Hermitian indefinite components: Bunch-Kaufman factorization, solve, inverse. More...

Functions/Subroutines
pure subroutine, public	la_cheswapr (uplo, n, a, lda, i1, i2)
	CHESWAPR: applies an elementary permutation on the rows and the columns of a hermitian matrix.

pure subroutine, public	la_zheswapr (uplo, n, a, lda, i1, i2)
	ZHESWAPR: applies an elementary permutation on the rows and the columns of a hermitian matrix.

pure subroutine, public	la_wheswapr (uplo, n, a, lda, i1, i2)
	WHESWAPR: applies an elementary permutation on the rows and the columns of a hermitian matrix.

pure subroutine, public	la_chetf2 (uplo, n, a, lda, ipiv, info)
	CHETF2: computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method: A = UDU*H or A = LDLH where U (or L) is a product of permutation and unit upper (lower) triangular matrices, U*H is the conjugate transpose of U, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. This is the unblocked version of the algorithm, calling Level 2 BLAS.

pure subroutine, public	la_zhetf2 (uplo, n, a, lda, ipiv, info)
	ZHETF2: computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method: A = UDU*H or A = LDLH where U (or L) is a product of permutation and unit upper (lower) triangular matrices, U*H is the conjugate transpose of U, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. This is the unblocked version of the algorithm, calling Level 2 BLAS.

pure subroutine, public	la_whetf2 (uplo, n, a, lda, ipiv, info)
	WHETF2: computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method: A = UDU*H or A = LDLH where U (or L) is a product of permutation and unit upper (lower) triangular matrices, U*H is the conjugate transpose of U, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. This is the unblocked version of the algorithm, calling Level 2 BLAS.

pure subroutine, public	la_chetri (uplo, n, a, lda, ipiv, work, info)
	CHETRI: computes the inverse of a complex Hermitian indefinite matrix A using the factorization A = UDU*H or A = LDL*H computed by CHETRF.

pure subroutine, public	la_zhetri (uplo, n, a, lda, ipiv, work, info)
	ZHETRI: computes the inverse of a complex Hermitian indefinite matrix A using the factorization A = UDU*H or A = LDL*H computed by ZHETRF.

pure subroutine, public	la_whetri (uplo, n, a, lda, ipiv, work, info)
	WHETRI: computes the inverse of a complex Hermitian indefinite matrix A using the factorization A = UDU*H or A = LDL*H computed by WHETRF.

pure subroutine, public	la_chetrs_3 (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)
	CHETRS_3: solves a system of linear equations A * X = B with a complex Hermitian matrix A using the factorization computed by CHETRF_RK or CHETRF_BK: A = PUD(UH)(P*T) or A = PLD(L*H)(PT), where U (or L) is unit upper (or lower) triangular matrix, UH (or LH) is the conjugate of U (or L), P is a permutation matrix, PT is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. This algorithm is using Level 3 BLAS.

pure subroutine, public	la_zhetrs_3 (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)
	ZHETRS_3: solves a system of linear equations A * X = B with a complex Hermitian matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK: A = PUD(UH)(P*T) or A = PLD(L*H)(PT), where U (or L) is unit upper (or lower) triangular matrix, UH (or LH) is the conjugate of U (or L), P is a permutation matrix, PT is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. This algorithm is using Level 3 BLAS.

pure subroutine, public	la_whetrs_3 (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)
	WHETRS_3: solves a system of linear equations A * X = B with a complex Hermitian matrix A using the factorization computed by WHETRF_RK or ZHETRF_BK: A = PUD(UH)(P*T) or A = PLD(L*H)(PT), where U (or L) is unit upper (or lower) triangular matrix, UH (or LH) is the conjugate of U (or L), P is a permutation matrix, PT is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. This algorithm is using Level 3 BLAS.

pure subroutine, public	la_chptrf (uplo, n, ap, ipiv, info)
	CHPTRF: computes the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method: A = UDU*H or A = LDL*H where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

pure subroutine, public	la_zhptrf (uplo, n, ap, ipiv, info)
	ZHPTRF: computes the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method: A = UDU*H or A = LDL*H where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

pure subroutine, public	la_whptrf (uplo, n, ap, ipiv, info)
	WHPTRF: computes the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method: A = UDU*H or A = LDL*H where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

pure subroutine, public	la_chptri (uplo, n, ap, ipiv, work, info)
	CHPTRI: computes the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = UDU*H or A = LDL*H computed by CHPTRF.

pure subroutine, public	la_zhptri (uplo, n, ap, ipiv, work, info)
	ZHPTRI: computes the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = UDU*H or A = LDL*H computed by ZHPTRF.

pure subroutine, public	la_whptri (uplo, n, ap, ipiv, work, info)
	WHPTRI: computes the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = UDU*H or A = LDL*H computed by WHPTRF.

pure subroutine, public	la_clahef (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
	CLAHEF: computes a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method. The partial factorization has the form: A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: ( 0 U22 ) ( 0 D ) ( U12H U22H ) A = ( L11 0 ) ( D 0 ) ( L11H L21H ) if UPLO = 'L' ( L21 I ) ( 0 A22 ) ( 0 I ) where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. Note that U**H denotes the conjugate transpose of U. CLAHEF is an auxiliary routine called by CHETRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L').

pure subroutine, public	la_zlahef (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
	ZLAHEF: computes a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method. The partial factorization has the form: A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: ( 0 U22 ) ( 0 D ) ( U12H U22H ) A = ( L11 0 ) ( D 0 ) ( L11H L21H ) if UPLO = 'L' ( L21 I ) ( 0 A22 ) ( 0 I ) where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. Note that U**H denotes the conjugate transpose of U. ZLAHEF is an auxiliary routine called by ZHETRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L').

pure subroutine, public	la_wlahef (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
	WLAHEF: computes a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method. The partial factorization has the form: A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: ( 0 U22 ) ( 0 D ) ( U12H U22H ) A = ( L11 0 ) ( D 0 ) ( L11H L21H ) if UPLO = 'L' ( L21 I ) ( 0 A22 ) ( 0 I ) where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. Note that U**H denotes the conjugate transpose of U. WLAHEF is an auxiliary routine called by WHETRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L').

pure subroutine, public	la_cheequb (uplo, n, a, lda, s, scond, amax, work, info)
	CHEEQUB: computes row and column scalings intended to equilibrate a Hermitian matrix A (with respect to the Euclidean norm) and reduce its condition number. The scale factors S are computed by the BIN algorithm (see references) so that the scaled matrix B with elements B(i,j) = S(i)A(i,j)S(j) has a condition number within a factor N of the smallest possible condition number over all possible diagonal scalings.

pure subroutine, public	la_zheequb (uplo, n, a, lda, s, scond, amax, work, info)
	ZHEEQUB: computes row and column scalings intended to equilibrate a Hermitian matrix A (with respect to the Euclidean norm) and reduce its condition number. The scale factors S are computed by the BIN algorithm (see references) so that the scaled matrix B with elements B(i,j) = S(i)A(i,j)S(j) has a condition number within a factor N of the smallest possible condition number over all possible diagonal scalings.

pure subroutine, public	la_wheequb (uplo, n, a, lda, s, scond, amax, work, info)
	WHEEQUB: computes row and column scalings intended to equilibrate a Hermitian matrix A (with respect to the Euclidean norm) and reduce its condition number. The scale factors S are computed by the BIN algorithm (see references) so that the scaled matrix B with elements B(i,j) = S(i)A(i,j)S(j) has a condition number within a factor N of the smallest possible condition number over all possible diagonal scalings.

pure subroutine, public	la_chetrf (uplo, n, a, lda, ipiv, work, lwork, info)
	CHETRF: computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method. The form of the factorization is A = UDU*H or A = LDL*H where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. This is the blocked version of the algorithm, calling Level 3 BLAS.

pure subroutine, public	la_zhetrf (uplo, n, a, lda, ipiv, work, lwork, info)
	ZHETRF: computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method. The form of the factorization is A = UDU*H or A = LDL*H where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. This is the blocked version of the algorithm, calling Level 3 BLAS.

pure subroutine, public	la_whetrf (uplo, n, a, lda, ipiv, work, lwork, info)
	WHETRF: computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method. The form of the factorization is A = UDU*H or A = LDL*H where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. This is the blocked version of the algorithm, calling Level 3 BLAS.

pure subroutine, public	la_chetrs (uplo, n, nrhs, a, lda, ipiv, b, ldb, info)
	CHETRS: solves a system of linear equations AX = B with a complex Hermitian matrix A using the factorization A = UDUH or A = LDL*H computed by CHETRF.

pure subroutine, public	la_zhetrs (uplo, n, nrhs, a, lda, ipiv, b, ldb, info)
	ZHETRS: solves a system of linear equations AX = B with a complex Hermitian matrix A using the factorization A = UDUH or A = LDL*H computed by ZHETRF.

pure subroutine, public	la_whetrs (uplo, n, nrhs, a, lda, ipiv, b, ldb, info)
	WHETRS: solves a system of linear equations AX = B with a complex Hermitian matrix A using the factorization A = UDUH or A = LDL*H computed by WHETRF.

pure subroutine, public	la_chetrs2 (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)
	CHETRS2: solves a system of linear equations AX = B with a complex Hermitian matrix A using the factorization A = UDUH or A = LDL*H computed by CHETRF and converted by CSYCONV.

pure subroutine, public	la_zhetrs2 (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)
	ZHETRS2: solves a system of linear equations AX = B with a complex Hermitian matrix A using the factorization A = UDUH or A = LDL*H computed by ZHETRF and converted by ZSYCONV.

pure subroutine, public	la_whetrs2 (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)
	WHETRS2: solves a system of linear equations AX = B with a complex Hermitian matrix A using the factorization A = UDUH or A = LDL*H computed by WHETRF and converted by WSYCONV.

pure subroutine, public	la_chptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info)
	CHPTRS: solves a system of linear equations AX = B with a complex Hermitian matrix A stored in packed format using the factorization A = UDUH or A = LDL*H computed by CHPTRF.

pure subroutine, public	la_zhptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info)
	ZHPTRS: solves a system of linear equations AX = B with a complex Hermitian matrix A stored in packed format using the factorization A = UDUH or A = LDL*H computed by ZHPTRF.

pure subroutine, public	la_whptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info)
	WHPTRS: solves a system of linear equations AX = B with a complex Hermitian matrix A stored in packed format using the factorization A = UDUH or A = LDL*H computed by WHPTRF.

pure subroutine, public	la_checon (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
	CHECON: estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = UDU*H or A = LDLH computed by CHETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM norm(inv(A))).

pure subroutine, public	la_zhecon (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
	ZHECON: estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = UDU*H or A = LDLH computed by ZHETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM norm(inv(A))).

pure subroutine, public	la_whecon (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
	WHECON: estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = UDU*H or A = LDLH computed by WHETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM norm(inv(A))).

pure subroutine, public	la_cherfs (uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
	CHERFS: improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution.

pure subroutine, public	la_zherfs (uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
	ZHERFS: improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution.

pure subroutine, public	la_wherfs (uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
	WHERFS: improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution.

pure subroutine, public	la_chpcon (uplo, n, ap, ipiv, anorm, rcond, work, info)
	CHPCON: estimates the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = UDU*H or A = LDLH computed by CHPTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM norm(inv(A))).

pure subroutine, public	la_zhpcon (uplo, n, ap, ipiv, anorm, rcond, work, info)
	ZHPCON: estimates the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = UDU*H or A = LDLH computed by ZHPTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM norm(inv(A))).

pure subroutine, public	la_whpcon (uplo, n, ap, ipiv, anorm, rcond, work, info)
	WHPCON: estimates the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = UDU*H or A = LDLH computed by WHPTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM norm(inv(A))).

Detailed Description

Hermitian indefinite components: Bunch-Kaufman factorization, solve, inverse.

Function/Subroutine Documentation

◆ la_checon()

pure subroutine, public la_lapack_solve_ldl_comp3::la_checon	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		complex(sp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(sp), intent(in)	anorm,
		real(sp), intent(out)	rcond,
		complex(sp), dimension(*), intent(out)	work,
		integer(ilp), intent(out)	info )

CHECON: estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).