Decomposition Operations<TReal, TComplex>.Band Cholesky Estimate Condition Method
Definition
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3
Overload List
Band | Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = UT*U or A = L*LT computed by DPBTRF. |
Band | Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = UH*U or A = L*LH computed by ZPBTRF. |
Band | Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = UH*U or A = L*LH computed by ZPBTRF. |
Band | Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = UT*U or A = L*LT computed by DPBTRF. |
Band | Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = UH*U or A = L*LH computed by ZPBTRF. |
Band | Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = UT*U or A = L*LT computed by DPBTRF. |
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Array2D<TReal>, TReal, TReal, Int32)
Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = UT*U or A = L*LT computed by DPBTRF.
public void BandCholeskyEstimateCondition(
MatrixTriangle storedTriangle,
int n,
int kd,
Array2D<TReal> ab,
TReal aNorm,
out TReal rcond,
out int info
)
Parameters
- storedTriangle MatrixTriangle
= 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB.
- n Int32
The order of the matrix A. N >= 0.
- kd Int32
The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
- ab Array2D<TReal>
AB is TReal array, dimension (LDAB,N) The triangular factor U or L from the Cholesky factorization A = UT*U or A = L*LT of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
The leading dimension of the array AB. LDAB >= KD+1.
- aNorm TReal
ANORM is TReal The 1-norm (or infinity-norm) of the symmetric band matrix A.
- rcond TReal
RCOND is TReal The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.
- info Int32
= 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Remarks
An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
This method corresponds to the LAPACK routine DPBCON.
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Array2D<TComplex>, TReal, TReal, Int32)
Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = UH*U or A = L*LH computed by ZPBTRF.
public void BandCholeskyEstimateCondition(
MatrixTriangle uplo,
int n,
int kd,
Array2D<TComplex> ab,
TReal anorm,
out TReal rcond,
out int info
)
Parameters
- uplo MatrixTriangle
= 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB.
- n Int32
The order of the matrix A. N >= 0.
- kd Int32
The number of superdiagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
- ab Array2D<TComplex>
AB is TComplex array, dimension (LDAB,N) The triangular factor U or L from the Cholesky factorization A = UH*U or A = L*LH of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
The leading dimension of the array AB. LDAB >= KD+1.
- anorm TReal
ANORM is TReal The 1-norm (or infinity-norm) of the Hermitian band matrix A.
- rcond TReal
RCOND is TReal The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.
- info Int32
= 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Remarks
An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, ReadOnlySpan2D<TComplex>, TReal, TReal, Int32)
Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = UH*U or A = L*LH computed by ZPBTRF.
public void BandCholeskyEstimateCondition(
MatrixTriangle uplo,
int n,
int kd,
ReadOnlySpan2D<TComplex> ab,
TReal anorm,
out TReal rcond,
out int info
)
Parameters
- uplo MatrixTriangle
= 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB.
- n Int32
The order of the matrix A. N >= 0.
- kd Int32
The number of superdiagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
- ab ReadOnlySpan2D<TComplex>
AB is TComplex array, dimension (LDAB,N) The triangular factor U or L from the Cholesky factorization A = UH*U or A = L*LH of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
The leading dimension of the array AB. LDAB >= KD+1.
- anorm TReal
ANORM is TReal The 1-norm (or infinity-norm) of the Hermitian band matrix A.
- rcond TReal
RCOND is TReal The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.
- info Int32
= 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Remarks
An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Span2D<TReal>, TReal, TReal, Int32)
Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = UT*U or A = L*LT computed by DPBTRF.
public void BandCholeskyEstimateCondition(
MatrixTriangle storedTriangle,
int n,
int kd,
Span2D<TReal> ab,
TReal aNorm,
out TReal rcond,
out int info
)
Parameters
- storedTriangle MatrixTriangle
= 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB.
- n Int32
The order of the matrix A. N >= 0.
- kd Int32
The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
- ab Span2D<TReal>
AB is TReal array, dimension (LDAB,N) The triangular factor U or L from the Cholesky factorization A = UT*U or A = L*LT of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
The leading dimension of the array AB. LDAB >= KD+1.
- aNorm TReal
ANORM is TReal The 1-norm (or infinity-norm) of the symmetric band matrix A.
- rcond TReal
RCOND is TReal The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.
- info Int32
= 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Remarks
An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
This method corresponds to the LAPACK routine DPBCON.
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, ReadOnlySpan<TComplex>, Int32, TReal, TReal, Int32)
Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = UH*U or A = L*LH computed by ZPBTRF.
public abstract void BandCholeskyEstimateCondition(
MatrixTriangle uplo,
int n,
int kd,
ReadOnlySpan<TComplex> ab,
int ldab,
TReal anorm,
out TReal rcond,
out int info
)
Parameters
- uplo MatrixTriangle
= 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB.
- n Int32
The order of the matrix A. N >= 0.
- kd Int32
The number of superdiagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
- ab ReadOnlySpan<TComplex>
AB is TComplex array, dimension (LDAB,N) The triangular factor U or L from the Cholesky factorization A = UH*U or A = L*LH of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
- ldab Int32
The leading dimension of the array AB. LDAB >= KD+1.
- anorm TReal
ANORM is TReal The 1-norm (or infinity-norm) of the Hermitian band matrix A.
- rcond TReal
RCOND is TReal The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.
- info Int32
= 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Remarks
An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Span<TReal>, Int32, TReal, TReal, Int32)
Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = UT*U or A = L*LT computed by DPBTRF.
public abstract void BandCholeskyEstimateCondition(
MatrixTriangle storedTriangle,
int n,
int kd,
Span<TReal> ab,
int ldab,
TReal aNorm,
out TReal rcond,
out int info
)
Parameters
- storedTriangle MatrixTriangle
= 'U': Upper triangular factor stored in AB; = 'L': Lower triangular factor stored in AB.
- n Int32
The order of the matrix A. N >= 0.
- kd Int32
The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
- ab Span<TReal>
AB is TReal array, dimension (LDAB,N) The triangular factor U or L from the Cholesky factorization A = UT*U or A = L*LT of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
- ldab Int32
The leading dimension of the array AB. LDAB >= KD+1.
- aNorm TReal
ANORM is TReal The 1-norm (or infinity-norm) of the symmetric band matrix A.
- rcond TReal
RCOND is TReal The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.
- info Int32
= 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Remarks
An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
This method corresponds to the LAPACK routine DPBCON.