JNIEXPORT void JNICALL Java_uncomplicate_neanderthal_CBLAS_srot
(JNIEnv *env, jclass clazz, jint N,
jobject X, jint offsetX, jint incX,
jobject Y, jint offsetY, jint incY,
float c, float s) {
float *cX = (float *) (*env)->GetDirectBufferAddress(env, X);
float *cY = (float *) (*env)->GetDirectBufferAddress(env, Y);
cblas_srot(N, cX + offsetX, incX, cY + offsetY, incY, c, s);
};
void
test_rot (void) {
const double flteps = 1e-4, dbleps = 1e-6;
{
int N = 1;
float c = 0.0f;
float s = 0.0f;
float X[] = { -0.314f };
int incX = 1;
float Y[] = { -0.406f };
int incY = -1;
float x_expected[] = { 0.0f };
float y_expected[] = { 0.0f };
cblas_srot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], flteps, "srot(case 558)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], flteps, "srot(case 559)");
}
};
};
{
int N = 1;
float c = 0.866025403784f;
float s = 0.5f;
float X[] = { -0.314f };
int incX = 1;
float Y[] = { -0.406f };
int incY = -1;
float x_expected[] = { -0.474932f };
float y_expected[] = { -0.194606f };
cblas_srot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], flteps, "srot(case 560)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], flteps, "srot(case 561)");
}
};
};
{
int N = 1;
float c = 0.0f;
float s = -1.0f;
float X[] = { -0.314f };
int incX = 1;
float Y[] = { -0.406f };
int incY = -1;
float x_expected[] = { 0.406f };
float y_expected[] = { -0.314f };
cblas_srot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], flteps, "srot(case 562)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], flteps, "srot(case 563)");
}
};
};
{
int N = 1;
float c = -1.0f;
float s = 0.0f;
float X[] = { -0.314f };
int incX = 1;
float Y[] = { -0.406f };
int incY = -1;
float x_expected[] = { 0.314f };
float y_expected[] = { 0.406f };
cblas_srot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], flteps, "srot(case 564)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], flteps, "srot(case 565)");
}
};
};
{
int N = 1;
double c = 0;
double s = 0;
double X[] = { -0.493 };
int incX = 1;
double Y[] = { -0.014 };
int incY = -1;
double x_expected[] = { 0.0 };
double y_expected[] = { 0.0 };
cblas_drot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], dbleps, "drot(case 566)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], dbleps, "drot(case 567)");
}
};
};
{
int N = 1;
double c = 0.866025403784;
double s = 0.5;
double X[] = { -0.493 };
int incX = 1;
double Y[] = { -0.014 };
int incY = -1;
double x_expected[] = { -0.433950524066 };
double y_expected[] = { 0.234375644347 };
cblas_drot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], dbleps, "drot(case 568)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], dbleps, "drot(case 569)");
}
};
};
{
int N = 1;
double c = 0;
double s = -1;
double X[] = { -0.493 };
int incX = 1;
double Y[] = { -0.014 };
int incY = -1;
double x_expected[] = { 0.014 };
double y_expected[] = { -0.493 };
cblas_drot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], dbleps, "drot(case 570)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], dbleps, "drot(case 571)");
}
};
};
{
int N = 1;
double c = -1;
double s = 0;
double X[] = { -0.493 };
int incX = 1;
double Y[] = { -0.014 };
int incY = -1;
double x_expected[] = { 0.493 };
double y_expected[] = { 0.014 };
cblas_drot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], dbleps, "drot(case 572)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], dbleps, "drot(case 573)");
}
};
};
{
int N = 1;
float c = 0.0f;
float s = 0.0f;
float X[] = { -0.808f };
int incX = -1;
float Y[] = { -0.511f };
int incY = 1;
float x_expected[] = { 0.0f };
float y_expected[] = { 0.0f };
cblas_srot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], flteps, "srot(case 574)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], flteps, "srot(case 575)");
}
};
};
{
int N = 1;
float c = 0.866025403784f;
float s = 0.5f;
float X[] = { -0.808f };
int incX = -1;
float Y[] = { -0.511f };
int incY = 1;
float x_expected[] = { -0.955249f };
float y_expected[] = { -0.038539f };
cblas_srot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], flteps, "srot(case 576)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], flteps, "srot(case 577)");
}
};
};
{
int N = 1;
float c = 0.0f;
float s = -1.0f;
float X[] = { -0.808f };
int incX = -1;
float Y[] = { -0.511f };
int incY = 1;
float x_expected[] = { 0.511f };
float y_expected[] = { -0.808f };
cblas_srot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], flteps, "srot(case 578)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], flteps, "srot(case 579)");
}
};
};
{
int N = 1;
float c = -1.0f;
float s = 0.0f;
float X[] = { -0.808f };
int incX = -1;
float Y[] = { -0.511f };
int incY = 1;
float x_expected[] = { 0.808f };
float y_expected[] = { 0.511f };
cblas_srot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], flteps, "srot(case 580)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], flteps, "srot(case 581)");
}
};
};
{
int N = 1;
double c = 0;
double s = 0;
double X[] = { -0.176 };
int incX = -1;
double Y[] = { -0.165 };
int incY = 1;
double x_expected[] = { 0.0 };
double y_expected[] = { 0.0 };
cblas_drot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], dbleps, "drot(case 582)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], dbleps, "drot(case 583)");
}
};
};
{
int N = 1;
double c = 0.866025403784;
double s = 0.5;
double X[] = { -0.176 };
int incX = -1;
double Y[] = { -0.165 };
int incY = 1;
double x_expected[] = { -0.234920471066 };
double y_expected[] = { -0.0548941916244 };
cblas_drot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], dbleps, "drot(case 584)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], dbleps, "drot(case 585)");
}
};
};
{
int N = 1;
double c = 0;
double s = -1;
double X[] = { -0.176 };
int incX = -1;
double Y[] = { -0.165 };
int incY = 1;
double x_expected[] = { 0.165 };
double y_expected[] = { -0.176 };
cblas_drot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], dbleps, "drot(case 586)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], dbleps, "drot(case 587)");
}
};
};
{
int N = 1;
double c = -1;
double s = 0;
double X[] = { -0.176 };
int incX = -1;
double Y[] = { -0.165 };
int incY = 1;
double x_expected[] = { 0.176 };
double y_expected[] = { 0.165 };
cblas_drot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], dbleps, "drot(case 588)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], dbleps, "drot(case 589)");
}
};
};
{
int N = 1;
float c = 0.0f;
float s = 0.0f;
float X[] = { -0.201f };
int incX = -1;
float Y[] = { 0.087f };
int incY = -1;
float x_expected[] = { 0.0f };
float y_expected[] = { 0.0f };
cblas_srot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], flteps, "srot(case 590)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], flteps, "srot(case 591)");
}
};
};
{
int N = 1;
float c = 0.866025403784f;
float s = 0.5f;
float X[] = { -0.201f };
int incX = -1;
float Y[] = { 0.087f };
int incY = -1;
float x_expected[] = { -0.130571f };
float y_expected[] = { 0.175844f };
cblas_srot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], flteps, "srot(case 592)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], flteps, "srot(case 593)");
}
};
};
{
int N = 1;
float c = 0.0f;
float s = -1.0f;
float X[] = { -0.201f };
int incX = -1;
float Y[] = { 0.087f };
int incY = -1;
float x_expected[] = { -0.087f };
float y_expected[] = { -0.201f };
cblas_srot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], flteps, "srot(case 594)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], flteps, "srot(case 595)");
}
};
};
{
int N = 1;
float c = -1.0f;
float s = 0.0f;
float X[] = { -0.201f };
int incX = -1;
float Y[] = { 0.087f };
int incY = -1;
float x_expected[] = { 0.201f };
float y_expected[] = { -0.087f };
cblas_srot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], flteps, "srot(case 596)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], flteps, "srot(case 597)");
}
};
};
{
int N = 1;
double c = 0;
double s = 0;
double X[] = { -0.464 };
int incX = -1;
double Y[] = { 0.7 };
int incY = -1;
double x_expected[] = { 0.0 };
double y_expected[] = { 0.0 };
cblas_drot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], dbleps, "drot(case 598)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], dbleps, "drot(case 599)");
}
};
};
{
int N = 1;
double c = 0.866025403784;
double s = 0.5;
double X[] = { -0.464 };
int incX = -1;
double Y[] = { 0.7 };
int incY = -1;
double x_expected[] = { -0.051835787356 };
double y_expected[] = { 0.838217782649 };
cblas_drot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], dbleps, "drot(case 600)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], dbleps, "drot(case 601)");
}
};
};
{
int N = 1;
double c = 0;
double s = -1;
double X[] = { -0.464 };
int incX = -1;
double Y[] = { 0.7 };
int incY = -1;
double x_expected[] = { -0.7 };
double y_expected[] = { -0.464 };
cblas_drot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], dbleps, "drot(case 602)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], dbleps, "drot(case 603)");
}
};
};
{
int N = 1;
double c = -1;
double s = 0;
double X[] = { -0.464 };
int incX = -1;
double Y[] = { 0.7 };
int incY = -1;
double x_expected[] = { 0.464 };
double y_expected[] = { -0.7 };
cblas_drot(N, X, incX, Y, incY, c, s);
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(X[i], x_expected[i], dbleps, "drot(case 604)");
}
};
{
int i;
for (i = 0; i < 1; i++) {
gsl_test_rel(Y[i], y_expected[i], dbleps, "drot(case 605)");
}
};
};
}
extern "C" magma_int_t
magma_sgeev(magma_vec_t jobvl, magma_vec_t jobvr, magma_int_t n,
float *a, magma_int_t lda,
float *WR, float *WI,
float *vl, magma_int_t ldvl,
float *vr, magma_int_t ldvr,
float *work, magma_int_t lwork,
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
=======
SGEEV computes for an N-by-N real 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)**T * A = lambda(j) * u(j)**T
where u(j)**T denotes the 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) DOUBLE PRECISION 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).
WR (output) DOUBLE PRECISION array, dimension (N)
WI (output) DOUBLE PRECISION array, dimension (N)
WR and WI contain the real and imaginary parts,
respectively, of the computed eigenvalues. Complex
conjugate pairs of eigenvalues appear consecutively
with the eigenvalue having the positive imaginary part
first.
VL (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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.
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 c_n1 = -1;
magma_int_t a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3;
float d__1, d__2;
magma_int_t i__, k, ihi, ilo;
float r__, cs, sn, scl;
float dum[1], eps;
magma_int_t ibal;
float anrm;
magma_int_t ierr, itau, iwrk, nout;
magma_int_t scalea;
float cscale;
float bignum;
magma_int_t minwrk;
magma_int_t wantvl;
float smlnum;
magma_int_t lquery, wantvr, select[1];
magma_int_t nb = 0;
magmaFloat_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 = -9;
} else if ( (ldvr < 1) || (wantvr && (ldvr < n))) {
*info = -11;
}
/* Compute workspace */
if (*info == 0) {
nb = magma_get_sgehrd_nb(n);
minwrk = (2+nb)*n;
work[0] = (float) minwrk;
if (lwork < minwrk && ! lquery) {
*info = -13;
}
}
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(float) )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
#endif
// subtract row and col for 1-based indexing
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;
/* 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_slange("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_slascl("G", &c__0, &c__0, &anrm, &cscale, &n, &n,
&a[a_offset], &lda, &ierr);
}
/* Balance the matrix
(Workspace: need N) */
ibal = 1;
lapackf77_sgebal("B", &n, &a[a_offset], &lda, &ilo, &ihi, &work[ibal], &ierr);
/* Reduce to upper Hessenberg form
(Workspace: need 3*N, prefer 2*N+N*NB) */
itau = ibal + n;
iwrk = itau + n;
i__1 = lwork - iwrk + 1;
//start = get_current_time();
#if defined(VERSION1)
/*
* Version 1 - LAPACK
*/
lapackf77_sgehrd(&n, &ilo, &ihi, &a[a_offset], &lda,
&work[itau], &work[iwrk], &i__1, &ierr);
#elif defined(VERSION2)
/*
* Version 2 - LAPACK consistent HRD
*/
magma_sgehrd2(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_sgehrd(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 sgehrd = %5.2f sec\n", GetTimerValue(start,end)/1000.);
if (wantvl) {
/* Want left eigenvectors
Copy Householder vectors to VL */
side[0] = 'L';
lapackf77_slacpy(MagmaLowerStr, &n, &n,
&a[a_offset], &lda, &vl[vl_offset], &ldvl);
/*
* Generate orthogonal matrix in VL
* (Workspace: need 3*N-1, prefer 2*N+(N-1)*NB)
*/
i__1 = lwork - iwrk + 1;
//start = get_current_time();
#if defined(VERSION1) || defined(VERSION2)
/*
* Version 1 & 2 - LAPACK
*/
lapackf77_sorghr(&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_sorghr(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau],
dT, 0, nb, &ierr, queue);
#endif
//end = get_current_time();
//printf(" Time for sorghr = %5.2f sec\n", GetTimerValue(start,end)/1000.);
/*
* Perform QR iteration, accumulating Schur vectors in VL
* (Workspace: need N+1, prefer N+HSWORK (see comments) )
*/
iwrk = itau;
i__1 = lwork - iwrk + 1;
lapackf77_shseqr("S", "V", &n, &ilo, &ihi, &a[a_offset], &lda, WR, WI,
&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_slacpy("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_slacpy("L", &n, &n, &a[a_offset], &lda, &vr[vr_offset], &ldvr);
/*
* Generate orthogonal matrix in VR
* (Workspace: need 3*N-1, prefer 2*N+(N-1)*NB)
*/
i__1 = lwork - iwrk + 1;
//start = get_current_time();
#if defined(VERSION1) || defined(VERSION2)
/*
* Version 1 & 2 - LAPACK
*/
lapackf77_sorghr(&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_sorghr(n, ilo, ihi, &vr[vr_offset], ldvr,
&work[itau], dT, 0, nb, &ierr, queue);
#endif
//end = get_current_time();
//printf(" Time for sorghr = %5.2f sec\n", GetTimerValue(start,end)/1000.);
/*
* Perform QR iteration, accumulating Schur vectors in VR
* (Workspace: need N+1, prefer N+HSWORK (see comments) )
*/
iwrk = itau;
i__1 = lwork - iwrk + 1;
lapackf77_shseqr("S", "V", &n, &ilo, &ihi, &a[a_offset], &lda, WR, WI,
&vr[vr_offset], &ldvr, &work[iwrk], &i__1, info);
} else {
/*
* Compute eigenvalues only
* (Workspace: need N+1, prefer N+HSWORK (see comments) )
*/
iwrk = itau;
i__1 = lwork - iwrk + 1;
lapackf77_shseqr("E", "N", &n, &ilo, &ihi, &a[a_offset], &lda, WR, WI,
&vr[vr_offset], &ldvr, &work[iwrk], &i__1, info);
}
/* If INFO > 0 from SHSEQR, then quit */
if (*info > 0) {
fprintf(stderr, "SHSEQR returned with info = %d\n", (int) *info);
goto L50;
}
if (wantvl || wantvr) {
/*
* Compute left and/or right eigenvectors
* (Workspace: need 4*N)
*/
lapackf77_strevc(side, "B", select, &n, &a[a_offset], &lda, &vl[vl_offset], &ldvl,
&vr[vr_offset], &ldvr, &n, &nout, &work[iwrk], &ierr);
}
if (wantvl) {
/*
* Undo balancing of left eigenvectors
* (Workspace: need N)
*/
lapackf77_sgebak("B", "L", &n, &ilo, &ihi,
&work[ibal], &n, &vl[vl_offset], &ldvl, &ierr);
/* Normalize left eigenvectors and make largest component real */
for (i__ = 1; i__ <= n; ++i__) {
if ( WI[i__-1] == 0.) {
scl = cblas_snrm2(n, &vl[i__ * vl_dim1 + 1], 1);
scl = 1. / scl;
cblas_sscal(n, (scl), &vl[i__ * vl_dim1 + 1], 1);
} else if (WI[i__-1] > 0.) {
d__1 = cblas_snrm2(n, &vl[ i__ * vl_dim1 + 1], 1);
d__2 = cblas_snrm2(n, &vl[(i__ + 1) * vl_dim1 + 1], 1);
scl = lapackf77_slapy2(&d__1, &d__2);
scl = 1. / scl;
cblas_sscal(n, (scl), &vl[ i__ * vl_dim1 + 1], 1);
cblas_sscal(n, (scl), &vl[(i__ + 1) * vl_dim1 + 1], 1);
i__2 = n;
for (k = 1; k <= i__2; ++k) {
/* Computing 2nd power */
d__1 = vl[k + i__ * vl_dim1];
/* Computing 2nd power */
d__2 = vl[k + (i__ + 1) * vl_dim1];
work[iwrk + 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_isamax */
k = cblas_isamax(n, &work[iwrk], 1)+1;
lapackf77_slartg(&vl[k + i__ * vl_dim1],
&vl[k + (i__ + 1) * vl_dim1], &cs, &sn, &r__);
cblas_srot(n, &vl[ i__ * vl_dim1 + 1], 1,
&vl[(i__ + 1) * vl_dim1 + 1], 1, cs, (sn));
vl[k + (i__ + 1) * vl_dim1] = 0.;
}
}
}
if (wantvr) {
/*
* Undo balancing of right eigenvectors
* (Workspace: need N)
*/
lapackf77_sgebak("B", "R", &n, &ilo, &ihi, &work[ibal], &n,
&vr[vr_offset], &ldvr, &ierr);
/* Normalize right eigenvectors and make largest component real */
for (i__ = 1; i__ <= n; ++i__) {
if (WI[i__-1] == 0.) {
scl = 1. / cblas_snrm2(n, &vr[i__ * vr_dim1 + 1], 1);
cblas_sscal(n, (scl), &vr[i__ * vr_dim1 + 1], 1);
} else if (WI[i__-1] > 0.) {
d__1 = cblas_snrm2(n, &vr[ i__ * vr_dim1 + 1], 1);
d__2 = cblas_snrm2(n, &vr[(i__ + 1) * vr_dim1 + 1], 1);
scl = lapackf77_slapy2(&d__1, &d__2);
scl = 1. / scl;
cblas_sscal(n, (scl), &vr[ i__ * vr_dim1 + 1], 1);
cblas_sscal(n, (scl), &vr[(i__ + 1) * vr_dim1 + 1], 1);
i__2 = n;
for (k = 1; k <= i__2; ++k) {
/* Computing 2nd power */
d__1 = vr[k + i__ * vr_dim1];
/* Computing 2nd power */
d__2 = vr[k + (i__ + 1) * vr_dim1];
work[iwrk + 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_isamax */
k = cblas_isamax(n, &work[iwrk], 1)+1;
lapackf77_slartg(&vr[k + i__ * vr_dim1], &vr[k + (i__ + 1) * vr_dim1],
&cs, &sn, &r__);
cblas_srot(n, &vr[ i__ * vr_dim1 + 1], 1,
&vr[(i__ + 1) * vr_dim1 + 1], 1, cs, (sn));
vr[k + (i__ + 1) * vr_dim1] = 0.;
}
}
}
/* Undo scaling if necessary */
L50:
if (scalea) {
i__1 = n - *info;
/* Computing MAX */
i__3 = n - *info;
i__2 = max(i__3,1);
lapackf77_slascl("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1,
WR + (*info), &i__2, &ierr);
i__1 = n - *info;
/* Computing MAX */
i__3 = n - *info;
i__2 = max(i__3,1);
lapackf77_slascl("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1,
WI + (*info), &i__2, &ierr);
if (*info > 0) {
i__1 = ilo - 1;
lapackf77_slascl("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1,
WR, &n, &ierr);
i__1 = ilo - 1;
lapackf77_slascl("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1,
WI, &n, &ierr);
}
}
#if defined(VERSION3)
magma_free( dT );
#endif
return *info;
} /* magma_sgeev */
//
// Overloaded function for dispatching to
// * CBLAS backend, and
// * float value-type.
//
inline void rot( const int n, float* x, const int incx, float* y,
const int incy, const float c, const float s ) {
cblas_srot( n, x, incx, y, incy, c, s );
}