/**
Purpose
-------
ZUNGTR generates a complex unitary matrix Q which is defined as the
product of n-1 elementary reflectors of order N, as returned by
ZHETRD:
if UPLO = MagmaUpper, Q = H(n-1) . . . H(2) H(1),
if UPLO = MagmaLower, Q = H(1) H(2) . . . H(n-1).
Arguments
---------
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A contains elementary reflectors
from ZHETRD;
- = MagmaLower: Lower triangle of A contains elementary reflectors
from ZHETRD.
@param[in]
n INTEGER
The order of the matrix Q. N >= 0.
@param[in,out]
A COMPLEX_16 array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by ZHETRD.
On exit, the N-by-N unitary matrix Q.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= N.
@param[in]
tau COMPLEX_16 array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZHETRD.
@param[out]
work (workspace) COMPLEX_16 array, dimension (LWORK)
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= N-1.
For optimum performance LWORK >= N*NB, where NB is
the optimal blocksize.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[in]
dT COMPLEX_16 array on the GPU device.
DT contains the T matrices used in blocking the elementary
reflectors H(i) as returned by magma_zhetrd.
@param[in]
nb INTEGER
This is the block size used in ZHETRD, and correspondingly
the size of the T matrices, used in the factorization, and
stored in DT.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_zheev_comp
********************************************************************/
extern "C" magma_int_t
magma_zungtr(
magma_uplo_t uplo, magma_int_t n,
magmaDoubleComplex *A, magma_int_t lda,
magmaDoubleComplex *tau,
magmaDoubleComplex *work, magma_int_t lwork,
magmaDoubleComplex *dT, magma_int_t nb,
magma_int_t *info)
{
#define A(i,j) (A + (j)*lda+ (i))
magma_int_t i__1;
magma_int_t i, j;
magma_int_t iinfo;
magma_int_t upper, lwkopt, lquery;
*info = 0;
lquery = (lwork == -1);
upper = (uplo == MagmaUpper);
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,n)) {
*info = -4;
} else /* if (complicated condition) */ {
/* Computing MAX */
if (lwork < max(1, n-1) && ! lquery) {
*info = -7;
}
}
lwkopt = max(1, n) * nb;
if (*info == 0) {
work[0] = magma_zmake_lwork( lwkopt );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
work[0] = MAGMA_Z_ONE;
return *info;
}
if (upper) {
/* Q was determined by a call to ZHETRD with UPLO = MagmaUpper
Shift the vectors which define the elementary reflectors one
column to the left, and set the last row and column of Q to
those of the unit matrix */
for (j = 0; j < n-1; ++j) {
for (i = 0; i < j-1; ++i)
*A(i, j) = *A(i, j + 1);
*A(n-1, j) = MAGMA_Z_ZERO;
}
for (i = 0; i < n-1; ++i) {
*A(i, n-1) = MAGMA_Z_ZERO;
}
*A(n-1, n-1) = MAGMA_Z_ONE;
/* Generate Q(1:n-1,1:n-1) */
i__1 = n - 1;
lapackf77_zungql(&i__1, &i__1, &i__1, A(0,0), &lda, tau, work,
&lwork, &iinfo);
} else {
/* Q was determined by a call to ZHETRD with UPLO = MagmaLower.
Shift the vectors which define the elementary reflectors one
column to the right, and set the first row and column of Q to
those of the unit matrix */
for (j = n-1; j > 0; --j) {
*A(0, j) = MAGMA_Z_ZERO;
for (i = j; i < n-1; ++i)
*A(i, j) = *A(i, j - 1);
}
*A(0, 0) = MAGMA_Z_ONE;
for (i = 1; i < n-1; ++i)
*A(i, 0) = MAGMA_Z_ZERO;
if (n > 1) {
/* Generate Q(2:n,2:n) */
magma_zungqr(n-1, n-1, n-1, A(1, 1), lda, tau, dT, nb, &iinfo);
}
}
work[0] = magma_zmake_lwork( lwkopt );
return *info;
} /* magma_zungtr */
/**
Purpose
-------
ZUNGHR generates a COMPLEX_16 unitary matrix Q which is defined as the
product of IHI-ILO elementary reflectors of order N, as returned by
ZGEHRD:
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Arguments
---------
@param[in]
n INTEGER
The order of the matrix Q. N >= 0.
@param[in]
ilo INTEGER
@param[in]
ihi INTEGER
ILO and IHI must have the same values as in the previous call
of ZGEHRD. Q is equal to the unit matrix except in the
submatrix Q(ilo+1:ihi,ilo+1:ihi).
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
@param[in,out]
A COMPLEX_16 array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by ZGEHRD.
On exit, the N-by-N unitary matrix Q.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in]
tau COMPLEX_16 array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEHRD.
@param[in]
dT COMPLEX_16 array on the GPU device.
DT contains the T matrices used in blocking the elementary
reflectors H(i), e.g., this can be the 9th argument of
magma_zgehrd.
@param[in]
nb INTEGER
This is the block size used in ZGEHRD, and correspondingly
the size of the T matrices, used in the factorization, and
stored in DT.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_zgeev_comp
********************************************************************/
extern "C" magma_int_t
magma_zunghr(magma_int_t n, magma_int_t ilo, magma_int_t ihi,
magmaDoubleComplex *A, magma_int_t lda,
magmaDoubleComplex *tau,
magmaDoubleComplex *dT, magma_int_t nb,
magma_int_t *info)
{
#define A(i,j) (A + (j)*lda+ (i))
magma_int_t i, j, nh, iinfo;
*info = 0;
nh = ihi - ilo;
if (n < 0)
*info = -1;
else if (ilo < 1 || ilo > max(1,n))
*info = -2;
else if (ihi < min(ilo,n) || ihi > n)
*info = -3;
else if (lda < max(1,n))
*info = -5;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (n == 0)
return *info;
/* Shift the vectors which define the elementary reflectors one
column to the right, and set the first ilo and the last n-ihi
rows and columns to those of the unit matrix */
for (j = ihi-1; j >= ilo; --j) {
for (i = 0; i < j; ++i)
*A(i, j) = MAGMA_Z_ZERO;
for (i = j+1; i < ihi; ++i)
*A(i, j) = *A(i, j - 1);
for (i = ihi; i < n; ++i)
*A(i, j) = MAGMA_Z_ZERO;
}
for (j = 0; j < ilo; ++j) {
for (i = 0; i < n; ++i)
*A(i, j) = MAGMA_Z_ZERO;
*A(j, j) = MAGMA_Z_ONE;
}
for (j = ihi; j < n; ++j) {
for (i = 0; i < n; ++i)
*A(i, j) = MAGMA_Z_ZERO;
*A(j, j) = MAGMA_Z_ONE;
}
if (nh > 0) {
/* Generate Q(ilo+1:ihi,ilo+1:ihi) */
magma_zungqr(nh, nh, nh,
A(ilo, ilo), lda,
tau+ilo-1, dT, nb, &iinfo);
}
return *info;
} /* magma_zunghr */
extern "C" magma_int_t
magma_zunghr(magma_int_t n, magma_int_t ilo, magma_int_t ihi,
cuDoubleComplex *a, magma_int_t lda,
cuDoubleComplex *tau,
cuDoubleComplex *dT, magma_int_t nb,
magma_int_t *info)
{
/* -- MAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
November 2012
Purpose
=======
ZUNGHR generates a COMPLEX_16 unitary matrix Q which is defined as the
product of IHI-ILO elementary reflectors of order N, as returned by
ZGEHRD:
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Arguments
=========
N (input) INTEGER
The order of the matrix Q. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER
ILO and IHI must have the same values as in the previous call
of ZGEHRD. Q is equal to the unit matrix except in the
submatrix Q(ilo+1:ihi,ilo+1:ihi).
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
A (input/output) COMPLEX_16 array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by ZGEHRD.
On exit, the N-by-N unitary matrix Q.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TAU (input) COMPLEX_16 array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEHRD.
DT (input) COMPLEX_16 array on the GPU device.
DT contains the T matrices used in blocking the elementary
reflectors H(i), e.g., this can be the 9th argument of
magma_zgehrd.
NB (input) INTEGER
This is the block size used in ZGEHRD, and correspondingly
the size of the T matrices, used in the factorization, and
stored in DT.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
===================================================================== */
#define a_ref(i,j) (a + (j)*lda+ (i))
magma_int_t i, j, nh, iinfo;
*info = 0;
nh = ihi - ilo;
if (n < 0)
*info = -1;
else if (ilo < 1 || ilo > max(1,n))
*info = -2;
else if (ihi < min(ilo,n) || ihi > n)
*info = -3;
else if (lda < max(1,n))
*info = -5;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (n == 0)
return *info;
/* Shift the vectors which define the elementary reflectors one
column to the right, and set the first ilo and the last n-ihi
rows and columns to those of the unit matrix */
for (j = ihi-1; j >= ilo; --j) {
for (i = 0; i < j; ++i)
*a_ref(i, j) = MAGMA_Z_ZERO;
for (i = j+1; i < ihi; ++i)
*a_ref(i, j) = *a_ref(i, j - 1);
for (i = ihi; i < n; ++i)
*a_ref(i, j) = MAGMA_Z_ZERO;
}
for (j = 0; j < ilo; ++j) {
for (i = 0; i < n; ++i)
*a_ref(i, j) = MAGMA_Z_ZERO;
*a_ref(j, j) = MAGMA_Z_ONE;
}
for (j = ihi; j < n; ++j) {
for (i = 0; i < n; ++i)
*a_ref(i, j) = MAGMA_Z_ZERO;
*a_ref(j, j) = MAGMA_Z_ONE;
}
if (nh > 0)
/* Generate Q(ilo+1:ihi,ilo+1:ihi) */
magma_zungqr(nh, nh, nh,
a_ref(ilo, ilo), lda,
tau+ilo-1, dT, nb, &iinfo);
return *info;
} /* magma_zunghr */
extern "C" magma_int_t
magma_zungtr(char uplo, magma_int_t n, magmaDoubleComplex *a,
magma_int_t lda, magmaDoubleComplex *tau,
magmaDoubleComplex *work, magma_int_t lwork,
magmaDoubleComplex *dT, magma_int_t nb,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
ZUNGTR generates a complex unitary matrix Q which is defined as the
product of n-1 elementary reflectors of order N, as returned by
ZHETRD:
if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A contains elementary reflectors
from ZHETRD;
= 'L': Lower triangle of A contains elementary reflectors
from ZHETRD.
N (input) INTEGER
The order of the matrix Q. N >= 0.
A (input/output) COMPLEX_16 array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by ZHETRD.
On exit, the N-by-N unitary matrix Q.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= N.
TAU (input) COMPLEX_16 array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZHETRD.
WORK (workspace/output) COMPLEX_16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= N-1.
For optimum performance LWORK >= N*NB, where NB is
the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
DT (input) COMPLEX_16 array on the GPU device.
DT contains the T matrices used in blocking the elementary
reflectors H(i) as returned by magma_zhetrd.
NB (input) INTEGER
This is the block size used in ZHETRD, and correspondingly
the size of the T matrices, used in the factorization, and
stored in DT.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
===================================================================== */
#define a_ref(i,j) ( a + (j)*lda+ (i))
char uplo_[2] = {uplo, 0};
magma_int_t i__1;
magma_int_t i, j;
magma_int_t iinfo;
magma_int_t upper, lwkopt, lquery;
*info = 0;
lquery = lwork == -1;
upper = lapackf77_lsame(uplo_, "U");
if (! upper && ! lapackf77_lsame(uplo_, "L")) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,n)) {
*info = -4;
} else /* if(complicated condition) */ {
/* Computing MAX */
if (lwork < max(1, n-1) && ! lquery) {
*info = -7;
}
}
lwkopt = max(1, n) * nb;
if (*info == 0) {
MAGMA_Z_SET2REAL( work[0], lwkopt);
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
work[0] = MAGMA_Z_ONE;
return *info;
}
if (upper) {
/* Q was determined by a call to ZHETRD with UPLO = 'U'
Shift the vectors which define the elementary reflectors one
column to the left, and set the last row and column of Q to
those of the unit matrix */
for (j = 0; j < n-1; ++j) {
for (i = 0; i < j-1; ++i)
*a_ref(i, j) = *a_ref(i, j + 1);
*a_ref(n-1, j) = MAGMA_Z_ZERO;
}
for (i = 0; i < n-1; ++i) {
*a_ref(i, n-1) = MAGMA_Z_ZERO;
}
*a_ref(n-1, n-1) = MAGMA_Z_ONE;
/* Generate Q(1:n-1,1:n-1) */
i__1 = n - 1;
lapackf77_zungql(&i__1, &i__1, &i__1, a_ref(0,0), &lda, tau, work,
&lwork, &iinfo);
} else {
/* Q was determined by a call to ZHETRD with UPLO = 'L'.
Shift the vectors which define the elementary reflectors one
column to the right, and set the first row and column of Q to
those of the unit matrix */
for (j = n-1; j > 0; --j) {
*a_ref(0, j) = MAGMA_Z_ZERO;
for (i = j; i < n-1; ++i)
*a_ref(i, j) = *a_ref(i, j - 1);
}
*a_ref(0, 0) = MAGMA_Z_ONE;
for (i = 1; i < n-1; ++i)
*a_ref(i, 0) = MAGMA_Z_ZERO;
if (n > 1) {
/* Generate Q(2:n,2:n) */
magma_zungqr(n-1, n-1, n-1, a_ref(1, 1), lda, tau, dT, nb, &iinfo);
}
}
MAGMA_Z_SET2REAL( work[0], lwkopt);
return *info;
} /* magma_zungtr */