/*
* Automatically Tuned Linear Algebra Software v3.10.2
* (C) Copyright 1999 R. Clint Whaley
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions, and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. The name of the ATLAS group or the names of its contributers may
* not be used to endorse or promote products derived from this
* software without specific written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
* TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE ATLAS GROUP OR ITS CONTRIBUTORS
* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*/
#ifdef TCPLX
static int ATL_potrf2(const int N, TYPE *A, const int lda)
{
int j, k;
static const TYPE one[2] = {ATL_rone, ATL_rzero};
static const TYPE none[2] = {ATL_rnone, ATL_rzero};
const size_t lda2 = lda+lda;
TYPE Ajj, *Ac=A, *An=A+lda2;
for (k=j=0; j != N; j++, k += 2)
{
Ajj = Ac[k] - llt_dot(k, Ac, 1, Ac, 1);
Ac[k+1] = ATL_rzero;
if (Ajj > ATL_rzero)
{
Ac[k] = Ajj = sqrt(Ajj);
if (j != N-1)
{
llt_scal(j, ATL_rnone, Ac+1, 2);
cblas_gemv(CblasColMajor, CblasTrans, j, N-j-1, none,
An, lda, Ac, 1, one, An+k, lda);
llt_scal(j, ATL_rnone, Ac+1, 2);
llt_rscal(N-j-1, ATL_rone/Ajj, An+k, lda);
Ac = An;
An += lda2;
}
}
else
{
Ac[k] = Ajj;
return(j+1);
}
}
return(0);
}
#else /* real version */
static int ATL_potrf2(const int N, TYPE *A, const int lda)
{
int j;
TYPE Ajj, *Ac=A, *An=A+lda;
for (j=0; j != N; j++)
{
Ajj = Ac[j] - cblas_dot(j, Ac, 1, Ac, 1);
if (Ajj > ATL_rzero)
{
Ac[j] = Ajj = sqrt(Ajj);
if (j != N-1)
{
cblas_gemv(CblasColMajor, CblasTrans, j, N-j-1, ATL_rnone,
An, lda, Ac, 1, ATL_rone, An+j, lda);
cblas_scal(N-j-1, ATL_rone/Ajj, An+j, lda);
Ac = An;
An += lda;
}
}
else
{
Ac[j] = Ajj;
return(j+1);
}
}
return(0);
}
static int ATL_potrf2(const int N, TYPE *A, const int lda)
{
int j, k;
static const TYPE one[2] = {ATL_rone, ATL_rzero};
static const TYPE none[2] = {ATL_rnone, ATL_rzero};
const size_t lda2 = lda+lda;
TYPE Ajj, *Ac=A, *An=A+lda2;
for (k=j=0; j != N; j++, k += 2)
{
Ajj = Ac[k] - llt_dot(k, Ac, 1, Ac, 1);
Ac[k+1] = ATL_rzero;
if (Ajj > ATL_rzero)
{
Ac[k] = Ajj = sqrt(Ajj);
if (j != N-1)
{
llt_scal(j, ATL_rnone, Ac+1, 2);
cblas_gemv(CblasColMajor, CblasTrans, j, N-j-1, none,
An, lda, Ac, 1, one, An+k, lda);
llt_scal(j, ATL_rnone, Ac+1, 2);
llt_rscal(N-j-1, ATL_rone/Ajj, An+k, lda);
Ac = An;
An += lda2;
}
}
else
{
Ac[k] = Ajj;
return(j+1);
}
}
return(0);
}
static int L2LU(const int M, const int N, TYPE *A, const int lda, int *ipiv)
/*
* Complex Level 2 based left-looking LU
*/
{
TYPE *Ac=A;
TYPE t0, tmp[2];
const TYPE one[2] = {ATL_rone, ATL_rzero}, none[2] = {ATL_rnone, ATL_rzero};
const int MN=Mmin(M,N), MN_1=MN-1, lda2=lda+lda;
int ip, ip2, j, j2, jn, jn2, iret=0;
for (j=0, j2=0, jn=1, jn2=2; j != MN; j=jn++, j2 += 2, jn2 += 2)
{
ipiv[j] = ip = j + cblas_iamax(M-j, Ac+j2, 1);
ip2 = ip + ip;
if (Ac[ip2] != ATL_rzero || Ac[ip2+1] != ATL_rzero)
{
Mjoin(PATL,cplxinvert)(1, Ac+ip2, 1, tmp, 1);
cblas_swap(N, A+j2, lda, A+ip2, lda);
cblas_scal(M-jn, tmp, Ac+jn2, 1);
if (j != MN_1)
{
Ac += lda2;
cblas_trsv(CblasColMajor, CblasLower, CblasNoTrans, CblasUnit, jn,
A, lda, Ac, 1);
cblas_gemv(CblasColMajor, CblasNoTrans, M-jn, jn, none,
A+jn2, lda, Ac, 1, one, Ac+jn2, 1);
}
}
else if (!iret) iret = jn;
}
return(iret);
}
static int L2LU(const int M, const int N, TYPE *A, const int lda, int *ipiv)
/*
* Level 2 based left-looking LU
*/
{
TYPE *Ac=A;
TYPE t0;
const int MN=Mmin(M,N), MN_1=MN-1;
int ip, j, jn, iret=0;
if (N == 2) return(LU2(M, A, lda, ipiv));
for (j=0, jn=1; j != MN; j=jn++)
{
ipiv[j] = ip = j + cblas_iamax(M-j, Ac+j, 1);
t0 = Ac[ip];
if (t0 != ATL_rzero)
{
MySwap(N, A+j, lda, ip-j);
cblas_scal(M-jn, ATL_rone/t0, Ac+jn, 1);
if (j != MN_1)
{
Ac += lda;
cblas_trsv(CblasColMajor, CblasLower, CblasNoTrans, CblasUnit, jn,
A, lda, Ac, 1);
cblas_gemv(CblasColMajor, CblasNoTrans, M-jn, jn, ATL_rnone,
A+jn, lda, Ac, 1, ATL_rone, Ac+jn, 1);
}
}
else if (!iret) iret = jn;
}
return(iret);
}
/*
* Automatically Tuned Linear Algebra Software v3.11.28
* (C) Copyright 1999 R. Clint Whaley
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions, and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. The name of the ATLAS group or the names of its contributers may
* not be used to endorse or promote products derived from this
* software without specific written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
* TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE ATLAS GROUP OR ITS CONTRIBUTORS
* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*/
static int ATL_potrf2(const int N, TYPE *A, const int lda)
{
#ifdef TREAL
TYPE Ajj, *Ac=A;
const int N_1 = N-1;
int j;
for (j=0; j != N_1; j++, Ac += lda)
{
Ajj = Ac[j] - cblas_dot(j, A+j, lda, A+j, lda);
if (Ajj > ATL_rzero)
{
Ac[j] = Ajj = sqrt(Ajj);
cblas_gemv(CblasColMajor, CblasNoTrans, N-j-1, j, ATL_rnone,
A+j+1, lda, A+j, lda, ATL_rone, Ac+j+1, 1);
cblas_scal(N-j-1, ATL_rone/Ajj, Ac+j+1, 1);
}
else
{
Ac[j] = Ajj;
return(j+1);
}
}
Ajj = Ac[j] - cblas_dot(j, A+j, lda, A+j, lda);
if (Ajj > ATL_rzero) Ac[j] = Ajj = sqrt(Ajj);
else
{
Ac[j] = Ajj;
return(N);
}
#else
TYPE Ajj, *Ac=A;
TYPE one[2] = {ATL_rone, ATL_rzero};
TYPE none[2] = {ATL_rnone, ATL_rzero};
const int N_1 = N-1, lda2 = lda<<1;
int j, j2;
for (j2=j=0; j != N_1; j++, j2 += 2, Ac += lda2)
{
Ajj = Ac[j2];
cblas_dotc_sub(j, A+j2, lda, A+j2, lda, Ac+j2);
Ajj -= Ac[j2];
if (Ajj > ATL_rzero)
{
Ac[j2] = Ajj = sqrt(Ajj);
llt_scal(j, ATL_rnone, A+j2+1, lda2);
cblas_gemv(CblasColMajor, CblasNoTrans, N-j-1, j, none,
A+j2+2, lda, A+j2, lda, one, Ac+j2+2, 1);
llt_scal(j, ATL_rnone, A+j2+1, lda2);
llt_scal((N-j-1)<<1, ATL_rone/Ajj, Ac+j2+2, 1);
}
else
{
Ac[j2] = Ajj;
return(j+1);
}
}
Ajj = Ac[j2];
cblas_dotc_sub(j, A+j2, lda, A+j2, lda, Ac+j2);
Ajj -= Ac[j2];
if (Ajj > ATL_rzero) Ac[j2] = sqrt(Ajj);
else
{
Ac[j2] = Ajj;
return(N);
}
#endif
return(0);
}
