geqrt3#

Functions

void sgeqrt3(
    const INT           m,
    const INT           n,
          f32* restrict A,
    const INT           lda,
          f32* restrict T,
    const INT           ldt,
          INT*          info
);
void sgeqrt3(const INT m, const INT n, f32 *restrict A, const INT lda, f32 *restrict T, const INT ldt, INT *info)#

SGEQRT3 recursively computes a QR factorization of a real M-by-N matrix A, using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

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. The block reflector H is then given by 
         H = I - V * T * V**T
where V**T is the transpose of V.

Parameters

in
m

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

in
n

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

inout
A

Double precision array, dimension (lda, n). On entry, the real M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; 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, n). The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used.

in
ldt

The leading dimension of the array T. ldt >= max(1, n).

out
info

  • = 0: successful exit

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

Functions

void dgeqrt3(
    const INT           m,
    const INT           n,
          f64* restrict A,
    const INT           lda,
          f64* restrict T,
    const INT           ldt,
          INT*          info
);
void dgeqrt3(const INT m, const INT n, f64 *restrict A, const INT lda, f64 *restrict T, const INT ldt, INT *info)#

DGEQRT3 recursively computes a QR factorization of a real M-by-N matrix A, using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

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. The block reflector H is then given by 
         H = I - V * T * V**T
where V**T is the transpose of V.

Parameters

in
m

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

in
n

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

inout
A

Double precision array, dimension (lda, n). On entry, the real M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; 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, n). The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used.

in
ldt

The leading dimension of the array T. ldt >= max(1, n).

out
info

  • = 0: successful exit

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

Functions

void cgeqrt3(
    const INT           m,
    const INT           n,
          c64* restrict A,
    const INT           lda,
          c64* restrict T,
    const INT           ldt,
          INT*          info
);
void cgeqrt3(const INT m, const INT n, c64 *restrict A, const INT lda, c64 *restrict T, const INT ldt, INT *info)#

CGEQRT3 recursively computes a QR factorization of a complex M-by-N matrix A, using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

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. The block reflector H is then given by 
         H = I - V * T * V**H
where V**H is the conjugate transpose of V.

Parameters

in
m

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

in
n

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

inout
A

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

Single complex array, dimension (ldt, n). The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used.

in
ldt

The leading dimension of the array T. ldt >= max(1, n).

out
info

  • = 0: successful exit

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

Functions

void zgeqrt3(
    const INT            m,
    const INT            n,
          c128* restrict A,
    const INT            lda,
          c128* restrict T,
    const INT            ldt,
          INT*           info
);
void zgeqrt3(const INT m, const INT n, c128 *restrict A, const INT lda, c128 *restrict T, const INT ldt, INT *info)#

ZGEQRT3 recursively computes a QR factorization of a complex M-by-N matrix A, using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

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. The block reflector H is then given by 
         H = I - V * T * V**H
where V**H is the conjugate transpose of V.

Parameters

in
m

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

in
n

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

inout
A

Double complex array, dimension (lda, n). On entry, the complex M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; 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 complex array, dimension (ldt, n). The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used.

in
ldt

The leading dimension of the array T. ldt >= max(1, n).

out
info

  • = 0: successful exit

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