tzrzf#

Functions

void stzrzf(
    const INT           m,
    const INT           n,
          f32* restrict A,
    const INT           lda,
          f32* restrict tau,
          f32* restrict work,
    const INT           lwork,
          INT*          info
);
void stzrzf(const INT m, const INT n, f32 *restrict A, const INT lda, f32 *restrict tau, f32 *restrict work, const INT lwork, INT *info)#

STZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations.

The upper trapezoidal matrix A is factored as

A = ( R 0 ) * Z,

where Z is an N-by-N orthogonal matrix and R is an M-by-M upper triangular matrix.

Parameters

in
m

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

in
n

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

inout
A

Double precision array, dimension (lda, n). On entry, the leading M-by-N upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading M-by-M upper triangular part of A contains the upper triangular matrix R, and elements M+1 to N of the first M rows of A, with the array TAU, represent the orthogonal matrix Z as a product of M elementary reflectors.

in
lda

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

out
tau

Double precision array, dimension (m). The scalar factors of the elementary reflectors.

out
work

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

in
lwork

The dimension of the array work. lwork >= max(1, m). For optimum performance lwork >= m*nb, where nb is the optimal blocksize. If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla.

out
info

  • = 0: successful exit

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

Functions

void dtzrzf(
    const INT           m,
    const INT           n,
          f64* restrict A,
    const INT           lda,
          f64* restrict tau,
          f64* restrict work,
    const INT           lwork,
          INT*          info
);
void dtzrzf(const INT m, const INT n, f64 *restrict A, const INT lda, f64 *restrict tau, f64 *restrict work, const INT lwork, INT *info)#

DTZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations.

The upper trapezoidal matrix A is factored as

A = ( R 0 ) * Z,

where Z is an N-by-N orthogonal matrix and R is an M-by-M upper triangular matrix.

Parameters

in
m

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

in
n

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

inout
A

Double precision array, dimension (lda, n). On entry, the leading M-by-N upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading M-by-M upper triangular part of A contains the upper triangular matrix R, and elements M+1 to N of the first M rows of A, with the array TAU, represent the orthogonal matrix Z as a product of M elementary reflectors.

in
lda

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

out
tau

Double precision array, dimension (m). The scalar factors of the elementary reflectors.

out
work

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

in
lwork

The dimension of the array work. lwork >= max(1, m). For optimum performance lwork >= m*nb, where nb is the optimal blocksize. If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla.

out
info

  • = 0: successful exit

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

Functions

void ctzrzf(
    const INT           m,
    const INT           n,
          c64* restrict A,
    const INT           lda,
          c64* restrict tau,
          c64* restrict work,
    const INT           lwork,
          INT*          info
);
void ctzrzf(const INT m, const INT n, c64 *restrict A, const INT lda, c64 *restrict tau, c64 *restrict work, const INT lwork, INT *info)#

CTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations.

The upper trapezoidal matrix A is factored as

A = ( R 0 ) * Z,

where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular matrix.

Parameters

in
m

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

in
n

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

inout
A

Single complex array, dimension (lda, n). On entry, the leading M-by-N upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading M-by-M upper triangular part of A contains the upper triangular matrix R, and elements M+1 to N of the first M rows of A, with the array TAU, represent the unitary matrix Z as a product of M elementary reflectors.

in
lda

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

out
tau

Single complex array, dimension (m). The scalar factors of the elementary reflectors.

out
work

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

in
lwork

The dimension of the array work. lwork >= max(1, m). For optimum performance lwork >= m*nb, where nb is the optimal blocksize. If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla.

out
info

  • = 0: successful exit

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

Functions

void ztzrzf(
    const INT            m,
    const INT            n,
          c128* restrict A,
    const INT            lda,
          c128* restrict tau,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);
void ztzrzf(const INT m, const INT n, c128 *restrict A, const INT lda, c128 *restrict tau, c128 *restrict work, const INT lwork, INT *info)#

ZTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations.

The upper trapezoidal matrix A is factored as

A = ( R 0 ) * Z,

where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular matrix.

Parameters

in
m

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

in
n

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

inout
A

Double complex array, dimension (lda, n). On entry, the leading M-by-N upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading M-by-M upper triangular part of A contains the upper triangular matrix R, and elements M+1 to N of the first M rows of A, with the array TAU, represent the unitary matrix Z as a product of M elementary reflectors.

in
lda

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

out
tau

Double complex array, dimension (m). The scalar factors of the elementary reflectors.

out
work

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

in
lwork

The dimension of the array work. lwork >= max(1, m). For optimum performance lwork >= m*nb, where nb is the optimal blocksize. If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla.

out
info

  • = 0: successful exit

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

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