VALUE rb_blas_ixamax(int argc, VALUE *argv, VALUE self)
{
Matrix *dx;
int incx;
int incy;
int n;
//char error_msg[64];
VALUE n_value, incx_value;
rb_scan_args(argc, argv, "02", &incx_value, &n_value);
Data_Get_Struct(self, Matrix, dx);
if(incx_value == Qnil)
incx = 1;
else
incx = NUM2INT(incx_value);
if(n_value == Qnil)
n = dx->nrows;
else
n = NUM2INT(n_value);
if(dx == NULL || dx->ncols != 1)
{ //sprintf(error_msg, );
rb_raise(rb_eRuntimeError, "Self is not a Vector");
}
switch(dx->data_type)
{
case Single_t: //s
return INT2FIX(cblas_isamax(n , (float *)dx->data, incx));
case Double_t: //d
return INT2FIX(cblas_idamax(n , (double *)dx->data, incx));
case Complex_t: //c
return INT2FIX(cblas_icamax(n , dx->data, incx));
case Double_Complex_t: //z
return INT2FIX(cblas_izamax(n , dx->data, incx));
default:
//sprintf(error_msg, "Invalid data_type (%d) in Matrix", dx->data_type);
rb_raise(rb_eRuntimeError, "Invalid data_type (%d) in Matrix", dx->data_type);
return Qnil; //Never reaches here.
}
}
JNIEXPORT jint JNICALL Java_uncomplicate_neanderthal_CBLAS_isamax
(JNIEnv *env, jclass clazz, jint N, jobject X, jint offsetX, jint incX) {
float *cX = (float *) (*env)->GetDirectBufferAddress(env, X);
return cblas_isamax(N, cX + offsetX, incX);
};
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 */
void
test_amax (void) {
{
int N = 1;
float X[] = { -0.388f };
int incX = -1;
int expected = 0;
int k;
k = cblas_isamax(N, X, incX);
gsl_test_int(k, expected, "samax(case 52)");
};
{
int N = 1;
double X[] = { 0.247 };
int incX = -1;
int expected = 0;
int k;
k = cblas_idamax(N, X, incX);
gsl_test_int(k, expected, "damax(case 53)");
};
{
int N = 1;
float X[] = { 0.704f, 0.665f };
int incX = -1;
int expected = 0;
int k;
k = cblas_icamax(N, X, incX);
gsl_test_int(k, expected, "camax(case 54)");
};
{
int N = 1;
double X[] = { -0.599, -0.758 };
int incX = -1;
int expected = 0;
int k;
k = cblas_izamax(N, X, incX);
gsl_test_int(k, expected, "zamax(case 55)");
};
{
int N = 2;
float X[] = { 0.909f, 0.037f };
int incX = 1;
int expected = 0;
int k;
k = cblas_isamax(N, X, incX);
gsl_test_int(k, expected, "samax(case 56)");
};
{
int N = 2;
double X[] = { 0.271, -0.426 };
int incX = 1;
int expected = 1;
int k;
k = cblas_idamax(N, X, incX);
gsl_test_int(k, expected, "damax(case 57)");
};
{
int N = 2;
float X[] = { -0.648f, 0.317f, 0.62f, 0.392f };
int incX = 1;
int expected = 1;
int k;
k = cblas_icamax(N, X, incX);
gsl_test_int(k, expected, "camax(case 58)");
};
{
int N = 2;
double X[] = { -0.789, 0.352, 0.562, 0.697 };
int incX = 1;
int expected = 1;
int k;
k = cblas_izamax(N, X, incX);
gsl_test_int(k, expected, "zamax(case 59)");
};
{
int N = 2;
float X[] = { 0.487f, 0.918f };
int incX = -1;
int expected = 0;
int k;
k = cblas_isamax(N, X, incX);
gsl_test_int(k, expected, "samax(case 60)");
};
{
int N = 2;
double X[] = { 0.537, 0.826 };
int incX = -1;
int expected = 0;
int k;
k = cblas_idamax(N, X, incX);
gsl_test_int(k, expected, "damax(case 61)");
};
{
int N = 2;
float X[] = { 0.993f, 0.172f, -0.825f, 0.873f };
int incX = -1;
int expected = 0;
int k;
k = cblas_icamax(N, X, incX);
gsl_test_int(k, expected, "camax(case 62)");
};
{
int N = 2;
double X[] = { 0.913, -0.436, -0.134, 0.129 };
int incX = -1;
int expected = 0;
int k;
k = cblas_izamax(N, X, incX);
gsl_test_int(k, expected, "zamax(case 63)");
};
}
/**
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 */
//
// Overloaded function for dispatching to
// * CBLAS backend, and
// * float value-type.
//
inline std::ptrdiff_t iamax( const int n, const float* x, const int incx ) {
return cblas_isamax( n, x, incx );
}
extern "C" magma_int_t
magma_slaqps(magma_int_t m, magma_int_t n, magma_int_t offset,
magma_int_t nb, magma_int_t *kb,
float *A, magma_int_t lda,
float *dA, magma_int_t ldda,
magma_int_t *jpvt, float *tau, float *vn1, float *vn2,
float *auxv,
float *F, magma_int_t ldf,
float *dF, magma_int_t lddf)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
SLAQPS computes a step of QR factorization with column pivoting
of a real M-by-N matrix A by using Blas-3. It tries to factorize
NB columns from A starting from the row OFFSET+1, and updates all
of the matrix with Blas-3 xGEMM.
In some cases, due to catastrophic cancellations, it cannot
factorize NB columns. Hence, the actual number of factorized
columns is returned in KB.
Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0
OFFSET (input) INTEGER
The number of rows of A that have been factorized in
previous steps.
NB (input) INTEGER
The number of columns to factorize.
KB (output) INTEGER
The number of columns actually factorized.
A (input/output) REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, block A(OFFSET+1:M,1:KB) is the triangular
factor obtained and block A(1:OFFSET,1:N) has been
accordingly pivoted, but no factorized.
The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
been updated.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
JPVT (input/output) INTEGER array, dimension (N)
JPVT(I) = K <==> Column K of the full matrix A has been
permuted into position I in AP.
TAU (output) REAL array, dimension (KB)
The scalar factors of the elementary reflectors.
VN1 (input/output) DOUBLE PRECISION array, dimension (N)
The vector with the partial column norms.
VN2 (input/output) DOUBLE PRECISION array, dimension (N)
The vector with the exact column norms.
AUXV (input/output) REAL array, dimension (NB)
Auxiliar vector.
F (input/output) REAL array, dimension (LDF,NB)
Matrix F' = L*Y'*A.
LDF (input) INTEGER
The leading dimension of the array F. LDF >= max(1,N).
===================================================================== */
#define A(i, j) (A + (i) + (j)*(lda ))
#define dA(i, j) (dA + (i) + (j)*(ldda))
#define F(i, j) (F + (i) + (j)*(ldf ))
#define dF(i, j) (dF + (i) + (j)*(lddf))
float c_zero = MAGMA_S_MAKE( 0.,0.);
float c_one = MAGMA_S_MAKE( 1.,0.);
float c_neg_one = MAGMA_S_MAKE(-1.,0.);
magma_int_t ione = 1;
magma_int_t i__1, i__2;
float d__1;
float z__1;
magma_int_t j, k, rk;
float Akk;
magma_int_t pvt;
float temp, temp2, tol3z;
magma_int_t itemp;
magma_int_t lsticc;
magma_int_t lastrk;
lastrk = min( m, n + offset );
tol3z = magma_ssqrt( lapackf77_slamch("Epsilon"));
magma_queue_t stream;
magma_queue_create( &stream );
lsticc = 0;
k = 0;
while( k < nb && lsticc == 0 ) {
rk = offset + k;
/* Determine ith pivot column and swap if necessary */
// Fortran: pvt, k, isamax are all 1-based; subtract 1 from k.
// C: pvt, k, isamax are all 0-based; don't subtract 1.
pvt = k + cblas_isamax( n-k, &vn1[k], ione );
if (pvt != k) {
if (pvt >= nb) {
/* 1. Start copy from GPU */
magma_sgetmatrix_async( m - offset - nb, 1,
dA(offset + nb, pvt), ldda,
A (offset + nb, pvt), lda, stream );
}
/* F gets swapped so F must be sent at the end to GPU */
i__1 = k;
blasf77_sswap( &i__1, F(pvt,0), &ldf, F(k,0), &ldf );
itemp = jpvt[pvt];
jpvt[pvt] = jpvt[k];
jpvt[k] = itemp;
vn1[pvt] = vn1[k];
vn2[pvt] = vn2[k];
if (pvt < nb){
/* no need of transfer if pivot is within the panel */
blasf77_sswap( &m, A(0, pvt), &ione, A(0, k), &ione );
}
else {
/* 1. Finish copy from GPU */
magma_queue_sync( stream );
/* 2. Swap as usual on CPU */
blasf77_sswap(&m, A(0, pvt), &ione, A(0, k), &ione);
/* 3. Restore the GPU */
magma_ssetmatrix_async( m - offset - nb, 1,
A (offset + nb, pvt), lda,
dA(offset + nb, pvt), ldda, stream);
}
}
/* Apply previous Householder reflectors to column K:
A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'.
Optimization: multiply with beta=0; wait for vector and subtract */
if (k > 0) {
#if defined(PRECISION_c) || defined(PRECISION_z)
for (j = 0; j < k; ++j){
*F(k,j) = MAGMA_S_CNJG( *F(k,j) );
}
#endif
i__1 = m - rk;
i__2 = k;
blasf77_sgemv( MagmaNoTransStr, &i__1, &i__2,
&c_neg_one, A(rk, 0), &lda,
F(k, 0), &ldf,
&c_one, A(rk, k), &ione );
#if defined(PRECISION_c) || defined(PRECISION_z)
for (j = 0; j < k; ++j) {
*F(k,j) = MAGMA_S_CNJG( *F(k,j) );
}
#endif
}
/* Generate elementary reflector H(k). */
if (rk < m-1) {
i__1 = m - rk;
lapackf77_slarfg( &i__1, A(rk, k), A(rk + 1, k), &ione, &tau[k] );
} else {
lapackf77_slarfg( &ione, A(rk, k), A(rk, k), &ione, &tau[k] );
}
Akk = *A(rk, k);
*A(rk, k) = c_one;
/* Compute Kth column of F:
Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K) on the GPU */
if (k < n-1) {
i__1 = m - rk;
i__2 = n - k - 1;
/* Send the vector to the GPU */
magma_ssetmatrix( i__1, 1, A(rk, k), lda, dA(rk,k), ldda );
/* Multiply on GPU */
// was CALL SGEMV( 'Conjugate transpose', M-RK+1, N-K,
// TAU( K ), A( RK, K+1 ), LDA,
// A( RK, K ), 1,
// CZERO, F( K+1, K ), 1 )
magma_int_t i__3 = nb-k-1;
magma_int_t i__4 = i__2 - i__3;
magma_int_t i__5 = nb-k;
magma_sgemv( MagmaTrans, i__1 - i__5, i__2 - i__3,
tau[k], dA(rk +i__5, k+1+i__3), ldda,
dA(rk +i__5, k ), ione,
c_zero, dF(k+1+i__3, k ), ione );
magma_sgetmatrix_async( i__2-i__3, 1,
dF(k + 1 +i__3, k), i__2,
F (k + 1 +i__3, k), i__2, stream );
blasf77_sgemv( MagmaTransStr, &i__1, &i__3,
&tau[k], A(rk, k+1), &lda,
A(rk, k ), &ione,
&c_zero, F(k+1, k ), &ione );
magma_queue_sync( stream );
blasf77_sgemv( MagmaTransStr, &i__5, &i__4,
&tau[k], A(rk, k+1+i__3), &lda,
A(rk, k ), &ione,
&c_one, F(k+1+i__3, k ), &ione );
}
/* Padding F(1:K,K) with zeros. */
for (j = 0; j < k; ++j) {
*F(j, k) = c_zero;
}
/* Incremental updating of F:
F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)'*A(RK:M,K). */
if (k > 0) {
i__1 = m - rk;
i__2 = k;
z__1 = MAGMA_S_NEGATE( tau[k] );
blasf77_sgemv( MagmaTransStr, &i__1, &i__2,
&z__1, A(rk, 0), &lda,
A(rk, k), &ione,
&c_zero, auxv, &ione );
i__1 = k;
blasf77_sgemv( MagmaNoTransStr, &n, &i__1,
&c_one, F(0,0), &ldf,
auxv, &ione,
&c_one, F(0,k), &ione );
}
/* Optimization: On the last iteration start sending F back to the GPU */
/* Update the current row of A:
A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'. */
if (k < n-1) {
i__1 = n - k - 1;
i__2 = k + 1;
blasf77_sgemm( MagmaNoTransStr, MagmaTransStr, &ione, &i__1, &i__2,
&c_neg_one, A(rk, 0 ), &lda,
F(k+1,0 ), &ldf,
&c_one, A(rk, k+1), &lda );
}
/* Update partial column norms. */
if (rk < lastrk) {
for (j = k + 1; j < n; ++j) {
if (vn1[j] != 0.) {
/* NOTE: The following 4 lines follow from the analysis in
Lapack Working Note 176. */
temp = MAGMA_S_ABS( *A(rk,j) ) / vn1[j];
temp = max( 0., ((1. + temp) * (1. - temp)) );
d__1 = vn1[j] / vn2[j];
temp2 = temp * (d__1 * d__1);
if (temp2 <= tol3z) {
vn2[j] = (float) lsticc;
lsticc = j;
} else {
vn1[j] *= magma_ssqrt(temp);
}
}
}
}
*A(rk, k) = Akk;
++k;
}
// leave k as the last column done
--k;
*kb = k + 1;
rk = offset + *kb - 1;
/* Apply the block reflector to the rest of the matrix:
A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)' */
if (*kb < min(n, m - offset)) {
i__1 = m - rk - 1;
i__2 = n - *kb;
/* Send F to the GPU */
magma_ssetmatrix( i__2, *kb,
F (*kb, 0), ldf,
dF(*kb, 0), i__2 );
magma_sgemm( MagmaNoTrans, MagmaTrans, i__1, i__2, *kb,
c_neg_one, dA(rk+1, 0 ), ldda,
dF(*kb, 0 ), i__2,
c_one, dA(rk+1, *kb), ldda );
}
/* Recomputation of difficult columns. */
while( lsticc > 0 ) {
itemp = (magma_int_t)(vn2[lsticc] >= 0. ? floor(vn2[lsticc] + .5) : -floor(.5 - vn2[lsticc]));
i__1 = m - rk - 1;
if (lsticc <= nb)
vn1[lsticc] = cblas_snrm2(i__1, A(rk + 1, lsticc), ione);
else {
/* Where is the data, CPU or GPU ? */
float r1, r2;
r1 = cblas_snrm2(nb-k, A(rk + 1, lsticc), ione);
r2 = magma_snrm2(m-offset-nb, dA(offset + nb + 1, lsticc), ione);
//vn1[lsticc] = magma_snrm2(i__1, dA(rk + 1, lsticc), ione);
vn1[lsticc] = magma_ssqrt(r1*r1+r2*r2);
}
/* NOTE: The computation of VN1( LSTICC ) relies on the fact that
SNRM2 does not fail on vectors with norm below the value of SQRT(SLAMCH('S')) */
vn2[lsticc] = vn1[lsticc];
lsticc = itemp;
}
magma_queue_destroy( stream );
return MAGMA_SUCCESS;
} /* magma_slaqps */
int CORE_ststrf(int M, int N, int IB, int NB,
float *U, int LDU,
float *A, int LDA,
float *L, int LDL,
int *IPIV,
float *WORK, int LDWORK,
int *INFO)
{
static float zzero = 0.0;
static float mzone =-1.0;
float alpha;
int i, j, ii, sb;
int im, ip;
/* Check input arguments */
*INFO = 0;
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 ((LDU < max(1,NB)) && (NB > 0)) {
coreblas_error(6, "Illegal value of LDU");
return -6;
}
if ((LDA < max(1,M)) && (M > 0)) {
coreblas_error(8, "Illegal value of LDA");
return -8;
}
if ((LDL < max(1,IB)) && (IB > 0)) {
coreblas_error(10, "Illegal value of LDL");
return -10;
}
/* Quick return */
if ((M == 0) || (N == 0) || (IB == 0))
return PLASMA_SUCCESS;
/* Set L to 0 */
memset(L, 0, LDL*N*sizeof(float));
ip = 0;
for (ii = 0; ii < N; ii += IB) {
sb = min(N-ii, IB);
for (i = 0; i < sb; i++) {
im = cblas_isamax(M, &A[LDA*(ii+i)], 1);
IPIV[ip] = ii+i+1;
if (fabsf(A[LDA*(ii+i)+im]) > fabsf(U[LDU*(ii+i)+ii+i])) {
/*
* Swap behind.
*/
cblas_sswap(i, &L[LDL*ii+i], LDL, &WORK[im], LDWORK );
/*
* Swap ahead.
*/
cblas_sswap(sb-i, &U[LDU*(ii+i)+ii+i], LDU, &A[LDA*(ii+i)+im], LDA );
/*
* Set IPIV.
*/
IPIV[ip] = NB + im + 1;
for (j = 0; j < i; j++) {
A[LDA*(ii+j)+im] = zzero;
}
}
if ((*INFO == 0) && (fabsf(A[LDA*(ii+i)+im]) == zzero)
&& (fabsf(U[LDU*(ii+i)+ii+i]) == zzero)) {
*INFO = ii+i+1;
}
alpha = ((float)1. / U[LDU*(ii+i)+ii+i]);
cblas_sscal(M, (alpha), &A[LDA*(ii+i)], 1);
cblas_scopy(M, &A[LDA*(ii+i)], 1, &WORK[LDWORK*i], 1);
cblas_sger(
CblasColMajor, M, sb-i-1,
(mzone), &A[LDA*(ii+i)], 1,
&U[LDU*(ii+i+1)+ii+i], LDU,
&A[LDA*(ii+i+1)], LDA );
ip = ip+1;
}
/*
* Apply the subpanel to the rest of the panel.
*/
if(ii+i < N) {
for(j = ii; j < ii+sb; j++) {
if (IPIV[j] <= NB) {
IPIV[j] = IPIV[j] - ii;
}
}
CORE_sssssm(
NB, N-(ii+sb), M, N-(ii+sb), sb, sb,
&U[LDU*(ii+sb)+ii], LDU,
&A[LDA*(ii+sb)], LDA,
&L[LDL*ii], LDL,
WORK, LDWORK, &IPIV[ii]);
for(j = ii; j < ii+sb; j++) {
if (IPIV[j] <= NB) {
IPIV[j] = IPIV[j] + ii;
}
}
}
}
return PLASMA_SUCCESS;
}
int STARPU_ISAMAX (const int n, float *X, const int incX)
{
int retVal;
retVal = cblas_isamax(n, X, incX);
return retVal;
}
