single precision
[GPU kernels for non-symmetric sparse LA]

Functions

magma_int_t magma_sbajac_csr (magma_int_t localiters, magma_s_matrix D, magma_s_matrix R, magma_s_matrix b, magma_s_matrix *x, magma_queue_t queue)
 This routine is a block-asynchronous Jacobi iteration performing s local Jacobi-updates within the block.
magma_int_t magma_scompact (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dnorms, float tol, magmaInt_ptr active, magmaInt_ptr cBlock, magma_queue_t queue)
 ZCOMPACT takes a set of n vectors of size m (in dA) and their norms and compacts them into the cBlock size<=n vectors that have norms > tol.
magma_int_t magma_siteric_csr (magma_s_matrix A, magma_s_matrix A_CSR, magma_queue_t queue)
 This routine iteratively computes an incomplete Cholesky factorization.
magma_int_t magma_siterilu_csr (magma_s_matrix A, magma_s_matrix L, magma_s_matrix U, magma_queue_t queue)
 This routine iteratively computes an incomplete LU factorization.
magma_int_t magma_sjacobisetup_vector_gpu (int num_rows, magma_s_matrix b, magma_s_matrix d, magma_s_matrix c, magma_s_matrix *x, magma_queue_t queue)
 Prepares the Jacobi Iteration according to x^(k+1) = D^(-1) * b - D^(-1) * (L+U) * x^k x^(k+1) = c - M * x^k.
magma_int_t magma_slobpcg_maxpy (magma_int_t num_rows, magma_int_t num_vecs, magmaFloat_ptr X, magmaFloat_ptr Y, magma_queue_t queue)
 This routine computes a axpy for a mxn matrix:.
int magma_sbicgmerge1 (int n, magmaFloat_ptr skp, magmaFloat_ptr v, magmaFloat_ptr r, magmaFloat_ptr p)
 Mergels multiple operations into one kernel:.
int magma_sbicgmerge2 (int n, magmaFloat_ptr skp, magmaFloat_ptr r, magmaFloat_ptr v, magmaFloat_ptr s)
 Mergels multiple operations into one kernel:.
int magma_sbicgmerge3 (int n, magmaFloat_ptr skp, magmaFloat_ptr p, magmaFloat_ptr s, magmaFloat_ptr t, magmaFloat_ptr x, magmaFloat_ptr r)
 Mergels multiple operations into one kernel:.
int magma_sbicgmerge4 (int type, magmaFloat_ptr skp)
 Performs some parameter operations for the BiCGSTAB with scalars on GPU.
magma_int_t magma_sbicgmerge_spmv1 (magma_s_matrix A, magmaFloat_ptr d1, magmaFloat_ptr d2, magmaFloat_ptr dp, magmaFloat_ptr dr, magmaFloat_ptr dv, magmaFloat_ptr skp, magma_queue_t queue)
 Merges the first SpmV using CSR with the dot product and the computation of alpha.
magma_int_t magma_sbicgmerge_spmv2 (magma_s_matrix A, magmaFloat_ptr d1, magmaFloat_ptr d2, magmaFloat_ptr ds, magmaFloat_ptr dt, magmaFloat_ptr skp, magma_queue_t queue)
 Merges the second SpmV using CSR with the dot product and the computation of omega.
magma_int_t magma_sbicgmerge_xrbeta (int n, magmaFloat_ptr d1, magmaFloat_ptr d2, magmaFloat_ptr rr, magmaFloat_ptr r, magmaFloat_ptr p, magmaFloat_ptr s, magmaFloat_ptr t, magmaFloat_ptr x, magmaFloat_ptr skp, magma_queue_t queue)
 Merges the second SpmV using CSR with the dot product and the computation of omega.
magma_int_t magma_scgmerge_spmv1 (magma_s_matrix A, magmaFloat_ptr d1, magmaFloat_ptr d2, magmaFloat_ptr dd, magmaFloat_ptr dz, magmaFloat_ptr skp, magma_queue_t queue)
 Merges the first SpmV using different formats with the dot product and the computation of rho.

Function Documentation

magma_int_t magma_sbajac_csr ( magma_int_t  localiters,
magma_s_matrix  D,
magma_s_matrix  R,
magma_s_matrix  b,
magma_s_matrix *  x,
magma_queue_t  queue 
)

This routine is a block-asynchronous Jacobi iteration performing s local Jacobi-updates within the block.

Input format is two CSR matrices, one containing the diagonal blocks, one containing the rest.

Parameters:
[in] localiters magma_int_t number of local Jacobi-like updates
[in] D magma_s_matrix input matrix with diagonal blocks
[in] R magma_s_matrix input matrix with non-diagonal parts
[in] b magma_s_matrix RHS
[in] x magma_s_matrix* iterate/solution
[in] queue magma_queue_t Queue to execute in.
int magma_sbicgmerge1 ( int  n,
magmaFloat_ptr  skp,
magmaFloat_ptr  v,
magmaFloat_ptr  r,
magmaFloat_ptr  p 
)

Mergels multiple operations into one kernel:.

p = beta*p p = p-omega*beta*v p = p+r

-> p = r + beta * ( p - omega * v )

Parameters:
[in] n int dimension n
[in] skp magmaFloat_ptr set of scalar parameters
[in] v magmaFloat_ptr input v
[in] r magmaFloat_ptr input r
in/out] p magmaFloat_ptr input/output p
[in] queue magma_queue_t Queue to execute in.
int magma_sbicgmerge2 ( int  n,
magmaFloat_ptr  skp,
magmaFloat_ptr  r,
magmaFloat_ptr  v,
magmaFloat_ptr  s 
)

Mergels multiple operations into one kernel:.

s=r s=s-alpha*v

-> s = r - alpha * v

Parameters:
[in] n int dimension n
[in] skp magmaFloat_ptr set of scalar parameters
[in] r magmaFloat_ptr input r
[in] v magmaFloat_ptr input v
s] s magmaFloat_ptr output s
[in] queue magma_queue_t Queue to execute in.
int magma_sbicgmerge3 ( int  n,
magmaFloat_ptr  skp,
magmaFloat_ptr  p,
magmaFloat_ptr  s,
magmaFloat_ptr  t,
magmaFloat_ptr  x,
magmaFloat_ptr  r 
)

Mergels multiple operations into one kernel:.

x=x+alpha*p x=x+omega*s r=s r=r-omega*t

-> x = x + alpha * p + omega * s -> r = s - omega * t

Parameters:
[in] n int dimension n
[in] skp magmaFloat_ptr set of scalar parameters
[in] p magmaFloat_ptr input p
[in] s magmaFloat_ptr input s
[in] t magmaFloat_ptr input t
in/out] x magmaFloat_ptr input/output x
in/out] r magmaFloat_ptr input/output r
[in] queue magma_queue_t Queue to execute in.
int magma_sbicgmerge4 ( int  type,
magmaFloat_ptr  skp 
)

Performs some parameter operations for the BiCGSTAB with scalars on GPU.

Parameters:
[in] type int kernel type
in/out] skp magmaFloat_ptr vector with parameters
[in] queue magma_queue_t Queue to execute in.
magma_int_t magma_sbicgmerge_spmv1 ( magma_s_matrix  A,
magmaFloat_ptr  d1,
magmaFloat_ptr  d2,
magmaFloat_ptr  dp,
magmaFloat_ptr  dr,
magmaFloat_ptr  dv,
magmaFloat_ptr  skp,
magma_queue_t  queue 
)

Merges the first SpmV using CSR with the dot product and the computation of alpha.

Parameters:
[in] A magma_s_matrix system matrix
[in] d1 magmaFloat_ptr temporary vector
[in] d2 magmaFloat_ptr temporary vector
[in] dp magmaFloat_ptr input vector p
[in] dr magmaFloat_ptr input vector r
[in] dv magmaFloat_ptr output vector v
in/out] skp magmaFloat_ptr array for parameters ( skp[0]=alpha )
[in] queue magma_queue_t Queue to execute in.
magma_int_t magma_sbicgmerge_spmv2 ( magma_s_matrix  A,
magmaFloat_ptr  d1,
magmaFloat_ptr  d2,
magmaFloat_ptr  ds,
magmaFloat_ptr  dt,
magmaFloat_ptr  skp,
magma_queue_t  queue 
)

Merges the second SpmV using CSR with the dot product and the computation of omega.

Parameters:
[in] A magma_s_matrix input matrix
[in] d1 magmaFloat_ptr temporary vector
[in] d2 magmaFloat_ptr temporary vector
[in] ds magmaFloat_ptr input vector s
[in] dt magmaFloat_ptr output vector t
in/out] skp magmaFloat_ptr array for parameters
[in] queue magma_queue_t Queue to execute in.
magma_int_t magma_sbicgmerge_xrbeta ( int  n,
magmaFloat_ptr  d1,
magmaFloat_ptr  d2,
magmaFloat_ptr  rr,
magmaFloat_ptr  r,
magmaFloat_ptr  p,
magmaFloat_ptr  s,
magmaFloat_ptr  t,
magmaFloat_ptr  x,
magmaFloat_ptr  skp,
magma_queue_t  queue 
)

Merges the second SpmV using CSR with the dot product and the computation of omega.

Parameters:
[in] n int dimension n
[in] d1 magmaFloat_ptr temporary vector
[in] d2 magmaFloat_ptr temporary vector
[in] rr magmaFloat_ptr input vector rr
[in] r magmaFloat_ptr input/output vector r
[in] p magmaFloat_ptr input vector p
[in] s magmaFloat_ptr input vector s
[in] t magmaFloat_ptr input vector t
[out] x magmaFloat_ptr output vector x
[in] skp magmaFloat_ptr array for parameters
[in] queue magma_queue_t Queue to execute in.
magma_int_t magma_scgmerge_spmv1 ( magma_s_matrix  A,
magmaFloat_ptr  d1,
magmaFloat_ptr  d2,
magmaFloat_ptr  dd,
magmaFloat_ptr  dz,
magmaFloat_ptr  skp,
magma_queue_t  queue 
)

Merges the first SpmV using different formats with the dot product and the computation of rho.

Parameters:
[in] A magma_s_matrix input matrix
[in] d1 magmaFloat_ptr temporary vector
[in] d2 magmaFloat_ptr temporary vector
[in] dd magmaFloat_ptr input vector d
[out] dz magmaFloat_ptr input vector z
[out] skp magmaFloat_ptr array for parameters ( skp[3]=rho )
[in] queue magma_queue_t Queue to execute in.
magma_int_t magma_scompact ( magma_int_t  m,
magma_int_t  n,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dnorms,
float  tol,
magmaInt_ptr  active,
magmaInt_ptr  cBlock,
magma_queue_t  queue 
)

ZCOMPACT takes a set of n vectors of size m (in dA) and their norms and compacts them into the cBlock size<=n vectors that have norms > tol.

The active mask array has 1 or 0, showing if a vector remained or not in the compacted resulting set of vectors.

Parameters:
[in] m INTEGER The number of rows of the matrix dA. M >= 0.
[in] n INTEGER The number of columns of the matrix dA. N >= 0.
[in] in,out] dA COMPLEX REAL array, dimension (LDDA,N) The m by n matrix dA.
[in] ldda INTEGER The leading dimension of the array dA. LDDA >= max(1,M).
[in] dnorms REAL array, dimension N The norms of the N vectors in dA
[in] tol DOUBLE PRECISON The tolerance value used in the criteria to compact or not.
[in] out] active INTEGER array, dimension N A mask of 1s and 0s showing if a vector remains or has been removed
[in] out] cBlock magmaInt_ptr The number of vectors that remain in dA (i.e., with norms > tol).
[in] queue magma_queue_t Queue to execute in.
magma_int_t magma_siteric_csr ( magma_s_matrix  A,
magma_s_matrix  A_CSR,
magma_queue_t  queue 
)

This routine iteratively computes an incomplete Cholesky factorization.

The idea is according to Edmond Chow's presentation at SIAM 2014. This routine was used in the ISC 2015 paper: E. Chow et al.: 'Study of an Asynchronous Iterative Algorithm for Computing Incomplete Factorizations on GPUs'

The input format of the initial guess matrix A is Magma_CSRCOO, A_CSR is CSR or CSRCOO format.

Parameters:
[in] A magma_s_matrix input matrix A - initial guess (lower triangular)
[in] out] A_CSR magma_s_matrix input/output matrix containing the IC approximation
[in] A_CSR magma_s_matrix input/output matrix containing the IC approximation
magma_int_t magma_siterilu_csr ( magma_s_matrix  A,
magma_s_matrix  L,
magma_s_matrix  U,
magma_queue_t  queue 
)

This routine iteratively computes an incomplete LU factorization.

The idea is according to Edmond Chow's presentation at SIAM 2014. This routine was used in the ISC 2015 paper: E. Chow et al.: 'Study of an Asynchronous Iterative Algorithm for Computing Incomplete Factorizations on GPUs'

The input format of the matrix is Magma_CSRCOO for the upper and lower triangular parts. Note however, that we flip col and rowidx for the U-part. Every component of L and U is handled by one thread.

Parameters:
[in] A magma_s_matrix input matrix A determing initial guess & processing order
[in] out] L magma_s_matrix input/output matrix L containing the ILU approximation
[in] out] U magma_s_matrix input/output matrix U containing the ILU approximation
[in] A_CSR magma_s_matrix input/output matrix containing the IC approximation
magma_int_t magma_sjacobisetup_vector_gpu ( int  num_rows,
magma_s_matrix  b,
magma_s_matrix  d,
magma_s_matrix  c,
magma_s_matrix *  x,
magma_queue_t  queue 
)

Prepares the Jacobi Iteration according to x^(k+1) = D^(-1) * b - D^(-1) * (L+U) * x^k x^(k+1) = c - M * x^k.

Returns the vector c. It calls a GPU kernel

Parameters:
[in] num_rows magma_int_t number of rows
[in] b magma_s_matrix RHS b
[in] d magma_s_matrix vector with diagonal entries
[out] c magma_s_matrix* c = D^(-1) * b
[out] x magma_s_matrix* iteration vector
[in] queue magma_queue_t Queue to execute in.
magma_int_t magma_slobpcg_maxpy ( magma_int_t  num_rows,
magma_int_t  num_vecs,
magmaFloat_ptr  X,
magmaFloat_ptr  Y,
magma_queue_t  queue 
)

This routine computes a axpy for a mxn matrix:.

Y = X + Y

It replaces: magma_saxpy(m*n, c_one, Y, 1, X, 1);

/ x1[0] x2[0] x3[0] \ | x1[1] x2[1] x3[1] | X = | x1[2] x2[2] x3[2] | = x1[0] x1[1] x1[2] x1[3] x1[4] x2[0] x2[1] . | x1[3] x2[3] x3[3] | \ x1[4] x2[4] x3[4] /

Parameters:
[in] num_rows magma_int_t number of rows
[in] num_vecs magma_int_t number of vectors
[in] X magmaFloat_ptr input vector X
in/out] Y magmaFloat_ptr input/output vector Y
[in] queue magma_queue_t Queue to execute in.

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