MAGMA
2.3.0
Matrix Algebra for GPU and Multicore Architectures

Functions  
magma_int_t  magma_dsytrd_sy2sb (magma_uplo_t uplo, magma_int_t n, magma_int_t nb, double *A, magma_int_t lda, double *tau, double *work, magma_int_t lwork, magmaDouble_ptr dT, magma_int_t *info) 
DSYTRD_HE2HB reduces a real symmetric matrix A to real symmetric banddiagonal form T by an orthogonal similarity transformation: Q**H * A * Q = T. More...  
magma_int_t  magma_dsytrd_sy2sb_mgpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nb, double *A, magma_int_t lda, double *tau, double *work, magma_int_t lwork, magmaDouble_ptr dAmgpu[], magma_int_t ldda, magmaDouble_ptr dTmgpu[], magma_int_t lddt, magma_int_t ngpu, magma_int_t distblk, magma_queue_t queues[][20], magma_int_t nqueue, magma_int_t *info) 
DSYTRD_HE2HB reduces a real symmetric matrix A to real symmetric banddiagonal form T by an orthogonal similarity transformation: Q**H * A * Q = T. More...  
magma_int_t  magma_ssytrd_sy2sb (magma_uplo_t uplo, magma_int_t n, magma_int_t nb, float *A, magma_int_t lda, float *tau, float *work, magma_int_t lwork, magmaFloat_ptr dT, magma_int_t *info) 
SSYTRD_HE2HB reduces a real symmetric matrix A to real symmetric banddiagonal form T by an orthogonal similarity transformation: Q**H * A * Q = T. More...  
magma_int_t  magma_ssytrd_sy2sb_mgpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nb, float *A, magma_int_t lda, float *tau, float *work, magma_int_t lwork, magmaFloat_ptr dAmgpu[], magma_int_t ldda, magmaFloat_ptr dTmgpu[], magma_int_t lddt, magma_int_t ngpu, magma_int_t distblk, magma_queue_t queues[][20], magma_int_t nqueue, magma_int_t *info) 
SSYTRD_HE2HB reduces a real symmetric matrix A to real symmetric banddiagonal form T by an orthogonal similarity transformation: Q**H * A * Q = T. More...  
magma_int_t magma_dsytrd_sy2sb  (  magma_uplo_t  uplo, 
magma_int_t  n,  
magma_int_t  nb,  
double *  A,  
magma_int_t  lda,  
double *  tau,  
double *  work,  
magma_int_t  lwork,  
magmaDouble_ptr  dT,  
magma_int_t *  info  
) 
DSYTRD_HE2HB reduces a real symmetric matrix A to real symmetric banddiagonal form T by an orthogonal similarity transformation: Q**H * A * Q = T.
This version stores the triangular matrices T used in the accumulated Householder transformations (I  V T V').
[in]  uplo  magma_uplo_t

[in]  n  INTEGER The order of the matrix A. n >= 0. 
[in]  nb  INTEGER The inner blocking. nb >= 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, if UPLO = MagmaUpper, the Upper banddiagonal of A is overwritten by the corresponding elements of the banddiagonal matrix T, and the elements above the band diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors; if UPLO = MagmaLower, the the Lower banddiagonal of A is overwritten by the corresponding elements of the banddiagonal matrix T, and the elements below the banddiagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. See Further Details. 
[in]  lda  INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[out]  tau  DOUBLE PRECISION array, dimension (N1) The scalar factors of the elementary reflectors (see Further Details). 
[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 dimension of the array WORK. LWORK >= 1. For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. 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. 
[out]  dT  DOUBLE PRECISION array on the GPU, dimension N*NB, where NB is the optimal blocksize. On exit dT holds the upper triangular matrices T from the accumulated Householder transformations (I  V T V') used in the factorization. The nb x nb matrices T are ordered consecutively in memory one after another. 
[out]  info  INTEGER

If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary reflectors
Q = H(n1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I  tau * v * v'
where tau is a real scalar, and v is a real vector with v(i+1:n) = 0 and v(i) = 1; v(1:i1) is stored on exit in A(1:i1,i+1), and tau in TAU(i).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(n1).
Each H(i) has the form
H(i) = I  tau * v * v'
where tau is a real scalar, and v is a real vector with v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), and tau in TAU(i).
The contents of A on exit are illustrated by the following examples with n = 5:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( d e v2 v3 v4 ) ( d ) ( d e v3 v4 ) ( e d ) ( d e v4 ) ( v1 e d ) ( d e ) ( v1 v2 e d ) ( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and offdiagonal elements of T, and vi denotes an element of the vector defining H(i).
magma_int_t magma_dsytrd_sy2sb_mgpu  (  magma_uplo_t  uplo, 
magma_int_t  n,  
magma_int_t  nb,  
double *  A,  
magma_int_t  lda,  
double *  tau,  
double *  work,  
magma_int_t  lwork,  
magmaDouble_ptr  dAmgpu[],  
magma_int_t  ldda,  
magmaDouble_ptr  dTmgpu[],  
magma_int_t  lddt,  
magma_int_t  ngpu,  
magma_int_t  distblk,  
magma_queue_t  queues[][20],  
magma_int_t  nqueue,  
magma_int_t *  info  
) 
DSYTRD_HE2HB reduces a real symmetric matrix A to real symmetric banddiagonal form T by an orthogonal similarity transformation: Q**H * A * Q = T.
This version stores the triangular matrices T used in the accumulated Householder transformations (I  V T V').
[in]  uplo  magma_uplo_t

[in]  n  INTEGER The order of the matrix A. N >= 0. 
[in]  nb  INTEGER The inner blocking. nb >= 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, if UPLO = MagmaUpper, the Upper banddiagonal of A is overwritten by the corresponding elements of the banddiagonal matrix T, and the elements above the band diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors; if UPLO = MagmaLower, the the Lower banddiagonal of A is overwritten by the corresponding elements of the banddiagonal matrix T, and the elements below the banddiagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. See Further Details. 
[in]  lda  INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[out]  tau  DOUBLE PRECISION array, dimension (N1) The scalar factors of the elementary reflectors (see Further Details). 
[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 dimension of the array WORK. LWORK >= 1. For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. 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. 
[in,out]  dAmgpu  DOUBLE PRECISION array of pointer, dimension (ngpu) Each point to a DOUBLE PRECISION array, dimension (LDDA, nlocal) which hold the local matrix on each GPU. 
[in]  ldda  INTEGER The leading dimension of the array dAmgpu. ldda >= max(1,n). 
[in,out]  dTmgpu  DOUBLE PRECISION array of pointer, dimension (ngpu) Each point to a DOUBLE PRECISION array on the GPU, dimension n*nb, where nb is the optimal blocksize. On exit dT holds the upper triangular matrices T from the accumulated Householder transformations (I  V T V') used in the factorization. The nb x nb matrices T are ordered consecutively in memory one after another. 
[in]  lddt  INTEGER The leading dimension of each array dT. lddt >= max(1,nb). 
[in]  ngpu  INTEGER The number of GPUs. 
[in]  distblk  INTEGER Internal parameter for performance tuning. The size of the distribution/computation. 
[in]  queues  Array of magma_queue_t that point to the queues to be used in execution/communications. Dimension >= max(3, ngpu+1) Queue to execute in. 
[in]  nqueue  INTEGER The number of queues should be >= max(3, ngpu+1). 
[out]  info  INTEGER

If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary reflectors
Q = H(n1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I  tau * v * v'
where tau is a real scalar, and v is a real vector with v(i+1:n) = 0 and v(i) = 1; v(1:i1) is stored on exit in A(1:i1,i+1), and tau in TAU(i).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(n1).
Each H(i) has the form
H(i) = I  tau * v * v'
where tau is a real scalar, and v is a real vector with v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), and tau in TAU(i).
The contents of A on exit are illustrated by the following examples with n = 5:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( d e v2 v3 v4 ) ( d ) ( d e v3 v4 ) ( e d ) ( d e v4 ) ( v1 e d ) ( d e ) ( v1 v2 e d ) ( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and offdiagonal elements of T, and vi denotes an element of the vector defining H(i).
magma_int_t magma_ssytrd_sy2sb  (  magma_uplo_t  uplo, 
magma_int_t  n,  
magma_int_t  nb,  
float *  A,  
magma_int_t  lda,  
float *  tau,  
float *  work,  
magma_int_t  lwork,  
magmaFloat_ptr  dT,  
magma_int_t *  info  
) 
SSYTRD_HE2HB reduces a real symmetric matrix A to real symmetric banddiagonal form T by an orthogonal similarity transformation: Q**H * A * Q = T.
This version stores the triangular matrices T used in the accumulated Householder transformations (I  V T V').
[in]  uplo  magma_uplo_t

[in]  n  INTEGER The order of the matrix A. n >= 0. 
[in]  nb  INTEGER The inner blocking. nb >= 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, if UPLO = MagmaUpper, the Upper banddiagonal of A is overwritten by the corresponding elements of the banddiagonal matrix T, and the elements above the band diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors; if UPLO = MagmaLower, the the Lower banddiagonal of A is overwritten by the corresponding elements of the banddiagonal matrix T, and the elements below the banddiagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. See Further Details. 
[in]  lda  INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[out]  tau  REAL array, dimension (N1) The scalar factors of the elementary reflectors (see Further Details). 
[out]  work  (workspace) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. 
[in]  lwork  INTEGER The dimension of the array WORK. LWORK >= 1. For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. 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. 
[out]  dT  REAL array on the GPU, dimension N*NB, where NB is the optimal blocksize. On exit dT holds the upper triangular matrices T from the accumulated Householder transformations (I  V T V') used in the factorization. The nb x nb matrices T are ordered consecutively in memory one after another. 
[out]  info  INTEGER

If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary reflectors
Q = H(n1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I  tau * v * v'
where tau is a real scalar, and v is a real vector with v(i+1:n) = 0 and v(i) = 1; v(1:i1) is stored on exit in A(1:i1,i+1), and tau in TAU(i).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(n1).
Each H(i) has the form
H(i) = I  tau * v * v'
where tau is a real scalar, and v is a real vector with v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), and tau in TAU(i).
The contents of A on exit are illustrated by the following examples with n = 5:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( d e v2 v3 v4 ) ( d ) ( d e v3 v4 ) ( e d ) ( d e v4 ) ( v1 e d ) ( d e ) ( v1 v2 e d ) ( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and offdiagonal elements of T, and vi denotes an element of the vector defining H(i).
magma_int_t magma_ssytrd_sy2sb_mgpu  (  magma_uplo_t  uplo, 
magma_int_t  n,  
magma_int_t  nb,  
float *  A,  
magma_int_t  lda,  
float *  tau,  
float *  work,  
magma_int_t  lwork,  
magmaFloat_ptr  dAmgpu[],  
magma_int_t  ldda,  
magmaFloat_ptr  dTmgpu[],  
magma_int_t  lddt,  
magma_int_t  ngpu,  
magma_int_t  distblk,  
magma_queue_t  queues[][20],  
magma_int_t  nqueue,  
magma_int_t *  info  
) 
SSYTRD_HE2HB reduces a real symmetric matrix A to real symmetric banddiagonal form T by an orthogonal similarity transformation: Q**H * A * Q = T.
This version stores the triangular matrices T used in the accumulated Householder transformations (I  V T V').
[in]  uplo  magma_uplo_t

[in]  n  INTEGER The order of the matrix A. N >= 0. 
[in]  nb  INTEGER The inner blocking. nb >= 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, if UPLO = MagmaUpper, the Upper banddiagonal of A is overwritten by the corresponding elements of the banddiagonal matrix T, and the elements above the band diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors; if UPLO = MagmaLower, the the Lower banddiagonal of A is overwritten by the corresponding elements of the banddiagonal matrix T, and the elements below the banddiagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. See Further Details. 
[in]  lda  INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[out]  tau  REAL array, dimension (N1) The scalar factors of the elementary reflectors (see Further Details). 
[out]  work  (workspace) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. 
[in]  lwork  INTEGER The dimension of the array WORK. LWORK >= 1. For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. 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. 
[in,out]  dAmgpu  REAL array of pointer, dimension (ngpu) Each point to a REAL array, dimension (LDDA, nlocal) which hold the local matrix on each GPU. 
[in]  ldda  INTEGER The leading dimension of the array dAmgpu. ldda >= max(1,n). 
[in,out]  dTmgpu  REAL array of pointer, dimension (ngpu) Each point to a REAL array on the GPU, dimension n*nb, where nb is the optimal blocksize. On exit dT holds the upper triangular matrices T from the accumulated Householder transformations (I  V T V') used in the factorization. The nb x nb matrices T are ordered consecutively in memory one after another. 
[in]  lddt  INTEGER The leading dimension of each array dT. lddt >= max(1,nb). 
[in]  ngpu  INTEGER The number of GPUs. 
[in]  distblk  INTEGER Internal parameter for performance tuning. The size of the distribution/computation. 
[in]  queues  Array of magma_queue_t that point to the queues to be used in execution/communications. Dimension >= max(3, ngpu+1) Queue to execute in. 
[in]  nqueue  INTEGER The number of queues should be >= max(3, ngpu+1). 
[out]  info  INTEGER

If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary reflectors
Q = H(n1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I  tau * v * v'
where tau is a real scalar, and v is a real vector with v(i+1:n) = 0 and v(i) = 1; v(1:i1) is stored on exit in A(1:i1,i+1), and tau in TAU(i).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(n1).
Each H(i) has the form
H(i) = I  tau * v * v'
where tau is a real scalar, and v is a real vector with v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), and tau in TAU(i).
The contents of A on exit are illustrated by the following examples with n = 5:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( d e v2 v3 v4 ) ( d ) ( d e v3 v4 ) ( e d ) ( d e v4 ) ( v1 e d ) ( d e ) ( v1 v2 e d ) ( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and offdiagonal elements of T, and vi denotes an element of the vector defining H(i).