MAGMA
2.3.0
Matrix Algebra for GPU and Multicore Architectures

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 BunchKaufman diagonal pivoting method. More...  
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 BunchKaufman diagonal pivoting method. More...  
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 BunchKaufman diagonal pivoting method. More...  
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 BunchKaufman diagonal pivoting method. More...  
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 BunchKaufman 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 1by1 and 2by2 diagonal blocks.
This is the blocked version of the algorithm, calling Level 3 BLAS.
[in]  uplo  magma_uplo_t

[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 NbyN 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 NbyN 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 1by1 diagonal block. If UPLO = MagmaUpper and IPIV(k) = IPIV(k1) < 0, then rows and columns k1 and IPIV(k) were interchanged and D(k1:k,k1:k) is a 2by2 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 2by2 diagonal block. 
[out]  info  INTEGER

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 1by1 and 2by2 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 ) ks
U(k) = ( 0 I 0 ) s ( 0 0 I ) nk ks s nk
If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k1,k). If s = 2, the upper triangle of D(k) overwrites A(k1,k1), A(k1,k), and A(k,k), and v overwrites A(1:k2,k1: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 1by1 and 2by2 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 ) k1
L(k) = ( 0 I 0 ) s ( 0 v I ) nks+1 k1 s nks+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_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 BunchKaufman 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 1by1 and 2by2 diagonal blocks.
This is the blocked version of the algorithm, calling Level 3 BLAS.
[in]  uplo  magma_uplo_t

[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 NbyN 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 NbyN 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 1by1 diagonal block. If UPLO = MagmaUpper and IPIV(k) = IPIV(k1) < 0, then rows and columns k1 and IPIV(k) were interchanged and D(k1:k,k1:k) is a 2by2 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 2by2 diagonal block. 
[out]  info  INTEGER

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 1by1 and 2by2 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 ) ks
U(k) = ( 0 I 0 ) s ( 0 0 I ) nk ks s nk
If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k1,k). If s = 2, the upper triangle of D(k) overwrites A(k1,k1), A(k1,k), and A(k,k), and v overwrites A(1:k2,k1: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 1by1 and 2by2 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 ) k1
L(k) = ( 0 I 0 ) s ( 0 v I ) nks+1 k1 s nks+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_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 BunchKaufman 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 1by1 and 2by2 diagonal blocks.
This is the blocked version of the algorithm, calling Level 3 BLAS.
[in]  uplo  magma_uplo_t

[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 NbyN 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 NbyN 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 1by1 diagonal block. If UPLO = MagmaUpper and IPIV(k) = IPIV(k1) < 0, then rows and columns k1 and IPIV(k) were interchanged and D(k1:k,k1:k) is a 2by2 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 2by2 diagonal block. 
[out]  info  INTEGER

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 1by1 and 2by2 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 ) ks
U(k) = ( 0 I 0 ) s ( 0 0 I ) nk ks s nk
If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k1,k). If s = 2, the upper triangle of D(k) overwrites A(k1,k1), A(k1,k), and A(k,k), and v overwrites A(1:k2,k1: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 1by1 and 2by2 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 ) k1
L(k) = ( 0 I 0 ) s ( 0 v I ) nks+1 k1 s nks+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_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 BunchKaufman 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 1by1 and 2by2 diagonal blocks.
This is the blocked version of the algorithm, calling Level 3 BLAS.
[in]  uplo  magma_uplo_t

[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 NbyN 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 NbyN 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 1by1 diagonal block. If UPLO = MagmaUpper and IPIV(k) = IPIV(k1) < 0, then rows and columns k1 and IPIV(k) were interchanged and D(k1:k,k1:k) is a 2by2 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 2by2 diagonal block. 
[out]  info  INTEGER

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 1by1 and 2by2 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 ) ks
U(k) = ( 0 I 0 ) s ( 0 0 I ) nk ks s nk
If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k1,k). If s = 2, the upper triangle of D(k) overwrites A(k1,k1), A(k1,k), and A(k,k), and v overwrites A(1:k2,k1: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 1by1 and 2by2 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 ) k1
L(k) = ( 0 I 0 ) s ( 0 v I ) nks+1 k1 s nks+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).