| @@ -160,7 +160,7 @@ | |||||
| *> i off-diagonal elements of an intermediate | *> i off-diagonal elements of an intermediate | ||||
| *> tridiagonal form did not converge to zero; | *> tridiagonal form did not converge to zero; | ||||
| *> > N: if INFO = N + i, for 1 <= i <= N, then the leading | *> > 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 | *> The factorization of B could not be completed and | ||||
| *> no eigenvalues or eigenvectors were computed. | *> no eigenvalues or eigenvectors were computed. | ||||
| *> \endverbatim | *> \endverbatim | ||||
| @@ -179,7 +179,7 @@ | |||||
| *> i off-diagonal elements of an intermediate | *> i off-diagonal elements of an intermediate | ||||
| *> tridiagonal form did not converge to zero; | *> tridiagonal form did not converge to zero; | ||||
| *> > N: if INFO = N + i, for 1 <= i <= N, then the leading | *> > 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 | *> The factorization of B could not be completed and | ||||
| *> no eigenvalues or eigenvectors were computed. | *> no eigenvalues or eigenvectors were computed. | ||||
| *> \endverbatim | *> \endverbatim | ||||
| @@ -212,7 +212,7 @@ | |||||
| *> the submatrix lying in rows and columns INFO/(N+1) | *> the submatrix lying in rows and columns INFO/(N+1) | ||||
| *> through mod(INFO,N+1); | *> through mod(INFO,N+1); | ||||
| *> > N: if INFO = N + i, for 1 <= i <= N, then the leading | *> > 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 | *> The factorization of B could not be completed and | ||||
| *> no eigenvalues or eigenvectors were computed. | *> no eigenvalues or eigenvectors were computed. | ||||
| *> \endverbatim | *> \endverbatim | ||||
| @@ -280,7 +280,7 @@ | |||||
| *> i eigenvectors failed to converge. Their indices | *> i eigenvectors failed to converge. Their indices | ||||
| *> are stored in array IFAIL. | *> are stored in array IFAIL. | ||||
| *> > N: if INFO = N + i, for 1 <= i <= N, then the leading | *> > 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 | *> The factorization of B could not be completed and | ||||
| *> no eigenvalues or eigenvectors were computed. | *> no eigenvalues or eigenvectors were computed. | ||||
| *> \endverbatim | *> \endverbatim | ||||
| @@ -144,7 +144,7 @@ | |||||
| *> i off-diagonal elements of an intermediate | *> i off-diagonal elements of an intermediate | ||||
| *> tridiagonal form did not convergeto zero; | *> tridiagonal form did not convergeto zero; | ||||
| *> > N: if INFO = N + i, for 1 <= i <= n, then the leading | *> > 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 | *> The factorization of B could not be completed and | ||||
| *> no eigenvalues or eigenvectors were computed. | *> no eigenvalues or eigenvectors were computed. | ||||
| *> \endverbatim | *> \endverbatim | ||||
| @@ -205,7 +205,7 @@ | |||||
| *> i off-diagonal elements of an intermediate | *> i off-diagonal elements of an intermediate | ||||
| *> tridiagonal form did not convergeto zero; | *> tridiagonal form did not convergeto zero; | ||||
| *> > N: if INFO = N + i, for 1 <= i <= n, then the leading | *> > 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 | *> The factorization of B could not be completed and | ||||
| *> no eigenvalues or eigenvectors were computed. | *> no eigenvalues or eigenvectors were computed. | ||||
| *> \endverbatim | *> \endverbatim | ||||
| @@ -250,7 +250,7 @@ | |||||
| *> i eigenvectors failed to converge. Their indices | *> i eigenvectors failed to converge. Their indices | ||||
| *> are stored in array IFAIL. | *> are stored in array IFAIL. | ||||
| *> > N: if INFO = N + i, for 1 <= i <= n, then the leading | *> > 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 | *> The factorization of B could not be completed and | ||||
| *> no eigenvalues or eigenvectors were computed. | *> no eigenvalues or eigenvectors were computed. | ||||
| *> \endverbatim | *> \endverbatim | ||||
| @@ -140,9 +140,9 @@ | |||||
| * .. Executable Statements .. | * .. Executable Statements .. | ||||
| UPPER = LSAME( 'Upper', UPLO ) | 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 | RPVGRW = 1.0 | ||||
| DO I = 1, 2*NCOLS | DO I = 1, 2*NCOLS | ||||
| @@ -119,9 +119,9 @@ | |||||
| *> INFO is INTEGER | *> INFO is INTEGER | ||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -i, the i-th argument had an illegal value | *> < 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 | *> \endverbatim | ||||
| * | * | ||||
| * Authors: | * Authors: | ||||
| @@ -70,7 +70,7 @@ | |||||
| *> where U is an upper triangular band matrix, and L is a lower | *> where U is an upper triangular band matrix, and L is a lower | ||||
| *> triangular band matrix. | *> 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 | *> then the routine returns with INFO = i. Otherwise, the factored | ||||
| *> form of A is used to estimate the condition number of the matrix | *> 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 | *> A. If the reciprocal of the condition number is less than machine | ||||
| @@ -280,10 +280,10 @@ | |||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -i, the i-th argument had an illegal value | *> < 0: if INFO = -i, the i-th argument had an illegal value | ||||
| *> > 0: if INFO = i, and i is | *> > 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 | *> = N+1: U is nonsingular, but RCOND is less than machine | ||||
| *> precision, meaning that the matrix is singular | *> precision, meaning that the matrix is singular | ||||
| *> to working precision. Nevertheless, the | *> to working precision. Nevertheless, the | ||||
| @@ -97,8 +97,8 @@ | |||||
| *> INFO is INTEGER | *> INFO is INTEGER | ||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -k, the k-th argument had an illegal value | *> < 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. | *> completed. | ||||
| *> \endverbatim | *> \endverbatim | ||||
| * | * | ||||
| @@ -92,8 +92,8 @@ | |||||
| *> INFO is INTEGER | *> INFO is INTEGER | ||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -i, the i-th argument had an illegal value | *> < 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. | *> completed. | ||||
| *> \endverbatim | *> \endverbatim | ||||
| * | * | ||||
| @@ -91,8 +91,8 @@ | |||||
| *> INFO is INTEGER | *> INFO is INTEGER | ||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -i, the i-th argument had an illegal value | *> < 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. | *> completed. | ||||
| *> | *> | ||||
| *> Further Notes on RFP Format: | *> Further Notes on RFP Format: | ||||
| @@ -110,9 +110,9 @@ | |||||
| *> INFO is INTEGER | *> INFO is INTEGER | ||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -i, the i-th argument had an illegal value | *> < 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 | *> \endverbatim | ||||
| * | * | ||||
| * Authors: | * Authors: | ||||
| @@ -70,7 +70,7 @@ | |||||
| *> where U is an upper triangular matrix and L is a lower triangular | *> where U is an upper triangular matrix and L is a lower triangular | ||||
| *> matrix. | *> 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 | *> then the routine returns with INFO = i. Otherwise, the factored | ||||
| *> form of A is used to estimate the condition number of the matrix | *> 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 | *> A. If the reciprocal of the condition number is less than machine | ||||
| @@ -276,10 +276,10 @@ | |||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -i, the i-th argument had an illegal value | *> < 0: if INFO = -i, the i-th argument had an illegal value | ||||
| *> > 0: if INFO = i, and i is | *> > 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 | *> = N+1: U is nonsingular, but RCOND is less than machine | ||||
| *> precision, meaning that the matrix is singular | *> precision, meaning that the matrix is singular | ||||
| *> to working precision. Nevertheless, the | *> to working precision. Nevertheless, the | ||||
| @@ -87,7 +87,7 @@ | |||||
| *> where U is an upper triangular matrix and L is a lower triangular | *> where U is an upper triangular matrix and L is a lower triangular | ||||
| *> matrix. | *> 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 | *> then the routine returns with INFO = i. Otherwise, the factored | ||||
| *> form of A is used to estimate the condition number of the matrix | *> form of A is used to estimate the condition number of the matrix | ||||
| *> A (see argument RCOND). If the reciprocal of the condition number | *> A (see argument RCOND). If the reciprocal of the condition number | ||||
| @@ -89,8 +89,8 @@ | |||||
| *> INFO is INTEGER | *> INFO is INTEGER | ||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -k, the k-th argument had an illegal value | *> < 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. | *> completed. | ||||
| *> \endverbatim | *> \endverbatim | ||||
| * | * | ||||
| @@ -87,8 +87,8 @@ | |||||
| *> INFO is INTEGER | *> INFO is INTEGER | ||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -i, the i-th argument had an illegal value | *> < 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. | *> completed. | ||||
| *> \endverbatim | *> \endverbatim | ||||
| * | * | ||||
| @@ -86,8 +86,8 @@ | |||||
| *> INFO is INTEGER | *> INFO is INTEGER | ||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -i, the i-th argument had an illegal value | *> < 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. | *> completed. | ||||
| *> \endverbatim | *> \endverbatim | ||||
| * | * | ||||
| @@ -104,9 +104,9 @@ | |||||
| *> INFO is INTEGER | *> INFO is INTEGER | ||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -i, the i-th argument had an illegal value | *> < 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 | *> \endverbatim | ||||
| * | * | ||||
| * Authors: | * Authors: | ||||
| @@ -69,7 +69,7 @@ | |||||
| *> where U is an upper triangular matrix, L is a lower triangular | *> where U is an upper triangular matrix, L is a lower triangular | ||||
| *> matrix, and **H indicates conjugate transpose. | *> 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 | *> then the routine returns with INFO = i. Otherwise, the factored | ||||
| *> form of A is used to estimate the condition number of the matrix | *> 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 | *> A. If the reciprocal of the condition number is less than machine | ||||
| @@ -262,10 +262,10 @@ | |||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -i, the i-th argument had an illegal value | *> < 0: if INFO = -i, the i-th argument had an illegal value | ||||
| *> > 0: if INFO = i, and i is | *> > 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 | *> = N+1: U is nonsingular, but RCOND is less than machine | ||||
| *> precision, meaning that the matrix is singular | *> precision, meaning that the matrix is singular | ||||
| *> to working precision. Nevertheless, the | *> to working precision. Nevertheless, the | ||||
| @@ -79,9 +79,9 @@ | |||||
| *> INFO is INTEGER | *> INFO is INTEGER | ||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -i, the i-th argument had an illegal value | *> < 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 | *> \endverbatim | ||||
| * | * | ||||
| * Authors: | * Authors: | ||||
| @@ -123,8 +123,8 @@ | |||||
| *> < 0: if INFO = -i, the i-th argument had an illegal value. | *> < 0: if INFO = -i, the i-th argument had an illegal value. | ||||
| *> > 0: if INFO = i, and i is: | *> > 0: if INFO = i, and i is: | ||||
| *> <= N the Cholesky factorization of the matrix could | *> <= 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; | *> > N the SVD algorithm failed to converge; | ||||
| *> if INFO = N+i, i off-diagonal elements of the | *> if INFO = N+i, i off-diagonal elements of the | ||||
| *> bidiagonal factor did not converge to zero. | *> bidiagonal factor did not converge to zero. | ||||
| @@ -94,8 +94,8 @@ | |||||
| *> INFO is INTEGER | *> INFO is INTEGER | ||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -i, the i-th argument had an illegal value | *> < 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 | *> computed. The factorization has not been completed | ||||
| *> unless i = N. | *> unless i = N. | ||||
| *> \endverbatim | *> \endverbatim | ||||
| @@ -60,7 +60,7 @@ | |||||
| *> factorization can also be regarded as having the form | *> factorization can also be regarded as having the form | ||||
| *> A = U**H*D*U. | *> 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 | *> then the routine returns with INFO = i. Otherwise, the factored | ||||
| *> form of A is used to estimate the condition number of the matrix | *> 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 | *> A. If the reciprocal of the condition number is less than machine | ||||
| @@ -205,10 +205,10 @@ | |||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -i, the i-th argument had an illegal value | *> < 0: if INFO = -i, the i-th argument had an illegal value | ||||
| *> > 0: if INFO = i, and i is | *> > 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 | *> = N+1: U is nonsingular, but RCOND is less than machine | ||||
| *> precision, meaning that the matrix is singular | *> precision, meaning that the matrix is singular | ||||
| *> to working precision. Nevertheless, the | *> to working precision. Nevertheless, the | ||||
| @@ -71,8 +71,8 @@ | |||||
| *> INFO is INTEGER | *> INFO is INTEGER | ||||
| *> = 0: successful exit | *> = 0: successful exit | ||||
| *> < 0: if INFO = -k, the k-th argument had an illegal value | *> < 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 | *> be completed, while if k = N, the factorization was | ||||
| *> completed, but D(N) <= 0. | *> completed, but D(N) <= 0. | ||||
| *> \endverbatim | *> \endverbatim | ||||