latsqr#

Functions

void slatsqr(
    const INT           m,
    const INT           n,
    const INT           mb,
    const INT           nb,
          f32* restrict A,
    const INT           lda,
          f32* restrict T,
    const INT           ldt,
          f32* restrict work,
    const INT           lwork,
          INT*          info
);
void slatsqr(const INT m, const INT n, const INT mb, const INT nb, f32 *restrict A, const INT lda, f32 *restrict T, const INT ldt, f32 *restrict work, const INT lwork, INT *info)#

SLATSQR computes a blocked Tall-Skinny QR factorization of a real M-by-N matrix A for M >= N:

A = Q * ( R ), ( 0 )

where:

Q is a M-by-M orthogonal matrix, stored on exit in an implicit form in the elements below the diagonal of the array A and in the elements of the array T;

R is an upper-triangular N-by-N matrix, stored on exit in the elements on and above the diagonal of the array A.

0 is a (M-N)-by-N zero matrix, and is not stored.

Parameters

in
m

The number of rows of the matrix A. m >= 0.

in
n

The number of columns of the matrix A. m >= n >= 0.

in
mb

The row block size to be used in the blocked QR. mb > 0.

in
nb

The column block size to be used in the blocked QR. n >= nb >= 1.

inout
A

Double precision array, dimension (lda, n). On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the N-by-N upper triangular matrix R; the elements below the diagonal represent Q by the columns of blocked V.

in
lda

The leading dimension of the array A. lda >= max(1, m).

out
T

Double precision array, dimension (ldt, n * Number_of_row_blocks) where Number_of_row_blocks = CEIL((m-n)/(mb-n)). The blocked upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks.

in
ldt

The leading dimension of the array T. ldt >= nb.

out
work

Workspace array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the minimal lwork.

in
lwork

The dimension of the array work. lwork >= 1, if min(m,n) = 0, and lwork >= nb*n, otherwise. If lwork = -1, then a workspace query is assumed.

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value

Functions

void dlatsqr(
    const INT           m,
    const INT           n,
    const INT           mb,
    const INT           nb,
          f64* restrict A,
    const INT           lda,
          f64* restrict T,
    const INT           ldt,
          f64* restrict work,
    const INT           lwork,
          INT*          info
);
void dlatsqr(const INT m, const INT n, const INT mb, const INT nb, f64 *restrict A, const INT lda, f64 *restrict T, const INT ldt, f64 *restrict work, const INT lwork, INT *info)#

DLATSQR computes a blocked Tall-Skinny QR factorization of a real M-by-N matrix A for M >= N:

A = Q * ( R ), ( 0 )

where:

Q is a M-by-M orthogonal matrix, stored on exit in an implicit form in the elements below the diagonal of the array A and in the elements of the array T;

R is an upper-triangular N-by-N matrix, stored on exit in the elements on and above the diagonal of the array A.

0 is a (M-N)-by-N zero matrix, and is not stored.

Parameters

in
m

The number of rows of the matrix A. m >= 0.

in
n

The number of columns of the matrix A. m >= n >= 0.

in
mb

The row block size to be used in the blocked QR. mb > 0.

in
nb

The column block size to be used in the blocked QR. n >= nb >= 1.

inout
A

Double precision array, dimension (lda, n). On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the N-by-N upper triangular matrix R; the elements below the diagonal represent Q by the columns of blocked V.

in
lda

The leading dimension of the array A. lda >= max(1, m).

out
T

Double precision array, dimension (ldt, n * Number_of_row_blocks) where Number_of_row_blocks = CEIL((m-n)/(mb-n)). The blocked upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks.

in
ldt

The leading dimension of the array T. ldt >= nb.

out
work

Workspace array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the minimal lwork.

in
lwork

The dimension of the array work. lwork >= 1, if min(m,n) = 0, and lwork >= nb*n, otherwise. If lwork = -1, then a workspace query is assumed.

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value

Functions

void clatsqr(
    const INT           m,
    const INT           n,
    const INT           mb,
    const INT           nb,
          c64* restrict A,
    const INT           lda,
          c64* restrict T,
    const INT           ldt,
          c64* restrict work,
    const INT           lwork,
          INT*          info
);
void clatsqr(const INT m, const INT n, const INT mb, const INT nb, c64 *restrict A, const INT lda, c64 *restrict T, const INT ldt, c64 *restrict work, const INT lwork, INT *info)#

CLATSQR computes a blocked Tall-Skinny QR factorization of a complex M-by-N matrix A for M >= N:

A = Q * ( R ), ( 0 )

where:

Q is a M-by-M orthogonal matrix, stored on exit in an implicit form in the elements below the diagonal of the array A and in the elements of the array T;

R is an upper-triangular N-by-N matrix, stored on exit in the elements on and above the diagonal of the array A.

0 is a (M-N)-by-N zero matrix, and is not stored.

Parameters

in
m

The number of rows of the matrix A. m >= 0.

in
n

The number of columns of the matrix A. m >= n >= 0.

in
mb

The row block size to be used in the blocked QR. mb > 0.

in
nb

The column block size to be used in the blocked QR. n >= nb >= 1.

inout
A

Single complex array, dimension (lda, n). On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the N-by-N upper triangular matrix R; the elements below the diagonal represent Q by the columns of blocked V.

in
lda

The leading dimension of the array A. lda >= max(1, m).

out
T

Single complex array, dimension (ldt, n * Number_of_row_blocks) where Number_of_row_blocks = CEIL((m-n)/(mb-n)). The blocked upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks.

in
ldt

The leading dimension of the array T. ldt >= nb.

out
work

Workspace array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the minimal lwork.

in
lwork

The dimension of the array work. lwork >= 1, if min(m,n) = 0, and lwork >= nb*n, otherwise. If lwork = -1, then a workspace query is assumed.

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value

Functions

void zlatsqr(
    const INT            m,
    const INT            n,
    const INT            mb,
    const INT            nb,
          c128* restrict A,
    const INT            lda,
          c128* restrict T,
    const INT            ldt,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);
void zlatsqr(const INT m, const INT n, const INT mb, const INT nb, c128 *restrict A, const INT lda, c128 *restrict T, const INT ldt, c128 *restrict work, const INT lwork, INT *info)#

ZLATSQR computes a blocked Tall-Skinny QR factorization of a complex M-by-N matrix A for M >= N:

A = Q * ( R ), ( 0 )

where:

Q is a M-by-M orthogonal matrix, stored on exit in an implicit form in the elements below the diagonal of the array A and in the elements of the array T;

R is an upper-triangular N-by-N matrix, stored on exit in the elements on and above the diagonal of the array A.

0 is a (M-N)-by-N zero matrix, and is not stored.

Parameters

in
m

The number of rows of the matrix A. m >= 0.

in
n

The number of columns of the matrix A. m >= n >= 0.

in
mb

The row block size to be used in the blocked QR. mb > 0.

in
nb

The column block size to be used in the blocked QR. n >= nb >= 1.

inout
A

Double complex array, dimension (lda, n). On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the N-by-N upper triangular matrix R; the elements below the diagonal represent Q by the columns of blocked V.

in
lda

The leading dimension of the array A. lda >= max(1, m).

out
T

Double complex array, dimension (ldt, n * Number_of_row_blocks) where Number_of_row_blocks = CEIL((m-n)/(mb-n)). The blocked upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks.

in
ldt

The leading dimension of the array T. ldt >= nb.

out
work

Workspace array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the minimal lwork.

in
lwork

The dimension of the array work. lwork >= 1, if min(m,n) = 0, and lwork >= nb*n, otherwise. If lwork = -1, then a workspace query is assumed.

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value