geqr#

Functions

void sgeqr(
    const INT           m,
    const INT           n,
          f32* restrict A,
    const INT           lda,
          f32* restrict T,
    const INT           tsize,
          f32* restrict work,
    const INT           lwork,
          INT*          info
);
void sgeqr(const INT m, const INT n, f32 *restrict A, const INT lda, f32 *restrict T, const INT tsize, f32 *restrict work, const INT lwork, INT *info)#

SGEQR computes a QR factorization of a real M-by-N matrix A:

A = Q * ( R ), ( 0 )

where:

Q is a M-by-M orthogonal matrix; R is an upper-triangular N-by-N matrix; 0 is a (M-N)-by-N zero matrix, if M > N.

Parameters

in
m

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

in
n

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

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 contain the min(m,n)-by-n upper trapezoidal matrix R; the elements below the diagonal are used to store part of the data structure to represent Q.

in
lda

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

out
T

Double precision array, dimension (max(5, tsize)). On exit, if info = 0, T[0] returns optimal (or minimal) tsize. T[1] = MB, T[2] = NB (block sizes). Remaining T contains part of the data structure for Q.

in
tsize

If tsize >= 5, the dimension of array T. If tsize = -1 or -2, workspace query is assumed.

out
work

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

in
lwork

The dimension of array work. lwork >= 1. If lwork = -1 or -2, workspace query is assumed.

out
info

  • = 0: successful exit

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

Functions

void dgeqr(
    const INT           m,
    const INT           n,
          f64* restrict A,
    const INT           lda,
          f64* restrict T,
    const INT           tsize,
          f64* restrict work,
    const INT           lwork,
          INT*          info
);
void dgeqr(const INT m, const INT n, f64 *restrict A, const INT lda, f64 *restrict T, const INT tsize, f64 *restrict work, const INT lwork, INT *info)#

DGEQR computes a QR factorization of a real M-by-N matrix A:

A = Q * ( R ), ( 0 )

where:

Q is a M-by-M orthogonal matrix; R is an upper-triangular N-by-N matrix; 0 is a (M-N)-by-N zero matrix, if M > N.

Parameters

in
m

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

in
n

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

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 contain the min(m,n)-by-n upper trapezoidal matrix R; the elements below the diagonal are used to store part of the data structure to represent Q.

in
lda

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

out
T

Double precision array, dimension (max(5, tsize)). On exit, if info = 0, T[0] returns optimal (or minimal) tsize. T[1] = MB, T[2] = NB (block sizes). Remaining T contains part of the data structure for Q.

in
tsize

If tsize >= 5, the dimension of array T. If tsize = -1 or -2, workspace query is assumed.

out
work

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

in
lwork

The dimension of array work. lwork >= 1. If lwork = -1 or -2, workspace query is assumed.

out
info

  • = 0: successful exit

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

Functions

void cgeqr(
    const INT           m,
    const INT           n,
          c64* restrict A,
    const INT           lda,
          c64* restrict T,
    const INT           tsize,
          c64* restrict work,
    const INT           lwork,
          INT*          info
);
void cgeqr(const INT m, const INT n, c64 *restrict A, const INT lda, c64 *restrict T, const INT tsize, c64 *restrict work, const INT lwork, INT *info)#

CGEQR computes a QR factorization of a complex M-by-N matrix A:

A = Q * ( R ), ( 0 )

where:

Q is a M-by-M orthogonal matrix; R is an upper-triangular N-by-N matrix; 0 is a (M-N)-by-N zero matrix, if M > N.

Parameters

in
m

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

in
n

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

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 contain the min(m,n)-by-n upper trapezoidal matrix R; the elements below the diagonal are used to store part of the data structure to represent Q.

in
lda

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

out
T

Single complex array, dimension (max(5, tsize)). On exit, if info = 0, T[0] returns optimal (or minimal) tsize. T[1] = MB, T[2] = NB (block sizes). Remaining T contains part of the data structure for Q.

in
tsize

If tsize >= 5, the dimension of array T. If tsize = -1 or -2, workspace query is assumed.

out
work

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

in
lwork

The dimension of array work. lwork >= 1. If lwork = -1 or -2, workspace query is assumed.

out
info

  • = 0: successful exit

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

Functions

void zgeqr(
    const INT            m,
    const INT            n,
          c128* restrict A,
    const INT            lda,
          c128* restrict T,
    const INT            tsize,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);
void zgeqr(const INT m, const INT n, c128 *restrict A, const INT lda, c128 *restrict T, const INT tsize, c128 *restrict work, const INT lwork, INT *info)#

ZGEQR computes a QR factorization of a complex M-by-N matrix A:

A = Q * ( R ), ( 0 )

where:

Q is a M-by-M orthogonal matrix; R is an upper-triangular N-by-N matrix; 0 is a (M-N)-by-N zero matrix, if M > N.

Parameters

in
m

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

in
n

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

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 contain the min(m,n)-by-n upper trapezoidal matrix R; the elements below the diagonal are used to store part of the data structure to represent Q.

in
lda

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

out
T

Double complex array, dimension (max(5, tsize)). On exit, if info = 0, T[0] returns optimal (or minimal) tsize. T[1] = MB, T[2] = NB (block sizes). Remaining T contains part of the data structure for Q.

in
tsize

If tsize >= 5, the dimension of array T. If tsize = -1 or -2, workspace query is assumed.

out
work

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

in
lwork

The dimension of array work. lwork >= 1. If lwork = -1 or -2, workspace query is assumed.

out
info

  • = 0: successful exit

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

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