void CORE_cgemm_quark(Quark *quark)
{
int transA;
int transB;
int m;
int n;
int k;
PLASMA_Complex32_t alpha;
PLASMA_Complex32_t *A;
int lda;
PLASMA_Complex32_t *B;
int ldb;
PLASMA_Complex32_t beta;
PLASMA_Complex32_t *C;
int ldc;
quark_unpack_args_13(quark, transA, transB, m, n, k, alpha, A, lda, B, ldb, beta, C, ldc);
cblas_cgemm(
CblasColMajor,
(CBLAS_TRANSPOSE)transA, (CBLAS_TRANSPOSE)transB,
m, n, k,
CBLAS_SADDR(alpha), A, lda,
B, ldb,
CBLAS_SADDR(beta), C, ldc);
}
static inline void CORE_cgetrf_reclap_update(const int M, const int column, const int n1, const int n2,
PLASMA_Complex32_t *A, const int LDA, int *IPIV,
const int thidx, const int thcnt)
{
static PLASMA_Complex32_t posone = 1.0;
static PLASMA_Complex32_t negone = -1.0;
PLASMA_Complex32_t *Atop = A + column*LDA;
PLASMA_Complex32_t *Atop2 = Atop + n1 *LDA;
int coff, ccnt, lm, loff;
CORE_cbarrier_thread( thidx, thcnt );
psplit( n2, thidx, thcnt, &coff, &ccnt );
if (ccnt > 0) {
CORE_claswap1( ccnt, Atop2 + coff*LDA, LDA, column, n1 + column, IPIV ); /* swap to the right */
cblas_ctrsm( CblasColMajor, CblasLeft, CblasLower, CblasNoTrans, CblasUnit,
n1, ccnt, CBLAS_SADDR(posone), Atop + column, LDA, Atop2 + coff*LDA + column, LDA );
}
/* __sync_synchronize(); */ /* hopefully we will not need memory fences */
/* need to wait for pivoting and triangular solve to finish */
CORE_cbarrier_thread( thidx, thcnt );
psplit( M, thidx, thcnt, &loff, &lm );
if (thidx == 0) {
loff = column + n1;
lm -= column + n1;
};
cblas_cgemm( CblasColMajor, CblasNoTrans, CblasNoTrans, lm, n2, n1,
CBLAS_SADDR(negone), Atop+loff, LDA, Atop2 + column, LDA, CBLAS_SADDR(posone), Atop2+loff, LDA );
}
void CORE_cgemm_p2f1_quark(Quark* quark)
{
int transA;
int transB;
int M;
int N;
int K;
PLASMA_Complex32_t alpha;
PLASMA_Complex32_t *A;
int LDA;
PLASMA_Complex32_t **B;
int LDB;
PLASMA_Complex32_t beta;
PLASMA_Complex32_t *C;
int LDC;
void *fake1;
quark_unpack_args_14(quark, transA, transB, M, N, K, alpha,
A, LDA, B, LDB, beta, C, LDC, fake1);
cblas_cgemm(
CblasColMajor,
(CBLAS_TRANSPOSE)transA, (CBLAS_TRANSPOSE)transB,
M, N, K,
CBLAS_SADDR(alpha), A, LDA,
*B, LDB,
CBLAS_SADDR(beta), C, LDC);
}
void CORE_zgemm_p3_quark(Quark* quark)
{
int transA;
int transB;
int M;
int N;
int K;
PLASMA_Complex64_t alpha;
PLASMA_Complex64_t *A;
int LDA;
PLASMA_Complex64_t *B;
int LDB;
PLASMA_Complex64_t beta;
PLASMA_Complex64_t **C;
int LDC;
quark_unpack_args_13(quark, transA, transB, M, N, K, alpha,
A, LDA, B, LDB, beta, C, LDC);
cblas_zgemm(
CblasColMajor,
(CBLAS_TRANSPOSE)transA, (CBLAS_TRANSPOSE)transB,
M, N, K,
CBLAS_SADDR(alpha), A, LDA,
B, LDB,
CBLAS_SADDR(beta), *C, LDC);
}
static int check_solution(PLASMA_enum uplo, PLASMA_enum trans, int N, int K,
PLASMA_Complex32_t alpha, PLASMA_Complex32_t *A, int LDA,
PLASMA_Complex32_t *B, int LDB,
float beta, PLASMA_Complex32_t *Cref, PLASMA_Complex32_t *Cplasma, int LDC)
{
int info_solution;
float Anorm, Bnorm, Cinitnorm, Cplasmanorm, Clapacknorm, Rnorm, result;
float eps;
PLASMA_Complex32_t beta_const;
float *work = (float *)malloc(max(N, K)* sizeof(float));
beta_const = -1.0;
Anorm = LAPACKE_clange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm),
(trans == PlasmaNoTrans) ? N : K,
(trans == PlasmaNoTrans) ? K : N, A, LDA, work);
Bnorm = LAPACKE_clange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm),
(trans == PlasmaNoTrans) ? N : K,
(trans == PlasmaNoTrans) ? K : N, B, LDB, work);
Cinitnorm = LAPACKE_clange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, N, Cref, LDC, work);
Cplasmanorm = LAPACKE_clange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, N, Cplasma, LDC, work);
cblas_cher2k(CblasColMajor, (CBLAS_UPLO)uplo, (CBLAS_TRANSPOSE)trans,
N, K, CBLAS_SADDR(alpha), A, LDA, B, LDB, (beta), Cref, LDC);
Clapacknorm = LAPACKE_clange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, N, Cref, LDC, work);
cblas_caxpy(LDC*N, CBLAS_SADDR(beta_const), Cplasma, 1, Cref, 1);
Rnorm = LAPACKE_clange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, N, Cref, LDC, work);
eps = LAPACKE_slamch_work('e');
printf("Rnorm %e, Anorm %e, Cinitnorm %e, Cplasmanorm %e, Clapacknorm %e\n",
Rnorm, Anorm, Cinitnorm, Cplasmanorm, Clapacknorm);
result = Rnorm / ((Anorm + Bnorm + Cinitnorm) * N * eps);
printf("============\n");
printf("Checking the norm of the difference against reference CHER2K \n");
printf("-- ||Cplasma - Clapack||_oo/((||A||_oo+||C||_oo).N.eps) = %e \n", result);
if ( isnan(Rnorm) || isinf(Rnorm) || isnan(result) || isinf(result) || (result > 10.0) ) {
printf("-- The solution is suspicious ! \n");
info_solution = 1;
}
else {
printf("-- The solution is CORRECT ! \n");
info_solution= 0 ;
}
free(work);
return info_solution;
}
void CORE_caxpy(int M, int N, PLASMA_Complex32_t alpha,
PLASMA_Complex32_t *A, int LDA,
PLASMA_Complex32_t *B, int LDB)
{
int j;
if (M == LDA)
cblas_caxpy(M*N, CBLAS_SADDR(alpha), A, 1, B, 1);
else {
for (j = 0; j < N; j++)
cblas_caxpy(M, CBLAS_SADDR(alpha), &A[j*LDA], 1, &B[j*LDA], 1);
}
}
int check_solution(int M, int N, int NRHS, PLASMA_Complex64_t *A1, int LDA, PLASMA_Complex64_t *B1, PLASMA_Complex64_t *B2, int LDB)
{
int info_solution;
double Rnorm, Anorm, Xnorm, Bnorm;
PLASMA_Complex64_t alpha, beta;
double *work = (double *)malloc(max(M, N)* sizeof(double));
double eps;
eps = LAPACKE_dlamch_work('e');
alpha = 1.0;
beta = -1.0;
Anorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), M, N, A1, LDA, work);
Xnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), M, NRHS, B2, LDB, work);
Bnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, NRHS, B1, LDB, work);
cblas_zgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, M, NRHS, N, CBLAS_SADDR(alpha), A1, LDA, B2, LDB, CBLAS_SADDR(beta), B1, LDB);
if (M >= N) {
PLASMA_Complex64_t *Residual = (PLASMA_Complex64_t *)malloc(M*NRHS*sizeof(PLASMA_Complex64_t));
memset((void*)Residual, 0, M*NRHS*sizeof(PLASMA_Complex64_t));
cblas_zgemm(CblasColMajor, CblasConjTrans, CblasNoTrans, N, NRHS, M, CBLAS_SADDR(alpha), A1, LDA, B1, LDB, CBLAS_SADDR(beta), Residual, M);
Rnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), M, NRHS, Residual, M, work);
free(Residual);
}
else {
PLASMA_Complex64_t *Residual = (PLASMA_Complex64_t *)malloc(N*NRHS*sizeof(PLASMA_Complex64_t));
memset((void*)Residual, 0, N*NRHS*sizeof(PLASMA_Complex64_t));
cblas_zgemm(CblasColMajor, CblasConjTrans, CblasNoTrans, N, NRHS, M, CBLAS_SADDR(alpha), A1, LDA, B1, LDB, CBLAS_SADDR(beta), Residual, N);
Rnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, NRHS, Residual, N, work);
free(Residual);
}
printf("============\n");
printf("Checking the Residual of the solution \n");
printf("-- ||Ax-B||_oo/((||A||_oo||x||_oo+||B||)_oo.N.eps) = %e \n",Rnorm/((Anorm*Xnorm+Bnorm)*N*eps));
if (isnan(Rnorm / ((Anorm * Xnorm + Bnorm) * N * eps)) || (Rnorm / ((Anorm * Xnorm + Bnorm) * N * eps) > 10.0) ) {
printf("-- The solution is suspicious ! \n");
info_solution = 1;
}
else {
printf("-- The solution is CORRECT ! \n");
info_solution= 0 ;
}
free(work);
return info_solution;
}
static int check_solution(int M, int N, int NRHS, PLASMA_Complex32_t *A1, int LDA, PLASMA_Complex32_t *B1, PLASMA_Complex32_t *B2, int LDB, float eps)
{
int info_solution;
float Rnorm, Anorm, Xnorm, Bnorm;
PLASMA_Complex32_t alpha, beta;
float result;
float *work = (float *)malloc(max(M, N)* sizeof(float));
alpha = 1.0;
beta = -1.0;
BLAS_cge_norm( blas_colmajor, blas_inf_norm, M, N, A1, LDA, &Anorm );
BLAS_cge_norm( blas_colmajor, blas_inf_norm, M, NRHS, B2, LDB, &Xnorm );
BLAS_cge_norm( blas_colmajor, blas_inf_norm, N, NRHS, B1, LDB, &Bnorm );
cblas_cgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, M, NRHS, N, CBLAS_SADDR(alpha), A1, LDA, B2, LDB, CBLAS_SADDR(beta), B1, LDB);
if (M >= N) {
PLASMA_Complex32_t *Residual = (PLASMA_Complex32_t *)malloc(M*NRHS*sizeof(PLASMA_Complex32_t));
memset((void*)Residual, 0, M*NRHS*sizeof(PLASMA_Complex32_t));
cblas_cgemm(CblasColMajor, CblasConjTrans, CblasNoTrans, N, NRHS, M, CBLAS_SADDR(alpha), A1, LDA, B1, LDB, CBLAS_SADDR(beta), Residual, M);
BLAS_cge_norm( blas_colmajor, blas_inf_norm, M, NRHS, Residual, M, &Rnorm );
free(Residual);
}
else {
PLASMA_Complex32_t *Residual = (PLASMA_Complex32_t *)malloc(N*NRHS*sizeof(PLASMA_Complex32_t));
memset((void*)Residual, 0, N*NRHS*sizeof(PLASMA_Complex32_t));
cblas_cgemm(CblasColMajor, CblasConjTrans, CblasNoTrans, N, NRHS, M, CBLAS_SADDR(alpha), A1, LDA, B1, LDB, CBLAS_SADDR(beta), Residual, N);
BLAS_cge_norm( blas_colmajor, blas_inf_norm, N, NRHS, Residual, N, &Rnorm );
free(Residual);
}
if (getenv("PLASMA_TESTING_VERBOSE"))
printf( "||A||_oo=%f\n||X||_oo=%f\n||B||_oo=%f\n||A X - B||_oo=%e\n", Anorm, Xnorm, Bnorm, Rnorm );
result = Rnorm / ( (Anorm*Xnorm+Bnorm)*N*eps ) ;
printf("============\n");
printf("Checking the Residual of the solution \n");
printf("-- ||Ax-B||_oo/((||A||_oo||x||_oo+||B||_oo).N.eps) = %e \n", result);
if ( isnan(Xnorm) || isinf(Xnorm) || isnan(result) || isinf(result) || (result > 60.0) ) {
printf("-- The solution is suspicious ! \n");
info_solution = 1;
}
else{
printf("-- The solution is CORRECT ! \n");
info_solution = 0;
}
free(work);
return info_solution;
}
void CORE_cgemm(int transA, int transB,
int M, int N, int K,
PLASMA_Complex32_t alpha, PLASMA_Complex32_t *A, int LDA,
PLASMA_Complex32_t *B, int LDB,
PLASMA_Complex32_t beta, PLASMA_Complex32_t *C, int LDC)
{
cblas_cgemm(
CblasColMajor,
(CBLAS_TRANSPOSE)transA, (CBLAS_TRANSPOSE)transB,
M, N, K,
CBLAS_SADDR(alpha), A, LDA,
B, LDB,
CBLAS_SADDR(beta), C, LDC);
}
static int check_solution(PLASMA_enum side, PLASMA_enum uplo, int M, int N,
PLASMA_Complex64_t alpha, PLASMA_Complex64_t *A, int LDA,
PLASMA_Complex64_t *B, int LDB,
PLASMA_Complex64_t beta, PLASMA_Complex64_t *Cref, PLASMA_Complex64_t *Cplasma, int LDC)
{
int info_solution, NrowA;
double Anorm, Bnorm, Cinitnorm, Cplasmanorm, Clapacknorm, Rnorm;
double eps;
PLASMA_Complex64_t beta_const;
double result;
double *work = (double *)malloc(max(M, N)* sizeof(double));
beta_const = (PLASMA_Complex64_t)-1.0;
NrowA = (side == PlasmaLeft) ? M : N;
Anorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), NrowA, NrowA, A, LDA, work);
Bnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), M, N, B, LDB, work);
Cinitnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), M, N, Cref, LDC, work);
Cplasmanorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), M, N, Cplasma, LDC, work);
cblas_zsymm(CblasColMajor, (CBLAS_SIDE)side, (CBLAS_UPLO)uplo, M, N, CBLAS_SADDR(alpha), A, LDA, B, LDB, CBLAS_SADDR(beta), Cref, LDC);
Clapacknorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), M, N, Cref, LDC, work);
cblas_zaxpy(LDC * N, CBLAS_SADDR(beta_const), Cplasma, 1, Cref, 1);
Rnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), M, N, Cref, LDC, work);
eps = LAPACKE_dlamch_work('e');
printf("Rnorm %e, Anorm %e, Bnorm %e, Cinitnorm %e, Cplasmanorm %e, Clapacknorm %e\n",Rnorm,Anorm,Bnorm,Cinitnorm,Cplasmanorm,Clapacknorm);
result = Rnorm / ((Anorm + Bnorm + Cinitnorm) * N * eps);
printf("============\n");
printf("Checking the norm of the difference against reference ZSYMM \n");
printf("-- ||Cplasma - Clapack||_oo/((||A||_oo+||B||_oo+||C||_oo).N.eps) = %e \n", result );
if ( isinf(Clapacknorm) || isinf(Cplasmanorm) || isnan(result) || isinf(result) || (result > 10.0) ) {
printf("-- The solution is suspicious ! \n");
info_solution = 1;
}
else {
printf("-- The solution is CORRECT ! \n");
info_solution= 0 ;
}
free(work);
return info_solution;
}
void CORE_zgemm_tile_quark(Quark *quark)
{
PLASMA_enum transA, transB;
int m, n, k, lda, ldb, ldc;
const PLASMA_Complex64_t *alpha, *beta;
const PLASMA_Complex64_t *A, *B;
PLASMA_Complex64_t *C;
quark_unpack_args_13( quark, transA, transB, m, n, k, alpha, A, lda, B, ldb, beta, C, ldc );
cblas_zgemm(
CblasColMajor,
(CBLAS_TRANSPOSE)transA, (CBLAS_TRANSPOSE)transB,
m, n, k,
CBLAS_SADDR(*alpha), A, lda,
B, ldb,
CBLAS_SADDR(*beta), C, ldc );
}
void CORE_zgemv_quark(Quark *quark)
{
PLASMA_enum trans;
int m, n, lda, incx, incy;
PLASMA_Complex64_t alpha, beta;
const PLASMA_Complex64_t *A, *x;
PLASMA_Complex64_t *y;
quark_unpack_args_11( quark, trans, m, n, alpha, A, lda, x, incx, beta, y, incy );
cblas_zgemv(
CblasColMajor,
(CBLAS_TRANSPOSE)trans,
m, n,
CBLAS_SADDR(alpha), A, lda,
x, incx,
CBLAS_SADDR(beta), y, incy);
}
void CORE_caxpy_quark(Quark *quark)
{
int M;
int N;
PLASMA_Complex32_t alpha;
PLASMA_Complex32_t *A;
int LDA;
PLASMA_Complex32_t *B;
int LDB;
int j;
quark_unpack_args_7(quark, M, N, alpha, A, LDA, B, LDB);
if (M == LDA)
cblas_caxpy(M*N, CBLAS_SADDR(alpha), A, 1, B, 1);
else {
for (j = 0; j < N; j++)
cblas_caxpy(M, CBLAS_SADDR(alpha), &A[j*LDA], 1, &B[j*LDA], 1);
}
}
void CORE_cher2k(int uplo, int trans,
int N, int K,
PLASMA_Complex32_t alpha, PLASMA_Complex32_t *A, int LDA,
PLASMA_Complex32_t *B, int LDB,
float beta, PLASMA_Complex32_t *C, int LDC)
{
cblas_cher2k(
CblasColMajor,
(CBLAS_UPLO)uplo, (CBLAS_TRANSPOSE)trans,
N, K,
CBLAS_SADDR(alpha), A, LDA, B, LDB,
beta, C, LDC);
}
static int check_solution(int N, int NRHS, PLASMA_Complex64_t *A1, int LDA, PLASMA_Complex64_t *B1, PLASMA_Complex64_t *B2, int LDB, double eps )
{
int info_solution;
double Rnorm, Anorm, Xnorm, Bnorm, result;
PLASMA_Complex64_t alpha, beta;
double *work = (double *)malloc(N*sizeof(double));
alpha = 1.0;
beta = -1.0;
Xnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, NRHS, B2, LDB, work);
Anorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, N, A1, LDA, work);
Bnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, NRHS, B1, LDB, work);
cblas_zgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, N, NRHS, N, CBLAS_SADDR(alpha), A1, LDA, B2, LDB, CBLAS_SADDR(beta), B1, LDB);
Rnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, NRHS, B1, LDB, work);
if (getenv("PLASMA_TESTING_VERBOSE"))
printf( "||A||_oo=%f\n||X||_oo=%f\n||B||_oo=%f\n||A X - B||_oo=%e\n", Anorm, Xnorm, Bnorm, Rnorm );
result = Rnorm / ( (Anorm*Xnorm+Bnorm)*N*eps ) ;
printf("============\n");
printf("Checking the Residual of the solution \n");
printf("-- ||Ax-B||_oo/((||A||_oo||x||_oo+||B||_oo).N.eps) = %e \n", result);
if ( isnan(Xnorm) || isinf(Xnorm) || isnan(result) || isinf(result) || (result > 60.0) ) {
printf("-- The solution is suspicious ! \n");
info_solution = 1;
}
else{
printf("-- The solution is CORRECT ! \n");
info_solution = 0;
}
free(work);
return info_solution;
}
int check_solution(int N, int NRHS, PLASMA_Complex32_t *A1, int LDA, PLASMA_Complex32_t *B1, PLASMA_Complex32_t *B2, int LDB )
{
int info_solution;
float Rnorm, Anorm, Xnorm, Bnorm;
PLASMA_Complex32_t alpha, beta;
float *work = (float *)malloc(N*sizeof(float));
float eps;
eps = LAPACKE_slamch_work('e');
/* Initialize A1 and A2 for Symmetric Positive Matrix */
alpha = 1.0;
beta = -1.0;
Xnorm = LAPACKE_clange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, NRHS, B2, LDB, work);
Anorm = LAPACKE_clange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, N, A1, LDA, work);
Bnorm = LAPACKE_clange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, NRHS, B1, LDB, work);
cblas_cgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, N, NRHS, N, CBLAS_SADDR(alpha), A1, LDA, B2, LDB, CBLAS_SADDR(beta), B1, LDB);
Rnorm = LAPACKE_clange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, NRHS, B1, LDB, work);
printf("============\n");
printf("Checking the Residual of the solution \n");
printf("-- ||Ax-B||_oo/((||A||_oo||x||_oo+||B||_oo).N.eps) = %e \n",Rnorm/((Anorm*Xnorm+Bnorm)*N*eps));
if (Rnorm/((Anorm*Xnorm+Bnorm)*N*eps) > 10.0){
printf("-- The solution is suspicious ! \n");
info_solution = 1;
}
else{
printf("-- The solution is CORRECT ! \n");
info_solution = 0;
}
free(work);
return info_solution;
}
int CORE_zttlqt(int M, int N, int IB,
PLASMA_Complex64_t *A1, int LDA1,
PLASMA_Complex64_t *A2, int LDA2,
PLASMA_Complex64_t *T, int LDT,
PLASMA_Complex64_t *TAU, PLASMA_Complex64_t *WORK)
{
static PLASMA_Complex64_t zone = 1.0;
static PLASMA_Complex64_t zzero = 0.0;
#ifdef COMPLEX
static int ione = 1;
#endif
PLASMA_Complex64_t alpha;
int i, j, l, ii, sb, mi, ni;
/* Check input arguments */
if (M < 0) {
coreblas_error(1, "Illegal value of M");
return -1;
}
if (N < 0) {
coreblas_error(2, "Illegal value of N");
return -2;
}
if (IB < 0) {
coreblas_error(3, "Illegal value of IB");
return -3;
}
if ((LDA2 < max(1,M)) && (M > 0)) {
coreblas_error(7, "Illegal value of LDA2");
return -7;
}
/* Quick return */
if ((M == 0) || (N == 0) || (IB == 0))
return PLASMA_SUCCESS;
/* TODO: Need to check why some cases require
* this to not have uninitialized values */
CORE_zlaset( PlasmaUpperLower, IB, N,
0., 0., T, LDT);
for(ii = 0; ii < M; ii += IB) {
sb = min(M-ii, IB);
for(i = 0; i < sb; i++) {
j = ii + i;
mi = sb-i-1;
ni = min( j + 1, N);
/*
* Generate elementary reflector H( II*IB+I ) to annihilate A( II*IB+I, II*IB+I:M ).
*/
#ifdef COMPLEX
LAPACKE_zlacgv_work(ni, &A2[j], LDA2);
LAPACKE_zlacgv_work(ione, &A1[LDA1*j+j], LDA1);
#endif
LAPACKE_zlarfg_work(ni+1, &A1[LDA1*j+j], &A2[j], LDA2, &TAU[j]);
if (mi > 0) {
/*
* Apply H( j-1 ) to A( j:II+IB-1, j-1:M ) from the right.
*/
cblas_zcopy(
mi,
&A1[LDA1*j+(j+1)], 1,
WORK, 1);
cblas_zgemv(
CblasColMajor, (CBLAS_TRANSPOSE)PlasmaNoTrans,
mi, ni,
CBLAS_SADDR(zone), &A2[j+1], LDA2,
&A2[j], LDA2,
CBLAS_SADDR(zone), WORK, 1);
alpha = -(TAU[j]);
cblas_zaxpy(
mi, CBLAS_SADDR(alpha),
WORK, 1,
&A1[LDA1*j+j+1], 1);
cblas_zgerc(
CblasColMajor, mi, ni,
CBLAS_SADDR(alpha), WORK, 1,
&A2[j], LDA2,
&A2[j+1], LDA2);
}
/*
* Calculate T.
*/
if (i > 0 ) {
l = min(i, max(0, N-ii));
alpha = -(TAU[j]);
CORE_zpemv(
PlasmaNoTrans, PlasmaRowwise,
i , min(j, N), l,
alpha, &A2[ii], LDA2,
&A2[j], LDA2,
zzero, &T[LDT*j], 1,
WORK);
/* T(0:i-1, j) = T(0:i-1, ii:j-1) * T(0:i-1, j) */
cblas_ztrmv(
CblasColMajor, (CBLAS_UPLO)PlasmaUpper,
(CBLAS_TRANSPOSE)PlasmaNoTrans,
(CBLAS_DIAG)PlasmaNonUnit,
i, &T[LDT*ii], LDT,
&T[LDT*j], 1);
}
#ifdef COMPLEX
LAPACKE_zlacgv_work(ni, &A2[j], LDA2 );
LAPACKE_zlacgv_work(ione, &A1[LDA1*j+j], LDA1 );
#endif
T[LDT*j+i] = TAU[j];
}
/* Apply Q to the rest of the matrix to the right */
if (M > ii+sb) {
mi = M-(ii+sb);
ni = min(ii+sb, N);
l = min(sb, max(0, ni-ii));
CORE_zparfb(
PlasmaRight, PlasmaNoTrans,
PlasmaForward, PlasmaRowwise,
mi, IB, mi, ni, sb, l,
&A1[LDA1*ii+ii+sb], LDA1,
&A2[ii+sb], LDA2,
&A2[ii], LDA2,
&T[LDT*ii], LDT,
WORK, M);
}
}
return PLASMA_SUCCESS;
}
int check_factorization(int N, PLASMA_Complex32_t *A1, PLASMA_Complex32_t *A2, int LDA, int uplo)
{
float Anorm, Rnorm;
PLASMA_Complex32_t alpha;
int info_factorization;
int i,j;
float eps;
eps = LAPACKE_slamch_work('e');
PLASMA_Complex32_t *Residual = (PLASMA_Complex32_t *)malloc(N*N*sizeof(PLASMA_Complex32_t));
PLASMA_Complex32_t *L1 = (PLASMA_Complex32_t *)malloc(N*N*sizeof(PLASMA_Complex32_t));
PLASMA_Complex32_t *L2 = (PLASMA_Complex32_t *)malloc(N*N*sizeof(PLASMA_Complex32_t));
float *work = (float *)malloc(N*sizeof(float));
memset((void*)L1, 0, N*N*sizeof(PLASMA_Complex32_t));
memset((void*)L2, 0, N*N*sizeof(PLASMA_Complex32_t));
alpha= 1.0;
LAPACKE_clacpy_work(LAPACK_COL_MAJOR,' ', N, N, A1, LDA, Residual, N);
/* Dealing with L'L or U'U */
if (uplo == PlasmaUpper){
LAPACKE_clacpy_work(LAPACK_COL_MAJOR,'u', N, N, A2, LDA, L1, N);
LAPACKE_clacpy_work(LAPACK_COL_MAJOR,'u', N, N, A2, LDA, L2, N);
cblas_ctrmm(CblasColMajor, CblasLeft, CblasUpper, CblasConjTrans, CblasNonUnit, N, N, CBLAS_SADDR(alpha), L1, N, L2, N);
}
else{
LAPACKE_clacpy_work(LAPACK_COL_MAJOR,'l', N, N, A2, LDA, L1, N);
LAPACKE_clacpy_work(LAPACK_COL_MAJOR,'l', N, N, A2, LDA, L2, N);
cblas_ctrmm(CblasColMajor, CblasRight, CblasLower, CblasConjTrans, CblasNonUnit, N, N, CBLAS_SADDR(alpha), L1, N, L2, N);
}
/* Compute the Residual || A -L'L|| */
for (i = 0; i < N; i++)
for (j = 0; j < N; j++)
Residual[j*N+i] = L2[j*N+i] - Residual[j*N+i];
Rnorm = LAPACKE_clange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, N, Residual, N, work);
Anorm = LAPACKE_clange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, N, A1, LDA, work);
printf("============\n");
printf("Checking the Cholesky Factorization \n");
printf("-- ||L'L-A||_oo/(||A||_oo.N.eps) = %e \n",Rnorm/(Anorm*N*eps));
if ( isnan(Rnorm/(Anorm*N*eps)) || (Rnorm/(Anorm*N*eps) > 10.0) ){
printf("-- Factorization is suspicious ! \n");
info_factorization = 1;
}
else{
printf("-- Factorization is CORRECT ! \n");
info_factorization = 0;
}
free(Residual); free(L1); free(L2); free(work);
return info_factorization;
}
extern "C" magma_int_t
magma_zgeev(magma_vec_t jobvl, magma_vec_t jobvr, magma_int_t n,
magmaDoubleComplex *a, magma_int_t lda,
magmaDoubleComplex *geev_w_array,
magmaDoubleComplex *vl, magma_int_t ldvl,
magmaDoubleComplex *vr, magma_int_t ldvr,
magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t *info, magma_queue_t queue)
{
/* -- clMAGMA (version 1.0.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
September 2012
Purpose
=======
ZGEEV 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
=========
JOBVL (input) CHARACTER*1
= 'N': left eigenvectors of A are not computed;
= 'V': left eigenvectors of are computed.
JOBVR (input) CHARACTER*1
= 'N': right eigenvectors of A are not computed;
= 'V': right eigenvectors of A are computed.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the N-by-N matrix A.
On exit, A has been overwritten.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) COMPLEX*16 array, dimension (N)
W contains the computed eigenvalues.
VL (output) COMPLEX*16 array, dimension (LDVL,N)
If JOBVL = 'V', the left eigenvectors u(j) are stored one
after another in the columns of VL, in the same order
as their eigenvalues.
If JOBVL = 'N', VL is not referenced.
u(j) = VL(:,j), the j-th column of VL.
LDVL (input) INTEGER
The leading dimension of the array VL. LDVL >= 1; if
JOBVL = 'V', LDVL >= N.
VR (output) COMPLEX*16 array, dimension (LDVR,N)
If JOBVR = 'V', the right eigenvectors v(j) are stored one
after another in the columns of VR, in the same order
as their eigenvalues.
If JOBVR = 'N', VR is not referenced.
v(j) = VR(:,j), the j-th column of VR.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= 1; if
JOBVR = 'V', LDVR >= N.
WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= (1+nb)*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.
RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
INFO (output) 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.
===================================================================== */
magma_int_t c__1 = 1;
magma_int_t c__0 = 0;
magma_int_t a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3;
double d__1, d__2;
magmaDoubleComplex z__1, z__2;
magma_int_t i__, k, ihi;
double scl;
magma_int_t ilo;
double dum[1], eps;
magmaDoubleComplex tmp;
magma_int_t ibal;
double anrm;
magma_int_t ierr, itau, iwrk, nout;
magma_int_t scalea;
double cscale;
magma_int_t select[1];
double bignum;
magma_int_t minwrk;
magma_int_t wantvl;
double smlnum;
magma_int_t irwork;
magma_int_t lquery, wantvr;
magma_int_t nb = 0;
magmaDoubleComplex_ptr dT;
//magma_timestr_t start, end;
char side[2] = {0, 0};
magma_vec_t jobvl_ = jobvl;
magma_vec_t jobvr_ = jobvr;
*info = 0;
lquery = lwork == -1;
wantvl = lapackf77_lsame(lapack_const(jobvl_), "V");
wantvr = lapackf77_lsame(lapack_const(jobvr_), "V");
if (! wantvl && ! lapackf77_lsame(lapack_const(jobvl_), "N")) {
*info = -1;
} else if (! wantvr && ! lapackf77_lsame(lapack_const(jobvr_), "N")) {
*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 */
if (*info == 0) {
nb = magma_get_zgehrd_nb(n);
minwrk = (1+nb)*n;
work[0] = MAGMA_Z_MAKE((double) minwrk, 0.);
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 eigenvectors are needed
#if defined(VERSION3)
if (MAGMA_SUCCESS != magma_malloc(&dT, nb*n*sizeof(magmaDoubleComplex) )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
#endif
a_dim1 = lda;
a_offset = 1 + a_dim1;
a -= a_offset;
vl_dim1 = ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--work;
--rwork;
/* Get machine constants */
eps = lapackf77_dlamch("P");
smlnum = lapackf77_dlamch("S");
bignum = 1. / smlnum;
lapackf77_dlabad(&smlnum, &bignum);
smlnum = magma_dsqrt(smlnum) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = lapackf77_zlange("M", &n, &n, &a[a_offset], &lda, dum);
scalea = 0;
if (anrm > 0. && anrm < smlnum) {
scalea = 1;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = 1;
cscale = bignum;
}
if (scalea) {
lapackf77_zlascl("G", &c__0, &c__0, &anrm, &cscale, &n, &n, &a[a_offset], &lda, &
ierr);
}
/* Balance the matrix
(CWorkspace: none)
(RWorkspace: need N) */
ibal = 1;
lapackf77_zgebal("B", &n, &a[a_offset], &lda, &ilo, &ihi, &rwork[ibal], &ierr);
/* Reduce to upper Hessenberg form
(CWorkspace: need 2*N, prefer N+N*NB)
(RWorkspace: none) */
itau = 1;
iwrk = itau + n;
i__1 = lwork - iwrk + 1;
//start = get_current_time();
#if defined(VERSION1)
/*
* Version 1 - LAPACK
*/
lapackf77_zgehrd(&n, &ilo, &ihi, &a[a_offset], &lda,
&work[itau], &work[iwrk], &i__1, &ierr);
#elif defined(VERSION2)
/*
* Version 2 - LAPACK consistent HRD
*/
magma_zgehrd2(n, ilo, ihi, &a[a_offset], lda,
&work[itau], &work[iwrk], &i__1, &ierr);
#elif defined(VERSION3)
/*
* Version 3 - LAPACK consistent MAGMA HRD + matrices T stored,
*/
magma_zgehrd(n, ilo, ihi, &a[a_offset], lda,
&work[itau], &work[iwrk], i__1, dT, 0, &ierr, queue);
#endif
//end = get_current_time();
//printf(" Time for zgehrd = %5.2f sec\n", GetTimerValue(start,end)/1000.);
if (wantvl) {
/* Want left eigenvectors
Copy Householder vectors to VL */
side[0] = 'L';
lapackf77_zlacpy(MagmaLowerStr, &n, &n,
&a[a_offset], &lda, &vl[vl_offset], &ldvl);
/* Generate unitary matrix in VL
(CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
(RWorkspace: none) */
i__1 = lwork - iwrk + 1;
//start = get_current_time();
#if defined(VERSION1) || defined(VERSION2)
/*
* Version 1 & 2 - LAPACK
*/
lapackf77_zunghr(&n, &ilo, &ihi, &vl[vl_offset], &ldvl,
&work[itau], &work[iwrk], &i__1, &ierr);
#elif defined(VERSION3)
/*
* Version 3 - LAPACK consistent MAGMA HRD + matrices T stored
*/
magma_zunghr(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau],
dT, 0, nb, &ierr, queue);
#endif
//end = get_current_time();
//printf(" Time for zunghr = %5.2f sec\n", GetTimerValue(start,end)/1000.);
/* Perform QR iteration, accumulating Schur vectors in VL
(CWorkspace: need 1, prefer HSWORK (see comments) )
(RWorkspace: none) */
iwrk = itau;
i__1 = lwork - iwrk + 1;
lapackf77_zhseqr("S", "V", &n, &ilo, &ihi, &a[a_offset], &lda, geev_w_array,
&vl[vl_offset], &ldvl, &work[iwrk], &i__1, info);
if (wantvr)
{
/* Want left and right eigenvectors
Copy Schur vectors to VR */
side[0] = 'B';
lapackf77_zlacpy("F", &n, &n, &vl[vl_offset], &ldvl, &vr[vr_offset], &ldvr);
}
} else if (wantvr) {
/* Want right eigenvectors
Copy Householder vectors to VR */
side[0] = 'R';
lapackf77_zlacpy("L", &n, &n, &a[a_offset], &lda, &vr[vr_offset], &ldvr);
/* Generate unitary matrix in VR
(CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
(RWorkspace: none) */
i__1 = lwork - iwrk + 1;
//start = get_current_time();
#if defined(VERSION1) || defined(VERSION2)
/*
* Version 1 & 2 - LAPACK
*/
lapackf77_zunghr(&n, &ilo, &ihi, &vr[vr_offset], &ldvr,
&work[itau], &work[iwrk], &i__1, &ierr);
#elif defined(VERSION3)
/*
* Version 3 - LAPACK consistent MAGMA HRD + matrices T stored
*/
magma_zunghr(n, ilo, ihi, &vr[vr_offset], ldvr,
&work[itau], dT, 0, nb, &ierr, queue);
#endif
//end = get_current_time();
//printf(" Time for zunghr = %5.2f sec\n", GetTimerValue(start,end)/1000.);
/* Perform QR iteration, accumulating Schur vectors in VR
(CWorkspace: need 1, prefer HSWORK (see comments) )
(RWorkspace: none) */
iwrk = itau;
i__1 = lwork - iwrk + 1;
lapackf77_zhseqr("S", "V", &n, &ilo, &ihi, &a[a_offset], &lda, geev_w_array,
&vr[vr_offset], &ldvr, &work[iwrk], &i__1, info);
} else {
/* Compute eigenvalues only
(CWorkspace: need 1, prefer HSWORK (see comments) )
(RWorkspace: none) */
iwrk = itau;
i__1 = lwork - iwrk + 1;
lapackf77_zhseqr("E", "N", &n, &ilo, &ihi, &a[a_offset], &lda, geev_w_array,
&vr[vr_offset], &ldvr, &work[iwrk], &i__1, info);
}
/* If INFO > 0 from ZHSEQR, then quit */
if (*info > 0) {
goto L50;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors
(CWorkspace: need 2*N)
(RWorkspace: need 2*N) */
irwork = ibal + n;
lapackf77_ztrevc(side, "B", select, &n, &a[a_offset], &lda, &vl[vl_offset], &ldvl,
&vr[vr_offset], &ldvr, &n, &nout, &work[iwrk], &rwork[irwork],
&ierr);
}
if (wantvl) {
/* Undo balancing of left eigenvectors
(CWorkspace: none)
(RWorkspace: need N) */
lapackf77_zgebak("B", "L", &n, &ilo, &ihi, &rwork[ibal], &n,
&vl[vl_offset], &ldvl, &ierr);
/* Normalize left eigenvectors and make largest component real */
for (i__ = 1; i__ <= n; ++i__) {
scl = 1. / cblas_dznrm2(n, &vl[i__ * vl_dim1 + 1], 1);
cblas_zdscal(n, scl, &vl[i__ * vl_dim1 + 1], 1);
i__2 = n;
for (k = 1; k <= i__2; ++k)
{
i__3 = k + i__ * vl_dim1;
/* Computing 2nd power */
d__1 = MAGMA_Z_REAL(vl[i__3]);
/* Computing 2nd power */
d__2 = MAGMA_Z_IMAG(vl[k + i__ * vl_dim1]);
rwork[irwork + k - 1] = d__1 * d__1 + d__2 * d__2;
}
/* Comment:
Fortran BLAS does not have to add 1
C BLAS must add one to cblas_idamax */
k = cblas_idamax(n, &rwork[irwork], 1)+1;
z__2 = MAGMA_Z_CNJG(vl[k + i__ * vl_dim1]);
d__1 = magma_dsqrt(rwork[irwork + k - 1]);
MAGMA_Z_DSCALE(z__1, z__2, d__1);
tmp = z__1;
cblas_zscal(n, CBLAS_SADDR(tmp), &vl[i__ * vl_dim1 + 1], 1);
i__2 = k + i__ * vl_dim1;
i__3 = k + i__ * vl_dim1;
d__1 = MAGMA_Z_REAL(vl[i__3]);
MAGMA_Z_SET2REAL(z__1, d__1);
vl[i__2] = z__1;
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors
(CWorkspace: none)
(RWorkspace: need N) */
lapackf77_zgebak("B", "R", &n, &ilo, &ihi, &rwork[ibal], &n,
&vr[vr_offset], &ldvr, &ierr);
/* Normalize right eigenvectors and make largest component real */
for (i__ = 1; i__ <= n; ++i__) {
scl = 1. / cblas_dznrm2(n, &vr[i__ * vr_dim1 + 1], 1);
cblas_zdscal(n, scl, &vr[i__ * vr_dim1 + 1], 1);
i__2 = n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * vr_dim1;
/* Computing 2nd power */
d__1 = MAGMA_Z_REAL(vr[i__3]);
/* Computing 2nd power */
d__2 = MAGMA_Z_IMAG(vr[k + i__ * vr_dim1]);
rwork[irwork + k - 1] = d__1 * d__1 + d__2 * d__2;
}
/* Comment:
Fortran BLAS does not have to add 1
C BLAS must add one to cblas_idamax */
k = cblas_idamax(n, &rwork[irwork], 1)+1;
z__2 = MAGMA_Z_CNJG(vr[k + i__ * vr_dim1]);
d__1 = magma_dsqrt(rwork[irwork + k - 1]);
MAGMA_Z_DSCALE(z__1, z__2, d__1);
tmp = z__1;
cblas_zscal(n, CBLAS_SADDR(tmp), &vr[i__ * vr_dim1 + 1], 1);
i__2 = k + i__ * vr_dim1;
i__3 = k + i__ * vr_dim1;
d__1 = MAGMA_Z_REAL(vr[i__3]);
MAGMA_Z_SET2REAL(z__1, d__1);
vr[i__2] = z__1;
}
}
/* Undo scaling if necessary */
L50:
if (scalea) {
i__1 = n - *info;
/* Computing MAX */
i__3 = n - *info;
i__2 = max(i__3,1);
lapackf77_zlascl("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1,
geev_w_array + *info, &i__2, &ierr);
if (*info > 0) {
i__1 = ilo - 1;
lapackf77_zlascl("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1,
geev_w_array, &n, &ierr);
}
}
#if defined(VERSION3)
magma_free( dT );
#endif
return *info;
} /* magma_zgeev */
int check_factorization(int M, int N, PLASMA_Complex64_t *A1, PLASMA_Complex64_t *A2, int LDA, PLASMA_Complex64_t *Q)
{
double Anorm, Rnorm;
PLASMA_Complex64_t alpha, beta;
int info_factorization;
int i,j;
double eps;
eps = LAPACKE_dlamch_work('e');
PLASMA_Complex64_t *Ql = (PLASMA_Complex64_t *)malloc(M*N*sizeof(PLASMA_Complex64_t));
PLASMA_Complex64_t *Residual = (PLASMA_Complex64_t *)malloc(M*N*sizeof(PLASMA_Complex64_t));
double *work = (double *)malloc(max(M,N)*sizeof(double));
alpha=1.0;
beta=0.0;
if (M >= N) {
/* Extract the R */
PLASMA_Complex64_t *R = (PLASMA_Complex64_t *)malloc(N*N*sizeof(PLASMA_Complex64_t));
memset((void*)R, 0, N*N*sizeof(PLASMA_Complex64_t));
LAPACKE_zlacpy_work(LAPACK_COL_MAJOR,'u', M, N, A2, LDA, R, N);
/* Perform Ql=Q*R */
memset((void*)Ql, 0, M*N*sizeof(PLASMA_Complex64_t));
cblas_zgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, M, N, N, CBLAS_SADDR(alpha), Q, LDA, R, N, CBLAS_SADDR(beta), Ql, M);
free(R);
}
else {
/* Extract the L */
PLASMA_Complex64_t *L = (PLASMA_Complex64_t *)malloc(M*M*sizeof(PLASMA_Complex64_t));
memset((void*)L, 0, M*M*sizeof(PLASMA_Complex64_t));
LAPACKE_zlacpy_work(LAPACK_COL_MAJOR,'l', M, N, A2, LDA, L, M);
/* Perform Ql=LQ */
memset((void*)Ql, 0, M*N*sizeof(PLASMA_Complex64_t));
cblas_zgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, M, N, M, CBLAS_SADDR(alpha), L, M, Q, LDA, CBLAS_SADDR(beta), Ql, M);
free(L);
}
/* Compute the Residual */
for (i = 0; i < M; i++)
for (j = 0 ; j < N; j++)
Residual[j*M+i] = A1[j*LDA+i]-Ql[j*M+i];
Rnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), M, N, Residual, M, work);
Anorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), M, N, A2, LDA, work);
if (M >= N) {
printf("============\n");
printf("Checking the QR Factorization \n");
printf("-- ||A-QR||_oo/(||A||_oo.N.eps) = %e \n",Rnorm/(Anorm*N*eps));
}
else {
printf("============\n");
printf("Checking the LQ Factorization \n");
printf("-- ||A-LQ||_oo/(||A||_oo.N.eps) = %e \n",Rnorm/(Anorm*N*eps));
}
if (isnan(Rnorm / (Anorm * N *eps)) || (Rnorm / (Anorm * N * eps) > 10.0) ) {
printf("-- Factorization is suspicious ! \n");
info_factorization = 1;
}
else {
printf("-- Factorization is CORRECT ! \n");
info_factorization = 0;
}
free(work); free(Ql); free(Residual);
return info_factorization;
}
int CORE_zttqrt(int M, int N, int IB,
PLASMA_Complex64_t *A1, int LDA1,
PLASMA_Complex64_t *A2, int LDA2,
PLASMA_Complex64_t *T, int LDT,
PLASMA_Complex64_t *TAU, PLASMA_Complex64_t *WORK)
{
static PLASMA_Complex64_t zone = 1.0;
static PLASMA_Complex64_t zzero = 0.0;
static int ione = 1;
PLASMA_Complex64_t alpha;
int i, j, ii, sb, mi, ni;
/* Check input arguments */
if (M < 0) {
coreblas_error(1, "Illegal value of M");
return -1;
}
if (N < 0) {
coreblas_error(2, "Illegal value of N");
return -2;
}
if (IB < 0) {
coreblas_error(3, "Illegal value of IB");
return -3;
}
if ((LDA2 < max(1,M)) && (M > 0)) {
coreblas_error(7, "Illegal value of LDA2");
return -7;
}
/* Quick return */
if ((M == 0) || (N == 0) || (IB == 0))
return PLASMA_SUCCESS;
for(ii = 0; ii < N; ii += IB) {
sb = min(N-ii, IB);
for(i = 0; i < sb; i++) {
/*
* Generate elementary reflector H( II*IB+I ) to annihilate
* A( II*IB+I:mi, II*IB+I ).
*/
mi = ii + i + 1;
LAPACKE_zlarfg_work(mi+1, &A1[LDA1*(ii+i)+ii+i], &A2[LDA2*(ii+i)], ione, &TAU[ii+i]);
if (sb-i-1>0) {
/*
* Apply H( II*IB+I ) to A( II*IB+I:M, II*IB+I+1:II*IB+IB ) from the left.
*/
ni = sb-i-1;
cblas_zcopy(
ni,
&A1[LDA1*(ii+i+1)+(ii+i)], LDA1,
WORK, 1);
#ifdef COMPLEX
LAPACKE_zlacgv_work(ni, WORK, ione);
#endif
cblas_zgemv(
CblasColMajor, (CBLAS_TRANSPOSE)PlasmaConjTrans,
mi, ni,
CBLAS_SADDR(zone), &A2[LDA2*(ii+i+1)], LDA2,
&A2[LDA2*(ii+i)], 1,
CBLAS_SADDR(zone), WORK, 1);
#ifdef COMPLEX
LAPACKE_zlacgv_work(ni, WORK, ione);
#endif
alpha = -conj(TAU[ii+i]);
cblas_zaxpy(
ni, CBLAS_SADDR(alpha),
WORK, 1,
&A1[LDA1*(ii+i+1)+ii+i], LDA1);
#ifdef COMPLEX
LAPACKE_zlacgv_work(ni, WORK, ione);
#endif
cblas_zgerc(
CblasColMajor, mi, ni,
CBLAS_SADDR(alpha), &A2[LDA2*(ii+i)], 1,
WORK, 1,
&A2[LDA2*(ii+i+1)], LDA2);
}
/*
* Calculate T.
*/
if (i > 0 ) {
cblas_zcopy(i, &A2[LDA2*(ii+i)+ii], 1, &WORK[ii], 1);
cblas_ztrmv(
CblasColMajor, (CBLAS_UPLO)PlasmaUpper,
(CBLAS_TRANSPOSE)PlasmaConjTrans, (CBLAS_DIAG)PlasmaNonUnit,
i, &A2[LDA2*ii+ii], LDA2,
&WORK[ii], 1);
alpha = -(TAU[ii+i]);
for(j = 0; j < i; j++) {
WORK[ii+j] = alpha * WORK[ii+j];
}
if (ii > 0) {
cblas_zgemv(
CblasColMajor, (CBLAS_TRANSPOSE)PlasmaConjTrans, ii, i,
CBLAS_SADDR(alpha), &A2[LDA2*ii], LDA2,
&A2[LDA2*(ii+i)], 1,
CBLAS_SADDR(zzero), WORK, 1);
cblas_zaxpy(i, CBLAS_SADDR(zone), &WORK[ii], 1, WORK, 1);
}
cblas_zcopy(i, WORK, 1, &T[LDT*(ii+i)], 1);
cblas_ztrmv(
CblasColMajor, (CBLAS_UPLO)PlasmaUpper,
(CBLAS_TRANSPOSE)PlasmaNoTrans, (CBLAS_DIAG)PlasmaNonUnit,
i, &T[LDT*ii], LDT,
&T[LDT*(ii+i)], 1);
}
T[LDT*(ii+i)+i] = TAU[ii+i];
}
/* Apply Q' to the rest of the matrix to the left */
if (N > ii+sb) {
CORE_zttrfb(
PlasmaLeft, PlasmaConjTrans,
PlasmaForward, PlasmaColumnwise,
sb, N-(ii+sb), ii+sb, N-(ii+sb), sb,
&A1[LDA1*(ii+sb)+ii], LDA1,
&A2[LDA2*(ii+sb)], LDA2,
&A2[LDA2*ii], LDA2,
&T[LDT*ii], LDT,
WORK, sb);
}
}
return PLASMA_SUCCESS;
}
/*------------------------------------------------------------------------
* Check the factorization of the matrix A2
*/
static int check_factorization(int N, PLASMA_Complex64_t *A1, PLASMA_Complex64_t *A2, int LDA, int uplo, double eps)
{
PLASMA_Complex64_t alpha = 1.0;
double Anorm, Rnorm, result;
int info_factorization;
int i,j;
PLASMA_Complex64_t *Residual = (PLASMA_Complex64_t *)malloc(N*N*sizeof(PLASMA_Complex64_t));
PLASMA_Complex64_t *L1 = (PLASMA_Complex64_t *)malloc(N*N*sizeof(PLASMA_Complex64_t));
PLASMA_Complex64_t *L2 = (PLASMA_Complex64_t *)malloc(N*N*sizeof(PLASMA_Complex64_t));
double *work = (double *)malloc(N*sizeof(double));
memset((void*)L1, 0, N*N*sizeof(PLASMA_Complex64_t));
memset((void*)L2, 0, N*N*sizeof(PLASMA_Complex64_t));
LAPACKE_zlacpy_work(LAPACK_COL_MAJOR,' ', N, N, A1, LDA, Residual, N);
/* Dealing with L'L or U'U */
LAPACKE_zlacpy_work(LAPACK_COL_MAJOR, lapack_const(uplo), N, N, A2, LDA, L1, N);
LAPACKE_zlacpy_work(LAPACK_COL_MAJOR, lapack_const(uplo), N, N, A2, LDA, L2, N);
if (uplo == PlasmaUpper)
cblas_ztrmm(CblasColMajor, CblasLeft, (CBLAS_UPLO)uplo, CblasConjTrans, CblasNonUnit, N, N, CBLAS_SADDR(alpha), L1, N, L2, N);
else
cblas_ztrmm(CblasColMajor, CblasRight, (CBLAS_UPLO)uplo, CblasConjTrans, CblasNonUnit, N, N, CBLAS_SADDR(alpha), L1, N, L2, N);
/* Compute the Residual || A - L'L|| */
for (i = 0; i < N; i++)
for (j = 0; j < N; j++)
Residual[j*N+i] = L2[j*N+i] - Residual[j*N+i];
Rnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, N, Residual, N, work);
Anorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, N, A1, LDA, work);
result = Rnorm / ( Anorm * N * eps );
printf("============\n");
printf("Checking the Cholesky Factorization \n");
printf("-- ||L'L-A||_oo/(||A||_oo.N.eps) = %e \n", result);
if ( isnan(result) || isinf(result) || (result > 60.0) ){
printf("-- Factorization is suspicious ! \n");
info_factorization = 1;
}
else{
printf("-- Factorization is CORRECT ! \n");
info_factorization = 0;
}
free(Residual); free(L1); free(L2); free(work);
return info_factorization;
}
extern "C" magma_int_t
magma_zgeev_m(
char jobvl, char jobvr, magma_int_t n,
magmaDoubleComplex *A, magma_int_t lda,
magmaDoubleComplex *W,
magmaDoubleComplex *vl, magma_int_t ldvl,
magmaDoubleComplex *vr, magma_int_t ldvr,
magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t *info )
{
/* -- MAGMA (version 1.4.1) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
December 2013
Purpose
=======
ZGEEV 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
=========
JOBVL (input) CHARACTER*1
= 'N': left eigenvectors of A are not computed;
= 'V': left eigenvectors of are computed.
JOBVR (input) CHARACTER*1
= 'N': right eigenvectors of A are not computed;
= 'V': right eigenvectors of A are computed.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the N-by-N matrix A.
On exit, A has been overwritten.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) COMPLEX*16 array, dimension (N)
W contains the computed eigenvalues.
VL (output) COMPLEX*16 array, dimension (LDVL,N)
If JOBVL = 'V', the left eigenvectors u(j) are stored one
after another in the columns of VL, in the same order
as their eigenvalues.
If JOBVL = 'N', VL is not referenced.
u(j) = VL(:,j), the j-th column of VL.
LDVL (input) INTEGER
The leading dimension of the array VL. LDVL >= 1; if
JOBVL = 'V', LDVL >= N.
VR (output) COMPLEX*16 array, dimension (LDVR,N)
If JOBVR = 'V', the right eigenvectors v(j) are stored one
after another in the columns of VR, in the same order
as their eigenvalues.
If JOBVR = 'N', VR is not referenced.
v(j) = VR(:,j), the j-th column of VR.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= 1; if
JOBVR = 'V', LDVR >= N.
WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= (1+nb)*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.
RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
INFO (output) 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.
===================================================================== */
#define vl(i,j) (vl + (i) + (j)*ldvl)
#define vr(i,j) (vr + (i) + (j)*ldvr)
magma_int_t c_one = 1;
magma_int_t c_zero = 0;
double d__1, d__2;
magmaDoubleComplex z__1, z__2;
magmaDoubleComplex tmp;
double scl;
double dum[1], eps;
double anrm, cscale, bignum, smlnum;
magma_int_t i, k, ilo, ihi;
magma_int_t ibal, ierr, itau, iwrk, nout, liwrk, i__1, i__2, nb;
magma_int_t scalea, minwrk, irwork, lquery, wantvl, wantvr, select[1];
char side[2] = {0, 0};
char jobvl_[2] = {jobvl, 0};
char jobvr_[2] = {jobvr, 0};
irwork = 0;
*info = 0;
lquery = lwork == -1;
wantvl = lapackf77_lsame( jobvl_, "V" );
wantvr = lapackf77_lsame( jobvr_, "V" );
if (! wantvl && ! lapackf77_lsame( jobvl_, "N" )) {
*info = -1;
} else if (! wantvr && ! lapackf77_lsame( jobvr_, "N" )) {
*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_zgehrd_nb( n );
if (*info == 0) {
minwrk = (1+nb)*n;
work[0] = MAGMA_Z_MAKE( minwrk, 0 );
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) || defined(Version4) || defined(Version5)
magmaDoubleComplex *dT;
if (MAGMA_SUCCESS != magma_zmalloc( &dT, nb*n )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
#endif
#if defined(Version4) || defined(Version5)
magmaDoubleComplex *T;
if (MAGMA_SUCCESS != magma_zmalloc_cpu( &T, nb*n )) {
magma_free( dT );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
#endif
/* Get machine constants */
eps = lapackf77_dlamch( "P" );
smlnum = lapackf77_dlamch( "S" );
bignum = 1. / smlnum;
lapackf77_dlabad( &smlnum, &bignum );
smlnum = magma_dsqrt( smlnum ) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = lapackf77_zlange( "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_zlascl( "G", &c_zero, &c_zero, &anrm, &cscale, &n, &n, A, &lda, &ierr );
}
/* Balance the matrix
* (CWorkspace: none)
* (RWorkspace: need N) */
ibal = 0;
lapackf77_zgebal( "B", &n, A, &lda, &ilo, &ihi, &rwork[ibal], &ierr );
/* Reduce to upper Hessenberg form
* (CWorkspace: need 2*N, prefer N + N*NB)
* (RWorkspace: none) */
itau = 0;
iwrk = itau + n;
liwrk = lwork - iwrk;
#if defined(Version1)
// Version 1 - LAPACK
lapackf77_zgehrd( &n, &ilo, &ihi, A, &lda,
&work[itau], &work[iwrk], &liwrk, &ierr );
#elif defined(Version2)
// Version 2 - LAPACK consistent HRD
magma_zgehrd2( n, ilo, ihi, A, lda,
&work[itau], &work[iwrk], &liwrk, &ierr );
#elif defined(Version3)
// Version 3 - LAPACK consistent MAGMA HRD + matrices T stored,
magma_zgehrd( n, ilo, ihi, A, lda,
&work[itau], &work[iwrk], liwrk, dT, &ierr );
#elif defined(Version4) || defined(Version5)
// Version 4 - Multi-GPU, T on host
magma_zgehrd_m( n, ilo, ihi, A, lda,
&work[itau], &work[iwrk], liwrk, T, &ierr );
magma_zsetmatrix( nb, n, T, nb, dT, nb );
#endif
if (wantvl) {
/* Want left eigenvectors
* Copy Householder vectors to VL */
side[0] = 'L';
lapackf77_zlacpy( MagmaLowerStr, &n, &n, A, &lda, vl, &ldvl );
/* Generate unitary matrix in VL
* (CWorkspace: need 2*N-1, prefer N + (N-1)*NB)
* (RWorkspace: none) */
#if defined(Version1) || defined(Version2)
// Version 1 & 2 - LAPACK
lapackf77_zunghr( &n, &ilo, &ihi, vl, &ldvl, &work[itau],
&work[iwrk], &liwrk, &ierr );
#elif defined(Version3) || defined(Version4)
// Version 3 - LAPACK consistent MAGMA HRD + matrices T stored
magma_zunghr( n, ilo, ihi, vl, ldvl, &work[itau], dT, nb, &ierr );
#elif defined(Version5)
// Version 5 - Multi-GPU, T on host
magma_zunghr_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: none) */
iwrk = itau;
liwrk = lwork - iwrk;
lapackf77_zhseqr( "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[0] = 'B';
lapackf77_zlacpy( "F", &n, &n, vl, &ldvl, vr, &ldvr );
}
}
else if (wantvr) {
/* Want right eigenvectors
* Copy Householder vectors to VR */
side[0] = 'R';
lapackf77_zlacpy( "L", &n, &n, A, &lda, vr, &ldvr );
/* Generate unitary matrix in VR
* (CWorkspace: need 2*N-1, prefer N + (N-1)*NB)
* (RWorkspace: none) */
#if defined(Version1) || defined(Version2)
// Version 1 & 2 - LAPACK
lapackf77_zunghr( &n, &ilo, &ihi, vr, &ldvr, &work[itau],
&work[iwrk], &liwrk, &ierr );
#elif defined(Version3) || defined(Version4)
// Version 3 - LAPACK consistent MAGMA HRD + matrices T stored
magma_zunghr( n, ilo, ihi, vr, ldvr, &work[itau], dT, nb, &ierr );
#elif defined(Version5)
// Version 5 - Multi-GPU, T on host
magma_zunghr_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: none) */
iwrk = itau;
liwrk = lwork - iwrk;
lapackf77_zhseqr( "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: none) */
iwrk = itau;
liwrk = lwork - iwrk;
lapackf77_zhseqr( "E", "N", &n, &ilo, &ihi, A, &lda, W,
vr, &ldvr, &work[iwrk], &liwrk, info );
}
/* If INFO > 0 from ZHSEQR, then quit */
if (*info > 0) {
goto CLEANUP;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors
* (CWorkspace: need 2*N)
* (RWorkspace: need 2*N) */
irwork = ibal + n;
lapackf77_ztrevc( side, "B", select, &n, A, &lda, vl, &ldvl,
vr, &ldvr, &n, &nout, &work[iwrk], &rwork[irwork], &ierr );
}
if (wantvl) {
/* Undo balancing of left eigenvectors
* (CWorkspace: none)
* (RWorkspace: need N) */
lapackf77_zgebak( "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. / cblas_dznrm2( n, vl(0,i), 1 );
cblas_zdscal( n, scl, vl(0,i), 1 );
for (k = 0; k < n; ++k) {
/* Computing 2nd power */
d__1 = MAGMA_Z_REAL( *vl(k,i) );
d__2 = MAGMA_Z_IMAG( *vl(k,i) );
rwork[irwork + k] = d__1*d__1 + d__2*d__2;
}
k = cblas_idamax( n, &rwork[irwork], 1 );
z__2 = MAGMA_Z_CNJG( *vl(k,i) );
d__1 = magma_dsqrt( rwork[irwork + k] );
MAGMA_Z_DSCALE( z__1, z__2, d__1 );
tmp = z__1;
cblas_zscal( n, CBLAS_SADDR(tmp), vl(0,i), 1 );
d__1 = MAGMA_Z_REAL( *vl(k,i) );
z__1 = MAGMA_Z_MAKE( d__1, 0 );
*vl(k,i) = z__1;
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors
* (CWorkspace: none)
* (RWorkspace: need N) */
lapackf77_zgebak( "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. / cblas_dznrm2( n, vr(0,i), 1 );
cblas_zdscal( n, scl, vr(0,i), 1 );
for (k = 0; k < n; ++k) {
/* Computing 2nd power */
d__1 = MAGMA_Z_REAL( *vr(k,i) );
d__2 = MAGMA_Z_IMAG( *vr(k,i) );
rwork[irwork + k] = d__1*d__1 + d__2*d__2;
}
k = cblas_idamax( n, &rwork[irwork], 1 );
z__2 = MAGMA_Z_CNJG( *vr(k,i) );
d__1 = magma_dsqrt( rwork[irwork + k] );
MAGMA_Z_DSCALE( z__1, z__2, d__1 );
tmp = z__1;
cblas_zscal( n, CBLAS_SADDR(tmp), vr(0,i), 1 );
d__1 = MAGMA_Z_REAL( *vr(k,i) );
z__1 = MAGMA_Z_MAKE( d__1, 0 );
*vr(k,i) = z__1;
}
}
CLEANUP:
/* Undo scaling if necessary */
if (scalea) {
i__1 = n - (*info);
i__2 = max( n - (*info), 1 );
lapackf77_zlascl( "G", &c_zero, &c_zero, &cscale, &anrm, &i__1, &c_one,
W + (*info), &i__2, &ierr );
if (*info > 0) {
i__1 = ilo - 1;
lapackf77_zlascl( "G", &c_zero, &c_zero, &cscale, &anrm, &i__1, &c_one,
W, &n, &ierr );
}
}
#if defined(Version3) || defined(Version4) || defined(Version5)
magma_free( dT );
#endif
#if defined(Version4) || defined(Version5)
magma_free_cpu( T );
#endif
return *info;
} /* magma_zgeev */
static int check_transformation(int itype, int uplo, int N, PLASMA_Complex64_t *A1, PLASMA_Complex64_t *A2, int LDA, PLASMA_Complex64_t *B2, int LDB, double eps)
{
PLASMA_Complex64_t alpha = 1.0;
double Anorm, Rnorm, result;
int info_transformation;
int i, j;
char *str;
PLASMA_Complex64_t *Residual = (PLASMA_Complex64_t *)malloc(N*N*sizeof(PLASMA_Complex64_t));
PLASMA_Complex64_t *Aorig = (PLASMA_Complex64_t *)malloc(N*N*sizeof(PLASMA_Complex64_t));
double *work = (double *)malloc(N*sizeof(double));
LAPACKE_zlacpy_work(LAPACK_COL_MAJOR, 'a', N, N, A1, LDA, Residual, N);
LAPACKE_zlacpy_work(LAPACK_COL_MAJOR, lapack_const(uplo), N, N, A2, LDA, Aorig, N);
/* Rebuild the symmetry of A2 */
if (uplo == PlasmaLower) {
for (j = 0; j < N; j++)
for (i = j+1; i < N; i++)
Aorig[j+i*N] = conj(Aorig[i+j*N]);
} else {
for (i = 0; i < N; i++)
for (j = i+1; j < N; j++)
Aorig[j+i*N] = conj(Aorig[i+j*N]);
}
if (itype == 1) {
if (uplo == PlasmaLower) {
str = "L*A2*L'";
cblas_ztrmm(CblasColMajor, CblasLeft, CblasLower, CblasNoTrans, CblasNonUnit, N, N, CBLAS_SADDR(alpha), B2, LDB, Aorig, N);
cblas_ztrmm(CblasColMajor, CblasRight, CblasLower, CblasConjTrans, CblasNonUnit, N, N, CBLAS_SADDR(alpha), B2, LDB, Aorig, N);
}
else{
str = "U'*A2*U";
cblas_ztrmm(CblasColMajor, CblasLeft, CblasUpper, CblasConjTrans, CblasNonUnit, N, N, CBLAS_SADDR(alpha), B2, LDB, Aorig, N);
cblas_ztrmm(CblasColMajor, CblasRight, CblasUpper, CblasNoTrans, CblasNonUnit, N, N, CBLAS_SADDR(alpha), B2, LDB, Aorig, N);
}
}
else {
if (uplo == PlasmaLower) {
str = "inv(L')*A2*inv(L)";
cblas_ztrsm(CblasColMajor, CblasLeft, CblasLower, CblasConjTrans, CblasNonUnit, N, N, CBLAS_SADDR(alpha), B2, LDB, Aorig, N);
cblas_ztrsm(CblasColMajor, CblasRight, CblasLower, CblasNoTrans, CblasNonUnit, N, N, CBLAS_SADDR(alpha), B2, LDB, Aorig, N);
}
else{
str = "inv(U)*A2*inv(U')";
cblas_ztrsm(CblasColMajor, CblasLeft, CblasUpper, CblasNoTrans, CblasNonUnit, N, N, CBLAS_SADDR(alpha), B2, LDB, Aorig, N);
cblas_ztrsm(CblasColMajor, CblasRight, CblasUpper, CblasConjTrans, CblasNonUnit, N, N, CBLAS_SADDR(alpha), B2, LDB, Aorig, N);
}
}
/* Compute the Residual ( A1 - W ) */
for (i = 0; i < N; i++)
for (j = 0; j < N; j++)
Residual[j*N+i] = Aorig[j*N+i] - Residual[j*N+i];
Rnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, N, Residual, N, work);
Anorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, lapack_const(PlasmaInfNorm), N, N, A1, LDA, work);
result = Rnorm / (Anorm * N *eps);
printf("============\n");
printf("Checking the global transformation \n");
printf("-- ||A1-%s||_oo/(||A1||_oo.N.eps) = %e \n", str, result );
if (isnan(result) || isinf(result) || (result > 60.0) ) {
printf("-- Transformation is suspicious ! \n");
info_transformation = 1;
}
else {
printf("-- Transformation is CORRECT ! \n");
info_transformation = 0;
}
free(Residual); free(Aorig); free(work);
return info_transformation;
}
static int check_factorization(int M, int N, PLASMA_Complex32_t *A1, PLASMA_Complex32_t *A2, int LDA, PLASMA_Complex32_t *Q, float eps )
{
float Anorm, Rnorm;
PLASMA_Complex32_t alpha, beta;
int info_factorization;
int i,j;
PLASMA_Complex32_t *Ql = (PLASMA_Complex32_t *)malloc(M*N*sizeof(PLASMA_Complex32_t));
PLASMA_Complex32_t *Residual = (PLASMA_Complex32_t *)malloc(M*N*sizeof(PLASMA_Complex32_t));
float *work = (float *)malloc(max(M,N)*sizeof(float));
alpha=1.0;
beta=0.0;
if (M >= N) {
/* Extract the R */
PLASMA_Complex32_t *R = (PLASMA_Complex32_t *)malloc(N*N*sizeof(PLASMA_Complex32_t));
memset((void*)R, 0, N*N*sizeof(PLASMA_Complex32_t));
LAPACKE_clacpy_work(LAPACK_COL_MAJOR,'u', M, N, A2, LDA, R, N);
/* Perform Ql=Q*R */
memset((void*)Ql, 0, M*N*sizeof(PLASMA_Complex32_t));
cblas_cgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, M, N, N, CBLAS_SADDR(alpha), Q, LDA, R, N, CBLAS_SADDR(beta), Ql, M);
free(R);
}
else {
/* Extract the L */
PLASMA_Complex32_t *L = (PLASMA_Complex32_t *)malloc(M*M*sizeof(PLASMA_Complex32_t));
memset((void*)L, 0, M*M*sizeof(PLASMA_Complex32_t));
LAPACKE_clacpy_work(LAPACK_COL_MAJOR,'l', M, N, A2, LDA, L, M);
/* Perform Ql=LQ */
memset((void*)Ql, 0, M*N*sizeof(PLASMA_Complex32_t));
cblas_cgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, M, N, M, CBLAS_SADDR(alpha), L, M, Q, LDA, CBLAS_SADDR(beta), Ql, M);
free(L);
}
/* Compute the Residual */
for (i = 0; i < M; i++)
for (j = 0 ; j < N; j++)
Residual[j*M+i] = A1[j*LDA+i]-Ql[j*M+i];
BLAS_cge_norm( blas_colmajor, blas_inf_norm, M, N, Residual, M, &Rnorm );
BLAS_cge_norm( blas_colmajor, blas_inf_norm, M, N, A2, LDA, &Anorm );
if (M >= N) {
printf("============\n");
printf("Checking the QR Factorization \n");
printf("-- ||A-QR||_oo/(||A||_oo.N.eps) = %e \n",Rnorm/(Anorm*N*eps));
}
else {
printf("============\n");
printf("Checking the LQ Factorization \n");
printf("-- ||A-LQ||_oo/(||A||_oo.N.eps) = %e \n",Rnorm/(Anorm*N*eps));
}
if (isnan(Rnorm / (Anorm * N *eps)) || isinf(Rnorm / (Anorm * N *eps)) || (Rnorm / (Anorm * N * eps) > 60.0) ) {
printf("-- Factorization is suspicious ! \n");
info_factorization = 1;
}
else {
printf("-- Factorization is CORRECT ! \n");
info_factorization = 0;
}
free(work); free(Ql); free(Residual);
return info_factorization;
}
int CORE_cgessm(int M, int N, int K, int IB,
int *IPIV,
PLASMA_Complex32_t *L, int LDL,
PLASMA_Complex32_t *A, int LDA)
{
static PLASMA_Complex32_t zone = 1.0;
static PLASMA_Complex32_t mzone = -1.0;
static int ione = 1;
int i, sb;
int tmp, tmp2;
/* Check input arguments */
if (M < 0) {
coreblas_error(1, "Illegal value of M");
return -1;
}
if (N < 0) {
coreblas_error(2, "Illegal value of N");
return -2;
}
if (K < 0) {
coreblas_error(3, "Illegal value of K");
return -3;
}
if (IB < 0) {
coreblas_error(4, "Illegal value of IB");
return -4;
}
if ((LDL < max(1,M)) && (M > 0)) {
coreblas_error(7, "Illegal value of LDL");
return -7;
}
if ((LDA < max(1,M)) && (M > 0)) {
coreblas_error(9, "Illegal value of LDA");
return -9;
}
/* Quick return */
if ((M == 0) || (N == 0) || (K == 0) || (IB == 0))
return PLASMA_SUCCESS;
for(i = 0; i < K; i += IB) {
sb = min(IB, K-i);
/*
* Apply interchanges to columns I*IB+1:IB*( I+1 )+1.
*/
tmp = i+1;
tmp2 = i+sb;
LAPACKE_claswp_work(LAPACK_COL_MAJOR, N, A, LDA, tmp, tmp2, IPIV, ione);
/*
* Compute block row of U.
*/
cblas_ctrsm(
CblasColMajor, CblasLeft, CblasLower, CblasNoTrans, CblasUnit,
sb, N, CBLAS_SADDR(zone),
&L[LDL*i+i], LDL,
&A[i], LDA );
if (i+sb < M) {
/*
* Update trailing submatrix.
*/
cblas_cgemm(
CblasColMajor, CblasNoTrans, CblasNoTrans,
M-(i+sb), N, sb,
CBLAS_SADDR(mzone), &L[LDL*i+(i+sb)], LDL,
&A[i], LDA,
CBLAS_SADDR(zone), &A[i+sb], LDA );
}
}
return PLASMA_SUCCESS;
}
int main(int argc, char **argv)
{
TESTING_INIT();
magma_setdevice(0);
magma_timestr_t start, end;
float flops, magma_perf, cuda_perf, error, work[1];
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magma_int_t n_local[4];
FILE *fp ;
magma_int_t N, m, i, j, lda, LDA, M;
magma_int_t matsize;
magma_int_t vecsize;
magma_int_t istart = 64;
magma_int_t incx = 1;
char uplo = MagmaLower;
magmaFloatComplex alpha = MAGMA_C_MAKE(1., 0.); // MAGMA_C_MAKE( 1.5, -2.3 );
magmaFloatComplex beta = MAGMA_C_MAKE(0., 0.); // MAGMA_C_MAKE( -0.6, 0.8 );
magmaFloatComplex *A, *X, *Y[4], *Ycublas, *Ymagma;
magmaFloatComplex *dA, *dX[4], *dY[4], *d_lA[4], *dYcublas ;
magma_queue_t stream[4][10];
magmaFloatComplex *C_work;
magmaFloatComplex *dC_work[4];
int max_num_gpus;
magma_int_t num_gpus = 1, nb;
magma_int_t blocks, lwork;
magma_int_t offset = 0;
M = 0;
N = 0;
if (argc != 1){
for(i = 1; i<argc; i++){
if (strcmp("-N", argv[i])==0)
{
N = atoi(argv[++i]);
istart = N;
}
else if (strcmp("-M", argv[i])==0)
M = atoi(argv[++i]);
else if (strcmp("-NGPU", argv[i])==0)
num_gpus = atoi(argv[++i]);
else if (strcmp("-offset", argv[i])==0)
offset = atoi(argv[++i]);
}
if ( M == 0 ) {
M = N;
}
if ( N == 0 ) {
N = M;
}
if (M>0 && N>0)
{ printf(" testing_chemv_mgpu -M %d -N %d -NGPU %d\n\n", (int) M, (int) N, (int) num_gpus);
printf(" in %c side \n", uplo);
}
else
{
printf("\nUsage: \n");
printf(" testing_chemv_mgpu -M %d -N %d -NGPU %d\n\n",
1024, 1024, 1);
exit(1);
}
}
else {
#if defined(PRECISION_z)
M = N = 8000;
#else
M = N = 12480;
#endif
num_gpus = 2;
offset = 0;
printf("\nUsage: \n");
printf(" testing_chemv_mgpu -M %d -N %d -NGPU %d\n\n", (int) M, (int) N, (int) num_gpus);
}
//////////////////////////////////////////////////////////////////////////
cudaGetDeviceCount(&max_num_gpus);
if (num_gpus > max_num_gpus){
printf("More GPUs requested than available. Have to change it.\n");
num_gpus = max_num_gpus;
}
printf("Number of GPUs to be used = %d\n", (int) num_gpus);
for(int i=0; i< num_gpus; i++)
{
magma_queue_create(&stream[i][0]);
}
LDA = ((N+31)/32)*32;
matsize = N*LDA;
vecsize = N*incx;
nb = 32;
//nb = 64;
printf("block size = %d\n", (int) nb);
TESTING_MALLOC_CPU( A, magmaFloatComplex, matsize );
TESTING_MALLOC_CPU( X, magmaFloatComplex, vecsize );
TESTING_MALLOC_CPU( Ycublas, magmaFloatComplex, vecsize );
TESTING_MALLOC_CPU( Ymagma, magmaFloatComplex, vecsize );
for(i=0; i<num_gpus; i++)
{
TESTING_MALLOC_CPU( Y[i], magmaFloatComplex, vecsize );
}
magma_setdevice(0);
TESTING_MALLOC_DEV( dA, magmaFloatComplex, matsize );
TESTING_MALLOC_DEV( dYcublas, magmaFloatComplex, vecsize );
for(i=0; i<num_gpus; i++)
{
n_local[i] = ((N/nb)/num_gpus)*nb;
if (i < (N/nb)%num_gpus)
n_local[i] += nb;
else if (i == (N/nb)%num_gpus)
n_local[i] += N%nb;
magma_setdevice(i);
TESTING_MALLOC_DEV( d_lA[i], magmaFloatComplex, LDA*n_local[i] );// potentially bugged
TESTING_MALLOC_DEV( dX[i], magmaFloatComplex, vecsize );
TESTING_MALLOC_DEV( dY[i], magmaFloatComplex, vecsize );
printf("device %2d n_local = %4d\n", (int) i, (int) n_local[i]);
}
magma_setdevice(0);
//////////////////////////////////////////////////////////////////////////
/* Initialize the matrix */
lapackf77_clarnv( &ione, ISEED, &matsize, A );
magma_cmake_hermitian( N, A, LDA );
blocks = N / nb + (N % nb != 0);
lwork = LDA * (blocks + 1);
TESTING_MALLOC_CPU( C_work, magmaFloatComplex, lwork );
for(i=0; i<num_gpus; i++){
magma_setdevice(i);
TESTING_MALLOC_DEV( dC_work[i], magmaFloatComplex, lwork );
//fillZero(dC_work[i], lwork);
}
magma_setdevice(0);
//////////////////////////////////////////////////////////////////////////
fp = fopen ("results_chemv_mgpu.csv", "w") ;
if( fp == NULL ){ printf("Couldn't open output file\n"); exit(1);}
printf("CHEMV magmaFloatComplex precision\n\n");
printf( " n CUBLAS,Gflop/s MAGMABLAS,Gflop/s \"error\"\n"
"==============================================================\n");
fprintf(fp, " n CUBLAS,Gflop/s MAGMABLAS,Gflop/s \"error\"\n"
"==============================================================\n");
// for( offset = 0; offset< N; offset ++ )
for(int size = istart ; size <= N ; size += 128)
{
// printf("offset = %d ", offset);
m = size ;
// m = N;
// lda = ((m+31)/32)*32;//
lda = LDA;
flops = FLOPS( (float)m ) / 1e6;
printf( "N %5d ", (int) m );
fprintf( fp, "%5d, ", (int) m );
vecsize = m * incx;
lapackf77_clarnv( &ione, ISEED, &vecsize, X );
lapackf77_clarnv( &ione, ISEED, &vecsize, Y[0] );
/* =====================================================================
Performs operation using CUDA-BLAS
=================================================================== */
magma_setdevice(0);
magma_csetmatrix_1D_col_bcyclic(m, m, A, LDA, d_lA, lda, num_gpus, nb);
magma_setdevice(0);
magma_csetmatrix( m, m, A, LDA, dA, lda );
magma_csetvector( m, Y[0], incx, dYcublas, incx );
for(i=0; i<num_gpus; i++){
magma_setdevice(i);
magma_csetvector( m, X, incx, dX[i], incx );
magma_csetvector( m, Y[0], incx, dY[i], incx );
blocks = m / nb + (m % nb != 0);
magma_csetmatrix( lda, blocks, C_work, LDA, dC_work[i], lda );
}
magma_setdevice(0);
start = get_current_time();
cublasChemv( uplo, m-offset, alpha, dA + offset + offset * lda, lda, dX[0] + offset, incx, beta, dYcublas + offset, incx );
end = get_current_time();
magma_cgetvector( m, dYcublas, incx, Ycublas, incx );
cuda_perf = flops / GetTimerValue(start,end);
printf( "%11.2f", cuda_perf );
fprintf(fp, "%11.2f,", cuda_perf );
magma_setdevice(0);
start = get_current_time();
if(nb == 32)
{
magmablas_chemv2_mgpu_32_offset( uplo, m, alpha, d_lA, lda, dX, incx, beta, dY, incx,
dC_work, lwork, num_gpus, nb, offset);
}
else // nb = 64
{
magmablas_chemv2_mgpu_offset( uplo, m, alpha, d_lA, lda, dX, incx, beta, dY, incx,
dC_work, lwork, num_gpus, nb, offset);
}
for(i=1; i<num_gpus; i++)
{
magma_setdevice(i);
cudaDeviceSynchronize();
}
end = get_current_time();
magma_perf = flops / GetTimerValue(start,end);
printf( "%11.2f", magma_perf );
fprintf(fp, "%11.2f,", magma_perf );
for(i=0; i<num_gpus; i++)
{
magma_setdevice(i);
magma_cgetvector( m, dY[i], incx, Y[i], incx );
}
magma_setdevice(0);
#ifdef validate
for( j= offset;j<m;j++)
{
for(i=1; i<num_gpus; i++)
{
// printf("Y[%d][%d] = %15.14f\n", i, j, Y[i][j].x);
#if defined(PRECISION_z) || defined(PRECISION_c)
Y[0][j].x = Y[0][j].x + Y[i][j].x;
Y[0][j].y = Y[0][j].y + Y[i][j].y;
#else
Y[0][j] = Y[0][j] + Y[i][j];
#endif
}
}
/*
#if defined(PRECISION_z) || defined(PRECISION_c)
for( j=offset;j<m;j++)
{
if(Y[0][j].x != Ycublas[j].x)
{
printf("Y-multi[%d] = %f, %f\n", j, Y[0][j].x, Y[0][j].y );
printf("Ycublas[%d] = %f, %f\n", j, Ycublas[j].x, Ycublas[j].y);
}
}
#else
for( j=offset;j<m;j++)
{
if(Y[0][j] != Ycublas[j])
{
printf("Y-multi[%d] = %f\n", j, Y[0][j] );
printf("Ycublas[%d] = %f\n", j, Ycublas[j]);
}
}
#endif
*/
/* =====================================================================
Computing the Difference Cublas VS Magma
=================================================================== */
magma_int_t nw = m - offset ;
blasf77_caxpy( &nw, &c_neg_one, Y[0] + offset, &incx, Ycublas + offset, &incx);
error = lapackf77_clange( "M", &nw, &ione, Ycublas + offset, &nw, work );
#if 0
printf( "\t\t %8.6e", error / m );
fprintf( fp, "\t\t %8.6e", error / m );
/*
* Extra check with cblas vs magma
*/
cblas_ccopy( m, Y, incx, Ycublas, incx );
cblas_chemv( CblasColMajor, CblasLower, m,
CBLAS_SADDR(alpha), A, LDA, X, incx,
CBLAS_SADDR(beta), Ycublas, incx );
blasf77_caxpy( &m, &c_neg_one, Ymagma, &incx, Ycublas, &incx);
error = lapackf77_clange( "M", &m, &ione, Ycublas, &m, work );
#endif
printf( "\t\t %8.6e", error / m );
fprintf( fp, "\t\t %8.6e", error / m );
#endif
printf("\n");
fprintf(fp, "\n");
}
fclose( fp ) ;
/* Free Memory */
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( X );
TESTING_FREE_CPU( Ycublas );
TESTING_FREE_CPU( Ymagma );
TESTING_FREE_CPU( C_work );
magma_setdevice(0);
TESTING_FREE_DEV( dA );
TESTING_FREE_DEV( dYcublas );
for(i=0; i<num_gpus; i++)
{
TESTING_FREE_CPU( Y[i] );
magma_setdevice(i);
TESTING_FREE_DEV( d_lA[i] );
TESTING_FREE_DEV( dX[i] );
TESTING_FREE_DEV( dY[i] );
TESTING_FREE_DEV( dC_work[i] );
}
magma_setdevice(0);
///////////////////////////////////////////////////////////
/* Free device */
TESTING_FINALIZE();
return 0;
}
/**
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(1) returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= (1+nb)*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_cgeev_driver
********************************************************************/
extern "C" magma_int_t
magma_cgeev(
magma_vec_t jobvl, magma_vec_t jobvr, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *W,
magmaFloatComplex *VL, magma_int_t ldvl,
magmaFloatComplex *VR, magma_int_t ldvr,
magmaFloatComplex *work, magma_int_t lwork,
float *rwork, magma_int_t *info )
{
#define VL(i,j) (VL + (i) + (j)*ldvl)
#define VR(i,j) (VR + (i) + (j)*ldvr)
magma_int_t c_one = 1;
magma_int_t c_zero = 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, irwork, lquery, wantvl, wantvr, select[1];
magma_side_t side = MagmaRight;
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)*n;
work[0] = MAGMA_C_MAKE( minwrk, 0 );
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
/* 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", &c_zero, &c_zero, &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)
* (RWorkspace: N)
* - 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 );
#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 );
#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 );
#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. / cblas_scnrm2( n, VL(0,i), 1 );
cblas_csscal( n, scl, VL(0,i), 1 );
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 = cblas_isamax( n, &rwork[irwork], 1 );
tmp = MAGMA_C_CNJG( *VL(k,i) ) / magma_ssqrt( rwork[irwork + k] );
cblas_cscal( n, CBLAS_SADDR(tmp), VL(0,i), 1 );
*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. / cblas_scnrm2( n, VR(0,i), 1 );
cblas_csscal( n, scl, VR(0,i), 1 );
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 = cblas_isamax( n, &rwork[irwork], 1 );
tmp = MAGMA_C_CNJG( *VR(k,i) ) / magma_ssqrt( rwork[irwork + k] );
cblas_cscal( n, CBLAS_SADDR(tmp), VR(0,i), 1 );
*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", &c_zero, &c_zero, &cscale, &anrm, &nval, &c_one, 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", &c_zero, &c_zero, &cscale, &anrm, &nval, &c_one, W, &n, &ierr );
}
}
#if defined(VERSION3)
magma_free( dT );
#endif
work[0] = MAGMA_C_MAKE( (float) minwrk, 0. ); // TODO use optwrk as in dgeev
return *info;
} /* magma_cgeev */
static void
CORE_cgetrf_reclap_rec(const int M, const int N,
PLASMA_Complex32_t *A, const int LDA,
int *IPIV, int *info,
const int thidx, const int thcnt, const int column)
{
int jp, n1, n2, lm, loff;
PLASMA_Complex32_t tmp1, tmp2, tmp3;
PLASMA_Complex32_t *Atop = A + column*LDA;
/* Assumption: N = min( M, N ); */
if (N > 1) {
int coff, ccnt;
n1 = N / 2;
n2 = N - n1;
CORE_cgetrf_reclap_rec( M, n1, A, LDA, IPIV, info,
thidx, thcnt, column );
if ( *info != 0 )
return;
CORE_cgetrf_reclap_update(M, column, n1, n2,
A, LDA, IPIV,
thidx, thcnt);
CORE_cgetrf_reclap_rec( M, n2, A, LDA, IPIV, info,
thidx, thcnt, column + n1 );
if ( *info != 0 )
return;
psplit( n1, thidx, thcnt, &coff, &ccnt );
if (ccnt > 0) {
CORE_claswap1( ccnt, Atop+coff*LDA, LDA, n1 + column, N + column, IPIV ); /* swap to the left */
}
} else {
int thrd;
CORE_cbarrier_thread( thidx, thcnt );
psplit( M, thidx, thcnt, &loff, &lm );
if (thidx == 0) {
loff = column;
lm -= column;
}
tmp2 = Atop[column]; /* all threads read the pivot element in case they need it */
jp = cblas_icamax( lm, Atop + loff, 1 );
tmp1 = Atop[loff + jp];
CORE_camax1_thread( tmp1, thidx, thcnt, &thrd,
&tmp3, loff + jp + 1, IPIV + column );
Atop[column] = tmp3; /* all threads set the pivot element: no need for synchronization */
if ( tmp3 != 0.0 ) {
if ( cabsf(tmp3) >= sfmin ) {
PLASMA_Complex32_t tmp = (PLASMA_Complex32_t)1.0 / tmp3;
n1 = (thidx == 0) ? 1 : 0;
cblas_cscal( lm - n1, CBLAS_SADDR(tmp), Atop + loff + n1, 1 );
} else {
int i;
PLASMA_Complex32_t *Atop2;
n1 = (thidx == 0) ? 1 : 0;
Atop2 = Atop + loff + n1;
for( i=0; i < lm-n1; i++, Atop2++)
*Atop2 = *Atop2 / tmp3;
}
if (thrd == thidx) { /* the thread that owns the best pivot */
if (loff + jp != column) /* if there is a need to exchange the pivot */
Atop[loff + jp] = tmp2 / tmp3;
}
} else {
*info = column + 1;
return;
}
CORE_cbarrier_thread( thidx, thcnt );
}
}
int CORE_ctsqrt(int M, int N, int IB,
PLASMA_Complex32_t *A1, int LDA1,
PLASMA_Complex32_t *A2, int LDA2,
PLASMA_Complex32_t *T, int LDT,
PLASMA_Complex32_t *TAU, PLASMA_Complex32_t *WORK)
{
static PLASMA_Complex32_t zone = 1.0;
static PLASMA_Complex32_t zzero = 0.0;
PLASMA_Complex32_t alpha;
int i, ii, sb;
/* Check input arguments */
if (M < 0) {
coreblas_error(1, "Illegal value of M");
return -1;
}
if (N < 0) {
coreblas_error(2, "Illegal value of N");
return -2;
}
if (IB < 0) {
coreblas_error(3, "Illegal value of IB");
return -3;
}
if ((LDA2 < max(1,M)) && (M > 0)) {
coreblas_error(8, "Illegal value of LDA2");
return -8;
}
/* Quick return */
if ((M == 0) || (N == 0) || (IB == 0))
return PLASMA_SUCCESS;
for(ii = 0; ii < N; ii += IB) {
sb = min(N-ii, IB);
for(i = 0; i < sb; i++) {
/*
* Generate elementary reflector H( II*IB+I ) to annihilate
* A( II*IB+I:M, II*IB+I )
*/
LAPACKE_clarfg_work(M+1, &A1[LDA1*(ii+i)+ii+i], &A2[LDA2*(ii+i)], 1, &TAU[ii+i]);
if (ii+i+1 < N) {
/*
* Apply H( II*IB+I ) to A( II*IB+I:M, II*IB+I+1:II*IB+IB ) from the left
*/
alpha = -conjf(TAU[ii+i]);
cblas_ccopy(
sb-i-1,
&A1[LDA1*(ii+i+1)+(ii+i)], LDA1,
WORK, 1);
#ifdef COMPLEX
LAPACKE_clacgv_work(sb-i-1, WORK, 1);
#endif
cblas_cgemv(
CblasColMajor, (CBLAS_TRANSPOSE)PlasmaConjTrans,
M, sb-i-1,
CBLAS_SADDR(zone), &A2[LDA2*(ii+i+1)], LDA2,
&A2[LDA2*(ii+i)], 1,
CBLAS_SADDR(zone), WORK, 1);
#ifdef COMPLEX
LAPACKE_clacgv_work(sb-i-1, WORK, 1 );
#endif
cblas_caxpy(
sb-i-1, CBLAS_SADDR(alpha),
WORK, 1,
&A1[LDA1*(ii+i+1)+ii+i], LDA1);
#ifdef COMPLEX
LAPACKE_clacgv_work(sb-i-1, WORK, 1 );
#endif
cblas_cgerc(
CblasColMajor, M, sb-i-1, CBLAS_SADDR(alpha),
&A2[LDA2*(ii+i)], 1,
WORK, 1,
&A2[LDA2*(ii+i+1)], LDA2);
}
/*
* Calculate T
*/
alpha = -TAU[ii+i];
cblas_cgemv(
CblasColMajor, (CBLAS_TRANSPOSE)PlasmaConjTrans, M, i,
CBLAS_SADDR(alpha), &A2[LDA2*ii], LDA2,
&A2[LDA2*(ii+i)], 1,
CBLAS_SADDR(zzero), &T[LDT*(ii+i)], 1);
cblas_ctrmv(
CblasColMajor, (CBLAS_UPLO)PlasmaUpper,
(CBLAS_TRANSPOSE)PlasmaNoTrans, (CBLAS_DIAG)PlasmaNonUnit, i,
&T[LDT*ii], LDT,
&T[LDT*(ii+i)], 1);
T[LDT*(ii+i)+i] = TAU[ii+i];
}
if (N > ii+sb) {
CORE_ctsmqr(
PlasmaLeft, PlasmaConjTrans,
sb, N-(ii+sb), M, N-(ii+sb), IB, IB,
&A1[LDA1*(ii+sb)+ii], LDA1,
&A2[LDA2*(ii+sb)], LDA2,
&A2[LDA2*ii], LDA2,
&T[LDT*ii], LDT,
WORK, sb);
}
}
return PLASMA_SUCCESS;
}