/* ////////////////////////////////////////////////////////////////////////////
-- Testing cgehrd
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
magmaFloatComplex *h_A, *h_R, *h_Q, *h_work, *tau, *twork;
magmaFloatComplex_ptr dT;
#if defined(PRECISION_z) || defined(PRECISION_c)
float *rwork;
#endif
float eps, result[2];
magma_int_t N, n2, lda, nb, lwork, ltwork, info;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
eps = lapackf77_slamch( "E" );
magma_opts opts;
parse_opts( argc, argv, &opts );
float tol = opts.tolerance * lapackf77_slamch("E");
printf(" N CPU GFlop/s (sec) GPU GFlop/s (sec) |A-QHQ'|/N|A| |I-QQ'|/N\n");
printf("=========================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
lda = N;
n2 = lda*N;
nb = magma_get_cgehrd_nb(N);
/* We suppose the magma nb is bigger than lapack nb */
lwork = N*nb;
gflops = FLOPS_CGEHRD( N ) / 1e9;
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, n2 );
TESTING_MALLOC_CPU( tau, magmaFloatComplex, N );
TESTING_MALLOC_PIN( h_R, magmaFloatComplex, n2 );
TESTING_MALLOC_PIN( h_work, magmaFloatComplex, lwork );
TESTING_MALLOC_DEV( dT, magmaFloatComplex, nb*N );
/* Initialize the matrices */
lapackf77_clarnv( &ione, ISEED, &n2, h_A );
lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_cgehrd( N, ione, N, h_R, lda, tau, h_work, lwork, dT, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_cgehrd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the factorization
=================================================================== */
if ( opts.check ) {
ltwork = 2*(N*N);
TESTING_MALLOC_PIN( h_Q, magmaFloatComplex, lda*N );
TESTING_MALLOC_CPU( twork, magmaFloatComplex, ltwork );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_MALLOC_CPU( rwork, float, N );
#endif
lapackf77_clacpy(MagmaUpperLowerStr, &N, &N, h_R, &lda, h_Q, &lda);
for( int j = 0; j < N-1; ++j )
for( int i = j+2; i < N; ++i )
h_R[i+j*lda] = MAGMA_C_ZERO;
magma_cunghr(N, ione, N, h_Q, lda, tau, dT, nb, &info);
if (info != 0) {
printf("magma_cunghr returned error %d: %s.\n",
(int) info, magma_strerror( info ));
exit(1);
}
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_chst01(&N, &ione, &N,
h_A, &lda, h_R, &lda,
h_Q, &lda, twork, <work, rwork, result);
#else
lapackf77_chst01(&N, &ione, &N,
h_A, &lda, h_R, &lda,
h_Q, &lda, twork, <work, result);
#endif
TESTING_FREE_PIN( h_Q );
TESTING_FREE_CPU( twork );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_FREE_CPU( rwork );
#endif
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_cgehrd(&N, &ione, &N, h_R, &lda, tau, h_work, &lwork, &info);
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_cgehrd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
Print performance and error.
=================================================================== */
if ( opts.lapack ) {
printf("%5d %7.2f (%7.2f) %7.2f (%7.2f)",
(int) N, cpu_perf, cpu_time, gpu_perf, gpu_time );
}
else {
printf("%5d --- ( --- ) %7.2f (%7.2f)",
(int) N, gpu_perf, gpu_time );
}
if ( opts.check ) {
printf(" %8.2e %8.2e %s\n",
result[0]*eps, result[1]*eps,
( ( (result[0]*eps < tol) && (result[1]*eps < tol) ) ? "ok" : "failed") );
status += ! (result[0]*eps < tol);
status += ! (result[1]*eps < tol);
}
else {
printf(" --- ---\n");
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( tau );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( h_work );
TESTING_FREE_DEV( dT );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
extern "C" magma_int_t
magma_cgehrd(magma_int_t n, magma_int_t ilo, magma_int_t ihi,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magmaFloatComplex *dT,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CGEHRD reduces a COMPLEX general matrix A to upper Hessenberg form H by
an orthogonal similarity transformation: Q' * A * Q = H . This version
stores the triangular matrices used in the factorization so that they can
be applied directly (i.e., without being recomputed) later. As a result,
the application of Q is much faster.
Arguments
=========
N (input) INTEGER
The order of the matrix A. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER
It is assumed that A is already upper triangular in rows
and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
set by a previous call to CGEBAL; otherwise they should be
set to 1 and N respectively. See Further Details.
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the N-by-N general matrix to be reduced.
On exit, the upper triangle and the first subdiagonal of A
are overwritten with the upper Hessenberg matrix H, and the
elements below the first subdiagonal, with the array TAU,
represent the orthogonal matrix Q as a product of elementary
reflectors. See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TAU (output) COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
zero.
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK. LWORK >= max(1,N).
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.
dT (output) COMPLEX array on the GPU, dimension NB*N,
where NB is the optimal blocksize. It stores the NB*NB blocks
of the triangular T matrices used in the reduction.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
===============
The matrix Q is represented as a product of (ihi-ilo) elementary
reflectors
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
exit in A(i+2:ihi,i), and tau in TAU(i).
The contents of A are illustrated by the following example, with
n = 7, ilo = 2 and ihi = 6:
on entry, on exit,
( a a a a a a a ) ( a a h h h h a )
( a a a a a a ) ( a h h h h a )
( a a a a a a ) ( h h h h h h )
( a a a a a a ) ( v2 h h h h h )
( a a a a a a ) ( v2 v3 h h h h )
( a a a a a a ) ( v2 v3 v4 h h h )
( a ) ( a )
where a denotes an element of the original matrix A, h denotes a
modified element of the upper Hessenberg matrix H, and vi denotes an
element of the vector defining H(i).
This implementation follows the hybrid algorithm and notations described in
S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg
form through hybrid GPU-based computing," University of Tennessee Computer
Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219),
May 24, 2009.
This version stores the T matrices in dT, for later use in magma_cunghr.
===================================================================== */
#define A( i, j ) ( A + (i) + (j)*lda)
#define dA( i, j ) (dA + (i) + (j-ilo)*ldda)
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_zero = MAGMA_C_ZERO;
magma_int_t nb = magma_get_cgehrd_nb(n);
magma_int_t ldda = n; // assumed in clahru
magma_int_t nh, iws;
magma_int_t iinfo;
magma_int_t ldwork;
magma_int_t lquery;
*info = 0;
iws = n*nb;
MAGMA_C_SET2REAL( work[0], (float) iws );
lquery = lwork == -1;
if (n < 0) {
*info = -1;
} else if (ilo < 1 || ilo > max(1,n)) {
*info = -2;
} else if (ihi < min(ilo,n) || ihi > n) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
} else if (lwork < max(1,n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
// Adjust from 1-based indexing
ilo -= 1;
// Quick return if possible
nh = ihi - ilo;
if (nh <= 1) {
work[0] = c_one;
return *info;
}
// GPU workspace is:
// nb*ldda for dwork for clahru
// nb*ldda for dV
// n*ldda for dA
magmaFloatComplex *dwork;
if (MAGMA_SUCCESS != magma_cmalloc( &dwork, 2*nb*ldda + n*ldda )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magmaFloatComplex *dV = dwork + nb*ldda;
magmaFloatComplex *dA = dwork + nb*ldda*2;
ldwork = n;
magma_int_t i;
magmaFloatComplex *T, *dTi;
magma_cmalloc_cpu( &T, nb*nb );
if ( T == NULL ) {
magma_free( dwork );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
// zero first block of V, which is lower triangular
czero_nbxnb_block(nb, dV, ldda);
// Set elements 0:ILO-1 and IHI-1:N-2 of TAU to zero
for(i = 0; i < ilo; ++i)
tau[i] = c_zero;
for(i = max(0,ihi-1); i < n-1; ++i)
tau[i] = c_zero;
for(i=0; i < nb*nb; i += 4)
T[i] = T[i+1] = T[i+2] = T[i+3] = c_zero;
magmablas_claset( 'F', nb, n, dT, nb );
// If not enough workspace, use unblocked code
if ( lwork < iws ) {
nb = 1;
}
if (nb == 1 || nb > nh) {
// Use unblocked code below
i = ilo;
}
else {
// Use blocked code
// Copy the matrix to the GPU
magma_csetmatrix( n, n-ilo, A(0,ilo), lda, dA, ldda );
for (i = ilo; i < ihi-1 - nb; i += nb) {
// Reduce columns i:i+nb-1 to Hessenberg form, returning the
// matrices V and T of the block reflector H = I - V*T*V'
// which performs the reduction, and also the matrix Y = A*V*T
// Get the current panel (no need for the 1st iteration)
magma_cgetmatrix( ihi-i, nb,
dA(i,i), ldda,
A (i,i), lda );
// add 1 to i for 1-based index
magma_clahr2( ihi, i+1, nb,
dA(0,i),
dV,
A (0,i), lda,
&tau[i], T, nb, work, ldwork);
// Copy T from the CPU to dT on the GPU
dTi = dT + (i - ilo)*nb;
magma_csetmatrix( nb, nb, T, nb, dTi, nb );
magma_clahru( n, ihi, i, nb,
A (0,i), lda,
dA(0,i), // dA
dA(i,i), // dY, stored over current panel
dV, dTi, dwork );
}
// Copy remainder to host
magma_cgetmatrix( n, n-i,
dA(0,i), ldda,
A (0,i), lda );
}
// Use unblocked code to reduce the rest of the matrix
// add 1 to i for 1-based index
i += 1;
lapackf77_cgehd2(&n, &i, &ihi, A, &lda, tau, work, &iinfo);
MAGMA_C_SET2REAL( work[0], (float) iws );
magma_free( dwork );
magma_free_cpu( T );
return *info;
} /* magma_cgehrd */
/**
Purpose
-------
CGEHRD reduces a COMPLEX general matrix A to upper Hessenberg form H by
an orthogonal similarity transformation: Q' * A * Q = H . This version
stores the triangular matrices used in the factorization so that they can
be applied directly (i.e., without being recomputed) later. As a result,
the application of Q is much faster.
Arguments
---------
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in]
ilo INTEGER
@param[in]
ihi INTEGER
It is assumed that A is already upper triangular in rows
and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
set by a previous call to CGEBAL; otherwise they should be
set to 1 and N respectively. See Further Details.
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the N-by-N general matrix to be reduced.
On exit, the upper triangle and the first subdiagonal of A
are overwritten with the upper Hessenberg matrix H, and the
elements below the first subdiagonal, with the array TAU,
represent the orthogonal matrix Q as a product of elementary
reflectors. See Further Details.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
tau COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
zero.
@param[out]
work (workspace) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK. LWORK >= max(1,N).
For optimum performance LWORK >= 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]
dT COMPLEX array on the GPU, dimension NB*N,
where NB is the optimal blocksize. It stores the NB*NB blocks
of the triangular T matrices used in the reduction.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
---------------
The matrix Q is represented as a product of (ihi-ilo) elementary
reflectors
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
exit in A(i+2:ihi,i), and tau in TAU(i).
The contents of A are illustrated by the following example, with
n = 7, ilo = 2 and ihi = 6:
@verbatim
on entry, on exit,
( a a a a a a a ) ( a a h h h h a )
( a a a a a a ) ( a h h h h a )
( a a a a a a ) ( h h h h h h )
( a a a a a a ) ( v2 h h h h h )
( a a a a a a ) ( v2 v3 h h h h )
( a a a a a a ) ( v2 v3 v4 h h h )
( a ) ( a )
@endverbatim
where a denotes an element of the original matrix A, h denotes a
modified element of the upper Hessenberg matrix H, and vi denotes an
element of the vector defining H(i).
This implementation follows the hybrid algorithm and notations described in
S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg
form through hybrid GPU-based computing," University of Tennessee Computer
Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219),
May 24, 2009.
This version stores the T matrices in dT, for later use in magma_cunghr.
@ingroup magma_cgeev_comp
********************************************************************/
extern "C" magma_int_t
magma_cgehrd(
magma_int_t n, magma_int_t ilo, magma_int_t ihi,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magmaFloatComplex_ptr dT,
magma_int_t *info)
{
#define A(i_,j_) ( A + (i_) + (j_)*lda)
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_zero = MAGMA_C_ZERO;
magma_int_t nb = magma_get_cgehrd_nb(n);
magma_int_t ldda = ((n+31)/32)*32;
magma_int_t i, nh, iws;
magma_int_t iinfo;
magma_int_t lquery;
*info = 0;
iws = n*nb;
work[0] = MAGMA_C_MAKE( iws, 0 );
lquery = (lwork == -1);
if (n < 0) {
*info = -1;
} else if (ilo < 1 || ilo > max(1,n)) {
*info = -2;
} else if (ihi < min(ilo,n) || ihi > n) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
} else if (lwork < max(1,n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
// Adjust from 1-based indexing
ilo -= 1;
// Quick return if possible
nh = ihi - ilo;
if (nh <= 1) {
work[0] = c_one;
return *info;
}
// If not enough workspace, use unblocked code
if ( lwork < iws ) {
nb = 1;
}
if (nb == 1 || nb > nh) {
// Use unblocked code below
i = ilo;
}
else {
// Use blocked code
// GPU workspace is:
// nb*ldda for dwork for clahru
// nb*ldda for dV
// n*ldda for dA
magmaFloatComplex *dwork;
if (MAGMA_SUCCESS != magma_cmalloc( &dwork, 2*nb*ldda + n*ldda )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magmaFloatComplex *dV = dwork + nb*ldda;
magmaFloatComplex *dA = dwork + nb*ldda*2;
magmaFloatComplex *dTi;
magmaFloatComplex *T;
magma_cmalloc_cpu( &T, nb*nb );
if ( T == NULL ) {
magma_free( dwork );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
// zero first block of V, which is lower triangular
magmablas_claset( MagmaFull, nb, nb, c_zero, c_zero, dV, ldda );
// Set elements 0:ILO-1 and IHI-1:N-2 of TAU to zero
for (i = 0; i < ilo; ++i)
tau[i] = c_zero;
for (i = max(0,ihi-1); i < n-1; ++i)
tau[i] = c_zero;
assert( nb % 4 == 0 );
for (i=0; i < nb*nb; i += 4)
T[i] = T[i+1] = T[i+2] = T[i+3] = c_zero;
magmablas_claset( MagmaFull, nb, n, c_zero, c_zero, dT, nb );
// Copy the matrix to the GPU
magma_csetmatrix( n, n-ilo, A(0,ilo), lda, dA, ldda );
for (i = ilo; i < ihi-1 - nb; i += nb) {
// Reduce columns i:i+nb-1 to Hessenberg form, returning the
// matrices V and T of the block reflector H = I - V*T*V'
// which performs the reduction, and also the matrix Y = A*V*T
// Get the current panel (no need for the 1st iteration)
magma_cgetmatrix( ihi-i, nb,
dA(i,i-ilo), ldda,
A(i,i), lda );
// add 1 to i for 1-based index
magma_clahr2( ihi, i+1, nb,
dA(0,i-ilo), ldda,
dV, ldda,
A(0,i), lda,
&tau[i], T, nb, work, n);
// Copy T from the CPU to dT on the GPU
dTi = dT + (i - ilo)*nb;
magma_csetmatrix( nb, nb, T, nb, dTi, nb );
magma_clahru( n, ihi, i, nb,
A(0,i), lda,
dA(0,i-ilo), ldda, // dA
dA(i,i-ilo), ldda, // dY, stored over current panel
dV, ldda,
dTi, dwork );
}
// Copy remainder to host
magma_cgetmatrix( n, n-i,
dA(0,i-ilo), ldda,
A(0,i), lda );
magma_free( dwork );
magma_free_cpu( T );
}
// Use unblocked code to reduce the rest of the matrix
// add 1 to i for 1-based index
i += 1;
lapackf77_cgehd2(&n, &i, &ihi, A, &lda, tau, work, &iinfo);
work[0] = MAGMA_C_MAKE( iws, 0 );
return *info;
} /* magma_cgehrd */
/***************************************************************************//**
Purpose
-------
CGEEV computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors.
The right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm
equal to 1 and largest component real.
Arguments
---------
@param[in]
jobvl magma_vec_t
- = MagmaNoVec: left eigenvectors of A are not computed;
- = MagmaVec: left eigenvectors of are computed.
@param[in]
jobvr magma_vec_t
- = MagmaNoVec: right eigenvectors of A are not computed;
- = MagmaVec: right eigenvectors of A are computed.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the N-by-N matrix A.
On exit, A has been overwritten.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
w COMPLEX array, dimension (N)
W contains the computed eigenvalues.
@param[out]
VL COMPLEX array, dimension (LDVL,N)
If JOBVL = MagmaVec, the left eigenvectors u(j) are stored one
after another in the columns of VL, in the same order
as their eigenvalues.
If JOBVL = MagmaNoVec, VL is not referenced.
u(j) = VL(:,j), the j-th column of VL.
@param[in]
ldvl INTEGER
The leading dimension of the array VL. LDVL >= 1; if
JOBVL = MagmaVec, LDVL >= N.
@param[out]
VR COMPLEX array, dimension (LDVR,N)
If JOBVR = MagmaVec, the right eigenvectors v(j) are stored one
after another in the columns of VR, in the same order
as their eigenvalues.
If JOBVR = MagmaNoVec, VR is not referenced.
v(j) = VR(:,j), the j-th column of VR.
@param[in]
ldvr INTEGER
The leading dimension of the array VR. LDVR >= 1; if
JOBVR = MagmaVec, LDVR >= N.
@param[out]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= (1 + nb + nb*ngpu)*N.
For optimal performance, LWORK >= (1 + 2*nb + nb*ngpu)*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 by XERBLA.
@param
rwork (workspace) REAL array, dimension (2*N)
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value.
- > 0: if INFO = i, the QR algorithm failed to compute all the
eigenvalues, and no eigenvectors have been computed;
elements and i+1:N of W contain eigenvalues which have
converged.
@ingroup magma_geev
*******************************************************************************/
extern "C" magma_int_t
magma_cgeev_m(
magma_vec_t jobvl, magma_vec_t jobvr, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
#ifdef COMPLEX
magmaFloatComplex *w,
#else
float *wr, float *wi,
#endif
magmaFloatComplex *VL, magma_int_t ldvl,
magmaFloatComplex *VR, magma_int_t ldvr,
magmaFloatComplex *work, magma_int_t lwork,
#ifdef COMPLEX
float *rwork,
#endif
magma_int_t *info )
{
#define VL(i,j) (VL + (i) + (j)*ldvl)
#define VR(i,j) (VR + (i) + (j)*ldvr)
const magma_int_t ione = 1;
const magma_int_t izero = 0;
float d__1, d__2;
magmaFloatComplex tmp;
float scl;
float dum[1], eps;
float anrm, cscale, bignum, smlnum;
magma_int_t i, k, ilo, ihi;
magma_int_t ibal, ierr, itau, iwrk, nout, liwrk, nb;
magma_int_t scalea, minwrk, optwrk, irwork, lquery, wantvl, wantvr, select[1];
magma_side_t side = MagmaRight;
magma_int_t ngpu = magma_num_gpus();
irwork = 0;
*info = 0;
lquery = (lwork == -1);
wantvl = (jobvl == MagmaVec);
wantvr = (jobvr == MagmaVec);
if (! wantvl && jobvl != MagmaNoVec) {
*info = -1;
} else if (! wantvr && jobvr != MagmaNoVec) {
*info = -2;
} else if (n < 0) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
} else if ( (ldvl < 1) || (wantvl && (ldvl < n))) {
*info = -8;
} else if ( (ldvr < 1) || (wantvr && (ldvr < n))) {
*info = -10;
}
/* Compute workspace */
nb = magma_get_cgehrd_nb( n );
if (*info == 0) {
minwrk = (1 + nb + nb*ngpu)*n;
optwrk = (1 + 2*nb + nb*ngpu)*n;
work[0] = magma_cmake_lwork( optwrk );
if (lwork < minwrk && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
#if defined(Version3)
magmaFloatComplex *dT;
if (MAGMA_SUCCESS != magma_cmalloc( &dT, nb*n )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
#endif
#if defined(Version5)
magmaFloatComplex *T;
if (MAGMA_SUCCESS != magma_cmalloc_cpu( &T, nb*n )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
#endif
/* Get machine constants */
eps = lapackf77_slamch( "P" );
smlnum = lapackf77_slamch( "S" );
bignum = 1. / smlnum;
lapackf77_slabad( &smlnum, &bignum );
smlnum = magma_ssqrt( smlnum ) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = lapackf77_clange( "M", &n, &n, A, &lda, dum );
scalea = 0;
if (anrm > 0. && anrm < smlnum) {
scalea = 1;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = 1;
cscale = bignum;
}
if (scalea) {
lapackf77_clascl( "G", &izero, &izero, &anrm, &cscale, &n, &n, A, &lda, &ierr );
}
/* Balance the matrix
* (CWorkspace: none)
* (RWorkspace: need N)
* - this space is reserved until after gebak */
ibal = 0;
lapackf77_cgebal( "B", &n, A, &lda, &ilo, &ihi, &rwork[ibal], &ierr );
/* Reduce to upper Hessenberg form
* (CWorkspace: need 2*N, prefer N + N*NB + NB*NGPU)
* (RWorkspace: N)
* - added NB*NGPU needed for multi-GPU magma_cgehrd_m
* - including N reserved for gebal/gebak, unused by cgehrd */
itau = 0;
iwrk = itau + n;
liwrk = lwork - iwrk;
#if defined(Version1)
// Version 1 - LAPACK
lapackf77_cgehrd( &n, &ilo, &ihi, A, &lda,
&work[itau], &work[iwrk], &liwrk, &ierr );
#elif defined(Version2)
// Version 2 - LAPACK consistent HRD
magma_cgehrd2( n, ilo, ihi, A, lda,
&work[itau], &work[iwrk], liwrk, &ierr );
#elif defined(Version3)
// Version 3 - LAPACK consistent MAGMA HRD + T matrices stored,
magma_cgehrd( n, ilo, ihi, A, lda,
&work[itau], &work[iwrk], liwrk, dT, &ierr );
#elif defined(Version5)
// Version 4 - Multi-GPU, T on host
magma_cgehrd_m( n, ilo, ihi, A, lda,
&work[itau], &work[iwrk], liwrk, T, &ierr );
#endif
if (wantvl) {
/* Want left eigenvectors
* Copy Householder vectors to VL */
side = MagmaLeft;
lapackf77_clacpy( MagmaLowerStr, &n, &n, A, &lda, VL, &ldvl );
/* Generate unitary matrix in VL
* (CWorkspace: need 2*N-1, prefer N + (N-1)*NB)
* (RWorkspace: N)
* - including N reserved for gebal/gebak, unused by cunghr */
#if defined(Version1) || defined(Version2)
// Version 1 & 2 - LAPACK
lapackf77_cunghr( &n, &ilo, &ihi, VL, &ldvl, &work[itau],
&work[iwrk], &liwrk, &ierr );
#elif defined(Version3)
// Version 3 - LAPACK consistent MAGMA HRD + T matrices stored
magma_cunghr( n, ilo, ihi, VL, ldvl, &work[itau], dT, nb, &ierr );
#elif defined(Version5)
// Version 5 - Multi-GPU, T on host
magma_cunghr_m( n, ilo, ihi, VL, ldvl, &work[itau], T, nb, &ierr );
#endif
/* Perform QR iteration, accumulating Schur vectors in VL
* (CWorkspace: need 1, prefer HSWORK (see comments) )
* (RWorkspace: N)
* - including N reserved for gebal/gebak, unused by chseqr */
iwrk = itau;
liwrk = lwork - iwrk;
lapackf77_chseqr( "S", "V", &n, &ilo, &ihi, A, &lda, w,
VL, &ldvl, &work[iwrk], &liwrk, info );
if (wantvr) {
/* Want left and right eigenvectors
* Copy Schur vectors to VR */
side = MagmaBothSides;
lapackf77_clacpy( "F", &n, &n, VL, &ldvl, VR, &ldvr );
}
}
else if (wantvr) {
/* Want right eigenvectors
* Copy Householder vectors to VR */
side = MagmaRight;
lapackf77_clacpy( "L", &n, &n, A, &lda, VR, &ldvr );
/* Generate unitary matrix in VR
* (CWorkspace: need 2*N-1, prefer N + (N-1)*NB)
* (RWorkspace: N)
* - including N reserved for gebal/gebak, unused by cunghr */
#if defined(Version1) || defined(Version2)
// Version 1 & 2 - LAPACK
lapackf77_cunghr( &n, &ilo, &ihi, VR, &ldvr, &work[itau],
&work[iwrk], &liwrk, &ierr );
#elif defined(Version3)
// Version 3 - LAPACK consistent MAGMA HRD + T matrices stored
magma_cunghr( n, ilo, ihi, VR, ldvr, &work[itau], dT, nb, &ierr );
#elif defined(Version5)
// Version 5 - Multi-GPU, T on host
magma_cunghr_m( n, ilo, ihi, VR, ldvr, &work[itau], T, nb, &ierr );
#endif
/* Perform QR iteration, accumulating Schur vectors in VR
* (CWorkspace: need 1, prefer HSWORK (see comments) )
* (RWorkspace: N)
* - including N reserved for gebal/gebak, unused by chseqr */
iwrk = itau;
liwrk = lwork - iwrk;
lapackf77_chseqr( "S", "V", &n, &ilo, &ihi, A, &lda, w,
VR, &ldvr, &work[iwrk], &liwrk, info );
}
else {
/* Compute eigenvalues only
* (CWorkspace: need 1, prefer HSWORK (see comments) )
* (RWorkspace: N)
* - including N reserved for gebal/gebak, unused by chseqr */
iwrk = itau;
liwrk = lwork - iwrk;
lapackf77_chseqr( "E", "N", &n, &ilo, &ihi, A, &lda, w,
VR, &ldvr, &work[iwrk], &liwrk, info );
}
/* If INFO > 0 from CHSEQR, then quit */
if (*info > 0) {
goto CLEANUP;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors
* (CWorkspace: need 2*N)
* (RWorkspace: need 2*N)
* - including N reserved for gebal/gebak, unused by ctrevc */
irwork = ibal + n;
#if TREVC_VERSION == 1
lapackf77_ctrevc( lapack_side_const(side), "B", select, &n, A, &lda, VL, &ldvl,
VR, &ldvr, &n, &nout, &work[iwrk], &rwork[irwork], &ierr );
#elif TREVC_VERSION == 2
liwrk = lwork - iwrk;
lapackf77_ctrevc3( lapack_side_const(side), "B", select, &n, A, &lda, VL, &ldvl,
VR, &ldvr, &n, &nout, &work[iwrk], &liwrk, &rwork[irwork], &ierr );
#elif TREVC_VERSION == 3
magma_ctrevc3( side, MagmaBacktransVec, select, n, A, lda, VL, ldvl,
VR, ldvr, n, &nout, &work[iwrk], liwrk, &rwork[irwork], &ierr );
#elif TREVC_VERSION == 4
magma_ctrevc3_mt( side, MagmaBacktransVec, select, n, A, lda, VL, ldvl,
VR, ldvr, n, &nout, &work[iwrk], liwrk, &rwork[irwork], &ierr );
#elif TREVC_VERSION == 5
magma_ctrevc3_mt_gpu( side, MagmaBacktransVec, select, n, A, lda, VL, ldvl,
VR, ldvr, n, &nout, &work[iwrk], liwrk, &rwork[irwork], &ierr );
#else
#error Unknown TREVC_VERSION
#endif
}
if (wantvl) {
/* Undo balancing of left eigenvectors
* (CWorkspace: none)
* (RWorkspace: need N) */
lapackf77_cgebak( "B", "L", &n, &ilo, &ihi, &rwork[ibal], &n,
VL, &ldvl, &ierr );
/* Normalize left eigenvectors and make largest component real */
for (i = 0; i < n; ++i) {
scl = 1. / magma_cblas_scnrm2( n, VL(0,i), 1 );
blasf77_csscal( &n, &scl, VL(0,i), &ione );
for (k = 0; k < n; ++k) {
/* Computing 2nd power */
d__1 = MAGMA_C_REAL( *VL(k,i) );
d__2 = MAGMA_C_IMAG( *VL(k,i) );
rwork[irwork + k] = d__1*d__1 + d__2*d__2;
}
k = blasf77_isamax( &n, &rwork[irwork], &ione ) - 1; // subtract 1; k is 0-based
tmp = MAGMA_C_CONJ( *VL(k,i) ) / magma_ssqrt( rwork[irwork + k] );
blasf77_cscal( &n, &tmp, VL(0,i), &ione );
*VL(k,i) = MAGMA_C_MAKE( MAGMA_C_REAL( *VL(k,i) ), 0 );
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors
* (CWorkspace: none)
* (RWorkspace: need N) */
lapackf77_cgebak( "B", "R", &n, &ilo, &ihi, &rwork[ibal], &n,
VR, &ldvr, &ierr );
/* Normalize right eigenvectors and make largest component real */
for (i = 0; i < n; ++i) {
scl = 1. / magma_cblas_scnrm2( n, VR(0,i), 1 );
blasf77_csscal( &n, &scl, VR(0,i), &ione );
for (k = 0; k < n; ++k) {
/* Computing 2nd power */
d__1 = MAGMA_C_REAL( *VR(k,i) );
d__2 = MAGMA_C_IMAG( *VR(k,i) );
rwork[irwork + k] = d__1*d__1 + d__2*d__2;
}
k = blasf77_isamax( &n, &rwork[irwork], &ione ) - 1; // subtract 1; k is 0-based
tmp = MAGMA_C_CONJ( *VR(k,i) ) / magma_ssqrt( rwork[irwork + k] );
blasf77_cscal( &n, &tmp, VR(0,i), &ione );
*VR(k,i) = MAGMA_C_MAKE( MAGMA_C_REAL( *VR(k,i) ), 0 );
}
}
CLEANUP:
/* Undo scaling if necessary */
if (scalea) {
// converged eigenvalues, stored in WR[i+1:n] and WI[i+1:n] for i = INFO
magma_int_t nval = n - (*info);
magma_int_t ld = max( nval, 1 );
lapackf77_clascl( "G", &izero, &izero, &cscale, &anrm, &nval, &ione, w + (*info), &ld, &ierr );
if (*info > 0) {
// first ilo columns were already upper triangular,
// so the corresponding eigenvalues are also valid.
nval = ilo - 1;
lapackf77_clascl( "G", &izero, &izero, &cscale, &anrm, &nval, &ione, w, &n, &ierr );
}
}
#if defined(Version3)
magma_free( dT );
#endif
#if defined(Version5)
magma_free_cpu( T );
#endif
work[0] = magma_cmake_lwork( minwrk ); // TODO use optwrk as in dgeev
return *info;
} /* magma_cgeev */
extern "C" int calc_bounding_box(magmaFloatComplex *M, magma_int_t M_lead_dim, float *wReEig, float *wImEig)
{
magma_int_t rslt = 0;
//magmaFloatComplex *AT = nullptr;
magmaFloatComplex *dA = nullptr, *dAT = nullptr,
*dreA = nullptr, *dimA = nullptr;
float *dreEig = nullptr;
float *dimEig = nullptr;
//magma_int_t *ipiv = NULL;
magma_int_t lda = M_lead_dim;
//magma_int_t ldx = lda;
magma_int_t info = 0;
magma_int_t nb = 0;
//magma_vec_t jobvl;
//magma_vec_t jobvr;
magmaFloatComplex *work = nullptr;
magma_int_t lwork = 0;
float *rwork = nullptr;
magma_int_t lrwork = 0;
magma_int_t *iwork = nullptr;
magma_int_t liwork = 0;
nb = magma_get_cgehrd_nb( M_lead_dim );
lwork = 2 * (M_lead_dim + M_lead_dim*nb); // MagmaNoVec
//lwork = 2 * max(M_lead_dim + M_lead_dim*nb, 2*M_lead_dim + M_lead_dim*M_lead_dim); // MagmaVec
lrwork = M_lead_dim; // MagmaNoVec
//lrwork = 1 + 5 * M_lead_dim + 2*M_lead_dim*M_lead_dim; // MagmaVec
liwork = 1; // MagmaNoVec
//liwork = 3 + 5*M_lead_dim; // MagmaVec
magma_imalloc_cpu(&iwork, liwork);
magma_smalloc_cpu(&rwork, lrwork);
//magma_cmalloc_cpu(&A, lda*M_lead_dim);
//magma_cmalloc_cpu(&AT, lda*M_lead_dim);
//magma_smalloc_cpu(&reEig, M_lead_dim);
//magma_smalloc_cpu(&imEig, M_lead_dim);
magma_cmalloc_pinned(&dA, lda*M_lead_dim);
magma_cmalloc_pinned(&dAT, lda*M_lead_dim);
magma_cmalloc_pinned(&dreA, lda*M_lead_dim);
magma_cmalloc_pinned(&dimA, lda*M_lead_dim);
//magma_cmalloc_pinned(&VL, lda*M_lead_dim);
//magma_cmalloc_pinned(&VR, lda*M_lead_dim);
magma_cmalloc_pinned(&work, lwork);
magma_smalloc_pinned(&dreEig, M_lead_dim);
magma_smalloc_pinned(&dimEig, M_lead_dim);
//matrix_fillzero(AT, M_lead_dim);
//vector_fillzero(reEig, M_lead_dim);
//vector_fillzero(imEig, M_lead_dim);
//prepare_matrix_2(M);
magma_csetmatrix(M_lead_dim, M_lead_dim, M, lda, dA, M_lead_dim, queue);
//magma_csetmatrix(M_lead_dim, M_lead_dim, AT, lda, dAT, M_lead_dim, queue);
//magma_ssetvector(M_lead_dim, wReEig, 1, dreEig, 1, queue);
//magma_ssetvector(M_lead_dim, wImEig, 1, dimEig, 1, queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dA, lda);
// reA = ( (A + A')/2.0 )
// A'
magmablas_ctranspose(M_lead_dim, M_lead_dim, dA, M_lead_dim, dAT, M_lead_dim, queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dAT, lda);
// AT = A + A'
magmablas_cgeadd(M_lead_dim, M_lead_dim, MAGMA_C_MAKE(1.0f, 0.0f), dA, M_lead_dim, dAT, M_lead_dim, queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dAT, lda);
// AT=AT*0.5
magma_cscal(lda*M_lead_dim, MAGMA_C_MAKE(0.5f, 0.0f), dAT, 1, queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dAT, lda);
// reA = AT
magma_ccopy(lda*M_lead_dim, dAT, 1, dreA, 1, queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dreA, lda);
magma_sync_wtime(queue);
// imA = ( -1im*(A - A')/2.0 )
// A'
magmablas_ctranspose(M_lead_dim, M_lead_dim, dA, M_lead_dim, dAT, M_lead_dim, queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dAT, lda);
// AT = A + A'
magmablas_cgeadd(M_lead_dim, M_lead_dim, MAGMA_C_MAKE(-1.0f, 0.0f), dAT, M_lead_dim, dA, M_lead_dim, queue);
// A=A*-1j*0.5
magma_cscal(lda*M_lead_dim, MAGMA_C_MAKE(0.0f, -0.5f), dA, 1, queue);
// imA = A
magma_ccopy(lda*M_lead_dim, dA, 1, dimA, 1, queue);
magma_sync_wtime(queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dreA, lda);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dimA, lda);
// reEig::Vector=eigvals(reA)
rslt = magma_cheevd(MagmaNoVec, MagmaLower,
M_lead_dim,
dreA, lda,
dreEig,
work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
// imEig::Vector=eigvals(imA)
rslt = magma_cheevd(MagmaNoVec, MagmaLower,
M_lead_dim,
dimA, lda,
dimEig,
work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
//magma_sprint_gpu(M_lead_dim, 1, dreEig, M_lead_dim);
//magma_sprint_gpu(M_lead_dim, 1, dimEig, M_lead_dim);
magma_sgetvector(M_lead_dim, dreEig, 1, wReEig, 1, queue);
//magma_sync_wtime(queue);
magma_sgetvector(M_lead_dim, dimEig, 1, wImEig, 1, queue);
//magma_sync_wtime(queue);
/*
maxReIdx = magma_isamax(M_lead_dim, dreEig, 1, queue) - 1;
minReIdx = magma_isamin(M_lead_dim, dreEig, 1, queue) - 1;
maxImIdx = magma_isamax(M_lead_dim, dimEig, 1, queue) - 1;
minImIdx = magma_isamin(M_lead_dim, dimEig, 1, queue) - 1;
printf("max re idx = %d\nmin re idx = %d\n", maxReIdx, minReIdx);
printf("%f %f\n", wReEig[maxReIdx], wReEig[minReIdx]);
printf("max im idx = %d\nmin im idx = %d\n", maxImIdx, minImIdx);
printf("%f %f\n", wImEig[maxImIdx], wImEig[minImIdx]);
*/
//printf("test wReEig: %f %f\n", wReEig[0], wReEig[1]);
//printf("test wImEig: %f %f\n", wImEig[0], wImEig[1]);
magma_free_cpu(iwork);
magma_free_cpu(rwork);
//magma_free_cpu(AT);
magma_free_pinned(dA);
magma_free_pinned(dAT);
magma_free_pinned(dreA);
magma_free_pinned(dimA);
magma_free_pinned(work);
magma_free_pinned(dreEig);
magma_free_pinned(dimEig);
return rslt;
}
extern "C" int calc_numerical_range(magmaFloatComplex *M, magma_int_t M_lead_dim, float _from, float _step, magma_int_t _steps, magmaFloatComplex *pts)
{
magma_int_t idx = 0, rslt = 0;
magmaFloatComplex p, scalar;
std::complex<float> vtmp;
float j;
magmaFloatComplex *dA = nullptr;
magmaFloatComplex *dAth = NULL, *dAthT = NULL,
*dX = NULL, *dY = NULL;
float *dE = NULL;
//float *hE = NULL;
//magma_int_t *ipiv = NULL;
magma_int_t lda = M_lead_dim;
//magma_int_t ldx = lda;
magma_int_t info = 0;
magma_int_t nb = 0;
//magma_vec_t jobvl;
//magma_vec_t jobvr;
magmaFloatComplex *work = nullptr;
magma_int_t lwork = 0;
float *rwork = nullptr;
magma_int_t lrwork = 0;
magma_int_t *iwork = nullptr;
magma_int_t liwork = 0;
nb = magma_get_cgehrd_nb( M_lead_dim );
lwork = 2 * max(M_lead_dim + M_lead_dim*nb, 2 * M_lead_dim + M_lead_dim*M_lead_dim); // MagmaVec
lrwork = 1 + 5 * M_lead_dim + 2 * M_lead_dim*M_lead_dim; // MagmaVec
liwork = (3 + 5 * M_lead_dim); // MagmaVec
magma_imalloc_cpu(&iwork, liwork);
magma_smalloc_cpu(&rwork, lrwork);
magma_cmalloc_pinned(&work, lwork);
magma_cmalloc_pinned(&dA, lda*M_lead_dim);
magma_cmalloc_pinned(&dAth, lda*M_lead_dim);
magma_cmalloc_pinned(&dAthT, lda*M_lead_dim);
magma_smalloc_pinned(&dE, M_lead_dim);
//magma_smalloc_cpu(&hE, M_lead_dim);
magma_cmalloc_pinned(&dX, M_lead_dim);
magma_cmalloc_pinned(&dY, M_lead_dim);
magma_csetmatrix(M_lead_dim, M_lead_dim, M, lda, dA, M_lead_dim, queue);
// th=[0:resolution:2*pi]
j = _from;
for (idx = 0; idx < _steps; idx++)
{
//scalar = exp( 1im * -j);
vtmp.real( 0.0f );
vtmp.imag( -j );
//vtmp = _FCbuild(0.0f, -j);
//printf("vtmp = %f + i%f\n", vtmp._Val[0], vtmp._Val[1]);
vtmp = exp(vtmp);
scalar.x = vtmp.real();
scalar.y = vtmp.imag();
//printf("scalar = %f + i%f\n", scalar.x, scalar.y);
magma_ccopy(lda * M_lead_dim, dA, 1, dAth, 1, queue);
// Ath = exp(1im * -j) * As
magma_cscal(lda * M_lead_dim, scalar, dAth, 1, queue);
//magma_cprint_gpu(N, N, dA, lda);
//magma_cprint_gpu(N, N, dAth, lda);
// AthT = (Ath + Ath')
magmablas_ctranspose_conj(M_lead_dim, M_lead_dim, dAth, M_lead_dim, dAthT, M_lead_dim, queue);
magmablas_cgeadd(M_lead_dim, M_lead_dim, MAGMA_C_MAKE(1.0f, 0.0f), dAth, M_lead_dim, dAthT, M_lead_dim, queue);
// AthT = AthT / 2
magma_cscal(lda*M_lead_dim, MAGMA_C_MAKE(0.5f, 0.0f), dAthT, 1, queue);
magma_sync_wtime(queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dAthT, lda);
// e, r = eig(AthT)
rslt = magma_cheevd(MagmaVec, MagmaLower,
M_lead_dim,
dAthT, lda,
dE,
work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
magma_sync_wtime(queue);
//printf("magma_cheevd info=%d\n", info);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dAthT, lda);
//magma_sprint_gpu(M_lead_dim, 1, dE, M_lead_dim);
//magma_sgetvector(M_lead_dim, dE, 1, hE, 1, queue);
//printf("%f %f\n", hE[0], hE[1]);
// p = r[:,s]' * A * r[:,s]
// r = r[:,s]
magma_ccopy(
M_lead_dim,
dAthT + (M_lead_dim*(M_lead_dim-1)), 1, // dAthT + (N), where (N) is a column offset
dX, 1,
queue);
magma_sync_wtime(queue);
//magma_cprint_gpu(M_lead_dim, 1, dX, M_lead_dim);
// pp = A * r[:,s]
magma_cgemv(MagmaNoTrans,
M_lead_dim, M_lead_dim,
MAGMA_C_MAKE(1.0f, 0.0f),
dA, lda,
dX, 1,
MAGMA_C_MAKE(0.0f, 0.0f),
dY, 1, queue);
magma_sync_wtime(queue);
//magma_cprint_gpu(M_lead_dim, 1, dY, M_lead_dim);
// p = r' * pp
p = magma_cdotc(M_lead_dim, dX, 1, dY, 1, queue);
magma_sync_wtime(queue);
pts[idx] = p;
//printf("p = %f %fi\n", p.x, p.y);
j += _step;
} // end of for (idx = 0; idx < _steps; idx++)
magma_free_pinned(dY);
magma_free_pinned(dX);
//magma_free_cpu(hE);
magma_free_pinned(dE);
magma_free_pinned(dAthT);
magma_free_pinned(dAth);
magma_free_pinned(dA);
magma_free_pinned(work);
magma_free_cpu(rwork);
magma_free_cpu(iwork);
//magma_free_cpu(w);
//magma_free_cpu(A);
return rslt;
}
extern "C" magma_int_t
magma_cgehrd2(magma_int_t n, magma_int_t ilo, magma_int_t ihi,
magmaFloatComplex *a, magma_int_t lda,
magmaFloatComplex *tau, magmaFloatComplex *work,
magma_int_t lwork, magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CGEHRD2 reduces a COMPLEX general matrix A to upper Hessenberg form H by
an orthogonal similarity transformation: Q' * A * Q = H .
Arguments
=========
N (input) INTEGER
The order of the matrix A. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER
It is assumed that A is already upper triangular in rows
and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
set by a previous call to CGEBAL; otherwise they should be
set to 1 and N respectively. See Further Details.
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the N-by-N general matrix to be reduced.
On exit, the upper triangle and the first subdiagonal of A
are overwritten with the upper Hessenberg matrix H, and the
elements below the first subdiagonal, with the array TAU,
represent the orthogonal matrix Q as a product of elementary
reflectors. See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TAU (output) COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
zero.
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK. LWORK >= max(1,N).
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.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
===============
The matrix Q is represented as a product of (ihi-ilo) elementary
reflectors
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
exit in A(i+2:ihi,i), and tau in TAU(i).
The contents of A are illustrated by the following example, with
n = 7, ilo = 2 and ihi = 6:
on entry, on exit,
( a a a a a a a ) ( a a h h h h a )
( a a a a a a ) ( a h h h h a )
( a a a a a a ) ( h h h h h h )
( a a a a a a ) ( v2 h h h h h )
( a a a a a a ) ( v2 v3 h h h h )
( a a a a a a ) ( v2 v3 v4 h h h )
( a ) ( a )
where a denotes an element of the original matrix A, h denotes a
modified element of the upper Hessenberg matrix H, and vi denotes an
element of the vector defining H(i).
This implementation follows the hybrid algorithm and notations described in
S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg
form through hybrid GPU-based computing," University of Tennessee Computer
Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219),
May 24, 2009.
===================================================================== */
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_zero = MAGMA_C_ZERO;
magma_int_t nb = magma_get_cgehrd_nb(n);
magma_int_t N = n, ldda = n;
magma_int_t ib;
magma_int_t nh, iws;
magma_int_t nbmin, iinfo;
magma_int_t ldwork;
magma_int_t lquery;
--tau;
*info = 0;
MAGMA_C_SET2REAL( work[0], (float) n * nb );
lquery = lwork == -1;
if (n < 0) {
*info = -1;
} else if (ilo < 1 || ilo > max(1,n)) {
*info = -2;
} else if (ihi < min(ilo,n) || ihi > n) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
} else if (lwork < max(1,n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Quick return if possible */
nh = ihi - ilo + 1;
if (nh <= 1) {
work[0] = c_one;
return *info;
}
magmaFloatComplex *da;
if (MAGMA_SUCCESS != magma_cmalloc( &da, N*ldda + 2*N*nb + nb*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magmaFloatComplex *d_A = da;
magmaFloatComplex *d_work = da + (N+nb)*ldda;
magma_int_t i__;
magmaFloatComplex *t, *d_t;
magma_cmalloc_cpu( &t, nb*nb );
if ( t == NULL ) {
magma_free( da );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
d_t = d_work + nb * ldda;
czero_nbxnb_block(nb, d_A+N*ldda, ldda);
/* Set elements 1:ILO-1 and IHI:N-1 of TAU to zero */
for (i__ = 1; i__ < ilo; ++i__)
tau[i__] = c_zero;
for (i__ = max(1,ihi); i__ < n; ++i__)
tau[i__] = c_zero;
for(i__=0; i__< nb*nb; i__+=4)
t[i__] = t[i__+1] = t[i__+2] = t[i__+3] = c_zero;
nbmin = 2;
iws = 1;
if (nb > 1 && nb < nh) {
/* Determine when to cross over from blocked to unblocked code
(last block is always handled by unblocked code) */
if (nb < nh) {
/* Determine if workspace is large enough for blocked code */
iws = n * nb;
if (lwork < iws) {
/* Not enough workspace to use optimal NB: determine the
minimum value of NB, and reduce NB or force use of
unblocked code */
nbmin = nb;
if (lwork >= n * nbmin)
nb = lwork / n;
else
nb = 1;
}
}
}
ldwork = n;
if (nb < nbmin || nb >= nh) {
/* Use unblocked code below */
i__ = ilo;
}
else {
/* Use blocked code */
/* Copy the matrix to the GPU */
magma_csetmatrix( N, N-ilo+1, a+(ilo-1)*(lda), lda, d_A, ldda );
for (i__ = ilo; i__ < ihi - nb; i__ += nb) {
/* Computing MIN */
ib = min(nb, ihi - i__);
/* Reduce columns i:i+ib-1 to Hessenberg form, returning the
matrices V and T of the block reflector H = I - V*T*V'
which performs the reduction, and also the matrix Y = A*V*T */
/* Get the current panel (no need for the 1st iteration) */
magma_cgetmatrix( ihi-i__+1, ib,
d_A + (i__ - ilo)*ldda + i__ - 1, ldda,
a + (i__ - 1 )*lda + i__ - 1, lda );
magma_clahr2(ihi, i__, ib,
d_A + (i__ - ilo)*ldda,
d_A + N*ldda + 1,
a + (i__ - 1 )*(lda) , lda,
&tau[i__], t, nb, work, ldwork);
/* Copy T from the CPU to D_T on the GPU */
magma_csetmatrix( nb, nb, t, nb, d_t, nb );
magma_clahru(n, ihi, i__ - 1, ib,
a + (i__ - 1 )*(lda), lda,
d_A + (i__ - ilo)*ldda,
d_A + (i__ - ilo)*ldda + i__ - 1,
d_A + N*ldda, d_t, d_work);
}
}
/* Use unblocked code to reduce the rest of the matrix */
if (!(nb < nbmin || nb >= nh)) {
magma_cgetmatrix( n, n-i__+1,
d_A+ (i__-ilo)*ldda, ldda,
a + (i__-1)*(lda), lda );
}
lapackf77_cgehd2(&n, &i__, &ihi, a, &lda, &tau[1], work, &iinfo);
MAGMA_C_SET2REAL( work[0], (float) iws );
magma_free( da );
magma_free_cpu(t);
return *info;
} /* magma_cgehrd2 */
/**
Purpose
-------
CGEHRD reduces a COMPLEX general matrix A to upper Hessenberg form H by
an orthogonal similarity transformation: Q' * A * Q = H . This version
stores the triangular matrices used in the factorization so that they can
be applied directly (i.e., without being recomputed) later. As a result,
the application of Q is much faster.
Arguments
---------
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in]
ilo INTEGER
@param[in]
ihi INTEGER
It is assumed that A is already upper triangular in rows
and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
set by a previous call to CGEBAL; otherwise they should be
set to 1 and N respectively. See Further Details.
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the N-by-N general matrix to be reduced.
On exit, the upper triangle and the first subdiagonal of A
are overwritten with the upper Hessenberg matrix H, and the
elements below the first subdiagonal, with the array TAU,
represent the orthogonal matrix Q as a product of elementary
reflectors. See Further Details.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
tau COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
zero.
@param[out]
work (workspace) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK. LWORK >= 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]
T COMPLEX array, dimension NB*N,
where NB is the optimal blocksize. It stores the NB*NB blocks
of the triangular T matrices used in the reduction.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
---------------
The matrix Q is represented as a product of (ihi-ilo) elementary
reflectors
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
exit in A(i+2:ihi,i), and tau in TAU(i).
The contents of A are illustrated by the following example, with
n = 7, ilo = 2 and ihi = 6:
@verbatim
on entry, on exit,
( a a a a a a a ) ( a a h h h h a )
( a a a a a a ) ( a h h h h a )
( a a a a a a ) ( h h h h h h )
( a a a a a a ) ( v2 h h h h h )
( a a a a a a ) ( v2 v3 h h h h )
( a a a a a a ) ( v2 v3 v4 h h h )
( a ) ( a )
@endverbatim
where a denotes an element of the original matrix A, h denotes a
modified element of the upper Hessenberg matrix H, and vi denotes an
element of the vector defining H(i).
This implementation follows the hybrid algorithm and notations described in
S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg
form through hybrid GPU-based computing," University of Tennessee Computer
Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219),
May 24, 2009.
This version stores the T matrices, for later use in magma_cunghr.
@ingroup magma_cgeev_comp
********************************************************************/
extern "C" magma_int_t
magma_cgehrd_m(
magma_int_t n, magma_int_t ilo, magma_int_t ihi,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magmaFloatComplex *T,
magma_int_t *info)
{
#define A( i, j ) (A + (i) + (j)*lda)
#define dA( d, i, j ) (data.A[d] + (i) + (j)*ldda)
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_zero = MAGMA_C_ZERO;
magma_int_t nb = magma_get_cgehrd_nb(n);
magma_int_t nh, iws, ldda, min_lblocks, max_lblocks, last_dev, d;
magma_int_t dpanel, di, nlocal, i, i2, ib, ldwork;
magma_int_t iinfo;
magma_int_t lquery;
struct cgehrd_data data;
magma_int_t ngpu = magma_num_gpus();
*info = 0;
iws = n*(nb + nb*ngpu);
work[0] = magma_cmake_lwork( iws );
lquery = (lwork == -1);
if (n < 0) {
*info = -1;
} else if (ilo < 1 || ilo > max(1,n)) {
*info = -2;
} else if (ihi < min(ilo,n) || ihi > n) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
} else if (lwork < iws && ! lquery) {
*info = -8;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
// Adjust from 1-based indexing
ilo -= 1;
// Quick return if possible
nh = ihi - ilo;
if (nh <= 1) {
work[0] = c_one;
return *info;
}
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
// Set elements 0:ILO-1 and IHI-1:N-2 of TAU to zero
for (i = 0; i < ilo; ++i)
tau[i] = c_zero;
for (i = max(0,ihi-1); i < n-1; ++i)
tau[i] = c_zero;
// set T to zero
lapackf77_claset( "Full", &nb, &n, &c_zero, &c_zero, T, &nb );
// set to null, to simplify cleanup code
for( d = 0; d < ngpu; ++d ) {
data.A[d] = NULL;
data.queues[d] = NULL;
}
// Now requires lwork >= iws; else dT won't be computed in unblocked code.
// If not enough workspace, use unblocked code
//if ( lwork < iws ) {
// nb = 1;
//}
if (nb == 1 || nb >= nh) {
// Use unblocked code below
i = ilo;
}
else {
// Use blocked code
// allocate memory on GPUs for A and workspaces
ldda = magma_roundup( n, 32 );
min_lblocks = (n / nb) / ngpu;
max_lblocks = ((n-1) / nb) / ngpu + 1;
last_dev = (n / nb) % ngpu;
// V and Vd need to be padded for copying in mclahr2
data.ngpu = ngpu;
data.ldda = ldda;
data.ldv = nb*max_lblocks*ngpu;
data.ldvd = nb*max_lblocks;
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
nlocal = min_lblocks*nb;
if ( d < last_dev ) {
nlocal += nb;
}
else if ( d == last_dev ) {
nlocal += (n % nb);
}
ldwork = nlocal*ldda // A
+ nb*data.ldv // V
+ nb*data.ldvd // Vd
+ nb*ldda // Y
+ nb*ldda // W
+ nb*nb; // Ti
if ( MAGMA_SUCCESS != magma_cmalloc( &data.A[d], ldwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto CLEANUP;
}
data.V [d] = data.A [d] + nlocal*ldda;
data.Vd[d] = data.V [d] + nb*data.ldv;
data.Y [d] = data.Vd[d] + nb*data.ldvd;
data.W [d] = data.Y [d] + nb*ldda;
data.Ti[d] = data.W [d] + nb*ldda;
magma_queue_create( d, &data.queues[d] );
}
// Copy the matrix to GPUs
magma_csetmatrix_1D_col_bcyclic( n, n, A, lda, data.A, ldda, ngpu, nb, data.queues );
// round ilo down to block boundary
ilo = (ilo/nb)*nb;
for (i = ilo; i < ihi - 1 - nb; i += nb) {
// Reduce columns i:i+nb-1 to Hessenberg form, returning the
// matrices V and T of the block reflector H = I - V*T*V'
// which performs the reduction, and also the matrix Y = A*V*T
// Get the current panel (no need for the 1st iteration)
dpanel = (i / nb) % ngpu;
di = ((i / nb) / ngpu) * nb;
if ( i > ilo ) {
magma_setdevice( dpanel );
magma_cgetmatrix( ihi-i, nb,
dA(dpanel, i, di), ldda,
A(i,i), lda, data.queues[dpanel] );
}
// add 1 to i for 1-based index
magma_clahr2_m( ihi, i+1, nb, A(0,i), lda,
&tau[i], &T[i*nb], nb, work, n, &data );
magma_clahru_m( n, ihi, i, nb, A, lda, &data );
// copy first i rows above panel to host
magma_setdevice( dpanel );
magma_cgetmatrix_async( i, nb,
dA(dpanel, 0, di), ldda,
A(0,i), lda, data.queues[dpanel] );
}
// Copy remainder to host, block-by-block
for( i2 = i; i2 < n; i2 += nb ) {
ib = min( nb, n-i2 );
d = (i2 / nb) % ngpu;
di = (i2 / nb) / ngpu * nb;
magma_setdevice( d );
magma_cgetmatrix( n, ib,
dA(d, 0, di), ldda,
A(0,i2), lda, data.queues[d] );
}
}
// Use unblocked code to reduce the rest of the matrix
// add 1 to i for 1-based index
i += 1;
lapackf77_cgehd2(&n, &i, &ihi, A, &lda, tau, work, &iinfo);
work[0] = magma_cmake_lwork( iws );
CLEANUP:
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
magma_free( data.A[d] );
magma_queue_destroy( data.queues[d] );
}
magma_setdevice( orig_dev );
return *info;
} /* magma_cgehrd */
