MAGMA
2.3.0
Matrix Algebra for GPU and Multicore Architectures

Functions  
magma_int_t  magma_chegvx (magma_int_t itype, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *B, magma_int_t ldb, float vl, float vu, magma_int_t il, magma_int_t iu, float abstol, magma_int_t *m, float *w, magmaFloatComplex *Z, magma_int_t ldz, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t *iwork, magma_int_t *ifail, magma_int_t *info) 
CHEGVX computes selected eigenvalues, and optionally, eigenvectors of a complex generalized Hermitiandefinite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. More...  
magma_int_t  magma_zhegvx (magma_int_t itype, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex *B, magma_int_t ldb, double vl, double vu, magma_int_t il, magma_int_t iu, double abstol, magma_int_t *m, double *w, magmaDoubleComplex *Z, magma_int_t ldz, magmaDoubleComplex *work, magma_int_t lwork, double *rwork, magma_int_t *iwork, magma_int_t *ifail, magma_int_t *info) 
ZHEGVX computes selected eigenvalues, and optionally, eigenvectors of a complex generalized Hermitiandefinite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. More...  
magma_int_t magma_chegvx  (  magma_int_t  itype, 
magma_vec_t  jobz,  
magma_range_t  range,  
magma_uplo_t  uplo,  
magma_int_t  n,  
magmaFloatComplex *  A,  
magma_int_t  lda,  
magmaFloatComplex *  B,  
magma_int_t  ldb,  
float  vl,  
float  vu,  
magma_int_t  il,  
magma_int_t  iu,  
float  abstol,  
magma_int_t *  m,  
float *  w,  
magmaFloatComplex *  Z,  
magma_int_t  ldz,  
magmaFloatComplex *  work,  
magma_int_t  lwork,  
float *  rwork,  
magma_int_t *  iwork,  
magma_int_t *  ifail,  
magma_int_t *  info  
) 
CHEGVX computes selected eigenvalues, and optionally, eigenvectors of a complex generalized Hermitiandefinite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
Here A and B are assumed to be Hermitian and B is also positive definite. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
[in]  itype  INTEGER Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x 
[in]  jobz  magma_vec_t

[in]  range  magma_range_t

[in]  uplo  magma_uplo_t

[in]  n  INTEGER The order of the matrices A and B. 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. If UPLO = MagmaLower, the leading NbyN lower triangular part of A contains the lower triangular part of the matrix A. On exit, the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed. 
[in]  lda  INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[in,out]  B  COMPLEX array, dimension (LDB, N) On entry, the Hermitian matrix B. If UPLO = MagmaUpper, the leading NbyN upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = MagmaLower, the leading NbyN lower triangular part of B contains the lower triangular part of the matrix B. On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H. 
[in]  ldb  INTEGER The leading dimension of the array B. LDB >= max(1,N). 
[in]  vl  REAL 
[in]  vu  REAL If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI. 
[in]  il  INTEGER 
[in]  iu  INTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV. 
[in]  abstol  REAL The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( a,b ), where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*T will be used in its place, where T is the 1norm of the tridiagonal matrix obtained by reducing A to tridiagonal form. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*SLAMCH('S'), not zero. If this routine returns with INFO > 0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*SLAMCH('S'). 
[out]  m  INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IUIL+1. 
[out]  w  REAL array, dimension (N) The first M elements contain the selected eigenvalues in ascending order. 
[out]  Z  COMPLEX array, dimension (LDZ, max(1,M)) If JOBZ = MagmaNoVec, then Z is not referenced. If JOBZ = MagmaVec, then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the ith column of Z holding the eigenvector associated with W(i). The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z = I. If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = MagmaRangeV, the exact value of M is not known in advance and an upper bound must be used. 
[in]  ldz  INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = MagmaVec, LDZ >= max(1,N). 
[out]  work  (workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. 
[in]  lwork  INTEGER The length of the array WORK. LWORK >= max(1,2*N). For optimal efficiency, LWORK >= (NB+1)*N, where NB is the blocksize for CHETRD returned by ILAENV. If LWORK = 1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 
rwork  (workspace) REAL array, dimension (7*N)  
iwork  (workspace) INTEGER array, dimension (5*N)  
[out]  ifail  INTEGER array, dimension (N) If JOBZ = MagmaVec, then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = MagmaNoVec, then IFAIL is not referenced. 
[out]  info  INTEGER

Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
magma_int_t magma_zhegvx  (  magma_int_t  itype, 
magma_vec_t  jobz,  
magma_range_t  range,  
magma_uplo_t  uplo,  
magma_int_t  n,  
magmaDoubleComplex *  A,  
magma_int_t  lda,  
magmaDoubleComplex *  B,  
magma_int_t  ldb,  
double  vl,  
double  vu,  
magma_int_t  il,  
magma_int_t  iu,  
double  abstol,  
magma_int_t *  m,  
double *  w,  
magmaDoubleComplex *  Z,  
magma_int_t  ldz,  
magmaDoubleComplex *  work,  
magma_int_t  lwork,  
double *  rwork,  
magma_int_t *  iwork,  
magma_int_t *  ifail,  
magma_int_t *  info  
) 
ZHEGVX computes selected eigenvalues, and optionally, eigenvectors of a complex generalized Hermitiandefinite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
Here A and B are assumed to be Hermitian and B is also positive definite. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
[in]  itype  INTEGER Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x 
[in]  jobz  magma_vec_t

[in]  range  magma_range_t

[in]  uplo  magma_uplo_t

[in]  n  INTEGER The order of the matrices A and B. 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. If UPLO = MagmaLower, the leading NbyN lower triangular part of A contains the lower triangular part of the matrix A. On exit, the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed. 
[in]  lda  INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[in,out]  B  COMPLEX_16 array, dimension (LDB, N) On entry, the Hermitian matrix B. If UPLO = MagmaUpper, the leading NbyN upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = MagmaLower, the leading NbyN lower triangular part of B contains the lower triangular part of the matrix B. On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H. 
[in]  ldb  INTEGER The leading dimension of the array B. LDB >= max(1,N). 
[in]  vl  DOUBLE PRECISION 
[in]  vu  DOUBLE PRECISION If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI. 
[in]  il  INTEGER 
[in]  iu  INTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV. 
[in]  abstol  DOUBLE PRECISION The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( a,b ), where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*T will be used in its place, where T is the 1norm of the tridiagonal matrix obtained by reducing A to tridiagonal form. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*DLAMCH('S'), not zero. If this routine returns with INFO > 0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*DLAMCH('S'). 
[out]  m  INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IUIL+1. 
[out]  w  DOUBLE PRECISION array, dimension (N) The first M elements contain the selected eigenvalues in ascending order. 
[out]  Z  COMPLEX_16 array, dimension (LDZ, max(1,M)) If JOBZ = MagmaNoVec, then Z is not referenced. If JOBZ = MagmaVec, then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the ith column of Z holding the eigenvector associated with W(i). The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z = I. If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = MagmaRangeV, the exact value of M is not known in advance and an upper bound must be used. 
[in]  ldz  INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = MagmaVec, LDZ >= max(1,N). 
[out]  work  (workspace) COMPLEX_16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. 
[in]  lwork  INTEGER The length of the array WORK. LWORK >= max(1,2*N). For optimal efficiency, LWORK >= (NB+1)*N, where NB is the blocksize for ZHETRD returned by ILAENV. If LWORK = 1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 
rwork  (workspace) DOUBLE PRECISION array, dimension (7*N)  
iwork  (workspace) INTEGER array, dimension (5*N)  
[out]  ifail  INTEGER array, dimension (N) If JOBZ = MagmaVec, then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = MagmaNoVec, then IFAIL is not referenced. 
[out]  info  INTEGER

Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA