Functions
magma_int_t	magma_chetrf (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex A, magma_int_t lda, magma_int_t ipiv, magma_int_t *info)
	CHETRF computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method.

magma_int_t	magma_chetrf_gpu (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex dA, magma_int_t ldda, magma_int_t ipiv, magma_int_t *info)
	CHETRF computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method.

magma_int_t	magma_dsidi (magma_uplo_t uplo, double A, magma_int_t lda, magma_int_t n, magma_int_t ipiv, double det, magma_int_t inert, double work, magma_int_t job, magma_int_t info)
	dsidi computes the determinant, inertia and inverse of a double precision symmetric matrix using the factors from dsytrf.

magma_int_t	magma_dsytrf (magma_uplo_t uplo, magma_int_t n, double A, magma_int_t lda, magma_int_t ipiv, magma_int_t *info)
	DSYTRF computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.

magma_int_t	magma_dsytrf_gpu (magma_uplo_t uplo, magma_int_t n, double dA, magma_int_t ldda, magma_int_t ipiv, magma_int_t *info)
	DSYTRF computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.

magma_int_t	magma_ssidi (magma_uplo_t uplo, float A, magma_int_t lda, magma_int_t n, magma_int_t ipiv, float det, magma_int_t inert, float work, magma_int_t job, magma_int_t info)
	ssidi computes the determinant, inertia and inverse of a float precision symmetric matrix using the factors from ssytrf.

magma_int_t	magma_ssytrf (magma_uplo_t uplo, magma_int_t n, float A, magma_int_t lda, magma_int_t ipiv, magma_int_t *info)
	SSYTRF computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.

magma_int_t	magma_ssytrf_gpu (magma_uplo_t uplo, magma_int_t n, float dA, magma_int_t ldda, magma_int_t ipiv, magma_int_t *info)
	SSYTRF computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.

magma_int_t	magma_zhetrf (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex A, magma_int_t lda, magma_int_t ipiv, magma_int_t *info)
	ZHETRF computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method.

magma_int_t	magma_zhetrf_gpu (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex dA, magma_int_t ldda, magma_int_t ipiv, magma_int_t *info)
	ZHETRF computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method.

magma_int_t	magmablas_cdiinertia (magma_int_t n, magmaFloatComplex_const_ptr dA, magma_int_t ldda, int *dneig, magma_queue_t queue)
	magmablas_cdiinertia computes the inertia of a real diagonal matrix.

magma_int_t	magmablas_cheinertia (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex_const_ptr dA, magma_int_t ldda, magma_int_t ipiv, int dneig, magma_queue_t queue)
	magmablas_cheinertia computes the inertia of a hermitian and block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks.

magma_int_t	magmablas_ddiinertia (magma_int_t n, magmaDouble_const_ptr dA, magma_int_t ldda, int *dneig, magma_queue_t queue)
	magmablas_ddiinertia computes the inertia of a real diagonal matrix.

magma_int_t	magmablas_dsiinertia (magma_uplo_t uplo, magma_int_t n, magmaDouble_const_ptr dA, magma_int_t ldda, magma_int_t ipiv, int dneig, magma_queue_t queue)
	magmablas_dsiinertia computes the inertia of a symmetric and block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks.

magma_int_t	magmablas_sdiinertia (magma_int_t n, magmaFloat_const_ptr dA, magma_int_t ldda, int *dneig, magma_queue_t queue)
	magmablas_sdiinertia computes the inertia of a real diagonal matrix.

magma_int_t	magmablas_ssiinertia (magma_uplo_t uplo, magma_int_t n, magmaFloat_const_ptr dA, magma_int_t ldda, magma_int_t ipiv, int dneig, magma_queue_t queue)
	magmablas_ssiinertia computes the inertia of a symmetric and block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks.

magma_int_t	magmablas_zdiinertia (magma_int_t n, magmaDoubleComplex_const_ptr dA, magma_int_t ldda, int *dneig, magma_queue_t queue)
	magmablas_zdiinertia computes the inertia of a real diagonal matrix.

magma_int_t	magmablas_zheinertia (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex_const_ptr dA, magma_int_t ldda, magma_int_t ipiv, int dneig, magma_queue_t queue)
	magmablas_zheinertia computes the inertia of a hermitian and block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks.

Detailed Description

Function Documentation

◆ magma_chetrf()

magma_int_t magma_chetrf	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magmaFloatComplex *	A,
		magma_int_t	lda,
		magma_int_t *	ipiv,
		magma_int_t *	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 = U*D*U^H  or  A = L*D*L^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.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in,out]	A	COMPLEX array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L (see below for further details).
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	ipiv	INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If UPLO = MagmaUpper and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = MagmaLower and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

Further Details

If UPLO = MagmaUpper, then A = U*D*U', where U = P(n)*U(n)* ... P(k)U(k) ..., i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and U(k) is a unit upper triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    v    0   )   k-s

U(k) = ( 0 I 0 ) s ( 0 0 I ) n-k k-s s n-k

If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k), and v overwrites A(1:k-2,k-1:k).

If UPLO = MagmaLower, then A = L*D*L', where L = P(1)*L(1)* ... P(k)*L(k) ..., i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and L(k) is a unit lower triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    0     0   )  k-1

L(k) = ( 0 I 0 ) s ( 0 v I ) n-k-s+1 k-1 s n-k-s+1

If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

◆ magma_chetrf_gpu()

magma_int_t magma_chetrf_gpu	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magmaFloatComplex *	dA,
		magma_int_t	ldda,
		magma_int_t *	ipiv,
		magma_int_t *	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 = U*D*U^H  or  A = L*D*L^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.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in,out]	dA	COMPLEX array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L (see below for further details).
[in]	ldda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	ipiv	INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If UPLO = MagmaUpper and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = MagmaLower and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

Further Details

If UPLO = MagmaUpper, then A = U*D*U', where U = P(n)*U(n)* ... P(k)U(k) ..., i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and U(k) is a unit upper triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    v    0   )   k-s

U(k) = ( 0 I 0 ) s ( 0 0 I ) n-k k-s s n-k

If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k), and v overwrites A(1:k-2,k-1:k).

If UPLO = MagmaLower, then A = L*D*L', where L = P(1)*L(1)* ... P(k)*L(k) ..., i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and L(k) is a unit lower triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    0     0   )  k-1

L(k) = ( 0 I 0 ) s ( 0 v I ) n-k-s+1 k-1 s n-k-s+1

If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

◆ magma_dsidi()

magma_int_t magma_dsidi	(	magma_uplo_t	uplo,
		double *	A,
		magma_int_t	lda,
		magma_int_t	n,
		magma_int_t *	ipiv,
		double *	det,
		magma_int_t *	inert,
		double *	work,
		magma_int_t	job,
		magma_int_t *	info )

dsidi computes the determinant, inertia and inverse of a double precision symmetric matrix using the factors from dsytrf.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in,out]	A	DOUBLE PRECISION array, dimension (LDA,N) On entry, the output from dsytrf. On exit, the upper triangle of the inverse of the original matrix. The strict lower triangle is never referenced.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	ipiv	INTEGER array, dimension (N) The pivot vector from dsytrf.
[out]	det	DOUBLE PRECISION array, dimension (2) Determinant of the original matrix: Determinant = det(0) * 10^det(1) with 1<=fabs(det(0))<10 or det(0) = 0.
[out]	inert	INTEGER array, dimension (3) The inertia of the original matrix: inert(0) = number of positive eigenvalues. inert(1) = number of negative eigenvalues. inert(2) = number of zero eigenvalues.
[in]	work	(workspace) DOUBLE PRECISION array, dimension (N) Work vector. Contents destroyed.
[in]	job	INTEGER JOB has the decimal expansion abc where if c != 0, the inverse is computed, if b != 0, the determinant is computed, if a != 0, the inertia is computed.

for example, job = 111 gives all three.

Further Details

Error condition: a division by zero may occur if the inverse is requested and dsytrf has set info != 0.

This routine is based on the LINPACK dsidi routine (see also LINPACK USERS' guide, page 5.15).

◆ magma_dsytrf()

magma_int_t magma_dsytrf	(	magma_uplo_t	uplo,
		magma_int_t	n,
		double *	A,
		magma_int_t	lda,
		magma_int_t *	ipiv,
		magma_int_t *	info )

DSYTRF computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.

The form of the factorization is

A = U*D*U^H  or  A = L*D*L^H

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric 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.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in,out]	A	DOUBLE PRECISION array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L (see below for further details).
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	ipiv	INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If UPLO = MagmaUpper and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = MagmaLower and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

Further Details

If UPLO = MagmaUpper, then A = U*D*U', where U = P(n)*U(n)* ... P(k)U(k) ..., i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and U(k) is a unit upper triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    v    0   )   k-s

U(k) = ( 0 I 0 ) s ( 0 0 I ) n-k k-s s n-k

If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k), and v overwrites A(1:k-2,k-1:k).

If UPLO = MagmaLower, then A = L*D*L', where L = P(1)*L(1)* ... P(k)*L(k) ..., i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and L(k) is a unit lower triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    0     0   )  k-1

L(k) = ( 0 I 0 ) s ( 0 v I ) n-k-s+1 k-1 s n-k-s+1

If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

◆ magma_dsytrf_gpu()

magma_int_t magma_dsytrf_gpu	(	magma_uplo_t	uplo,
		magma_int_t	n,
		double *	dA,
		magma_int_t	ldda,
		magma_int_t *	ipiv,
		magma_int_t *	info )

DSYTRF computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.

The form of the factorization is

A = U*D*U^H  or  A = L*D*L^H

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric 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.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in,out]	dA	DOUBLE PRECISION array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L (see below for further details).
[in]	ldda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	ipiv	INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If UPLO = MagmaUpper and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = MagmaLower and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

Further Details

If UPLO = MagmaUpper, then A = U*D*U', where U = P(n)*U(n)* ... P(k)U(k) ..., i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and U(k) is a unit upper triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    v    0   )   k-s

U(k) = ( 0 I 0 ) s ( 0 0 I ) n-k k-s s n-k

If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k), and v overwrites A(1:k-2,k-1:k).

If UPLO = MagmaLower, then A = L*D*L', where L = P(1)*L(1)* ... P(k)*L(k) ..., i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and L(k) is a unit lower triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    0     0   )  k-1

L(k) = ( 0 I 0 ) s ( 0 v I ) n-k-s+1 k-1 s n-k-s+1

If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

◆ magma_ssidi()

magma_int_t magma_ssidi	(	magma_uplo_t	uplo,
		float *	A,
		magma_int_t	lda,
		magma_int_t	n,
		magma_int_t *	ipiv,
		float *	det,
		magma_int_t *	inert,
		float *	work,
		magma_int_t	job,
		magma_int_t *	info )

ssidi computes the determinant, inertia and inverse of a float precision symmetric matrix using the factors from ssytrf.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in,out]	A	REAL array, dimension (LDA,N) On entry, the output from ssytrf. On exit, the upper triangle of the inverse of the original matrix. The strict lower triangle is never referenced.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	ipiv	INTEGER array, dimension (N) The pivot vector from ssytrf.
[out]	det	REAL array, dimension (2) Determinant of the original matrix: Determinant = det(0) * 10^det(1) with 1<=fabsf(det(0))<10 or det(0) = 0.
[out]	inert	INTEGER array, dimension (3) The inertia of the original matrix: inert(0) = number of positive eigenvalues. inert(1) = number of negative eigenvalues. inert(2) = number of zero eigenvalues.
[in]	work	(workspace) REAL array, dimension (N) Work vector. Contents destroyed.
[in]	job	INTEGER JOB has the decimal expansion abc where if c != 0, the inverse is computed, if b != 0, the determinant is computed, if a != 0, the inertia is computed.

for example, job = 111 gives all three.

Further Details

Error condition: a division by zero may occur if the inverse is requested and ssytrf has set info != 0.

This routine is based on the LINPACK ssidi routine (see also LINPACK USERS' guide, page 5.15).

◆ magma_ssytrf()

magma_int_t magma_ssytrf	(	magma_uplo_t	uplo,
		magma_int_t	n,
		float *	A,
		magma_int_t	lda,
		magma_int_t *	ipiv,
		magma_int_t *	info )

SSYTRF computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.

The form of the factorization is

A = U*D*U^H  or  A = L*D*L^H

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric 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.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in,out]	A	REAL array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L (see below for further details).
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	ipiv	INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If UPLO = MagmaUpper and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = MagmaLower and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

Further Details

If UPLO = MagmaUpper, then A = U*D*U', where U = P(n)*U(n)* ... P(k)U(k) ..., i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and U(k) is a unit upper triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    v    0   )   k-s

U(k) = ( 0 I 0 ) s ( 0 0 I ) n-k k-s s n-k

If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k), and v overwrites A(1:k-2,k-1:k).

If UPLO = MagmaLower, then A = L*D*L', where L = P(1)*L(1)* ... P(k)*L(k) ..., i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and L(k) is a unit lower triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    0     0   )  k-1

L(k) = ( 0 I 0 ) s ( 0 v I ) n-k-s+1 k-1 s n-k-s+1

If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

◆ magma_ssytrf_gpu()

magma_int_t magma_ssytrf_gpu	(	magma_uplo_t	uplo,
		magma_int_t	n,
		float *	dA,
		magma_int_t	ldda,
		magma_int_t *	ipiv,
		magma_int_t *	info )

SSYTRF computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.

The form of the factorization is

A = U*D*U^H  or  A = L*D*L^H

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric 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.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in,out]	dA	REAL array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L (see below for further details).
[in]	ldda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	ipiv	INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If UPLO = MagmaUpper and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = MagmaLower and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

Further Details

If UPLO = MagmaUpper, then A = U*D*U', where U = P(n)*U(n)* ... P(k)U(k) ..., i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and U(k) is a unit upper triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    v    0   )   k-s

U(k) = ( 0 I 0 ) s ( 0 0 I ) n-k k-s s n-k

If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k), and v overwrites A(1:k-2,k-1:k).

If UPLO = MagmaLower, then A = L*D*L', where L = P(1)*L(1)* ... P(k)*L(k) ..., i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and L(k) is a unit lower triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    0     0   )  k-1

L(k) = ( 0 I 0 ) s ( 0 v I ) n-k-s+1 k-1 s n-k-s+1

If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

◆ magma_zhetrf()

magma_int_t magma_zhetrf	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magmaDoubleComplex *	A,
		magma_int_t	lda,
		magma_int_t *	ipiv,
		magma_int_t *	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 = U*D*U^H  or  A = L*D*L^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.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in,out]	A	COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L (see below for further details).
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	ipiv	INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If UPLO = MagmaUpper and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = MagmaLower and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

Further Details

If UPLO = MagmaUpper, then A = U*D*U', where U = P(n)*U(n)* ... P(k)U(k) ..., i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and U(k) is a unit upper triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    v    0   )   k-s

U(k) = ( 0 I 0 ) s ( 0 0 I ) n-k k-s s n-k

If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k), and v overwrites A(1:k-2,k-1:k).

If UPLO = MagmaLower, then A = L*D*L', where L = P(1)*L(1)* ... P(k)*L(k) ..., i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and L(k) is a unit lower triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    0     0   )  k-1

L(k) = ( 0 I 0 ) s ( 0 v I ) n-k-s+1 k-1 s n-k-s+1

If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

◆ magma_zhetrf_gpu()

magma_int_t magma_zhetrf_gpu	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magmaDoubleComplex *	dA,
		magma_int_t	ldda,
		magma_int_t *	ipiv,
		magma_int_t *	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 = U*D*U^H  or  A = L*D*L^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.

Parameters

[in]	uplo	magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]	n	INTEGER The order of the matrix A. N >= 0.
[in,out]	dA	COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L (see below for further details).
[in]	ldda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	ipiv	INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If UPLO = MagmaUpper and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = MagmaLower and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

Further Details

If UPLO = MagmaUpper, then A = U*D*U', where U = P(n)*U(n)* ... P(k)U(k) ..., i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and U(k) is a unit upper triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    v    0   )   k-s

U(k) = ( 0 I 0 ) s ( 0 0 I ) n-k k-s s n-k

If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k), and v overwrites A(1:k-2,k-1:k).

If UPLO = MagmaLower, then A = L*D*L', where L = P(1)*L(1)* ... P(k)*L(k) ..., i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and L(k) is a unit lower triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

       (   I    0     0   )  k-1

L(k) = ( 0 I 0 ) s ( 0 v I ) n-k-s+1 k-1 s n-k-s+1

If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

◆ magmablas_cdiinertia()

magma_int_t magmablas_cdiinertia	(	magma_int_t	n,
		magmaFloatComplex_const_ptr	dA,
		magma_int_t	ldda,
		int *	dneig,
		magma_queue_t	queue )

magmablas_cdiinertia computes the inertia of a real diagonal matrix.

If matrix entries are complex, magmablas_cdiinertia considers the real part of the diagonal.

Parameters

[in]	n	INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
[in]	dA	COMPLEX array of DIMENSION ( LDDA, n ). The input matrix A with diagonal entries for which the inertia is computed. If dA is complex, the computation is done on the real part of the diagonal.
[in]	ldda	INTEGER. On entry, LDDA specifies the leading dimension of A. LDDA must be at least max( 1, n ).
[out]	dneig	INTEGER array of DIMENSION 3 on the GPU memory. The number of positive, negative, and zero eigenvalues in this order.
[in]	queue	magma_queue_t. Queue to execute in.

◆ magmablas_cheinertia()

magma_int_t magmablas_cheinertia	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magmaFloatComplex_const_ptr	dA,
		magma_int_t	ldda,
		magma_int_t *	ipiv,
		int *	dneig,
		magma_queue_t	queue )

magmablas_cheinertia computes the inertia of a hermitian and block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks.

These are matrices comming from the Bunch-Kaufman with diagonal pivoting factorizations (the CHETRF routine).

Parameters

[in]	n	INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
[in]	dA	COMPLEX array of DIMENSION ( LDDA, n ). The input matrix A with 1-by-1 and 2-by-2 diagonal block entries for which the inertia is computed.
[in]	ldda	INTEGER. On entry, LDDA specifies the leading dimension of A. LDDA must be at least max( 1, n ).
[in]	ipiv	INTEGER array, dimension (N) The pivot vector from dsytrf.
[out]	dneig	INTEGER array of DIMENSION 3 on the GPU memory. The number of positive, negative, and zero eigenvalues in this order.
[in]	queue	magma_queue_t. Queue to execute in.

◆ magmablas_ddiinertia()

magma_int_t magmablas_ddiinertia	(	magma_int_t	n,
		magmaDouble_const_ptr	dA,
		magma_int_t	ldda,
		int *	dneig,
		magma_queue_t	queue )

magmablas_ddiinertia computes the inertia of a real diagonal matrix.

If matrix entries are real, magmablas_ddiinertia considers the real part of the diagonal.

Parameters

[in]	n	INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
[in]	dA	DOUBLE PRECISION array of DIMENSION ( LDDA, n ). The input matrix A with diagonal entries for which the inertia is computed. If dA is real, the computation is done on the real part of the diagonal.
[in]	ldda	INTEGER. On entry, LDDA specifies the leading dimension of A. LDDA must be at least max( 1, n ).
[out]	dneig	INTEGER array of DIMENSION 3 on the GPU memory. The number of positive, negative, and zero eigenvalues in this order.
[in]	queue	magma_queue_t. Queue to execute in.

◆ magmablas_dsiinertia()

magma_int_t magmablas_dsiinertia	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magmaDouble_const_ptr	dA,
		magma_int_t	ldda,
		magma_int_t *	ipiv,
		int *	dneig,
		magma_queue_t	queue )

magmablas_dsiinertia computes the inertia of a symmetric and block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks.

These are matrices comming from the Bunch-Kaufman with diagonal pivoting factorizations (the DSYTRF routine).

Parameters

[in]	n	INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
[in]	dA	DOUBLE PRECISION array of DIMENSION ( LDDA, n ). The input matrix A with 1-by-1 and 2-by-2 diagonal block entries for which the inertia is computed.
[in]	ldda	INTEGER. On entry, LDDA specifies the leading dimension of A. LDDA must be at least max( 1, n ).
[in]	ipiv	INTEGER array, dimension (N) The pivot vector from dsytrf.
[out]	dneig	INTEGER array of DIMENSION 3 on the GPU memory. The number of positive, negative, and zero eigenvalues in this order.
[in]	queue	magma_queue_t. Queue to execute in.

◆ magmablas_sdiinertia()

magma_int_t magmablas_sdiinertia	(	magma_int_t	n,
		magmaFloat_const_ptr	dA,
		magma_int_t	ldda,
		int *	dneig,
		magma_queue_t	queue )

magmablas_sdiinertia computes the inertia of a real diagonal matrix.

If matrix entries are real, magmablas_sdiinertia considers the real part of the diagonal.

Parameters

[in]	n	INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
[in]	dA	REAL array of DIMENSION ( LDDA, n ). The input matrix A with diagonal entries for which the inertia is computed. If dA is real, the computation is done on the real part of the diagonal.
[in]	ldda	INTEGER. On entry, LDDA specifies the leading dimension of A. LDDA must be at least max( 1, n ).
[out]	dneig	INTEGER array of DIMENSION 3 on the GPU memory. The number of positive, negative, and zero eigenvalues in this order.
[in]	queue	magma_queue_t. Queue to execute in.

◆ magmablas_ssiinertia()

magma_int_t magmablas_ssiinertia	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magmaFloat_const_ptr	dA,
		magma_int_t	ldda,
		magma_int_t *	ipiv,
		int *	dneig,
		magma_queue_t	queue )

magmablas_ssiinertia computes the inertia of a symmetric and block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks.

These are matrices comming from the Bunch-Kaufman with diagonal pivoting factorizations (the SSYTRF routine).

Parameters

[in]	n	INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
[in]	dA	REAL array of DIMENSION ( LDDA, n ). The input matrix A with 1-by-1 and 2-by-2 diagonal block entries for which the inertia is computed.
[in]	ldda	INTEGER. On entry, LDDA specifies the leading dimension of A. LDDA must be at least max( 1, n ).
[in]	ipiv	INTEGER array, dimension (N) The pivot vector from dsytrf.
[out]	dneig	INTEGER array of DIMENSION 3 on the GPU memory. The number of positive, negative, and zero eigenvalues in this order.
[in]	queue	magma_queue_t. Queue to execute in.

◆ magmablas_zdiinertia()

magma_int_t magmablas_zdiinertia	(	magma_int_t	n,
		magmaDoubleComplex_const_ptr	dA,
		magma_int_t	ldda,
		int *	dneig,
		magma_queue_t	queue )

magmablas_zdiinertia computes the inertia of a real diagonal matrix.

If matrix entries are complex, magmablas_zdiinertia considers the real part of the diagonal.

Parameters

[in]	n	INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
[in]	dA	COMPLEX_16 array of DIMENSION ( LDDA, n ). The input matrix A with diagonal entries for which the inertia is computed. If dA is complex, the computation is done on the real part of the diagonal.
[in]	ldda	INTEGER. On entry, LDDA specifies the leading dimension of A. LDDA must be at least max( 1, n ).
[out]	dneig	INTEGER array of DIMENSION 3 on the GPU memory. The number of positive, negative, and zero eigenvalues in this order.
[in]	queue	magma_queue_t. Queue to execute in.

◆ magmablas_zheinertia()

magma_int_t magmablas_zheinertia	(	magma_uplo_t	uplo,
		magma_int_t	n,
		magmaDoubleComplex_const_ptr	dA,
		magma_int_t	ldda,
		magma_int_t *	ipiv,
		int *	dneig,
		magma_queue_t	queue )

magmablas_zheinertia computes the inertia of a hermitian and block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks.

These are matrices comming from the Bunch-Kaufman with diagonal pivoting factorizations (the ZHETRF routine).

Parameters

[in]	n	INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
[in]	dA	COMPLEX_16 array of DIMENSION ( LDDA, n ). The input matrix A with 1-by-1 and 2-by-2 diagonal block entries for which the inertia is computed.
[in]	ldda	INTEGER. On entry, LDDA specifies the leading dimension of A. LDDA must be at least max( 1, n ).
[in]	ipiv	INTEGER array, dimension (N) The pivot vector from dsytrf.
[out]	dneig	INTEGER array of DIMENSION 3 on the GPU memory. The number of positive, negative, and zero eigenvalues in this order.
[in]	queue	magma_queue_t. Queue to execute in.

Functions

Detailed Description

Function Documentation

◆ magma_chetrf()

Further Details

◆ magma_chetrf_gpu()

Further Details

◆ magma_dsidi()

Further Details

◆ magma_dsytrf()

Further Details

◆ magma_dsytrf_gpu()

Further Details

◆ magma_ssidi()

Further Details

◆ magma_ssytrf()

Further Details

◆ magma_ssytrf_gpu()

Further Details

◆ magma_zhetrf()

Further Details

◆ magma_zhetrf_gpu()

Further Details

◆ magmablas_cdiinertia()

◆ magmablas_cheinertia()

◆ magmablas_ddiinertia()

◆ magmablas_dsiinertia()

◆ magmablas_sdiinertia()

◆ magmablas_ssiinertia()

◆ magmablas_zdiinertia()

◆ magmablas_zheinertia()