geqrt#

Functions

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

SGEQRT computes a blocked QR factorization of a real M-by-N matrix A using the compact WY representation of Q.

The factorization has the form A = Q * R where Q is represented in the compact WY form as a product of elementary reflectors stored with their triangular block reflector factors T.

The matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is 

         V = (  1       )
             ( v1  1    )
             ( v1 v2  1 )
             ( v1 v2 v3 )
             ( v1 v2 v3 )
where the vi’s represent the vectors which define H(i), which are returned in the matrix A. The 1’s along the diagonal of V are not stored in A.

Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K - (B-1)*NB. For each of the B blocks, an upper triangular block reflector factor is computed: T1, T2, …, TB. The NB-by-NB (and IB-by-IB for the last block) T’s are stored in the NB-by-K matrix T as 

         T = (T1 T2 ... TB).

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.

in
nb

The block size to be used in the blocked QR. min(m,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 min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V.

in
lda

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

out
T

Double precision array, dimension (ldt, min(m,n)). The 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

Double precision array, dimension (nb*n).

out
info

  • = 0: successful exit

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

Functions

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

DGEQRT computes a blocked QR factorization of a real M-by-N matrix A using the compact WY representation of Q.

The factorization has the form A = Q * R where Q is represented in the compact WY form as a product of elementary reflectors stored with their triangular block reflector factors T.

The matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is 

         V = (  1       )
             ( v1  1    )
             ( v1 v2  1 )
             ( v1 v2 v3 )
             ( v1 v2 v3 )
where the vi’s represent the vectors which define H(i), which are returned in the matrix A. The 1’s along the diagonal of V are not stored in A.

Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K - (B-1)*NB. For each of the B blocks, an upper triangular block reflector factor is computed: T1, T2, …, TB. The NB-by-NB (and IB-by-IB for the last block) T’s are stored in the NB-by-K matrix T as 

         T = (T1 T2 ... TB).

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.

in
nb

The block size to be used in the blocked QR. min(m,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 min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V.

in
lda

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

out
T

Double precision array, dimension (ldt, min(m,n)). The 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

Double precision array, dimension (nb*n).

out
info

  • = 0: successful exit

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

Functions

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

CGEQRT computes a blocked QR factorization of a complex M-by-N matrix A using the compact WY representation of Q.

The factorization has the form A = Q * R where Q is represented in the compact WY form as a product of elementary reflectors stored with their triangular block reflector factors T.

The matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is 

         V = (  1       )
             ( v1  1    )
             ( v1 v2  1 )
             ( v1 v2 v3 )
             ( v1 v2 v3 )
where the vi’s represent the vectors which define H(i), which are returned in the matrix A. The 1’s along the diagonal of V are not stored in A.

Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K - (B-1)*NB. For each of the B blocks, an upper triangular block reflector factor is computed: T1, T2, …, TB. The NB-by-NB (and IB-by-IB for the last block) T’s are stored in the NB-by-K matrix T as 

         T = (T1 T2 ... TB).

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.

in
nb

The block size to be used in the blocked QR. min(m,n) >= nb >= 1.

inout
A

Complex*16 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 min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V.

in
lda

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

out
T

Complex*16 array, dimension (ldt, min(m,n)). The 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

Complex*16 array, dimension (nb*n).

out
info

  • = 0: successful exit

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

Functions

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

ZGEQRT computes a blocked QR factorization of a complex M-by-N matrix A using the compact WY representation of Q.

The factorization has the form A = Q * R where Q is represented in the compact WY form as a product of elementary reflectors stored with their triangular block reflector factors T.

The matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is 

         V = (  1       )
             ( v1  1    )
             ( v1 v2  1 )
             ( v1 v2 v3 )
             ( v1 v2 v3 )
where the vi’s represent the vectors which define H(i), which are returned in the matrix A. The 1’s along the diagonal of V are not stored in A.

Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K - (B-1)*NB. For each of the B blocks, an upper triangular block reflector factor is computed: T1, T2, …, TB. The NB-by-NB (and IB-by-IB for the last block) T’s are stored in the NB-by-K matrix T as 

         T = (T1 T2 ... TB).

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.

in
nb

The block size to be used in the blocked QR. min(m,n) >= nb >= 1.

inout
A

Complex*16 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 min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V.

in
lda

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

out
T

Complex*16 array, dimension (ldt, min(m,n)). The 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

Complex*16 array, dimension (nb*n).

out
info

  • = 0: successful exit

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

On this page

This Page