gebrd#

sgebrd

Functions

void sgebrd(
    const INT           m,
    const INT           n,
          f32* restrict A,
    const INT           lda,
          f32* restrict D,
          f32* restrict E,
          f32* restrict tauq,
          f32* restrict taup,
          f32* restrict work,
    const INT           lwork,
          INT*          info
);

void sgebrd(const INT m, const INT n, f32 *restrict A, const INT lda, f32 *restrict D, f32 *restrict E, f32 *restrict tauq, f32 *restrict taup, f32 *restrict work, const INT lwork, INT *info)#

SGEBRD reduces a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.

If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.

Parameters

in

m

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

in

n

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

inout

A

Double precision array, dimension (lda, n). On entry, the M-by-N general matrix to be reduced. On exit, if m >= n, the diagonal and the first superdiagonal are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors; if m < n, the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and the elements above the diagonal, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors.

in

lda

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

out

D

Double precision array, dimension (min(m,n)). The diagonal elements of the bidiagonal matrix B: D[i] = A[i,i].

out

E

Double precision array, dimension (min(m,n)-1). The off-diagonal elements of the bidiagonal matrix B: if m >= n, E[i] = A[i,i+1] for i = 0,1,…,n-2; if m < n, E[i] = A[i+1,i] for i = 0,1,…,m-2.

out

tauq

Double precision array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the orthogonal matrix Q.

out

taup

Double precision array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the orthogonal matrix P.

out

work

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

in

lwork

The length of the array work. lwork >= 1, if min(m,n) = 0, and lwork >= max(m,n), otherwise. For optimum performance lwork >= (m+n)*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.

dgebrd

Functions

void dgebrd(
    const INT           m,
    const INT           n,
          f64* restrict A,
    const INT           lda,
          f64* restrict D,
          f64* restrict E,
          f64* restrict tauq,
          f64* restrict taup,
          f64* restrict work,
    const INT           lwork,
          INT*          info
);

void dgebrd(const INT m, const INT n, f64 *restrict A, const INT lda, f64 *restrict D, f64 *restrict E, f64 *restrict tauq, f64 *restrict taup, f64 *restrict work, const INT lwork, INT *info)#

DGEBRD reduces a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.

If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.

Parameters

in

m

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

in

n

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

inout

A

Double precision array, dimension (lda, n). On entry, the M-by-N general matrix to be reduced. On exit, if m >= n, the diagonal and the first superdiagonal are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors; if m < n, the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and the elements above the diagonal, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors.

in

lda

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

out

D

Double precision array, dimension (min(m,n)). The diagonal elements of the bidiagonal matrix B: D[i] = A[i,i].

out

E

Double precision array, dimension (min(m,n)-1). The off-diagonal elements of the bidiagonal matrix B: if m >= n, E[i] = A[i,i+1] for i = 0,1,…,n-2; if m < n, E[i] = A[i+1,i] for i = 0,1,…,m-2.

out

tauq

Double precision array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the orthogonal matrix Q.

out

taup

Double precision array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the orthogonal matrix P.

out

work

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

in

lwork

The length of the array work. lwork >= 1, if min(m,n) = 0, and lwork >= max(m,n), otherwise. For optimum performance lwork >= (m+n)*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.

cgebrd

Functions

void cgebrd(
    const INT           m,
    const INT           n,
          c64* restrict A,
    const INT           lda,
          f32* restrict D,
          f32* restrict E,
          c64* restrict tauq,
          c64* restrict taup,
          c64* restrict work,
    const INT           lwork,
          INT*          info
);

void cgebrd(const INT m, const INT n, c64 *restrict A, const INT lda, f32 *restrict D, f32 *restrict E, c64 *restrict tauq, c64 *restrict taup, c64 *restrict work, const INT lwork, INT *info)#

CGEBRD reduces a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation: Q**H * A * P = B.

If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.

Parameters

in

m

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

in

n

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

inout

A

Complex*16 array, dimension (lda, n). On entry, the M-by-N general matrix to be reduced. On exit, if m >= n, the diagonal and the first superdiagonal are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the array TAUP, represent the unitary matrix P as a product of elementary reflectors; if m < n, the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the diagonal, with the array TAUP, represent the unitary matrix P as a product of elementary reflectors.

in

lda

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

out

D

Single precision array, dimension (min(m,n)). The diagonal elements of the bidiagonal matrix B: D[i] = A[i,i].

out

E

Single precision array, dimension (min(m,n)-1). The off-diagonal elements of the bidiagonal matrix B: if m >= n, E[i] = A[i,i+1] for i = 0,1,…,n-2; if m < n, E[i] = A[i+1,i] for i = 0,1,…,m-2.

out

tauq

Complex*16 array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the unitary matrix Q.

out

taup

Complex*16 array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the unitary matrix P.

out

work

Complex*16 array, dimension (max(1,lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in

lwork

The length of the array work. lwork >= 1, if min(m,n) = 0, and lwork >= max(m,n), otherwise. For optimum performance lwork >= (m+n)*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.

zgebrd

Functions

void zgebrd(
    const INT            m,
    const INT            n,
          c128* restrict A,
    const INT            lda,
          f64*  restrict D,
          f64*  restrict E,
          c128* restrict tauq,
          c128* restrict taup,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);

void zgebrd(const INT m, const INT n, c128 *restrict A, const INT lda, f64 *restrict D, f64 *restrict E, c128 *restrict tauq, c128 *restrict taup, c128 *restrict work, const INT lwork, INT *info)#

ZGEBRD reduces a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation: Q**H * A * P = B.

If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.

Parameters

in

m

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

in

n

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

inout

A

Complex*16 array, dimension (lda, n). On entry, the M-by-N general matrix to be reduced. On exit, if m >= n, the diagonal and the first superdiagonal are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the array TAUP, represent the unitary matrix P as a product of elementary reflectors; if m < n, the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the diagonal, with the array TAUP, represent the unitary matrix P as a product of elementary reflectors.

in

lda

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

out

D

Double precision array, dimension (min(m,n)). The diagonal elements of the bidiagonal matrix B: D[i] = A[i,i].

out

E

Double precision array, dimension (min(m,n)-1). The off-diagonal elements of the bidiagonal matrix B: if m >= n, E[i] = A[i,i+1] for i = 0,1,…,n-2; if m < n, E[i] = A[i+1,i] for i = 0,1,…,m-2.

out

tauq

Complex*16 array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the unitary matrix Q.

out

taup

Complex*16 array, dimension (min(m,n)). The scalar factors of the elementary reflectors which represent the unitary matrix P.

out

work

Complex*16 array, dimension (max(1,lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in

lwork

The length of the array work. lwork >= 1, if min(m,n) = 0, and lwork >= max(m,n), otherwise. For optimum performance lwork >= (m+n)*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.

gebrd#

This Page