/**
Purpose
-------
DGEQRF computes a QR factorization of a DOUBLE PRECISION M-by-N matrix A:
A = Q * R. This version does not require work space on the GPU
passed as input. GPU memory is allocated in the routine.
This uses 2 queues to overlap communication and computation.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
A DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[out]
tau DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
\n
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= max( N*NB, 2*NB*NB ),
where NB can be obtained through magma_get_dgeqrf_nb( M, N ).
\n
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.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
---------------
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
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-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
@ingroup magma_dgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_dgeqrf(
magma_int_t m, magma_int_t n,
double *A, magma_int_t lda,
double *tau,
double *work, magma_int_t lwork,
magma_int_t *info )
{
#define A(i_,j_) (A + (i_) + (j_)*lda)
#ifdef HAVE_clBLAS
#define dA(i_,j_) dA, ((i_) + (j_)*ldda + dA_offset)
#define dT(i_,j_) dT, ((i_) + (j_)*nb + dT_offset)
#define dwork(i_) dwork, ((i_) + dwork_offset)
#else
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define dT(i_,j_) (dT + (i_) + (j_)*nb)
#define dwork(i_) (dwork + (i_))
#endif
/* Constants */
const double c_one = MAGMA_D_ONE;
/* Local variables */
magmaDouble_ptr dA, dT, dwork;
magma_int_t i, ib, min_mn, ldda, lddwork, old_i, old_ib;
/* Function Body */
*info = 0;
magma_int_t nb = magma_get_dgeqrf_nb( m, n );
// need 2*nb*nb to store T and upper triangle of V simultaneously
magma_int_t lwkopt = max( n*nb, 2*nb*nb );
work[0] = magma_dmake_lwork( lwkopt );
bool lquery = (lwork == -1);
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
} else if (lwork < max(1, lwkopt) && ! lquery) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
min_mn = min( m, n );
if (min_mn == 0) {
work[0] = c_one;
return *info;
}
// largest N for larfb is n-nb (trailing matrix lacks 1st panel)
lddwork = magma_roundup( n, 32 ) - nb;
ldda = magma_roundup( m, 32 );
magma_int_t ngpu = magma_num_gpus();
if ( ngpu > 1 ) {
/* call multiple-GPU interface */
return magma_dgeqrf_m( ngpu, m, n, A, lda, tau, work, lwork, info );
}
// allocate space for dA, dwork, and dT
if (MAGMA_SUCCESS != magma_dmalloc( &dA, n*ldda + nb*lddwork + nb*nb )) {
/* alloc failed so call non-GPU-resident version */
return magma_dgeqrf_ooc( m, n, A, lda, tau, work, lwork, info );
}
dwork = dA + n*ldda;
dT = dA + n*ldda + nb*lddwork;
magma_queue_t queues[2];
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queues[0] );
magma_queue_create( cdev, &queues[1] );
//used for timing CPU and GPU
int iter = 0;
float cpu_time = 0.0;
float gpu_time = 0.0;
int affinity = map_cpu(0);
if(affinity != 0)
{
printf("affinity failed\n");
return -1;
}
magma_set_lapack_numthreads(1);
// for initial setting, better to be automatic in the future
// SetGPUFreq(324, 324);
// system("echo 1200000 > /sys/devices/system/cpu/cpu0/cpufreq/scaling_setspeed");
SetGPUFreq(2600, 705);
system("echo 2500000 > /sys/devices/system/cpu/cpu0/cpufreq/scaling_setspeed");
double gpu_iter1_low = 2096.544434;
double gpu_iter1_high = 478.825226;
double cpu_iter1_low = 1792.011230;
double cpu_iter1_high = 1413.732788;
double gpu_pred_high = gpu_iter1_high;
double gpu_pred_low = gpu_iter1_low;
double cpu_pred_high = cpu_iter1_high;
double cpu_pred_low = cpu_iter1_low;
double ratio_split_freq = 0;
double time_until_interrupt = 0;
cudaEvent_t start_cpu, stop_cpu;
cudaEvent_t start_gpu, stop_gpu;
// switches for different modes
bool timing = false; //for initial setting only, greatly impact performance
bool dvfs = false; //turn on dvfs energy saving
bool relax = false; //turn on relax scheme
bool r2h = false; // turn on race to halt
//these parameters need to be tuned in future works.
double dvfs_converage = 0.5;
double prediction_offset_gpu = 0.65;
double prediction_offset_cpu = 0.65;
//for nvprof profiler, brings slight constant performance overhead
//cudaProfilerStart();
if ( (nb > 1) && (nb < min_mn) ) {
/* Use blocked code initially.
Asynchronously send the matrix to the GPU except the first panel. */
magma_dsetmatrix_async( m, n-nb,
A(0,nb), lda,
dA(0,nb), ldda, queues[0] );
old_i = 0;
old_ib = nb;
for (i = 0; i < min_mn-nb; i += nb) {
ib = min( min_mn-i, nb );
if (i > 0) {
/* get i-th panel from device */
magma_queue_sync( queues[1] );
magma_dgetmatrix_async( m-i, ib,
dA(i,i), ldda,
A(i,i), lda, queues[0] );
if (timing) {
//start gpu timing
cudaEventCreate(&start_gpu);
cudaEventCreate(&stop_gpu);
cudaEventRecord(start_gpu, 0);
}
/* Apply H' to A(i:m,i+2*ib:n) from the left */
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
m-old_i, n-old_i-2*old_ib, old_ib,
dA(old_i, old_i), ldda, dT(0,0), nb,
dA(old_i, old_i+2*old_ib), ldda, dwork(0), lddwork, queues[1] );
double ratio_slack_pred = 1.0 - (double)nb/(m-iter*nb);
cpu_pred_high = cpu_pred_high * ratio_slack_pred;
cpu_pred_low = cpu_pred_low * ratio_slack_pred;
gpu_pred_high = gpu_pred_high * ratio_slack_pred * ratio_slack_pred;
gpu_pred_low = gpu_pred_low * ratio_slack_pred * ratio_slack_pred;
if (timing) {
printf("iter:%d GPU time pred:%f\n", iter, gpu_pred_high);
printf("iter:%d CPU time pred:%f\n", iter, cpu_pred_high);
}
if (iter < dvfs_converage*(min_mn-nb)/nb) {
if (cpu_pred_high > gpu_pred_high) { //slack on GPU
ratio_split_freq = (cpu_pred_high - gpu_pred_high) / (gpu_pred_high * ((gpu_iter1_low / gpu_iter1_high) - 1));
time_until_interrupt = gpu_pred_low * ratio_split_freq;
//printf("iter:%d time_until_interrupt:%f\n", iter, time_until_interrupt);
// printf("iter:%d ratio_split_freq:%f\n", iter, ratio_split_freq);
if (dvfs) {
if ((!relax) || (relax && ratio_split_freq > 0.05)) {
if (ratio_split_freq < 1)
dvfs_adjust(time_until_interrupt*prediction_offset_gpu, 'g');
else
dvfs_adjust(cpu_pred_high, 'g');
}
} else if (r2h) {
r2h_adjust(gpu_pred_high, cpu_pred_high - gpu_pred_high, 'g');
}
} else { //slack on CPU
ratio_split_freq = (gpu_pred_high - cpu_pred_high) / (cpu_pred_high * ((cpu_iter1_low / cpu_iter1_high) - 1));
time_until_interrupt = cpu_pred_low * ratio_split_freq;
if (dvfs) {
if ((!relax) || (relax && ratio_split_freq > 0.05)) {
if (ratio_split_freq < 1)
dvfs_adjust(time_until_interrupt*prediction_offset_cpu, 'c');
else
dvfs_adjust(gpu_pred_high, 'c');
}
} else if (r2h) {
r2h_adjust(cpu_pred_high, gpu_pred_high - cpu_pred_high, 'c');
}
}
}
if (timing) {
//end gpu timing
cudaEventRecord(stop_gpu, 0);
cudaEventSynchronize(stop_gpu);
cudaEventElapsedTime(&gpu_time, start_gpu, stop_gpu);
cudaEventDestroy(start_gpu);
cudaEventDestroy(stop_gpu);
printf("iter:%d GPU time:%f\n", iter, gpu_time);
}
magma_dgetmatrix_async( i, ib,
dA(0,i), ldda,
A(0,i), lda, queues[1] );
magma_queue_sync( queues[0] );
}
magma_int_t rows = m-i;
if (timing) {
//start cpu timing
cudaEventCreate(&start_cpu);
cudaEventCreate(&stop_cpu);
cudaEventRecord(start_cpu, 0);
}
lapackf77_dgeqrf( &rows, &ib, A(i,i), &lda, tau+i, work, &lwork, info );
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib, A(i,i), &lda, tau+i, work, &ib );
if (timing) {
//end cpu timing
cudaEventRecord(stop_cpu, 0);
cudaEventSynchronize(stop_cpu);
cudaEventElapsedTime(&cpu_time, start_cpu, stop_cpu);
cudaEventDestroy(start_cpu);
cudaEventDestroy(stop_cpu);
printf("iter:%d CPU time:%f\n", iter, cpu_time);
if (gpu_time < cpu_time) {
printf("slack: +\n");
} else {
printf("slack: -\n");
}
}
magma_dpanel_to_q( MagmaUpper, ib, A(i,i), lda, work+ib*ib );
/* put i-th V matrix onto device */
magma_dsetmatrix_async( rows, ib, A(i,i), lda, dA(i,i), ldda, queues[0] );
/* put T matrix onto device */
magma_queue_sync( queues[1] );
magma_dsetmatrix_async( ib, ib, work, ib, dT(0,0), nb, queues[0] );
magma_queue_sync( queues[0] );
if (i + ib < n) {
if (i+ib < min_mn-nb) {
/* Apply H' to A(i:m,i+ib:i+2*ib) from the left (look-ahead) */
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dA(i, i ), ldda, dT(0,0), nb,
dA(i, i+ib), ldda, dwork(0), lddwork, queues[1] );
magma_dq_to_panel( MagmaUpper, ib, A(i,i), lda, work+ib*ib );
}
else {
/* After last panel, update whole trailing matrix. */
/* Apply H' to A(i:m,i+ib:n) from the left */
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n-i-ib, ib,
dA(i, i ), ldda, dT(0,0), nb,
dA(i, i+ib), ldda, dwork(0), lddwork, queues[1] );
magma_dq_to_panel( MagmaUpper, ib, A(i,i), lda, work+ib*ib );
}
old_i = i;
old_ib = ib;
}
iter ++;
}
//for nvprof profiler.
//cudaProfilerStop();
} else {
i = 0;
}
/* Use unblocked code to factor the last or only block. */
if (i < min_mn) {
ib = n-i;
if (i != 0) {
magma_dgetmatrix( m, ib, dA(0,i), ldda, A(0,i), lda, queues[1] );
}
magma_int_t rows = m-i;
lapackf77_dgeqrf( &rows, &ib, A(i,i), &lda, tau+i, work, &lwork, info );
}
magma_queue_destroy( queues[0] );
magma_queue_destroy( queues[1] );
magma_free( dA );
return *info;
} /* magma_dgeqrf */
static void signal_handler(int signal) {
SetGPUFreq(2600, 758);
}
/**
Purpose
-------
DGEBRD reduces a general real M-by-N matrix A to upper or lower
bidiagonal form B by an orthogonal transformation: Q**H * A * P = B.
If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
Arguments
---------
@param[in]
m INTEGER
The number of rows in the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns in the matrix A. N >= 0.
@param[in,out]
A DOUBLE_PRECISION array, dimension (LDA,N)
On entry, the M-by-N general matrix to be reduced.
On exit,
if m >= n, the diagonal and the first superdiagonal are
overwritten with the upper bidiagonal matrix B; the
elements below the diagonal, with the array TAUQ, represent
the orthogonal matrix Q as a product of elementary
reflectors, and the elements above the first superdiagonal,
with the array TAUP, represent the orthogonal matrix P as
a product of elementary reflectors;
\n
if m < n, the diagonal and the first subdiagonal are
overwritten with the lower bidiagonal matrix B; the
elements below the first subdiagonal, with the array TAUQ,
represent the orthogonal matrix Q as a product of
elementary reflectors, and the elements above the diagonal,
with the array TAUP, represent the orthogonal matrix P as
a product of elementary reflectors.
See Further Details.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[out]
d double precision array, dimension (min(M,N))
The diagonal elements of the bidiagonal matrix B:
D(i) = A(i,i).
@param[out]
e double precision array, dimension (min(M,N)-1)
The off-diagonal elements of the bidiagonal matrix B:
if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
@param[out]
tauq DOUBLE_PRECISION array dimension (min(M,N))
The scalar factors of the elementary reflectors which
represent the orthogonal matrix Q. See Further Details.
@param[out]
taup DOUBLE_PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors which
represent the orthogonal matrix P. See Further Details.
@param[out]
work (workspace) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK. LWORK >= (M+N)*NB, where NB
is the optimal blocksize.
\n
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.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
---------------
The matrices Q and P are represented as products of elementary
reflectors:
If m >= n,
Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1)
Each H(i) and G(i) has the form:
H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'
where tauq and taup are real scalars, and v and u are real vectors;
v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i);
u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n);
tauq is stored in TAUQ(i) and taup in TAUP(i).
If m < n,
Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m)
Each H(i) and G(i) has the form:
H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'
where tauq and taup are real scalars, and v and u are real vectors;
v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n);
tauq is stored in TAUQ(i) and taup in TAUP(i).
The contents of A on exit are illustrated by the following examples:
@verbatim
m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n):
( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 )
( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 )
( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 )
( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 )
( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 )
( v1 v2 v3 v4 v5 )
@endverbatim
where d and e denote diagonal and off-diagonal elements of B, vi
denotes an element of the vector defining H(i), and ui an element of
the vector defining G(i).
@ingroup magma_dgesvd_comp
********************************************************************/
extern "C" magma_int_t
magma_dgebrd(
magma_int_t m, magma_int_t n,
double *A, magma_int_t lda, double *d, double *e,
double *tauq, double *taup,
double *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i, j) (A + (j)*lda + (i))
#define dA(i, j) (dA + (j)*ldda + (i))
double c_neg_one = MAGMA_D_NEG_ONE;
double c_one = MAGMA_D_ONE;
double *dA, *dwork;
magma_int_t ncol, nrow, jmax, nb, ldda;
magma_int_t i, j, nx;
magma_int_t iinfo;
magma_int_t minmn;
magma_int_t ldwrkx, ldwrky, lwkopt;
magma_int_t lquery;
nb = magma_get_dgebrd_nb(n);
ldda = m;
lwkopt = (m + n) * nb;
work[0] = MAGMA_D_MAKE( lwkopt, 0. );
lquery = (lwork == -1);
/* Check arguments */
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
} else if (lwork < lwkopt && (! lquery) ) {
*info = -10;
}
if (*info < 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Quick return if possible */
minmn = min(m,n);
if (minmn == 0) {
work[0] = c_one;
return *info;
}
if (MAGMA_SUCCESS != magma_dmalloc( &dA, n*ldda + (m + n)*nb )) {
fprintf (stderr, "!!!! device memory allocation error in dgebrd\n" );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dwork = dA + n*ldda;
ldwrkx = m;
ldwrky = n;
/* Set the block/unblock crossover point NX. */
nx = 128;
/* Copy the matrix to the GPU */
if (minmn - nx >= 1) {
magma_dsetmatrix( m, n, A, lda, dA, ldda );
}
for (i=0; i < (minmn - nx); i += nb) {
/* Reduce rows and columns i:i+nb-1 to bidiagonal form and return
the matrices X and Y which are needed to update the unreduced
part of the matrix */
nrow = m - i;
ncol = n - i;
/* Get the current panel (no need for the 1st iteration) */
if ( i > 0 ) {
magma_dgetmatrix( nrow, nb, dA(i, i), ldda, A( i, i), lda );
magma_dgetmatrix( nb, ncol - nb,
dA(i, i+nb), ldda,
A( i, i+nb), lda );
}
magma_queue_t stream;
magmablasGetKernelStream( &stream );
magma_queue_sync( stream );
SetGPUFreq(2600, 614);
magma_dlabrd_gpu(nrow, ncol, nb,
A(i, i), lda, dA(i, i), ldda,
d+i, e+i, tauq+i, taup+i,
work, ldwrkx, dwork, ldwrkx, // x, dx
work+(ldwrkx*nb), ldwrky, dwork+(ldwrkx*nb), ldwrky); // y, dy
magma_queue_sync( stream );
SetGPUFreq(2600, 705);
/* Update the trailing submatrix A(i+nb:m,i+nb:n), using an update
of the form A := A - V*Y' - X*U' */
nrow = m - i - nb;
ncol = n - i - nb;
// Send Y back to the GPU
magma_dsetmatrix( nrow, nb, work + nb, ldwrkx, dwork + nb, ldwrkx );
magma_dsetmatrix( ncol, nb,
work + (ldwrkx+1)*nb, ldwrky,
dwork + (ldwrkx+1)*nb, ldwrky );
magma_dgemm( MagmaNoTrans, MagmaConjTrans,
nrow, ncol, nb,
c_neg_one, dA(i+nb, i ), ldda,
dwork+(ldwrkx+1)*nb, ldwrky,
c_one, dA(i+nb, i+nb), ldda);
magma_dgemm( MagmaNoTrans, MagmaNoTrans,
nrow, ncol, nb,
c_neg_one, dwork+nb, ldwrkx,
dA( i, i+nb ), ldda,
c_one, dA( i+nb, i+nb ), ldda);
/* Copy diagonal and off-diagonal elements of B back into A */
if (m >= n) {
jmax = i + nb;
for (j = i; j < jmax; ++j) {
*A(j, j ) = MAGMA_D_MAKE( d[j], 0. );
*A(j, j+1) = MAGMA_D_MAKE( e[j], 0. );
}
} else {
jmax = i + nb;
for (j = i; j < jmax; ++j) {
*A(j, j ) = MAGMA_D_MAKE( d[j], 0. );
*A(j+1, j ) = MAGMA_D_MAKE( e[j], 0. );
}
}
}
/* Use unblocked code to reduce the remainder of the matrix */
nrow = m - i;
ncol = n - i;
if ( 0 < minmn - nx ) {
magma_dgetmatrix( nrow, ncol, dA(i, i), ldda, A(i, i), lda );
}
lapackf77_dgebrd( &nrow, &ncol,
A(i, i), &lda, d+i, e+i,
tauq+i, taup+i, work, &lwork, &iinfo);
work[0] = MAGMA_D_MAKE( lwkopt, 0. );
magma_free( dA );
return *info;
} /* magma_dgebrd */