MAGMA
2.3.0
Matrix Algebra for GPU and Multicore Architectures

Functions  
magma_int_t  magma_cgebrd (magma_int_t m, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, float *d, float *e, magmaFloatComplex *tauq, magmaFloatComplex *taup, magmaFloatComplex *work, magma_int_t lwork, magma_int_t *info) 
CGEBRD reduces a general complex MbyN matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Q**H * A * P = B. More...  
magma_int_t  magma_dgebrd (magma_int_t m, magma_int_t n, double *A, magma_int_t lda, double *d, double *e, double *tauq, double *taup, double *work, magma_int_t lwork, magma_int_t *info) 
DGEBRD reduces a general real MbyN matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Q**H * A * P = B. More...  
magma_int_t  magma_sgebrd (magma_int_t m, magma_int_t n, float *A, magma_int_t lda, float *d, float *e, float *tauq, float *taup, float *work, magma_int_t lwork, magma_int_t *info) 
SGEBRD reduces a general real MbyN matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Q**H * A * P = B. More...  
magma_int_t  magma_zgebrd (magma_int_t m, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, double *d, double *e, magmaDoubleComplex *tauq, magmaDoubleComplex *taup, magmaDoubleComplex *work, magma_int_t lwork, magma_int_t *info) 
ZGEBRD reduces a general complex MbyN matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Q**H * A * P = B. More...  
magma_int_t magma_cgebrd  (  magma_int_t  m, 
magma_int_t  n,  
magmaFloatComplex *  A,  
magma_int_t  lda,  
float *  d,  
float *  e,  
magmaFloatComplex *  tauq,  
magmaFloatComplex *  taup,  
magmaFloatComplex *  work,  
magma_int_t  lwork,  
magma_int_t *  info  
) 
CGEBRD reduces a general complex MbyN matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Q**H * A * P = B.
If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
[in]  m  INTEGER The number of rows in the matrix A. M >= 0. 
[in]  n  INTEGER The number of columns in the matrix A. N >= 0. 
[in,out]  A  COMPLEX array, dimension (LDA,N) On entry, the MbyN 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. See Further Details. 
[in]  lda  INTEGER The leading dimension of the array A. LDA >= max(1,M). 
[out]  d  real array, dimension (min(M,N)) The diagonal elements of the bidiagonal matrix B: D(i) = A(i,i). 
[out]  e  real array, dimension (min(M,N)1) The offdiagonal elements of the bidiagonal matrix B: if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n1; if m < n, E(i) = A(i+1,i) for i = 1,2,...,m1. 
[out]  tauq  COMPLEX array dimension (min(M,N)) The scalar factors of the elementary reflectors which represent the orthogonal matrix Q. See Further Details. 
[out]  taup  COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors which represent the orthogonal matrix P. See Further Details. 
[out]  work  (workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. 
[in]  lwork  INTEGER The length of the array WORK. 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  INTEGER

The matrices Q and P are represented as products of elementary reflectors:
If m >= n,
Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n1)
Each H(i) and G(i) has the form:
H(i) = I  tauq * v * v' and G(i) = I  taup * u * u'
where tauq and taup are complex scalars, and v and u are complex vectors; v(1:i1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
If m < n,
Q = H(1) H(2) . . . H(m1) and P = G(1) G(2) . . . G(m)
Each H(i) and G(i) has the form:
H(i) = I  tauq * v * v' and G(i) = I  taup * u * u'
where tauq and taup are complex scalars, and v and u are complex vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); u(1:i1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
The contents of A on exit are illustrated by the following examples:
m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) ( v1 v2 v3 v4 v5 )
where d and e denote diagonal and offdiagonal elements of B, vi denotes an element of the vector defining H(i), and ui an element of the vector defining G(i).
magma_int_t magma_dgebrd  (  magma_int_t  m, 
magma_int_t  n,  
double *  A,  
magma_int_t  lda,  
double *  d,  
double *  e,  
double *  tauq,  
double *  taup,  
double *  work,  
magma_int_t  lwork,  
magma_int_t *  info  
) 
DGEBRD reduces a general real MbyN matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Q**H * A * P = B.
If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
[in]  m  INTEGER The number of rows in the matrix A. M >= 0. 
[in]  n  INTEGER The number of columns in the matrix A. N >= 0. 
[in,out]  A  DOUBLE PRECISION array, dimension (LDA,N) On entry, the MbyN 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. See Further Details. 
[in]  lda  INTEGER 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 offdiagonal elements of the bidiagonal matrix B: if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n1; if m < n, E(i) = A(i+1,i) for i = 1,2,...,m1. 
[out]  tauq  DOUBLE PRECISION array dimension (min(M,N)) The scalar factors of the elementary reflectors which represent the orthogonal matrix Q. See Further Details. 
[out]  taup  DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors which represent the orthogonal matrix P. See Further Details. 
[out]  work  (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. 
[in]  lwork  INTEGER The length of the array WORK. 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  INTEGER

The matrices Q and P are represented as products of elementary reflectors:
If m >= n,
Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n1)
Each H(i) and G(i) has the form:
H(i) = I  tauq * v * v' and G(i) = I  taup * u * u'
where tauq and taup are real scalars, and v and u are real vectors; v(1:i1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
If m < n,
Q = H(1) H(2) . . . H(m1) and P = G(1) G(2) . . . G(m)
Each H(i) and G(i) has the form:
H(i) = I  tauq * v * v' and G(i) = I  taup * u * u'
where tauq and taup are real scalars, and v and u are real vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); u(1:i1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
The contents of A on exit are illustrated by the following examples:
m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) ( v1 v2 v3 v4 v5 )
where d and e denote diagonal and offdiagonal elements of B, vi denotes an element of the vector defining H(i), and ui an element of the vector defining G(i).
magma_int_t magma_sgebrd  (  magma_int_t  m, 
magma_int_t  n,  
float *  A,  
magma_int_t  lda,  
float *  d,  
float *  e,  
float *  tauq,  
float *  taup,  
float *  work,  
magma_int_t  lwork,  
magma_int_t *  info  
) 
SGEBRD reduces a general real MbyN matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Q**H * A * P = B.
If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
[in]  m  INTEGER The number of rows in the matrix A. M >= 0. 
[in]  n  INTEGER The number of columns in the matrix A. N >= 0. 
[in,out]  A  REAL array, dimension (LDA,N) On entry, the MbyN 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. See Further Details. 
[in]  lda  INTEGER The leading dimension of the array A. LDA >= max(1,M). 
[out]  d  real array, dimension (min(M,N)) The diagonal elements of the bidiagonal matrix B: D(i) = A(i,i). 
[out]  e  real array, dimension (min(M,N)1) The offdiagonal elements of the bidiagonal matrix B: if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n1; if m < n, E(i) = A(i+1,i) for i = 1,2,...,m1. 
[out]  tauq  REAL array dimension (min(M,N)) The scalar factors of the elementary reflectors which represent the orthogonal matrix Q. See Further Details. 
[out]  taup  REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors which represent the orthogonal matrix P. See Further Details. 
[out]  work  (workspace) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. 
[in]  lwork  INTEGER The length of the array WORK. 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  INTEGER

The matrices Q and P are represented as products of elementary reflectors:
If m >= n,
Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n1)
Each H(i) and G(i) has the form:
H(i) = I  tauq * v * v' and G(i) = I  taup * u * u'
where tauq and taup are real scalars, and v and u are real vectors; v(1:i1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
If m < n,
Q = H(1) H(2) . . . H(m1) and P = G(1) G(2) . . . G(m)
Each H(i) and G(i) has the form:
H(i) = I  tauq * v * v' and G(i) = I  taup * u * u'
where tauq and taup are real scalars, and v and u are real vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); u(1:i1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
The contents of A on exit are illustrated by the following examples:
m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) ( v1 v2 v3 v4 v5 )
where d and e denote diagonal and offdiagonal elements of B, vi denotes an element of the vector defining H(i), and ui an element of the vector defining G(i).
magma_int_t magma_zgebrd  (  magma_int_t  m, 
magma_int_t  n,  
magmaDoubleComplex *  A,  
magma_int_t  lda,  
double *  d,  
double *  e,  
magmaDoubleComplex *  tauq,  
magmaDoubleComplex *  taup,  
magmaDoubleComplex *  work,  
magma_int_t  lwork,  
magma_int_t *  info  
) 
ZGEBRD reduces a general complex MbyN matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Q**H * A * P = B.
If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
[in]  m  INTEGER The number of rows in the matrix A. M >= 0. 
[in]  n  INTEGER The number of columns in the matrix A. N >= 0. 
[in,out]  A  COMPLEX_16 array, dimension (LDA,N) On entry, the MbyN 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. See Further Details. 
[in]  lda  INTEGER 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 offdiagonal elements of the bidiagonal matrix B: if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n1; if m < n, E(i) = A(i+1,i) for i = 1,2,...,m1. 
[out]  tauq  COMPLEX_16 array dimension (min(M,N)) The scalar factors of the elementary reflectors which represent the orthogonal matrix Q. See Further Details. 
[out]  taup  COMPLEX_16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors which represent the orthogonal matrix P. See Further Details. 
[out]  work  (workspace) COMPLEX_16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. 
[in]  lwork  INTEGER The length of the array WORK. 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  INTEGER

The matrices Q and P are represented as products of elementary reflectors:
If m >= n,
Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n1)
Each H(i) and G(i) has the form:
H(i) = I  tauq * v * v' and G(i) = I  taup * u * u'
where tauq and taup are complex scalars, and v and u are complex vectors; v(1:i1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
If m < n,
Q = H(1) H(2) . . . H(m1) and P = G(1) G(2) . . . G(m)
Each H(i) and G(i) has the form:
H(i) = I  tauq * v * v' and G(i) = I  taup * u * u'
where tauq and taup are complex scalars, and v and u are complex vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); u(1:i1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
The contents of A on exit are illustrated by the following examples:
m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) ( v1 v2 v3 v4 v5 )
where d and e denote diagonal and offdiagonal elements of B, vi denotes an element of the vector defining H(i), and ui an element of the vector defining G(i).