Developer Reference for Intel® oneAPI Math Kernel Library for C
?orbdb/?unbdb
Simultaneously bidiagonalizes the blocks of a partitioned orthogonal/unitary matrix.
Syntax
lapack_int LAPACKE_sorbdb ( intmatrix_layout , chartrans , charsigns , lapack_intm , lapack_intp , lapack_intq , float*x11 , lapack_intldx11 , float*x12 , lapack_intldx12 , float*x21 , lapack_intldx21 , float*x22 , lapack_intldx22 , float*theta , float*phi , float*taup1 , float*taup2 , float*tauq1 , float*tauq2 );
lapack_int LAPACKE_dorbdb ( intmatrix_layout , chartrans , charsigns , lapack_intm , lapack_intp , lapack_intq , double*x11 , lapack_intldx11 , double*x12 , lapack_intldx12 , double*x21 , lapack_intldx21 , double*x22 , lapack_intldx22 , double*theta , double*phi , double*taup1 , double*taup2 , double*tauq1 , double*tauq );
lapack_int LAPACKE_cunbdb ( intmatrix_layout , chartrans , charsigns , lapack_intm , lapack_intp , lapack_intq , lapack_complex_float*x11 , lapack_intldx11 , lapack_complex_float*x12 , lapack_intldx12 , lapack_complex_float*x21 , lapack_intldx21 , lapack_complex_float*x22 , lapack_intldx22 , float*theta , float*phi , lapack_complex_float*taup1 , lapack_complex_float*taup2 , lapack_complex_float*tauq1 , lapack_complex_float*tauq2 );
lapack_int LAPACKE_zunbdb ( intmatrix_layout , chartrans , charsigns , lapack_intm , lapack_intp , lapack_intq , lapack_complex_double*x11 , lapack_intldx11 , lapack_complex_double*x12 , lapack_intldx12 , lapack_complex_double*x21 , lapack_intldx21 , lapack_complex_double*x22 , lapack_intldx22 , double*theta , double*phi , lapack_complex_double*taup1 , lapack_complex_double*taup2 , lapack_complex_double*tauq1 , lapack_complex_double*tauq2 );
Include Files
mkl.h
Description
The routines ?orbdb / ?unbdb simultaneously bidiagonalizes the blocks of an m -by- m partitioned orthogonal matrix X :
or unitary matrix:
x11 is p -by- q . q must not be larger than p , m - p , or m - q . Otherwise, x must be transposed and/or permuted in constant time using the trans and signs options.
The orthogonal/unitary matrices p1 , p2 , q1 , and q2 are p -by- p , (m-p) -by- (m-p) , q -by- q , (m-q) -by- (m-q) , respectively. They are represented implicitly by Housholder vectors.
The bidiagonal matrices b11 , b12 , b21 , and b22 are q -by- q bidiagonal matrices represented implicitly by angles theta(1) , …, theta(q) and phi(1) , …, phi(q-1)theta[0] , …, theta[q - 1] and phi[0] , …, phi[q - 2] . b11 and b12 are upper bidiagonal, while b21 and b22 are lower bidiagonal. Every entry in each bidiagonal band is a product of a sine or cosine of theta with a sine or cosine of phi . See [Sutton09] for details.
p1 , p2 , q1 , and q2 are represented as products of elementary reflectors. .
Input Parameters
- matrix_layout
-
Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).
- trans
-
CHARACTER
- signs
-
CHARACTER
m
The number of rows and columns of the matrix X .
p
The number of rows in x11 and x12 . 0 ≤p≤m .
q
The number of columns in x11 and x21 . 0 ≤q≤ min(p,m-p,m-q) .
- x11
-
REAL for sorbdb DOUBLE PRECISION for dorbdb COMPLEX for cunbdb DOUBLE COMPLEX for zunbdb
Array, size (size max(1, ldx11 * q ) for column major layout and max(1, ldx11 * p ) for row major layout) .
On entry, the top-left block of the orthogonal/unitary matrix to be reduced.
ldx11
The leading dimension of the array X11 . If trans = ‘ T ‘, ldx11≥p for column major layout and ldx11≥q for row major layout . Otherwise, ldx11≥q .
- x12
-
REAL for sorbdb DOUBLE PRECISION for dorbdb COMPLEX for cunbdb DOUBLE COMPLEX for zunbdb
Array, size (size max(1, ldx12 *( m - q )) for column major layout and max(1, ldx12 * p ) for row major layout) .
On entry, the top-right block of the orthogonal/unitary matrix to be reduced.
ldx12
The leading dimension of the array X12 . If trans = ‘ N ‘, ldx12≥p for column major layout and ldx12≥m - q for row major layout. . Otherwise, ldx12≥m-q .
- x21
-
REAL for sorbdb DOUBLE PRECISION for dorbdb COMPLEX for cunbdb DOUBLE COMPLEX for zunbdb
Array, size (size max(1, ldx21 * q ) for column major layout and max(1, ldx21 *( m - p )) for row major layout) .
On entry, the bottom-left block of the orthogonal/unitary matrix to be reduced.
ldx21
The leading dimension of the array X21 . If trans = ‘ N ‘, ldx21≥m-p for column major layout and ldx12≥q for row major layout. . Otherwise, ldx21≥q .
- x22
-
REAL for sorbdb DOUBLE PRECISION for dorbdb COMPLEX for cunbdb DOUBLE COMPLEX for zunbdb
Array, size ( (size max(1, ldx22 *( m - q )) for column major layout and max(1, ldx22 *( m - p )) for row major layout) .
On entry, the bottom-right block of the orthogonal/unitary matrix to be reduced.
ldx22
The leading dimension of the array X21 . If trans = ‘ N ‘, ldx22≥m-p for column major layout and ldx22≥m - q for row major layout. . Otherwise, ldx22≥m-q .
- work
-
REAL for sorbdb DOUBLE PRECISION for dorbdb COMPLEX for cunbdb DOUBLE COMPLEX for zunbdb
Workspace array, size lwork .
lwork
The size of the work array. lwork ≥ m - q
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 .
Output Parameters
- x11
-
On exit, the form depends on trans : If trans =’ N ‘, the columns of the lower triangle of x11 specify reflectors for p1 , the rows of the upper triangle of x11(1:q - 1, q:q - 1) specify reflectors for q1 otherwise trans =’ T ‘, the rows of the upper triangle of x11 specify reflectors for p1 , the columns of the lower triangle of x11(1:q - 1, q:q - 1) specify reflectors for q1
- x12
-
On exit, the form depends on trans : If trans =’ N ‘, the columns of the upper triangle of x12 specify the first p reflectors for q2 otherwise trans =’ T ‘, the columns of the lower triangle of x12 specify the first p reflectors for q2
- x21
-
On exit, the form depends on trans : If trans =’ N ‘, the columns of the lower triangle of x21 specify the reflectors for p2 otherwise trans =’ T ‘, the columns of the upper triangle of x21 specify the reflectors for p2
- x22
-
On exit, the form depends on trans : If trans =’ N ‘, the rows of the upper triangle of x22 ( q +1: m - p , p +1: m - q ) specify the last m-p-q reflectors for q2 otherwise trans =’ T ‘, the columns of the lower triangle of x22 ( p +1: m - q , q +1: m - p ) specify the last m-p-q reflectors for p2
- theta
-
REAL for sorbdb DOUBLE PRECISION for dorbdb COMPLEX for cunbdb DOUBLE COMPLEX for zunbdb
Array, size q . The entries of bidiagonal blocks b11 , b12 , b21 , and b22 can be computed from the angles theta and phi . See the Description section for details.
- phi
-
REAL for sorbdb DOUBLE PRECISION for dorbdb COMPLEX for cunbdb DOUBLE COMPLEX for zunbdb
Array, size q -1 . The entries of bidiagonal blocks b11 , b12 , b21 , and b22 can be computed from the angles theta and phi . See the Description section for details.
- taup1
-
REAL for sorbdb DOUBLE PRECISION for dorbdb COMPLEX for cunbdb DOUBLE COMPLEX for zunbdb
Array, size p .
- taup2
-
REAL for sorbdb DOUBLE PRECISION for dorbdb COMPLEX for cunbdb DOUBLE COMPLEX for zunbdb
Array, size m - p .
- tauq1
-
REAL for sorbdb DOUBLE PRECISION for dorbdb COMPLEX for cunbdb DOUBLE COMPLEX for zunbdb
Array, size q .
- tauq2
-
REAL for sorbdb DOUBLE PRECISION for dorbdb COMPLEX for cunbdb DOUBLE COMPLEX for zunbdb
Array, size m - q .
Return Values
This function returns a value info .
If info=0 , the execution is successful.
If info = -i , the i -th parameter had an illegal value.