lahr2#

Functions

void slahr2(
    const INT  n,
    const INT  k,
    const INT  nb,
          f32* A,
    const INT  lda,
          f32* tau,
          f32* T,
    const INT  ldt,
          f32* Y,
    const INT  ldy
);
void slahr2(const INT n, const INT k, const INT nb, f32 *A, const INT lda, f32 *tau, f32 *T, const INT ldt, f32 *Y, const INT ldy)#

SLAHR2 reduces the first NB columns of A real general n-BY-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero.

The reduction is performed by an orthogonal similarity transformation Q**T * A * Q. The routine returns the matrices V and T which determine Q as a block reflector I - V*T*V**T, and also the matrix Y = A * V * T.

This is an auxiliary routine called by SGEHRD.

Parameters

in
n

The order of the matrix A.

in
k

The offset for the reduction. Elements below the k-th subdiagonal in the first NB columns are reduced to zero. k < n. (0-based)

in
nb

The number of columns to be reduced.

inout
A

On entry, the n-by-(n-k) general matrix A. On exit, the elements on and above the k-th subdiagonal in the first NB columns are overwritten with the corresponding elements of the reduced matrix. Dimension (lda, n-k).

in
lda

The leading dimension of A. lda >= max(1, n).

out
tau

The scalar factors of the elementary reflectors. Dimension (nb).

out
T

The upper triangular matrix T. Dimension (ldt, nb).

in
ldt

The leading dimension of T. ldt >= nb.

out
Y

The n-by-nb matrix Y. Dimension (ldy, nb).

in
ldy

The leading dimension of Y. ldy >= n.

Functions

void dlahr2(
    const INT  n,
    const INT  k,
    const INT  nb,
          f64* A,
    const INT  lda,
          f64* tau,
          f64* T,
    const INT  ldt,
          f64* Y,
    const INT  ldy
);
void dlahr2(const INT n, const INT k, const INT nb, f64 *A, const INT lda, f64 *tau, f64 *T, const INT ldt, f64 *Y, const INT ldy)#

DLAHR2 reduces the first NB columns of A real general n-BY-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero.

The reduction is performed by an orthogonal similarity transformation Q**T * A * Q. The routine returns the matrices V and T which determine Q as a block reflector I - V*T*V**T, and also the matrix Y = A * V * T.

This is an auxiliary routine called by DGEHRD.

Parameters

in
n

The order of the matrix A.

in
k

The offset for the reduction. Elements below the k-th subdiagonal in the first NB columns are reduced to zero. k < n. (0-based)

in
nb

The number of columns to be reduced.

inout
A

On entry, the n-by-(n-k) general matrix A. On exit, the elements on and above the k-th subdiagonal in the first NB columns are overwritten with the corresponding elements of the reduced matrix. Dimension (lda, n-k).

in
lda

The leading dimension of A. lda >= max(1, n).

out
tau

The scalar factors of the elementary reflectors. Dimension (nb).

out
T

The upper triangular matrix T. Dimension (ldt, nb).

in
ldt

The leading dimension of T. ldt >= nb.

out
Y

The n-by-nb matrix Y. Dimension (ldy, nb).

in
ldy

The leading dimension of Y. ldy >= n.

Functions

void clahr2(
    const INT  n,
    const INT  k,
    const INT  nb,
          c64* A,
    const INT  lda,
          c64* tau,
          c64* T,
    const INT  ldt,
          c64* Y,
    const INT  ldy
);
void clahr2(const INT n, const INT k, const INT nb, c64 *A, const INT lda, c64 *tau, c64 *T, const INT ldt, c64 *Y, const INT ldy)#

CLAHR2 reduces the first NB columns of A complex general n-BY-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero.

The reduction is performed by an unitary similarity transformation Q**H * A * Q. The routine returns the matrices V and T which determine Q as a block reflector I - V*T*V**H, and also the matrix Y = A * V * T.

This is an auxiliary routine called by CGEHRD.

Parameters

in
n

The order of the matrix A.

in
k

The offset for the reduction. Elements below the k-th subdiagonal in the first NB columns are reduced to zero. k < n. (0-based)

in
nb

The number of columns to be reduced.

inout
A

On entry, the n-by-(n-k) general matrix A. On exit, the elements on and above the k-th subdiagonal in the first NB columns are overwritten with the corresponding elements of the reduced matrix. Dimension (lda, n-k).

in
lda

The leading dimension of A. lda >= max(1, n).

out
tau

The scalar factors of the elementary reflectors. Dimension (nb).

out
T

The upper triangular matrix T. Dimension (ldt, nb).

in
ldt

The leading dimension of T. ldt >= nb.

out
Y

The n-by-nb matrix Y. Dimension (ldy, nb).

in
ldy

The leading dimension of Y. ldy >= n.

Functions

void zlahr2(
    const INT   n,
    const INT   k,
    const INT   nb,
          c128* A,
    const INT   lda,
          c128* tau,
          c128* T,
    const INT   ldt,
          c128* Y,
    const INT   ldy
);
void zlahr2(const INT n, const INT k, const INT nb, c128 *A, const INT lda, c128 *tau, c128 *T, const INT ldt, c128 *Y, const INT ldy)#

ZLAHR2 reduces the first NB columns of A complex general n-BY-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero.

The reduction is performed by an unitary similarity transformation Q**H * A * Q. The routine returns the matrices V and T which determine Q as a block reflector I - V*T*V**H, and also the matrix Y = A * V * T.

This is an auxiliary routine called by ZGEHRD.

Parameters

in
n

The order of the matrix A.

in
k

The offset for the reduction. Elements below the k-th subdiagonal in the first NB columns are reduced to zero. k < n. (0-based)

in
nb

The number of columns to be reduced.

inout
A

On entry, the n-by-(n-k) general matrix A. On exit, the elements on and above the k-th subdiagonal in the first NB columns are overwritten with the corresponding elements of the reduced matrix. Dimension (lda, n-k).

in
lda

The leading dimension of A. lda >= max(1, n).

out
tau

The scalar factors of the elementary reflectors. Dimension (nb).

out
T

The upper triangular matrix T. Dimension (ldt, nb).

in
ldt

The leading dimension of T. ldt >= nb.

out
Y

The n-by-nb matrix Y. Dimension (ldy, nb).

in
ldy

The leading dimension of Y. ldy >= n.

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