/**
Purpose
-------
CLATRD2 reduces NB rows and columns of a complex Hermitian matrix A to
Hermitian tridiagonal form by an orthogonal similarity
transformation Q' * A * Q, and returns the matrices V and W which are
needed to apply the transformation to the unreduced part of A.
If UPLO = MagmaUpper, CLATRD reduces the last NB rows and columns of a
matrix, of which the upper triangle is supplied;
if UPLO = MagmaLower, CLATRD reduces the first NB rows and columns of a
matrix, of which the lower triangle is supplied.
This is an auxiliary routine called by CHETRD2_GPU. It uses an
accelerated HEMV that needs extra memory.
Arguments
---------
@param[in]
uplo magma_uplo_t
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
- = MagmaUpper: Upper triangular
- = MagmaLower: Lower triangular
@param[in]
n INTEGER
The order of the matrix A.
@param[in]
nb INTEGER
The number of rows and columns to be reduced.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading
n-by-n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = MagmaLower, the
leading n-by-n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit:
- if UPLO = MagmaUpper, the last NB columns have been reduced to
tridiagonal form, with the diagonal elements overwriting
the diagonal elements of A; the elements above the diagonal
with the array TAU, represent the orthogonal matrix Q as a
product of elementary reflectors;
- if UPLO = MagmaLower, the first NB columns have been reduced to
tridiagonal form, with the diagonal elements overwriting
the diagonal elements of A; the elements below the diagonal
with the array TAU, represent the orthogonal matrix Q as a
product of elementary reflectors.
See Further Details.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= (1,N).
@param[out]
e COMPLEX array, dimension (N-1)
If UPLO = MagmaUpper, E(n-nb:n-1) contains the superdiagonal
elements of the last NB columns of the reduced matrix;
if UPLO = MagmaLower, E(1:nb) contains the subdiagonal elements of
the first NB columns of the reduced matrix.
@param[out]
tau COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors, stored in
TAU(n-nb:n-1) if UPLO = MagmaUpper, and in TAU(1:nb) if UPLO = MagmaLower.
See Further Details.
@param[out]
W COMPLEX array, dimension (LDW,NB)
The n-by-nb matrix W required to update the unreduced part
of A.
@param[in]
ldw INTEGER
The leading dimension of the array W. LDW >= max(1,N).
Further Details
---------------
If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary
reflectors
Q = H(n) H(n-1) . . . H(n-nb+1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
and tau in TAU(i-1).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(nb).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
and tau in TAU(i).
The elements of the vectors v together form the n-by-nb matrix V
which is needed, with W, to apply the transformation to the unreduced
part of the matrix, using a Hermitian rank-2k update of the form:
A := A - V*W' - W*V'.
The contents of A on exit are illustrated by the following examples
with n = 5 and nb = 2:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( a a a v4 v5 ) ( d )
( a a v4 v5 ) ( 1 d )
( a 1 v5 ) ( v1 1 a )
( d 1 ) ( v1 v2 a a )
( d ) ( v1 v2 a a a )
where d denotes a diagonal element of the reduced matrix, a denotes
an element of the original matrix that is unchanged, and vi denotes
an element of the vector defining H(i).
@ingroup magma_cheev_aux
********************************************************************/
extern "C" magma_int_t
magma_clatrd2(magma_uplo_t uplo, magma_int_t n, magma_int_t nb,
magmaFloatComplex *A, magma_int_t lda,
float *e, magmaFloatComplex *tau,
magmaFloatComplex *W, magma_int_t ldw,
magmaFloatComplex *dA, magma_int_t ldda,
magmaFloatComplex *dW, magma_int_t lddw,
magmaFloatComplex *dwork, magma_int_t ldwork)
{
#define A(i, j) (A + (j)*lda + (i))
#define W(i, j) (W + (j)*ldw + (i))
#define dA(i, j) (dA + (j)*ldda + (i))
#define dW(i, j) (dW + (j)*lddw + (i))
magma_int_t i;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_zero = MAGMA_C_ZERO;
magmaFloatComplex value = MAGMA_C_ZERO;
magma_int_t ione = 1;
magma_int_t i_n, i_1, iw;
magmaFloatComplex alpha;
magmaFloatComplex *f;
if (n <= 0) {
return 0;
}
magma_queue_t stream;
magma_queue_create( &stream );
magma_cmalloc_cpu( &f, n );
assert( f != NULL ); // TODO return error, or allocate outside clatrd
if (uplo == MagmaUpper) {
/* Reduce last NB columns of upper triangle */
for (i = n-1; i >= n - nb; --i) {
i_1 = i + 1;
i_n = n - i - 1;
iw = i - n + nb;
if (i < n-1) {
/* Update A(1:i,i) */
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv(&i_n, W(i, iw+1), &ldw);
#endif
blasf77_cgemv("No transpose", &i_1, &i_n, &c_neg_one, A(0, i+1), &lda,
W(i, iw+1), &ldw, &c_one, A(0, i), &ione);
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv(&i_n, W(i, iw+1), &ldw);
lapackf77_clacgv(&i_n, A(i, i+1), &ldw);
#endif
blasf77_cgemv("No transpose", &i_1, &i_n, &c_neg_one, W(0, iw+1), &ldw,
A(i, i+1), &lda, &c_one, A(0, i), &ione);
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv(&i_n, A(i, i+1), &ldw);
#endif
}
if (i > 0) {
/* Generate elementary reflector H(i) to annihilate A(1:i-2,i) */
alpha = *A(i-1, i);
lapackf77_clarfg(&i, &alpha, A(0, i), &ione, &tau[i - 1]);
e[i-1] = MAGMA_C_REAL( alpha );
*A(i-1,i) = MAGMA_C_MAKE( 1, 0 );
/* Compute W(1:i-1,i) */
// 1. Send the block reflector A(0:n-i-1,i) to the GPU
magma_csetvector( i, A(0, i), 1, dA(0, i), 1 );
//#if (GPUSHMEM < 200)
//magma_chemv(MagmaUpper, i, c_one, dA(0, 0), ldda,
// dA(0, i), ione, c_zero, dW(0, iw), ione);
//#else
magmablas_chemv_work(MagmaUpper, i, c_one, dA(0, 0), ldda,
dA(0, i), ione, c_zero, dW(0, iw), ione,
dwork, ldwork);
//#endif
// 2. Start putting the result back (asynchronously)
magma_cgetmatrix_async( i, 1,
dW(0, iw), lddw,
W(0, iw) /*test*/, ldw, stream );
if (i < n-1) {
blasf77_cgemv(MagmaConjTransStr, &i, &i_n, &c_one, W(0, iw+1), &ldw,
A(0, i), &ione, &c_zero, W(i+1, iw), &ione);
}
// 3. Here is where we need it // TODO find the right place
magma_queue_sync( stream );
if (i < n-1) {
blasf77_cgemv("No transpose", &i, &i_n, &c_neg_one, A(0, i+1), &lda,
W(i+1, iw), &ione, &c_one, W(0, iw), &ione);
blasf77_cgemv(MagmaConjTransStr, &i, &i_n, &c_one, A(0, i+1), &lda,
A(0, i), &ione, &c_zero, W(i+1, iw), &ione);
blasf77_cgemv("No transpose", &i, &i_n, &c_neg_one, W(0, iw+1), &ldw,
W(i+1, iw), &ione, &c_one, W(0, iw), &ione);
}
blasf77_cscal(&i, &tau[i - 1], W(0, iw), &ione);
#if defined(PRECISION_z) || defined(PRECISION_c)
cblas_cdotc_sub( i, W(0,iw), ione, A(0,i), ione, &value );
#else
value = cblas_cdotc( i, W(0,iw), ione, A(0,i), ione );
#endif
alpha = tau[i - 1] * -0.5f * value;
blasf77_caxpy(&i, &alpha, A(0, i), &ione,
W(0, iw), &ione);
}
}
}
else {
/* Reduce first NB columns of lower triangle */
for (i = 0; i < nb; ++i) {
/* Update A(i:n,i) */
i_n = n - i;
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv(&i, W(i, 0), &ldw);
#endif
blasf77_cgemv("No transpose", &i_n, &i, &c_neg_one, A(i, 0), &lda,
W(i, 0), &ldw, &c_one, A(i, i), &ione);
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv(&i, W(i, 0), &ldw);
lapackf77_clacgv(&i, A(i, 0), &lda);
#endif
blasf77_cgemv("No transpose", &i_n, &i, &c_neg_one, W(i, 0), &ldw,
A(i, 0), &lda, &c_one, A(i, i), &ione);
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv(&i, A(i, 0), &lda);
#endif
if (i < n-1) {
/* Generate elementary reflector H(i) to annihilate A(i+2:n,i) */
i_n = n - i - 1;
alpha = *A(i+1, i);
lapackf77_clarfg(&i_n, &alpha, A(min(i+2,n-1), i), &ione, &tau[i]);
e[i] = MAGMA_C_REAL( alpha );
*A(i+1,i) = MAGMA_C_MAKE( 1, 0 );
/* Compute W(i+1:n,i) */
// 1. Send the block reflector A(i+1:n,i) to the GPU
magma_csetvector( i_n, A(i+1, i), 1, dA(i+1, i), 1 );
//#if (GPUSHMEM < 200)
//magma_chemv(MagmaLower, i_n, c_one, dA(i+1, i+1), ldda, dA(i+1, i), ione, c_zero,
// dW(i+1, i), ione);
//#else
magmablas_chemv_work(MagmaLower, i_n, c_one, dA(i+1, i+1), ldda, dA(i+1, i), ione, c_zero,
dW(i+1, i), ione,
dwork, ldwork);
//#endif
// 2. Start putting the result back (asynchronously)
magma_cgetmatrix_async( i_n, 1,
dW(i+1, i), lddw,
W(i+1, i), ldw, stream );
blasf77_cgemv(MagmaConjTransStr, &i_n, &i, &c_one, W(i+1, 0), &ldw,
A(i+1, i), &ione, &c_zero, W(0, i), &ione);
blasf77_cgemv("No transpose", &i_n, &i, &c_neg_one, A(i+1, 0), &lda,
W(0, i), &ione, &c_zero, f, &ione);
blasf77_cgemv(MagmaConjTransStr, &i_n, &i, &c_one, A(i+1, 0), &lda,
A(i+1, i), &ione, &c_zero, W(0, i), &ione);
// 3. Here is where we need it
magma_queue_sync( stream );
if (i != 0)
blasf77_caxpy(&i_n, &c_one, f, &ione, W(i+1, i), &ione);
blasf77_cgemv("No transpose", &i_n, &i, &c_neg_one, W(i+1, 0), &ldw,
W(0, i), &ione, &c_one, W(i+1, i), &ione);
blasf77_cscal(&i_n, &tau[i], W(i+1,i), &ione);
#if defined(PRECISION_z) || defined(PRECISION_c)
cblas_cdotc_sub( i_n, W(i+1,i), ione, A(i+1,i), ione, &value );
#else
value = cblas_cdotc( i_n, W(i+1,i), ione, A(i+1,i), ione );
#endif
alpha = tau[i] * -0.5f * value;
blasf77_caxpy(&i_n, &alpha, A(i+1, i), &ione, W(i+1,i), &ione);
}
}
}
magma_free_cpu(f);
magma_queue_destroy( stream );
return 0;
} /* magma_clatrd */
/**
Purpose
-------
CLATRD2 reduces NB rows and columns of a complex Hermitian matrix A to
Hermitian tridiagonal form by an orthogonal similarity
transformation Q' * A * Q, and returns the matrices V and W which are
needed to apply the transformation to the unreduced part of A.
If UPLO = MagmaUpper, CLATRD reduces the last NB rows and columns of a
matrix, of which the upper triangle is supplied;
if UPLO = MagmaLower, CLATRD reduces the first NB rows and columns of a
matrix, of which the lower triangle is supplied.
This is an auxiliary routine called by CHETRD2_GPU. It uses an
accelerated HEMV that needs extra memory.
Arguments
---------
@param[in]
uplo magma_uplo_t
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
- = MagmaUpper: Upper triangular
- = MagmaLower: Lower triangular
@param[in]
n INTEGER
The order of the matrix A.
@param[in]
nb INTEGER
The number of rows and columns to be reduced.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading
n-by-n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = MagmaLower, the
leading n-by-n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit:
- if UPLO = MagmaUpper, the last NB columns have been reduced to
tridiagonal form, with the diagonal elements overwriting
the diagonal elements of A; the elements above the diagonal
with the array TAU, represent the orthogonal matrix Q as a
product of elementary reflectors;
- if UPLO = MagmaLower, the first NB columns have been reduced to
tridiagonal form, with the diagonal elements overwriting
the diagonal elements of A; the elements below the diagonal
with the array TAU, represent the orthogonal matrix Q as a
product of elementary reflectors.
See Further Details.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= (1,N).
@param[out]
e COMPLEX array, dimension (N-1)
If UPLO = MagmaUpper, E(n-nb:n-1) contains the superdiagonal
elements of the last NB columns of the reduced matrix;
if UPLO = MagmaLower, E(1:nb) contains the subdiagonal elements of
the first NB columns of the reduced matrix.
@param[out]
tau COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors, stored in
TAU(n-nb:n-1) if UPLO = MagmaUpper, and in TAU(1:nb) if UPLO = MagmaLower.
See Further Details.
@param[out]
W COMPLEX array, dimension (LDW,NB)
The n-by-nb matrix W required to update the unreduced part
of A.
@param[in]
ldw INTEGER
The leading dimension of the array W. LDW >= max(1,N).
@param
dA TODO: dimension (ldda, n) ??
@param
ldda TODO: ldda >= n ??
@param
dW TODO: dimension (lddw, 2*nb) ??
@param
lddw TODO: lddw >= n ??
@param
dwork TODO: dimension (ldwork) ??
@param
ldwork TODO: ldwork >= ceil(n/64)*ldda ??
@param[in]
queue magma_queue_t
Queue to execute in.
Further Details
---------------
If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary
reflectors
Q = H(n) H(n-1) . . . H(n-nb+1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
and tau in TAU(i-1).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(nb).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
and tau in TAU(i).
The elements of the vectors v together form the n-by-nb matrix V
which is needed, with W, to apply the transformation to the unreduced
part of the matrix, using a Hermitian rank-2k update of the form:
A := A - V*W' - W*V'.
The contents of A on exit are illustrated by the following examples
with n = 5 and nb = 2:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( a a a v4 v5 ) ( d )
( a a v4 v5 ) ( 1 d )
( a 1 v5 ) ( v1 1 a )
( d 1 ) ( v1 v2 a a )
( d ) ( v1 v2 a a a )
where d denotes a diagonal element of the reduced matrix, a denotes
an element of the original matrix that is unchanged, and vi denotes
an element of the vector defining H(i).
@ingroup magma_cheev_aux
********************************************************************/
extern "C" magma_int_t
magma_clatrd2(
magma_uplo_t uplo, magma_int_t n, magma_int_t nb,
magmaFloatComplex *A, magma_int_t lda,
float *e, magmaFloatComplex *tau,
magmaFloatComplex *W, magma_int_t ldw,
magmaFloatComplex *work, magma_int_t lwork,
magmaFloatComplex_ptr dA, magma_int_t ldda,
magmaFloatComplex_ptr dW, magma_int_t lddw,
magmaFloatComplex_ptr dwork, magma_int_t ldwork,
magma_queue_t queue )
{
#define A(i_, j_) (A + (i_) + (j_)*lda)
#define W(i_, j_) (W + (i_) + (j_)*ldw)
#define dA(i_, j_) (dA + (i_) + (j_)*ldda)
#define dW(i_, j_) (dW + (i_) + (j_)*lddw)
/* Constants */
const magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
const magmaFloatComplex c_one = MAGMA_C_ONE;
const magmaFloatComplex c_zero = MAGMA_C_ZERO;
const magma_int_t ione = 1;
/* Local variables */
magmaFloatComplex alpha, value;
magma_int_t i, i_n, i_1, iw;
/* Check arguments */
magma_int_t info = 0;
if ( uplo != MagmaLower && uplo != MagmaUpper ) {
info = -1;
} else if ( n < 0 ) {
info = -2;
} else if ( nb < 1 ) {
info = -3;
} else if ( lda < max(1,n) ) {
info = -5;
} else if ( ldw < max(1,n) ) {
info = -9;
} else if ( lwork < max(1,n) ) {
info = -11;
} else if ( ldda < max(1,n) ) {
info = -13;
} else if ( lddw < max(1,n) ) {
info = -15;
} else if ( ldwork < ldda*magma_ceildiv(n,64) ) {
info = -17;
}
if (info != 0) {
magma_xerbla( __func__, -(info) );
return info;
}
/* Quick return if possible */
if (n == 0) {
return info;
}
if (uplo == MagmaUpper) {
/* Reduce last NB columns of upper triangle */
for (i = n-1; i >= n - nb; --i) {
i_1 = i + 1;
i_n = n - i - 1;
iw = i - n + nb;
if (i < n-1) {
/* Update A(1:i,i) */
#ifdef COMPLEX
lapackf77_clacgv( &i_n, W(i, iw+1), &ldw );
#endif
blasf77_cgemv( "No transpose", &i_1, &i_n, &c_neg_one, A(0, i+1), &lda,
W(i, iw+1), &ldw, &c_one, A(0, i), &ione );
#ifdef COMPLEX
lapackf77_clacgv( &i_n, W(i, iw+1), &ldw );
lapackf77_clacgv( &i_n, A(i, i+1), &lda );
#endif
blasf77_cgemv( "No transpose", &i_1, &i_n, &c_neg_one, W(0, iw+1), &ldw,
A(i, i+1), &lda, &c_one, A(0, i), &ione );
#ifdef COMPLEX
lapackf77_clacgv( &i_n, A(i, i+1), &lda );
#endif
}
if (i > 0) {
/* Generate elementary reflector H(i) to annihilate A(1:i-2,i) */
alpha = *A(i-1, i);
lapackf77_clarfg( &i, &alpha, A(0, i), &ione, &tau[i - 1] );
e[i-1] = MAGMA_C_REAL( alpha );
*A(i-1,i) = MAGMA_C_ONE;
/* Compute W(1:i-1,i) */
// 1. Send the block reflector A(0:n-i-1,i) to the GPU
magma_csetvector_async( i, A(0, i), 1, dA(0, i), 1, queue );
magmablas_chemv_work( MagmaUpper, i, c_one, dA(0, 0), ldda,
dA(0, i), ione, c_zero, dW(0, iw), ione,
dwork, ldwork, queue );
// 2. Start getting the result back (asynchronously)
magma_cgetmatrix_async( i, 1,
dW(0, iw), lddw,
W(0, iw), ldw, queue );
if (i < n-1) {
blasf77_cgemv( MagmaConjTransStr, &i, &i_n, &c_one, W(0, iw+1), &ldw,
A(0, i), &ione, &c_zero, W(i+1, iw), &ione );
}
// 3. Here we need chemv result W(0, iw)
magma_queue_sync( queue );
if (i < n-1) {
blasf77_cgemv( "No transpose", &i, &i_n, &c_neg_one, A(0, i+1), &lda,
W(i+1, iw), &ione, &c_one, W(0, iw), &ione );
blasf77_cgemv( MagmaConjTransStr, &i, &i_n, &c_one, A(0, i+1), &lda,
A(0, i), &ione, &c_zero, W(i+1, iw), &ione );
blasf77_cgemv( "No transpose", &i, &i_n, &c_neg_one, W(0, iw+1), &ldw,
W(i+1, iw), &ione, &c_one, W(0, iw), &ione );
}
blasf77_cscal( &i, &tau[i - 1], W(0, iw), &ione );
value = magma_cblas_cdotc( i, W(0,iw), ione, A(0,i), ione );
alpha = tau[i - 1] * -0.5f * value;
blasf77_caxpy( &i, &alpha, A(0, i), &ione,
W(0, iw), &ione );
}
}
}
else {
/* Reduce first NB columns of lower triangle */
for (i = 0; i < nb; ++i) {
/* Update A(i:n,i) */
i_n = n - i;
#ifdef COMPLEX
lapackf77_clacgv( &i, W(i, 0), &ldw );
#endif
blasf77_cgemv( "No transpose", &i_n, &i, &c_neg_one, A(i, 0), &lda,
W(i, 0), &ldw, &c_one, A(i, i), &ione );
#ifdef COMPLEX
lapackf77_clacgv( &i, W(i, 0), &ldw );
lapackf77_clacgv( &i, A(i, 0), &lda );
#endif
blasf77_cgemv( "No transpose", &i_n, &i, &c_neg_one, W(i, 0), &ldw,
A(i, 0), &lda, &c_one, A(i, i), &ione );
#ifdef COMPLEX
lapackf77_clacgv( &i, A(i, 0), &lda );
#endif
if (i < n-1) {
/* Generate elementary reflector H(i) to annihilate A(i+2:n,i) */
i_n = n - i - 1;
alpha = *A(i+1, i);
lapackf77_clarfg( &i_n, &alpha, A(min(i+2,n-1), i), &ione, &tau[i] );
e[i] = MAGMA_C_REAL( alpha );
*A(i+1,i) = MAGMA_C_ONE;
/* Compute W(i+1:n,i) */
// 1. Send the block reflector A(i+1:n,i) to the GPU
magma_csetvector_async( i_n, A(i+1, i), 1, dA(i+1, i), 1, queue );
magmablas_chemv_work( MagmaLower, i_n, c_one, dA(i+1, i+1), ldda,
dA(i+1, i), ione, c_zero, dW(i+1, i), ione,
dwork, ldwork, queue );
// 2. Start getting the result back (asynchronously)
magma_cgetmatrix_async( i_n, 1,
dW(i+1, i), lddw,
W(i+1, i), ldw, queue );
blasf77_cgemv( MagmaConjTransStr, &i_n, &i, &c_one, W(i+1, 0), &ldw,
A(i+1, i), &ione, &c_zero, W(0, i), &ione );
blasf77_cgemv( "No transpose", &i_n, &i, &c_neg_one, A(i+1, 0), &lda,
W(0, i), &ione, &c_zero, work, &ione );
blasf77_cgemv( MagmaConjTransStr, &i_n, &i, &c_one, A(i+1, 0), &lda,
A(i+1, i), &ione, &c_zero, W(0, i), &ione );
// 3. Here we need chemv result W(i+1, i)
magma_queue_sync( queue );
if (i != 0)
blasf77_caxpy( &i_n, &c_one, work, &ione, W(i+1, i), &ione );
blasf77_cgemv( "No transpose", &i_n, &i, &c_neg_one, W(i+1, 0), &ldw,
W(0, i), &ione, &c_one, W(i+1, i), &ione );
blasf77_cscal( &i_n, &tau[i], W(i+1,i), &ione );
value = magma_cblas_cdotc( i_n, W(i+1,i), ione, A(i+1,i), ione );
alpha = tau[i] * -0.5f * value;
blasf77_caxpy( &i_n, &alpha, A(i+1, i), &ione, W(i+1,i), &ione );
}
}
}
return info;
} /* magma_clatrd */
