TOP/spotrf.f index 65895502b..7401f8844 100644 --- a/lapack-netlib/SRC/VARIANTS/cholesky/TOP/spotrf.f +++ b/lapack-netlib/SRC/VARIANTS/cholesky/TOP/spotrf.f @@ -79,8 +79,8 @@ C> \verbatim C> INFO is INTEGER C> = 0: successful exit C> < 0: if INFO = -i, the i-th argument had an illegal value -C> > 0: if INFO = i, the leading minor of order i is not -C> positive definite, and the factorization could not be +C> > 0: if INFO = i, the leading principal minor of order i +C> is not positive, and the factorization could not be C> completed. C> \endverbatim C> diff --git a/lapack-netlib/SRC/VARIANTS/cholesky/TOP/zpotrf.f b/lapack-netlib/SRC/VARIANTS/cholesky/TOP/zpotrf.f index 449c7ac95..80b7c7f43 100644 --- a/lapack-netlib/SRC/VARIANTS/cholesky/TOP/zpotrf.f +++ b/lapack-netlib/SRC/VARIANTS/cholesky/TOP/zpotrf.f @@ -79,8 +79,8 @@ C> \verbatim C> INFO is INTEGER C> = 0: successful exit C> < 0: if INFO = -i, the i-th argument had an illegal value -C> > 0: if INFO = i, the leading minor of order i is not -C> positive definite, and the factorization could not be +C> > 0: if INFO = i, the leading principal minor of order i +C> is not positive, and the factorization could not be C> completed. C> \endverbatim C> From 219a73a394d8bf4cd31a7cd1c534f83f205c5c70 Mon Sep 17 00:00:00 2001 From: Martin Kroeker Date: Thu, 22 Jun 2023 16:18:58 +0200 Subject: [PATCH 3/6] Fix confusing use of "minor" in inline documentation (Reference-LAPACK PR849) --- lapack-netlib/SRC/zcposv.f | 8 ++++---- lapack-netlib/SRC/zhegv.f | 2 +- lapack-netlib/SRC/zhegv_2stage.f | 2 +- lapack-netlib/SRC/zhegvd.f | 2 +- lapack-netlib/SRC/zhegvx.f | 2 +- lapack-netlib/SRC/zhpgv.f | 2 +- lapack-netlib/SRC/zhpgvd.f | 2 +- lapack-netlib/SRC/zhpgvx.f | 2 +- lapack-netlib/SRC/zla_porpvgrw.f | 6 +++--- lapack-netlib/SRC/zpbsv.f | 6 +++--- lapack-netlib/SRC/zpbsvx.f | 10 +++++----- lapack-netlib/SRC/zpbtf2.f | 4 ++-- lapack-netlib/SRC/zpbtrf.f | 4 ++-- lapack-netlib/SRC/zpftrf.f | 4 ++-- lapack-netlib/SRC/zposv.f | 6 +++--- lapack-netlib/SRC/zposvx.f | 10 +++++----- lapack-netlib/SRC/zposvxx.f | 2 +- lapack-netlib/SRC/zpotf2.f | 4 ++-- lapack-netlib/SRC/zpotrf.f | 4 ++-- lapack-netlib/SRC/zpotrf2.f | 4 ++-- lapack-netlib/SRC/zppsv.f | 6 +++--- lapack-netlib/SRC/zppsvx.f | 10 +++++----- lapack-netlib/SRC/zpptrf.f | 4 ++-- lapack-netlib/SRC/zpteqr.f | 4 ++-- lapack-netlib/SRC/zptsv.f | 4 ++-- lapack-netlib/SRC/zptsvx.f | 10 +++++----- lapack-netlib/SRC/zpttrf.f | 4 ++-- 27 files changed, 64 insertions(+), 64 deletions(-) diff --git a/lapack-netlib/SRC/zcposv.f b/lapack-netlib/SRC/zcposv.f index 9b1940d60..649d2c049 100644 --- a/lapack-netlib/SRC/zcposv.f +++ b/lapack-netlib/SRC/zcposv.f @@ -187,10 +187,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i of -*> (COMPLEX*16) A is not positive definite, so the -*> factorization could not be completed, and the solution -*> has not been computed. +*> > 0: if INFO = i, the leading principal minor of order i +*> of (COMPLEX*16) A is not positive, so the factorization +*> could not be completed, and the solution has not been +*> computed. *> \endverbatim * * Authors: diff --git a/lapack-netlib/SRC/zhegv.f b/lapack-netlib/SRC/zhegv.f index 41657e3be..c973bd0fc 100644 --- a/lapack-netlib/SRC/zhegv.f +++ b/lapack-netlib/SRC/zhegv.f @@ -160,7 +160,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not converge to zero; *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/zhegv_2stage.f b/lapack-netlib/SRC/zhegv_2stage.f index fda651e5e..91ac09311 100644 --- a/lapack-netlib/SRC/zhegv_2stage.f +++ b/lapack-netlib/SRC/zhegv_2stage.f @@ -179,7 +179,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not converge to zero; *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/zhegvd.f b/lapack-netlib/SRC/zhegvd.f index eeda656ad..2c3586517 100644 --- a/lapack-netlib/SRC/zhegvd.f +++ b/lapack-netlib/SRC/zhegvd.f @@ -212,7 +212,7 @@ *> the submatrix lying in rows and columns INFO/(N+1) *> through mod(INFO,N+1); *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/zhegvx.f b/lapack-netlib/SRC/zhegvx.f index ac9f9ef1a..71ed1c4ca 100644 --- a/lapack-netlib/SRC/zhegvx.f +++ b/lapack-netlib/SRC/zhegvx.f @@ -280,7 +280,7 @@ *> i eigenvectors failed to converge. Their indices *> are stored in array IFAIL. *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/zhpgv.f b/lapack-netlib/SRC/zhpgv.f index 72876b6e4..b92168555 100644 --- a/lapack-netlib/SRC/zhpgv.f +++ b/lapack-netlib/SRC/zhpgv.f @@ -144,7 +144,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not convergeto zero; *> > N: if INFO = N + i, for 1 <= i <= n, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/zhpgvd.f b/lapack-netlib/SRC/zhpgvd.f index e96e39738..e9688f0c7 100644 --- a/lapack-netlib/SRC/zhpgvd.f +++ b/lapack-netlib/SRC/zhpgvd.f @@ -205,7 +205,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not convergeto zero; *> > N: if INFO = N + i, for 1 <= i <= n, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/zhpgvx.f b/lapack-netlib/SRC/zhpgvx.f index 94d7f7733..de75b486b 100644 --- a/lapack-netlib/SRC/zhpgvx.f +++ b/lapack-netlib/SRC/zhpgvx.f @@ -250,7 +250,7 @@ *> i eigenvectors failed to converge. Their indices *> are stored in array IFAIL. *> > N: if INFO = N + i, for 1 <= i <= n, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/zla_porpvgrw.f b/lapack-netlib/SRC/zla_porpvgrw.f index 9b381a072..897589aa0 100644 --- a/lapack-netlib/SRC/zla_porpvgrw.f +++ b/lapack-netlib/SRC/zla_porpvgrw.f @@ -142,9 +142,9 @@ * .. Executable Statements .. UPPER = LSAME( 'Upper', UPLO ) * -* DPOTRF will have factored only the NCOLSxNCOLS leading minor, so -* we restrict the growth search to that minor and use only the first -* 2*NCOLS workspace entries. +* DPOTRF will have factored only the NCOLSxNCOLS leading submatrix, +* so we restrict the growth search to that submatrix and use only +* the first 2*NCOLS workspace entries. * RPVGRW = 1.0D+0 DO I = 1, 2*NCOLS diff --git a/lapack-netlib/SRC/zpbsv.f b/lapack-netlib/SRC/zpbsv.f index fe6baf8b5..ef212bbc3 100644 --- a/lapack-netlib/SRC/zpbsv.f +++ b/lapack-netlib/SRC/zpbsv.f @@ -119,9 +119,9 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i of A is not -*> positive definite, so the factorization could not be -*> completed, and the solution has not been computed. +*> > 0: if INFO = i, the leading principal minor of order i +*> of A is not positive, so the factorization could not +*> be completed, and the solution has not been computed. *> \endverbatim * * Authors: diff --git a/lapack-netlib/SRC/zpbsvx.f b/lapack-netlib/SRC/zpbsvx.f index 1efd2fd1e..724102376 100644 --- a/lapack-netlib/SRC/zpbsvx.f +++ b/lapack-netlib/SRC/zpbsvx.f @@ -70,7 +70,7 @@ *> where U is an upper triangular band matrix, and L is a lower *> triangular band matrix. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -280,10 +280,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/zpbtf2.f b/lapack-netlib/SRC/zpbtf2.f index 7b90af47e..39bf6c3fa 100644 --- a/lapack-netlib/SRC/zpbtf2.f +++ b/lapack-netlib/SRC/zpbtf2.f @@ -97,8 +97,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value -*> > 0: if INFO = k, the leading minor of order k is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = k, the leading principal minor of order k +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/zpbtrf.f b/lapack-netlib/SRC/zpbtrf.f index 61cd1d434..80afb0836 100644 --- a/lapack-netlib/SRC/zpbtrf.f +++ b/lapack-netlib/SRC/zpbtrf.f @@ -92,8 +92,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/zpftrf.f b/lapack-netlib/SRC/zpftrf.f index 6d18f2cb3..4d4a5116e 100644 --- a/lapack-netlib/SRC/zpftrf.f +++ b/lapack-netlib/SRC/zpftrf.f @@ -91,8 +91,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> *> Further Notes on RFP Format: diff --git a/lapack-netlib/SRC/zposv.f b/lapack-netlib/SRC/zposv.f index 3bb625876..0e91cde2f 100644 --- a/lapack-netlib/SRC/zposv.f +++ b/lapack-netlib/SRC/zposv.f @@ -110,9 +110,9 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i of A is not -*> positive definite, so the factorization could not be -*> completed, and the solution has not been computed. +*> > 0: if INFO = i, the leading principal minor of order i +*> of A is not positive, so the factorization could not +*> be completed, and the solution has not been computed. *> \endverbatim * * Authors: diff --git a/lapack-netlib/SRC/zposvx.f b/lapack-netlib/SRC/zposvx.f index f9e9b1d5f..6c06dbd57 100644 --- a/lapack-netlib/SRC/zposvx.f +++ b/lapack-netlib/SRC/zposvx.f @@ -70,7 +70,7 @@ *> where U is an upper triangular matrix and L is a lower triangular *> matrix. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -276,10 +276,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/zposvxx.f b/lapack-netlib/SRC/zposvxx.f index 6735fab71..3886c66f0 100644 --- a/lapack-netlib/SRC/zposvxx.f +++ b/lapack-netlib/SRC/zposvxx.f @@ -87,7 +87,7 @@ *> where U is an upper triangular matrix and L is a lower triangular *> matrix. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A (see argument RCOND). If the reciprocal of the condition number diff --git a/lapack-netlib/SRC/zpotf2.f b/lapack-netlib/SRC/zpotf2.f index eb88d617c..b48f3d654 100644 --- a/lapack-netlib/SRC/zpotf2.f +++ b/lapack-netlib/SRC/zpotf2.f @@ -89,8 +89,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value -*> > 0: if INFO = k, the leading minor of order k is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = k, the leading principal minor of order k +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/zpotrf.f b/lapack-netlib/SRC/zpotrf.f index 3b7018276..3edae84fb 100644 --- a/lapack-netlib/SRC/zpotrf.f +++ b/lapack-netlib/SRC/zpotrf.f @@ -87,8 +87,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/zpotrf2.f b/lapack-netlib/SRC/zpotrf2.f index 859ddc75f..67430f231 100644 --- a/lapack-netlib/SRC/zpotrf2.f +++ b/lapack-netlib/SRC/zpotrf2.f @@ -86,8 +86,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/zppsv.f b/lapack-netlib/SRC/zppsv.f index 19536e204..f466266e4 100644 --- a/lapack-netlib/SRC/zppsv.f +++ b/lapack-netlib/SRC/zppsv.f @@ -104,9 +104,9 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i of A is not -*> positive definite, so the factorization could not be -*> completed, and the solution has not been computed. +*> > 0: if INFO = i, the leading principal minor of order i +*> of A is not positive, so the factorization could not +*> be completed, and the solution has not been computed. *> \endverbatim * * Authors: diff --git a/lapack-netlib/SRC/zppsvx.f b/lapack-netlib/SRC/zppsvx.f index f94badf78..60d07cbc7 100644 --- a/lapack-netlib/SRC/zppsvx.f +++ b/lapack-netlib/SRC/zppsvx.f @@ -69,7 +69,7 @@ *> where U is an upper triangular matrix, L is a lower triangular *> matrix, and **H indicates conjugate transpose. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -262,10 +262,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/zpptrf.f b/lapack-netlib/SRC/zpptrf.f index a34d63913..a103e5eca 100644 --- a/lapack-netlib/SRC/zpptrf.f +++ b/lapack-netlib/SRC/zpptrf.f @@ -79,8 +79,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/zpteqr.f b/lapack-netlib/SRC/zpteqr.f index a81a6ad94..897136c76 100644 --- a/lapack-netlib/SRC/zpteqr.f +++ b/lapack-netlib/SRC/zpteqr.f @@ -123,8 +123,8 @@ *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if INFO = i, and i is: *> <= N the Cholesky factorization of the matrix could -*> not be performed because the i-th principal minor -*> was not positive definite. +*> not be performed because the leading principal +*> minor of order i was not positive. *> > N the SVD algorithm failed to converge; *> if INFO = N+i, i off-diagonal elements of the *> bidiagonal factor did not converge to zero. diff --git a/lapack-netlib/SRC/zptsv.f b/lapack-netlib/SRC/zptsv.f index d53e17a34..191adaff6 100644 --- a/lapack-netlib/SRC/zptsv.f +++ b/lapack-netlib/SRC/zptsv.f @@ -94,8 +94,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the solution has not been +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the solution has not been *> computed. The factorization has not been completed *> unless i = N. *> \endverbatim diff --git a/lapack-netlib/SRC/zptsvx.f b/lapack-netlib/SRC/zptsvx.f index 4a40768f1..94409a7a1 100644 --- a/lapack-netlib/SRC/zptsvx.f +++ b/lapack-netlib/SRC/zptsvx.f @@ -60,7 +60,7 @@ *> factorization can also be regarded as having the form *> A = U**H*D*U. *> -*> 2. If the leading i-by-i principal minor is not positive definite, +*> 2. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -205,10 +205,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/zpttrf.f b/lapack-netlib/SRC/zpttrf.f index a106ec419..75ef847c4 100644 --- a/lapack-netlib/SRC/zpttrf.f +++ b/lapack-netlib/SRC/zpttrf.f @@ -71,8 +71,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value -*> > 0: if INFO = k, the leading minor of order k is not -*> positive definite; if k < N, the factorization could not +*> > 0: if INFO = k, the leading principal minor of order k +*> is not positive; if k < N, the factorization could not *> be completed, while if k = N, the factorization was *> completed, but D(N) <= 0. *> \endverbatim From d9a6cacef737593c5f6e7c91396da7e3769afede Mon Sep 17 00:00:00 2001 From: Martin Kroeker Date: Thu, 22 Jun 2023 16:20:49 +0200 Subject: [PATCH 4/6] Fix confusing use of "minor" in inline documentation (Reference-LAPACK PR849) --- lapack-netlib/SRC/sla_porpvgrw.f | 6 +++--- lapack-netlib/SRC/spbsv.f | 6 +++--- lapack-netlib/SRC/spbsvx.f | 10 +++++----- lapack-netlib/SRC/spbtf2.f | 4 ++-- lapack-netlib/SRC/spbtrf.f | 4 ++-- lapack-netlib/SRC/spftrf.f | 4 ++-- lapack-netlib/SRC/sposv.f | 6 +++--- lapack-netlib/SRC/sposvx.f | 10 +++++----- lapack-netlib/SRC/sposvxx.f | 2 +- lapack-netlib/SRC/spotf2.f | 4 ++-- lapack-netlib/SRC/spotrf.f | 4 ++-- lapack-netlib/SRC/spotrf2.f | 4 ++-- lapack-netlib/SRC/sppsv.f | 6 +++--- lapack-netlib/SRC/sppsvx.f | 10 +++++----- lapack-netlib/SRC/spptrf.f | 4 ++-- lapack-netlib/SRC/spteqr.f | 4 ++-- lapack-netlib/SRC/sptsv.f | 4 ++-- lapack-netlib/SRC/sptsvx.f | 10 +++++----- lapack-netlib/SRC/spttrf.f | 4 ++-- lapack-netlib/SRC/ssbgvx.f | 2 +- lapack-netlib/SRC/sspgv.f | 2 +- lapack-netlib/SRC/sspgvd.f | 2 +- lapack-netlib/SRC/sspgvx.f | 2 +- lapack-netlib/SRC/ssygv.f | 2 +- lapack-netlib/SRC/ssygv_2stage.f | 2 +- lapack-netlib/SRC/ssygvd.f | 2 +- lapack-netlib/SRC/ssygvx.f | 2 +- 27 files changed, 61 insertions(+), 61 deletions(-) diff --git a/lapack-netlib/SRC/sla_porpvgrw.f b/lapack-netlib/SRC/sla_porpvgrw.f index a97e7f72a..8064bf7fa 100644 --- a/lapack-netlib/SRC/sla_porpvgrw.f +++ b/lapack-netlib/SRC/sla_porpvgrw.f @@ -132,9 +132,9 @@ * UPPER = LSAME( 'Upper', UPLO ) * -* SPOTRF will have factored only the NCOLSxNCOLS leading minor, so -* we restrict the growth search to that minor and use only the first -* 2*NCOLS workspace entries. +* SPOTRF will have factored only the NCOLSxNCOLS leading submatrix, +* so we restrict the growth search to that submatrix and use only +* the first 2*NCOLS workspace entries. * RPVGRW = 1.0 DO I = 1, 2*NCOLS diff --git a/lapack-netlib/SRC/spbsv.f b/lapack-netlib/SRC/spbsv.f index 2d084424e..8929321ea 100644 --- a/lapack-netlib/SRC/spbsv.f +++ b/lapack-netlib/SRC/spbsv.f @@ -119,9 +119,9 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i of A is not -*> positive definite, so the factorization could not be -*> completed, and the solution has not been computed. +*> > 0: if INFO = i, the leading principal minor of order i +*> of A is not positive, so the factorization could not +*> be completed, and the solution has not been computed. *> \endverbatim * * Authors: diff --git a/lapack-netlib/SRC/spbsvx.f b/lapack-netlib/SRC/spbsvx.f index 27907eb85..6abb6caae 100644 --- a/lapack-netlib/SRC/spbsvx.f +++ b/lapack-netlib/SRC/spbsvx.f @@ -71,7 +71,7 @@ *> where U is an upper triangular band matrix, and L is a lower *> triangular band matrix. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -281,10 +281,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/spbtf2.f b/lapack-netlib/SRC/spbtf2.f index ff08bc327..b5aac1ccd 100644 --- a/lapack-netlib/SRC/spbtf2.f +++ b/lapack-netlib/SRC/spbtf2.f @@ -97,8 +97,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value -*> > 0: if INFO = k, the leading minor of order k is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = k, the leading principal minor of order k +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/spbtrf.f b/lapack-netlib/SRC/spbtrf.f index ef5dcbb98..d3ae216e5 100644 --- a/lapack-netlib/SRC/spbtrf.f +++ b/lapack-netlib/SRC/spbtrf.f @@ -92,8 +92,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/spftrf.f b/lapack-netlib/SRC/spftrf.f index 9e2c11eea..0ed0e3abd 100644 --- a/lapack-netlib/SRC/spftrf.f +++ b/lapack-netlib/SRC/spftrf.f @@ -91,8 +91,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/sposv.f b/lapack-netlib/SRC/sposv.f index fe0a35a56..336332d2d 100644 --- a/lapack-netlib/SRC/sposv.f +++ b/lapack-netlib/SRC/sposv.f @@ -110,9 +110,9 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i of A is not -*> positive definite, so the factorization could not be -*> completed, and the solution has not been computed. +*> > 0: if INFO = i, the leading principal minor of order i +*> of A is not positive, so the factorization could not +*> be completed, and the solution has not been computed. *> \endverbatim * * Authors: diff --git a/lapack-netlib/SRC/sposvx.f b/lapack-netlib/SRC/sposvx.f index bcf38c7ea..0770897d2 100644 --- a/lapack-netlib/SRC/sposvx.f +++ b/lapack-netlib/SRC/sposvx.f @@ -71,7 +71,7 @@ *> where U is an upper triangular matrix and L is a lower triangular *> matrix. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -277,10 +277,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/sposvxx.f b/lapack-netlib/SRC/sposvxx.f index 08adf1d58..19e599f64 100644 --- a/lapack-netlib/SRC/sposvxx.f +++ b/lapack-netlib/SRC/sposvxx.f @@ -88,7 +88,7 @@ *> where U is an upper triangular matrix and L is a lower triangular *> matrix. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A (see argument RCOND). If the reciprocal of the condition number diff --git a/lapack-netlib/SRC/spotf2.f b/lapack-netlib/SRC/spotf2.f index 5b3504834..773b768b2 100644 --- a/lapack-netlib/SRC/spotf2.f +++ b/lapack-netlib/SRC/spotf2.f @@ -89,8 +89,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value -*> > 0: if INFO = k, the leading minor of order k is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = k, the leading principal minor of order k +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/spotrf.f b/lapack-netlib/SRC/spotrf.f index 5d5771c86..12ef58a40 100644 --- a/lapack-netlib/SRC/spotrf.f +++ b/lapack-netlib/SRC/spotrf.f @@ -87,8 +87,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/spotrf2.f b/lapack-netlib/SRC/spotrf2.f index ae0484ce1..ef731ffa2 100644 --- a/lapack-netlib/SRC/spotrf2.f +++ b/lapack-netlib/SRC/spotrf2.f @@ -86,8 +86,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/sppsv.f b/lapack-netlib/SRC/sppsv.f index 2d3fb3d91..1f48dd4db 100644 --- a/lapack-netlib/SRC/sppsv.f +++ b/lapack-netlib/SRC/sppsv.f @@ -104,9 +104,9 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i of A is not -*> positive definite, so the factorization could not be -*> completed, and the solution has not been computed. +*> > 0: if INFO = i, the leading principal minor of order i +*> of A is not positive, so the factorization could not +*> be completed, and the solution has not been computed. *> \endverbatim * * Authors: diff --git a/lapack-netlib/SRC/sppsvx.f b/lapack-netlib/SRC/sppsvx.f index 7d71efcd5..bd2da20ee 100644 --- a/lapack-netlib/SRC/sppsvx.f +++ b/lapack-netlib/SRC/sppsvx.f @@ -69,7 +69,7 @@ *> where U is an upper triangular matrix and L is a lower triangular *> matrix. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -262,10 +262,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/spptrf.f b/lapack-netlib/SRC/spptrf.f index 0f90399cc..be51c4824 100644 --- a/lapack-netlib/SRC/spptrf.f +++ b/lapack-netlib/SRC/spptrf.f @@ -79,8 +79,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/spteqr.f b/lapack-netlib/SRC/spteqr.f index 0d6bf911b..6e6e9aa45 100644 --- a/lapack-netlib/SRC/spteqr.f +++ b/lapack-netlib/SRC/spteqr.f @@ -123,8 +123,8 @@ *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if INFO = i, and i is: *> <= N the Cholesky factorization of the matrix could -*> not be performed because the i-th principal minor -*> was not positive definite. +*> not be performed because the leading principal +*> minor of order i was not positive. *> > N the SVD algorithm failed to converge; *> if INFO = N+i, i off-diagonal elements of the *> bidiagonal factor did not converge to zero. diff --git a/lapack-netlib/SRC/sptsv.f b/lapack-netlib/SRC/sptsv.f index 46aadf4c3..f11c22594 100644 --- a/lapack-netlib/SRC/sptsv.f +++ b/lapack-netlib/SRC/sptsv.f @@ -93,8 +93,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the solution has not been +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the solution has not been *> computed. The factorization has not been completed *> unless i = N. *> \endverbatim diff --git a/lapack-netlib/SRC/sptsvx.f b/lapack-netlib/SRC/sptsvx.f index 8dd04b054..eaa691cef 100644 --- a/lapack-netlib/SRC/sptsvx.f +++ b/lapack-netlib/SRC/sptsvx.f @@ -59,7 +59,7 @@ *> factorization can also be regarded as having the form *> A = U**T*D*U. *> -*> 2. If the leading i-by-i principal minor is not positive definite, +*> 2. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -199,10 +199,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/spttrf.f b/lapack-netlib/SRC/spttrf.f index 2217a7338..e083b7456 100644 --- a/lapack-netlib/SRC/spttrf.f +++ b/lapack-netlib/SRC/spttrf.f @@ -70,8 +70,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value -*> > 0: if INFO = k, the leading minor of order k is not -*> positive definite; if k < N, the factorization could not +*> > 0: if INFO = k, the leading principal minor of order k +*> is not positive; if k < N, the factorization could not *> be completed, while if k = N, the factorization was *> completed, but D(N) <= 0. *> \endverbatim diff --git a/lapack-netlib/SRC/ssbgvx.f b/lapack-netlib/SRC/ssbgvx.f index 271f35964..3607fae82 100644 --- a/lapack-netlib/SRC/ssbgvx.f +++ b/lapack-netlib/SRC/ssbgvx.f @@ -267,7 +267,7 @@ *> Their indices are stored in IFAIL. *> > N: SPBSTF returned an error code; i.e., *> if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/sspgv.f b/lapack-netlib/SRC/sspgv.f index c73e94e60..e8bc66e5d 100644 --- a/lapack-netlib/SRC/sspgv.f +++ b/lapack-netlib/SRC/sspgv.f @@ -139,7 +139,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not converge to zero. *> > N: if INFO = n + i, for 1 <= i <= n, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/sspgvd.f b/lapack-netlib/SRC/sspgvd.f index 73862ed1b..8ce2311fa 100644 --- a/lapack-netlib/SRC/sspgvd.f +++ b/lapack-netlib/SRC/sspgvd.f @@ -184,7 +184,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not converge to zero; *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/sspgvx.f b/lapack-netlib/SRC/sspgvx.f index de581543a..6d5b4ed3d 100644 --- a/lapack-netlib/SRC/sspgvx.f +++ b/lapack-netlib/SRC/sspgvx.f @@ -245,7 +245,7 @@ *> i eigenvectors failed to converge. Their indices *> are stored in array IFAIL. *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/ssygv.f b/lapack-netlib/SRC/ssygv.f index 270957fce..f39947d92 100644 --- a/lapack-netlib/SRC/ssygv.f +++ b/lapack-netlib/SRC/ssygv.f @@ -154,7 +154,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not converge to zero; *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/ssygv_2stage.f b/lapack-netlib/SRC/ssygv_2stage.f index 49f357d90..3d9a44b5e 100644 --- a/lapack-netlib/SRC/ssygv_2stage.f +++ b/lapack-netlib/SRC/ssygv_2stage.f @@ -173,7 +173,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not converge to zero; *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/ssygvd.f b/lapack-netlib/SRC/ssygvd.f index 7c7e0de01..79f12a6f9 100644 --- a/lapack-netlib/SRC/ssygvd.f +++ b/lapack-netlib/SRC/ssygvd.f @@ -190,7 +190,7 @@ *> the submatrix lying in rows and columns INFO/(N+1) *> through mod(INFO,N+1); *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/ssygvx.f b/lapack-netlib/SRC/ssygvx.f index e93da60cc..344075c9f 100644 --- a/lapack-netlib/SRC/ssygvx.f +++ b/lapack-netlib/SRC/ssygvx.f @@ -270,7 +270,7 @@ *> i eigenvectors failed to converge. Their indices *> are stored in array IFAIL. *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim From a20f533b868a23c96374d7c6f897cf1c76772e8a Mon Sep 17 00:00:00 2001 From: Martin Kroeker Date: Thu, 22 Jun 2023 16:23:26 +0200 Subject: [PATCH 5/6] Fix confusing use of "minor" in inline documentation (Reference-LAPACK PR849) --- lapack-netlib/SRC/dla_porpvgrw.f | 6 +++--- lapack-netlib/SRC/dpbsv.f | 6 +++--- lapack-netlib/SRC/dpbsvx.f | 10 +++++----- lapack-netlib/SRC/dpbtf2.f | 4 ++-- lapack-netlib/SRC/dpbtrf.f | 4 ++-- lapack-netlib/SRC/dpftrf.f | 4 ++-- lapack-netlib/SRC/dposv.f | 6 +++--- lapack-netlib/SRC/dposvx.f | 10 +++++----- lapack-netlib/SRC/dposvxx.f | 2 +- lapack-netlib/SRC/dpotf2.f | 4 ++-- lapack-netlib/SRC/dpotrf.f | 4 ++-- lapack-netlib/SRC/dpotrf2.f | 4 ++-- lapack-netlib/SRC/dppsv.f | 6 +++--- lapack-netlib/SRC/dppsvx.f | 10 +++++----- lapack-netlib/SRC/dpptrf.f | 4 ++-- lapack-netlib/SRC/dpteqr.f | 4 ++-- lapack-netlib/SRC/dptsv.f | 4 ++-- lapack-netlib/SRC/dptsvx.f | 10 +++++----- lapack-netlib/SRC/dpttrf.f | 4 ++-- lapack-netlib/SRC/dsbgvx.f | 2 +- lapack-netlib/SRC/dspgv.f | 2 +- lapack-netlib/SRC/dspgvd.f | 2 +- lapack-netlib/SRC/dspgvx.f | 2 +- lapack-netlib/SRC/dsposv.f | 4 ++-- lapack-netlib/SRC/dsygv.f | 2 +- lapack-netlib/SRC/dsygv_2stage.f | 2 +- lapack-netlib/SRC/dsygvd.f | 2 +- lapack-netlib/SRC/dsygvx.f | 2 +- 28 files changed, 63 insertions(+), 63 deletions(-) diff --git a/lapack-netlib/SRC/dla_porpvgrw.f b/lapack-netlib/SRC/dla_porpvgrw.f index 93ad3eb6a..00fdd7ae1 100644 --- a/lapack-netlib/SRC/dla_porpvgrw.f +++ b/lapack-netlib/SRC/dla_porpvgrw.f @@ -134,9 +134,9 @@ * UPPER = LSAME( 'Upper', UPLO ) * -* DPOTRF will have factored only the NCOLSxNCOLS leading minor, so -* we restrict the growth search to that minor and use only the first -* 2*NCOLS workspace entries. +* DPOTRF will have factored only the NCOLSxNCOLS leading submatrix, +* so we restrict the growth search to that submatrix and use only +* the first 2*NCOLS workspace entries. * RPVGRW = 1.0D+0 DO I = 1, 2*NCOLS diff --git a/lapack-netlib/SRC/dpbsv.f b/lapack-netlib/SRC/dpbsv.f index a52e78309..2d8f06440 100644 --- a/lapack-netlib/SRC/dpbsv.f +++ b/lapack-netlib/SRC/dpbsv.f @@ -119,9 +119,9 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i of A is not -*> positive definite, so the factorization could not be -*> completed, and the solution has not been computed. +*> > 0: if INFO = i, the leading principal minor of order i +*> of A is not positive, so the factorization could not +*> be completed, and the solution has not been computed. *> \endverbatim * * Authors: diff --git a/lapack-netlib/SRC/dpbsvx.f b/lapack-netlib/SRC/dpbsvx.f index 1bf526fc7..142dda5da 100644 --- a/lapack-netlib/SRC/dpbsvx.f +++ b/lapack-netlib/SRC/dpbsvx.f @@ -71,7 +71,7 @@ *> where U is an upper triangular band matrix, and L is a lower *> triangular band matrix. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -281,10 +281,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/dpbtf2.f b/lapack-netlib/SRC/dpbtf2.f index 534629294..1284c9ec8 100644 --- a/lapack-netlib/SRC/dpbtf2.f +++ b/lapack-netlib/SRC/dpbtf2.f @@ -97,8 +97,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value -*> > 0: if INFO = k, the leading minor of order k is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = k, the leading principal minor of order k +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/dpbtrf.f b/lapack-netlib/SRC/dpbtrf.f index 8256f8938..29e9aaecd 100644 --- a/lapack-netlib/SRC/dpbtrf.f +++ b/lapack-netlib/SRC/dpbtrf.f @@ -92,8 +92,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/dpftrf.f b/lapack-netlib/SRC/dpftrf.f index 980debaf2..312dcdf84 100644 --- a/lapack-netlib/SRC/dpftrf.f +++ b/lapack-netlib/SRC/dpftrf.f @@ -91,8 +91,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/dposv.f b/lapack-netlib/SRC/dposv.f index ee2988e6f..cb76e9977 100644 --- a/lapack-netlib/SRC/dposv.f +++ b/lapack-netlib/SRC/dposv.f @@ -110,9 +110,9 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i of A is not -*> positive definite, so the factorization could not be -*> completed, and the solution has not been computed. +*> > 0: if INFO = i, the leading principal minor of order i +*> of A is not positive, so the factorization could not +*> be completed, and the solution has not been computed. *> \endverbatim * * Authors: diff --git a/lapack-netlib/SRC/dposvx.f b/lapack-netlib/SRC/dposvx.f index 4a0b9d605..faffff803 100644 --- a/lapack-netlib/SRC/dposvx.f +++ b/lapack-netlib/SRC/dposvx.f @@ -71,7 +71,7 @@ *> where U is an upper triangular matrix and L is a lower triangular *> matrix. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -277,10 +277,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/dposvxx.f b/lapack-netlib/SRC/dposvxx.f index e74b23c80..b5336cf63 100644 --- a/lapack-netlib/SRC/dposvxx.f +++ b/lapack-netlib/SRC/dposvxx.f @@ -88,7 +88,7 @@ *> where U is an upper triangular matrix and L is a lower triangular *> matrix. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A (see argument RCOND). If the reciprocal of the condition number diff --git a/lapack-netlib/SRC/dpotf2.f b/lapack-netlib/SRC/dpotf2.f index 08fa4957f..30da5c3f3 100644 --- a/lapack-netlib/SRC/dpotf2.f +++ b/lapack-netlib/SRC/dpotf2.f @@ -89,8 +89,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value -*> > 0: if INFO = k, the leading minor of order k is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = k, the leading principal minor of order k +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/dpotrf.f b/lapack-netlib/SRC/dpotrf.f index 1679fc3cd..65509feb8 100644 --- a/lapack-netlib/SRC/dpotrf.f +++ b/lapack-netlib/SRC/dpotrf.f @@ -87,8 +87,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/dpotrf2.f b/lapack-netlib/SRC/dpotrf2.f index 6c28ce6d6..aaf9b9c58 100644 --- a/lapack-netlib/SRC/dpotrf2.f +++ b/lapack-netlib/SRC/dpotrf2.f @@ -86,8 +86,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/dppsv.f b/lapack-netlib/SRC/dppsv.f index 435703b08..1888005d9 100644 --- a/lapack-netlib/SRC/dppsv.f +++ b/lapack-netlib/SRC/dppsv.f @@ -104,9 +104,9 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i of A is not -*> positive definite, so the factorization could not be -*> completed, and the solution has not been computed. +*> > 0: if INFO = i, the leading principal minor of order i +*> of A is not positive, so the factorization could not +*> be completed, and the solution has not been computed. *> \endverbatim * * Authors: diff --git a/lapack-netlib/SRC/dppsvx.f b/lapack-netlib/SRC/dppsvx.f index cb41d39ee..3b08fc821 100644 --- a/lapack-netlib/SRC/dppsvx.f +++ b/lapack-netlib/SRC/dppsvx.f @@ -69,7 +69,7 @@ *> where U is an upper triangular matrix and L is a lower triangular *> matrix. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -262,10 +262,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/dpptrf.f b/lapack-netlib/SRC/dpptrf.f index 2d8de5110..d9eed910d 100644 --- a/lapack-netlib/SRC/dpptrf.f +++ b/lapack-netlib/SRC/dpptrf.f @@ -79,8 +79,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/dpteqr.f b/lapack-netlib/SRC/dpteqr.f index aa1f1a80c..d07b065b0 100644 --- a/lapack-netlib/SRC/dpteqr.f +++ b/lapack-netlib/SRC/dpteqr.f @@ -123,8 +123,8 @@ *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if INFO = i, and i is: *> <= N the Cholesky factorization of the matrix could -*> not be performed because the i-th principal minor -*> was not positive definite. +*> not be performed because the leading principal +*> minor of order i was not positive. *> > N the SVD algorithm failed to converge; *> if INFO = N+i, i off-diagonal elements of the *> bidiagonal factor did not converge to zero. diff --git a/lapack-netlib/SRC/dptsv.f b/lapack-netlib/SRC/dptsv.f index addc34b88..41d8cff15 100644 --- a/lapack-netlib/SRC/dptsv.f +++ b/lapack-netlib/SRC/dptsv.f @@ -93,8 +93,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the solution has not been +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the solution has not been *> computed. The factorization has not been completed *> unless i = N. *> \endverbatim diff --git a/lapack-netlib/SRC/dptsvx.f b/lapack-netlib/SRC/dptsvx.f index 7fb6cf436..fcbf5aa3b 100644 --- a/lapack-netlib/SRC/dptsvx.f +++ b/lapack-netlib/SRC/dptsvx.f @@ -59,7 +59,7 @@ *> factorization can also be regarded as having the form *> A = U**T*D*U. *> -*> 2. If the leading i-by-i principal minor is not positive definite, +*> 2. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -199,10 +199,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/dpttrf.f b/lapack-netlib/SRC/dpttrf.f index e0022e3ad..156e845a3 100644 --- a/lapack-netlib/SRC/dpttrf.f +++ b/lapack-netlib/SRC/dpttrf.f @@ -70,8 +70,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value -*> > 0: if INFO = k, the leading minor of order k is not -*> positive definite; if k < N, the factorization could not +*> > 0: if INFO = k, the leading principal minor of order k +*> is not positive; if k < N, the factorization could not *> be completed, while if k = N, the factorization was *> completed, but D(N) <= 0. *> \endverbatim diff --git a/lapack-netlib/SRC/dsbgvx.f b/lapack-netlib/SRC/dsbgvx.f index 20de17931..53deae580 100644 --- a/lapack-netlib/SRC/dsbgvx.f +++ b/lapack-netlib/SRC/dsbgvx.f @@ -267,7 +267,7 @@ *> Their indices are stored in IFAIL. *> > N: DPBSTF returned an error code; i.e., *> if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/dspgv.f b/lapack-netlib/SRC/dspgv.f index d8ec3b1a4..96041c301 100644 --- a/lapack-netlib/SRC/dspgv.f +++ b/lapack-netlib/SRC/dspgv.f @@ -139,7 +139,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not converge to zero. *> > N: if INFO = n + i, for 1 <= i <= n, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/dspgvd.f b/lapack-netlib/SRC/dspgvd.f index df215ae1a..ec3cdc1ac 100644 --- a/lapack-netlib/SRC/dspgvd.f +++ b/lapack-netlib/SRC/dspgvd.f @@ -184,7 +184,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not converge to zero; *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/dspgvx.f b/lapack-netlib/SRC/dspgvx.f index ec93147aa..5afd73d02 100644 --- a/lapack-netlib/SRC/dspgvx.f +++ b/lapack-netlib/SRC/dspgvx.f @@ -245,7 +245,7 @@ *> i eigenvectors failed to converge. Their indices *> are stored in array IFAIL. *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/dsposv.f b/lapack-netlib/SRC/dsposv.f index c3b8de0e3..0bd75698d 100644 --- a/lapack-netlib/SRC/dsposv.f +++ b/lapack-netlib/SRC/dsposv.f @@ -177,8 +177,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i of (DOUBLE -*> PRECISION) A is not positive definite, so the +*> > 0: if INFO = i, the leading principal minor of order i +*> of (DOUBLE PRECISION) A is not positive, so the *> factorization could not be completed, and the solution *> has not been computed. *> \endverbatim diff --git a/lapack-netlib/SRC/dsygv.f b/lapack-netlib/SRC/dsygv.f index 5208dbb1f..02a4cc3ed 100644 --- a/lapack-netlib/SRC/dsygv.f +++ b/lapack-netlib/SRC/dsygv.f @@ -154,7 +154,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not converge to zero; *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/dsygv_2stage.f b/lapack-netlib/SRC/dsygv_2stage.f index 5c71ebf94..383304267 100644 --- a/lapack-netlib/SRC/dsygv_2stage.f +++ b/lapack-netlib/SRC/dsygv_2stage.f @@ -173,7 +173,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not converge to zero; *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/dsygvd.f b/lapack-netlib/SRC/dsygvd.f index 3b38665a7..d6682d4e5 100644 --- a/lapack-netlib/SRC/dsygvd.f +++ b/lapack-netlib/SRC/dsygvd.f @@ -190,7 +190,7 @@ *> the submatrix lying in rows and columns INFO/(N+1) *> through mod(INFO,N+1); *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/dsygvx.f b/lapack-netlib/SRC/dsygvx.f index 3fa55b97c..2dc27e8a8 100644 --- a/lapack-netlib/SRC/dsygvx.f +++ b/lapack-netlib/SRC/dsygvx.f @@ -270,7 +270,7 @@ *> i eigenvectors failed to converge. Their indices *> are stored in array IFAIL. *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim From 7b73666d709c7f77379a35d318fdc34bd3818efe Mon Sep 17 00:00:00 2001 From: Martin Kroeker Date: Thu, 22 Jun 2023 16:25:24 +0200 Subject: [PATCH 6/6] Fix confusing use of "minor" in inline documentation (Reference-LAPACK PR849) --- lapack-netlib/SRC/chegv.f | 2 +- lapack-netlib/SRC/chegv_2stage.f | 2 +- lapack-netlib/SRC/chegvd.f | 2 +- lapack-netlib/SRC/chegvx.f | 2 +- lapack-netlib/SRC/chpgv.f | 2 +- lapack-netlib/SRC/chpgvd.f | 2 +- lapack-netlib/SRC/chpgvx.f | 2 +- lapack-netlib/SRC/cla_porpvgrw.f | 6 +++--- lapack-netlib/SRC/cpbsv.f | 6 +++--- lapack-netlib/SRC/cpbsvx.f | 10 +++++----- lapack-netlib/SRC/cpbtf2.f | 4 ++-- lapack-netlib/SRC/cpbtrf.f | 4 ++-- lapack-netlib/SRC/cpftrf.f | 4 ++-- lapack-netlib/SRC/cposv.f | 6 +++--- lapack-netlib/SRC/cposvx.f | 10 +++++----- lapack-netlib/SRC/cposvxx.f | 2 +- lapack-netlib/SRC/cpotf2.f | 4 ++-- lapack-netlib/SRC/cpotrf.f | 4 ++-- lapack-netlib/SRC/cpotrf2.f | 4 ++-- lapack-netlib/SRC/cppsv.f | 6 +++--- lapack-netlib/SRC/cppsvx.f | 10 +++++----- lapack-netlib/SRC/cpptrf.f | 6 +++--- lapack-netlib/SRC/cpteqr.f | 4 ++-- lapack-netlib/SRC/cptsv.f | 4 ++-- lapack-netlib/SRC/cptsvx.f | 10 +++++----- lapack-netlib/SRC/cpttrf.f | 4 ++-- 26 files changed, 61 insertions(+), 61 deletions(-) diff --git a/lapack-netlib/SRC/chegv.f b/lapack-netlib/SRC/chegv.f index f7675a19f..198e5d102 100644 --- a/lapack-netlib/SRC/chegv.f +++ b/lapack-netlib/SRC/chegv.f @@ -160,7 +160,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not converge to zero; *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/chegv_2stage.f b/lapack-netlib/SRC/chegv_2stage.f index 472581c4b..d2b8fc795 100644 --- a/lapack-netlib/SRC/chegv_2stage.f +++ b/lapack-netlib/SRC/chegv_2stage.f @@ -179,7 +179,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not converge to zero; *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/chegvd.f b/lapack-netlib/SRC/chegvd.f index 4b7f43d52..c96f011af 100644 --- a/lapack-netlib/SRC/chegvd.f +++ b/lapack-netlib/SRC/chegvd.f @@ -212,7 +212,7 @@ *> the submatrix lying in rows and columns INFO/(N+1) *> through mod(INFO,N+1); *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/chegvx.f b/lapack-netlib/SRC/chegvx.f index 6e428242d..8e565222d 100644 --- a/lapack-netlib/SRC/chegvx.f +++ b/lapack-netlib/SRC/chegvx.f @@ -280,7 +280,7 @@ *> i eigenvectors failed to converge. Their indices *> are stored in array IFAIL. *> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/chpgv.f b/lapack-netlib/SRC/chpgv.f index 417f10121..660724e05 100644 --- a/lapack-netlib/SRC/chpgv.f +++ b/lapack-netlib/SRC/chpgv.f @@ -144,7 +144,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not convergeto zero; *> > N: if INFO = N + i, for 1 <= i <= n, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/chpgvd.f b/lapack-netlib/SRC/chpgvd.f index 65d08b783..5c9e417d3 100644 --- a/lapack-netlib/SRC/chpgvd.f +++ b/lapack-netlib/SRC/chpgvd.f @@ -205,7 +205,7 @@ *> i off-diagonal elements of an intermediate *> tridiagonal form did not convergeto zero; *> > N: if INFO = N + i, for 1 <= i <= n, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/chpgvx.f b/lapack-netlib/SRC/chpgvx.f index 711daf55f..2646800cc 100644 --- a/lapack-netlib/SRC/chpgvx.f +++ b/lapack-netlib/SRC/chpgvx.f @@ -250,7 +250,7 @@ *> i eigenvectors failed to converge. Their indices *> are stored in array IFAIL. *> > N: if INFO = N + i, for 1 <= i <= n, then the leading -*> minor of order i of B is not positive definite. +*> principal minor of order i of B is not positive. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim diff --git a/lapack-netlib/SRC/cla_porpvgrw.f b/lapack-netlib/SRC/cla_porpvgrw.f index 1eb706d1a..78cd19da9 100644 --- a/lapack-netlib/SRC/cla_porpvgrw.f +++ b/lapack-netlib/SRC/cla_porpvgrw.f @@ -140,9 +140,9 @@ * .. Executable Statements .. UPPER = LSAME( 'Upper', UPLO ) * -* SPOTRF will have factored only the NCOLSxNCOLS leading minor, so -* we restrict the growth search to that minor and use only the first -* 2*NCOLS workspace entries. +* SPOTRF will have factored only the NCOLSxNCOLS leading submatrix, +* so we restrict the growth search to that submatrix and use only +* the first 2*NCOLS workspace entries. * RPVGRW = 1.0 DO I = 1, 2*NCOLS diff --git a/lapack-netlib/SRC/cpbsv.f b/lapack-netlib/SRC/cpbsv.f index 248abbc1f..889bbde08 100644 --- a/lapack-netlib/SRC/cpbsv.f +++ b/lapack-netlib/SRC/cpbsv.f @@ -119,9 +119,9 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i of A is not -*> positive definite, so the factorization could not be -*> completed, and the solution has not been computed. +*> > 0: if INFO = i, the leading principal minor of order i +*> of A is not positive, so the factorization could not +*> be completed, and the solution has not been computed. *> \endverbatim * * Authors: diff --git a/lapack-netlib/SRC/cpbsvx.f b/lapack-netlib/SRC/cpbsvx.f index 652e18501..975c87768 100644 --- a/lapack-netlib/SRC/cpbsvx.f +++ b/lapack-netlib/SRC/cpbsvx.f @@ -70,7 +70,7 @@ *> where U is an upper triangular band matrix, and L is a lower *> triangular band matrix. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -280,10 +280,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/cpbtf2.f b/lapack-netlib/SRC/cpbtf2.f index 0be2c0a7f..f5bc9b3a6 100644 --- a/lapack-netlib/SRC/cpbtf2.f +++ b/lapack-netlib/SRC/cpbtf2.f @@ -97,8 +97,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value -*> > 0: if INFO = k, the leading minor of order k is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = k, the leading principal minor of order k +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/cpbtrf.f b/lapack-netlib/SRC/cpbtrf.f index a4c18efb3..af60780c8 100644 --- a/lapack-netlib/SRC/cpbtrf.f +++ b/lapack-netlib/SRC/cpbtrf.f @@ -92,8 +92,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/cpftrf.f b/lapack-netlib/SRC/cpftrf.f index cbaab6832..12799c6f7 100644 --- a/lapack-netlib/SRC/cpftrf.f +++ b/lapack-netlib/SRC/cpftrf.f @@ -91,8 +91,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> *> Further Notes on RFP Format: diff --git a/lapack-netlib/SRC/cposv.f b/lapack-netlib/SRC/cposv.f index f37dfa3c0..ea6fc37db 100644 --- a/lapack-netlib/SRC/cposv.f +++ b/lapack-netlib/SRC/cposv.f @@ -110,9 +110,9 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i of A is not -*> positive definite, so the factorization could not be -*> completed, and the solution has not been computed. +*> > 0: if INFO = i, the leading principal minor of order i +*> of A is not positive, so the factorization could not +*> be completed, and the solution has not been computed. *> \endverbatim * * Authors: diff --git a/lapack-netlib/SRC/cposvx.f b/lapack-netlib/SRC/cposvx.f index 78b9f4db1..322a26447 100644 --- a/lapack-netlib/SRC/cposvx.f +++ b/lapack-netlib/SRC/cposvx.f @@ -70,7 +70,7 @@ *> where U is an upper triangular matrix and L is a lower triangular *> matrix. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -276,10 +276,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/cposvxx.f b/lapack-netlib/SRC/cposvxx.f index 7834c75da..c40a2d856 100644 --- a/lapack-netlib/SRC/cposvxx.f +++ b/lapack-netlib/SRC/cposvxx.f @@ -87,7 +87,7 @@ *> where U is an upper triangular matrix and L is a lower triangular *> matrix. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A (see argument RCOND). If the reciprocal of the condition number diff --git a/lapack-netlib/SRC/cpotf2.f b/lapack-netlib/SRC/cpotf2.f index 2f4658bae..d84988949 100644 --- a/lapack-netlib/SRC/cpotf2.f +++ b/lapack-netlib/SRC/cpotf2.f @@ -89,8 +89,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value -*> > 0: if INFO = k, the leading minor of order k is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = k, the leading principal minor of order k +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/cpotrf.f b/lapack-netlib/SRC/cpotrf.f index 6aba3103e..e2b120a49 100644 --- a/lapack-netlib/SRC/cpotrf.f +++ b/lapack-netlib/SRC/cpotrf.f @@ -87,8 +87,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/cpotrf2.f b/lapack-netlib/SRC/cpotrf2.f index e1eae3e9d..ea2e4ca98 100644 --- a/lapack-netlib/SRC/cpotrf2.f +++ b/lapack-netlib/SRC/cpotrf2.f @@ -86,8 +86,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the factorization could not be *> completed. *> \endverbatim * diff --git a/lapack-netlib/SRC/cppsv.f b/lapack-netlib/SRC/cppsv.f index 1e6f02695..a8fd660c4 100644 --- a/lapack-netlib/SRC/cppsv.f +++ b/lapack-netlib/SRC/cppsv.f @@ -104,9 +104,9 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i of A is not -*> positive definite, so the factorization could not be -*> completed, and the solution has not been computed. +*> > 0: if INFO = i, the leading principal minor of order i +*> of A is not positive, so the factorization could not +*> be completed, and the solution has not been computed. *> \endverbatim * * Authors: diff --git a/lapack-netlib/SRC/cppsvx.f b/lapack-netlib/SRC/cppsvx.f index f6f07538c..2ef02100f 100644 --- a/lapack-netlib/SRC/cppsvx.f +++ b/lapack-netlib/SRC/cppsvx.f @@ -69,7 +69,7 @@ *> where U is an upper triangular matrix, L is a lower triangular *> matrix, and **H indicates conjugate transpose. *> -*> 3. If the leading i-by-i principal minor is not positive definite, +*> 3. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -262,10 +262,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/cpptrf.f b/lapack-netlib/SRC/cpptrf.f index 4e81458cb..e36f834cb 100644 --- a/lapack-netlib/SRC/cpptrf.f +++ b/lapack-netlib/SRC/cpptrf.f @@ -79,9 +79,9 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be -*> completed. +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive definite, and the factorization could +*> not be completed. *> \endverbatim * * Authors: diff --git a/lapack-netlib/SRC/cpteqr.f b/lapack-netlib/SRC/cpteqr.f index e3af59041..fc9c44908 100644 --- a/lapack-netlib/SRC/cpteqr.f +++ b/lapack-netlib/SRC/cpteqr.f @@ -123,8 +123,8 @@ *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if INFO = i, and i is: *> <= N the Cholesky factorization of the matrix could -*> not be performed because the i-th principal minor -*> was not positive definite. +*> not be performed because the leading principal +*> minor of order i was not positive. *> > N the SVD algorithm failed to converge; *> if INFO = N+i, i off-diagonal elements of the *> bidiagonal factor did not converge to zero. diff --git a/lapack-netlib/SRC/cptsv.f b/lapack-netlib/SRC/cptsv.f index 20ee32bbe..4c16f6a0a 100644 --- a/lapack-netlib/SRC/cptsv.f +++ b/lapack-netlib/SRC/cptsv.f @@ -94,8 +94,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the solution has not been +*> > 0: if INFO = i, the leading principal minor of order i +*> is not positive, and the solution has not been *> computed. The factorization has not been completed *> unless i = N. *> \endverbatim diff --git a/lapack-netlib/SRC/cptsvx.f b/lapack-netlib/SRC/cptsvx.f index db63a3c36..6f7d8cf5b 100644 --- a/lapack-netlib/SRC/cptsvx.f +++ b/lapack-netlib/SRC/cptsvx.f @@ -60,7 +60,7 @@ *> factorization can also be regarded as having the form *> A = U**H*D*U. *> -*> 2. If the leading i-by-i principal minor is not positive definite, +*> 2. If the leading principal minor of order i is not positive, *> then the routine returns with INFO = i. Otherwise, the factored *> form of A is used to estimate the condition number of the matrix *> A. If the reciprocal of the condition number is less than machine @@ -205,10 +205,10 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, and i is -*> <= N: the leading minor of order i of A is -*> not positive definite, so the factorization -*> could not be completed, and the solution has not -*> been computed. RCOND = 0 is returned. +*> <= N: the leading principal minor of order i of A +*> is not positive, so the factorization could not +*> be completed, and the solution has not been +*> computed. RCOND = 0 is returned. *> = N+1: U is nonsingular, but RCOND is less than machine *> precision, meaning that the matrix is singular *> to working precision. Nevertheless, the diff --git a/lapack-netlib/SRC/cpttrf.f b/lapack-netlib/SRC/cpttrf.f index c6379e923..111343b78 100644 --- a/lapack-netlib/SRC/cpttrf.f +++ b/lapack-netlib/SRC/cpttrf.f @@ -71,8 +71,8 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value -*> > 0: if INFO = k, the leading minor of order k is not -*> positive definite; if k < N, the factorization could not +*> > 0: if INFO = k, the leading principal minor of order k +*> is not positive; if k < N, the factorization could not *> be completed, while if k = N, the factorization was *> completed, but D(N) <= 0. *> \endverbatim