MAGMA
2.3.0
Matrix Algebra for GPU and Multicore Architectures

Functions  
magma_int_t  magma_chegvd (magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *B, magma_int_t ldb, float *w, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) 
CHEGVD computes all the eigenvalues, and optionally, the 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_chegvd_m (magma_int_t ngpu, magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *B, magma_int_t ldb, float *w, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) 
CHEGVD computes all the eigenvalues, and optionally, the 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_dsygvd (magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, double *A, magma_int_t lda, double *B, magma_int_t ldb, double *w, double *work, magma_int_t lwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) 
DSYGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. More...  
magma_int_t  magma_dsygvd_m (magma_int_t ngpu, magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, double *A, magma_int_t lda, double *B, magma_int_t ldb, double *w, double *work, magma_int_t lwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) 
DSYGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. More...  
magma_int_t  magma_ssygvd (magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, float *B, magma_int_t ldb, float *w, float *work, magma_int_t lwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) 
SSYGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. More...  
magma_int_t  magma_ssygvd_m (magma_int_t ngpu, magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, float *B, magma_int_t ldb, float *w, float *work, magma_int_t lwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) 
SSYGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. More...  
magma_int_t  magma_zhegvd (magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex *B, magma_int_t ldb, double *w, magmaDoubleComplex *work, magma_int_t lwork, double *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) 
ZHEGVD computes all the eigenvalues, and optionally, the 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_zhegvd_m (magma_int_t ngpu, magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex *B, magma_int_t ldb, double *w, magmaDoubleComplex *work, magma_int_t lwork, double *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) 
ZHEGVD computes all the eigenvalues, and optionally, the 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_chegvd  (  magma_int_t  itype, 
magma_vec_t  jobz,  
magma_uplo_t  uplo,  
magma_int_t  n,  
magmaFloatComplex *  A,  
magma_int_t  lda,  
magmaFloatComplex *  B,  
magma_int_t  ldb,  
float *  w,  
magmaFloatComplex *  work,  
magma_int_t  lwork,  
float *  rwork,  
magma_int_t  lrwork,  
magma_int_t *  iwork,  
magma_int_t  liwork,  
magma_int_t *  info  
) 
CHEGVD computes all the eigenvalues, and optionally, the 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. If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray XMP, Cray YMP, Cray C90, or Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[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]  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, if JOBZ = MagmaVec, then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I. If JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper) or the lower triangle (if UPLO=MagmaLower) 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). 
[out]  w  REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. 
[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.

[out]  rwork  (workspace) REAL array, dimension (MAX(1,LRWORK)) On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK. 
[in]  lrwork  INTEGER The dimension of the array RWORK.

[out]  iwork  (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. 
[in]  liwork  INTEGER The dimension of the array IWORK.

[out]  info  INTEGER

Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Modified so that no backsubstitution is performed if CHEEVD fails to converge (NEIG in old code could be greater than N causing out of bounds reference to A  reported by Ralf Meyer). Also corrected the description of INFO and the test on ITYPE. Sven, 16 Feb 05.
magma_int_t magma_chegvd_m  (  magma_int_t  ngpu, 
magma_int_t  itype,  
magma_vec_t  jobz,  
magma_uplo_t  uplo,  
magma_int_t  n,  
magmaFloatComplex *  A,  
magma_int_t  lda,  
magmaFloatComplex *  B,  
magma_int_t  ldb,  
float *  w,  
magmaFloatComplex *  work,  
magma_int_t  lwork,  
float *  rwork,  
magma_int_t  lrwork,  
magma_int_t *  iwork,  
magma_int_t  liwork,  
magma_int_t *  info  
) 
CHEGVD computes all the eigenvalues, and optionally, the 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. If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray XMP, Cray YMP, Cray C90, or Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[in]  ngpu  INTEGER Number of GPUs to use. ngpu > 0. 
[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]  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, if JOBZ = MagmaVec, then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I. If JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper) or the lower triangle (if UPLO=MagmaLower) 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). 
[out]  w  REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. 
[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.

[out]  rwork  (workspace) REAL array, dimension (MAX(1,LRWORK)) On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK. 
[in]  lrwork  INTEGER The dimension of the array RWORK.

[out]  iwork  (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. 
[in]  liwork  INTEGER The dimension of the array IWORK.

[out]  info  INTEGER

Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Modified so that no backsubstitution is performed if CHEEVD fails to converge (NEIG in old code could be greater than N causing out of bounds reference to A  reported by Ralf Meyer). Also corrected the description of INFO and the test on ITYPE. Sven, 16 Feb 05.
magma_int_t magma_dsygvd  (  magma_int_t  itype, 
magma_vec_t  jobz,  
magma_uplo_t  uplo,  
magma_int_t  n,  
double *  A,  
magma_int_t  lda,  
double *  B,  
magma_int_t  ldb,  
double *  w,  
double *  work,  
magma_int_t  lwork,  
magma_int_t *  iwork,  
magma_int_t  liwork,  
magma_int_t *  info  
) 
DSYGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite 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 symmetric and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray XMP, Cray YMP, Cray C90, or Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[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]  uplo  magma_uplo_t

[in]  n  INTEGER The order of the matrices A and B. 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. If UPLO = MagmaLower, the leading NbyN lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the matrix Z of eigenvectors. 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 JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper) or the lower triangle (if UPLO=MagmaLower) of A, including the diagonal, is destroyed. 
[in]  lda  INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[in,out]  B  DOUBLE PRECISION array, dimension (LDB, N) On entry, the symmetric 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**T * U or B = L * L**T. 
[in]  ldb  INTEGER The leading dimension of the array B. LDB >= max(1,N). 
[out]  w  DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. 
[out]  work  (workspace) DOUBLE PRECISION 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.

[out]  iwork  (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. 
[in]  liwork  INTEGER The dimension of the array IWORK.

[out]  info  INTEGER

Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Modified so that no backsubstitution is performed if DSYEVD fails to converge (NEIG in old code could be greater than N causing out of bounds reference to A  reported by Ralf Meyer). Also corrected the description of INFO and the test on ITYPE. Sven, 16 Feb 05.
magma_int_t magma_dsygvd_m  (  magma_int_t  ngpu, 
magma_int_t  itype,  
magma_vec_t  jobz,  
magma_uplo_t  uplo,  
magma_int_t  n,  
double *  A,  
magma_int_t  lda,  
double *  B,  
magma_int_t  ldb,  
double *  w,  
double *  work,  
magma_int_t  lwork,  
magma_int_t *  iwork,  
magma_int_t  liwork,  
magma_int_t *  info  
) 
DSYGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite 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 symmetric and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray XMP, Cray YMP, Cray C90, or Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[in]  ngpu  INTEGER Number of GPUs to use. ngpu > 0. 
[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]  uplo  magma_uplo_t

[in]  n  INTEGER The order of the matrices A and B. 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. If UPLO = MagmaLower, the leading NbyN lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the matrix Z of eigenvectors. 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 JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper) or the lower triangle (if UPLO=MagmaLower) of A, including the diagonal, is destroyed. 
[in]  lda  INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[in,out]  B  DOUBLE PRECISION array, dimension (LDB, N) On entry, the symmetric 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**T * U or B = L * L**T. 
[in]  ldb  INTEGER The leading dimension of the array B. LDB >= max(1,N). 
[out]  w  DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. 
[out]  work  (workspace) DOUBLE PRECISION 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.

[out]  iwork  (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. 
[in]  liwork  INTEGER The dimension of the array IWORK.

[out]  info  INTEGER

Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Modified so that no backsubstitution is performed if DSYEVD fails to converge (NEIG in old code could be greater than N causing out of bounds reference to A  reported by Ralf Meyer). Also corrected the description of INFO and the test on ITYPE. Sven, 16 Feb 05.
magma_int_t magma_ssygvd  (  magma_int_t  itype, 
magma_vec_t  jobz,  
magma_uplo_t  uplo,  
magma_int_t  n,  
float *  A,  
magma_int_t  lda,  
float *  B,  
magma_int_t  ldb,  
float *  w,  
float *  work,  
magma_int_t  lwork,  
magma_int_t *  iwork,  
magma_int_t  liwork,  
magma_int_t *  info  
) 
SSYGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite 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 symmetric and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray XMP, Cray YMP, Cray C90, or Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[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]  uplo  magma_uplo_t

[in]  n  INTEGER The order of the matrices A and B. 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. If UPLO = MagmaLower, the leading NbyN lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the matrix Z of eigenvectors. 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 JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper) or the lower triangle (if UPLO=MagmaLower) of A, including the diagonal, is destroyed. 
[in]  lda  INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[in,out]  B  REAL array, dimension (LDB, N) On entry, the symmetric 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**T * U or B = L * L**T. 
[in]  ldb  INTEGER The leading dimension of the array B. LDB >= max(1,N). 
[out]  w  REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. 
[out]  work  (workspace) REAL 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.

[out]  iwork  (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. 
[in]  liwork  INTEGER The dimension of the array IWORK.

[out]  info  INTEGER

Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Modified so that no backsubstitution is performed if SSYEVD fails to converge (NEIG in old code could be greater than N causing out of bounds reference to A  reported by Ralf Meyer). Also corrected the description of INFO and the test on ITYPE. Sven, 16 Feb 05.
magma_int_t magma_ssygvd_m  (  magma_int_t  ngpu, 
magma_int_t  itype,  
magma_vec_t  jobz,  
magma_uplo_t  uplo,  
magma_int_t  n,  
float *  A,  
magma_int_t  lda,  
float *  B,  
magma_int_t  ldb,  
float *  w,  
float *  work,  
magma_int_t  lwork,  
magma_int_t *  iwork,  
magma_int_t  liwork,  
magma_int_t *  info  
) 
SSYGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite 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 symmetric and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray XMP, Cray YMP, Cray C90, or Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[in]  ngpu  INTEGER Number of GPUs to use. ngpu > 0. 
[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]  uplo  magma_uplo_t

[in]  n  INTEGER The order of the matrices A and B. 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. If UPLO = MagmaLower, the leading NbyN lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the matrix Z of eigenvectors. 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 JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper) or the lower triangle (if UPLO=MagmaLower) of A, including the diagonal, is destroyed. 
[in]  lda  INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[in,out]  B  REAL array, dimension (LDB, N) On entry, the symmetric 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**T * U or B = L * L**T. 
[in]  ldb  INTEGER The leading dimension of the array B. LDB >= max(1,N). 
[out]  w  REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. 
[out]  work  (workspace) REAL 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.

[out]  iwork  (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. 
[in]  liwork  INTEGER The dimension of the array IWORK.

[out]  info  INTEGER

Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Modified so that no backsubstitution is performed if SSYEVD fails to converge (NEIG in old code could be greater than N causing out of bounds reference to A  reported by Ralf Meyer). Also corrected the description of INFO and the test on ITYPE. Sven, 16 Feb 05.
magma_int_t magma_zhegvd  (  magma_int_t  itype, 
magma_vec_t  jobz,  
magma_uplo_t  uplo,  
magma_int_t  n,  
magmaDoubleComplex *  A,  
magma_int_t  lda,  
magmaDoubleComplex *  B,  
magma_int_t  ldb,  
double *  w,  
magmaDoubleComplex *  work,  
magma_int_t  lwork,  
double *  rwork,  
magma_int_t  lrwork,  
magma_int_t *  iwork,  
magma_int_t  liwork,  
magma_int_t *  info  
) 
ZHEGVD computes all the eigenvalues, and optionally, the 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. If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray XMP, Cray YMP, Cray C90, or Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[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]  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, if JOBZ = MagmaVec, then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I. If JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper) or the lower triangle (if UPLO=MagmaLower) 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). 
[out]  w  DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. 
[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.

[out]  rwork  (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK. 
[in]  lrwork  INTEGER The dimension of the array RWORK.

[out]  iwork  (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. 
[in]  liwork  INTEGER The dimension of the array IWORK.

[out]  info  INTEGER

Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Modified so that no backsubstitution is performed if ZHEEVD fails to converge (NEIG in old code could be greater than N causing out of bounds reference to A  reported by Ralf Meyer). Also corrected the description of INFO and the test on ITYPE. Sven, 16 Feb 05.
magma_int_t magma_zhegvd_m  (  magma_int_t  ngpu, 
magma_int_t  itype,  
magma_vec_t  jobz,  
magma_uplo_t  uplo,  
magma_int_t  n,  
magmaDoubleComplex *  A,  
magma_int_t  lda,  
magmaDoubleComplex *  B,  
magma_int_t  ldb,  
double *  w,  
magmaDoubleComplex *  work,  
magma_int_t  lwork,  
double *  rwork,  
magma_int_t  lrwork,  
magma_int_t *  iwork,  
magma_int_t  liwork,  
magma_int_t *  info  
) 
ZHEGVD computes all the eigenvalues, and optionally, the 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. If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray XMP, Cray YMP, Cray C90, or Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
[in]  ngpu  INTEGER Number of GPUs to use. ngpu > 0. 
[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]  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, if JOBZ = MagmaVec, then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I. If JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper) or the lower triangle (if UPLO=MagmaLower) 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). 
[out]  w  DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. 
[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.

[out]  rwork  (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK. 
[in]  lrwork  INTEGER The dimension of the array RWORK.

[out]  iwork  (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. 
[in]  liwork  INTEGER The dimension of the array IWORK.

[out]  info  INTEGER

Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Modified so that no backsubstitution is performed if ZHEEVD fails to converge (NEIG in old code could be greater than N causing out of bounds reference to A  reported by Ralf Meyer). Also corrected the description of INFO and the test on ITYPE. Sven, 16 Feb 05.