Computes the CS decomposition of a block-partitioned orthogonal/unitary matrix.
Syntax
lapack_int LAPACKE_sorcsd( int matrix_layout, char jobu1, char jobu2, char jobv1t, char jobv2t, char trans, char signs, lapack_int m, lapack_int p, lapack_int q, float* x11, lapack_int ldx11, float* x12, lapack_int ldx12, float* x21, lapack_int ldx21, float* x22, lapack_int ldx22, float* theta, float* u1, lapack_int ldu1, float* u2, lapack_int ldu2, float* v1t, lapack_int ldv1t, float* v2t, lapack_int ldv2t );
lapack_int LAPACKE_dorcsd( int matrix_layout, char jobu1, char jobu2, char jobv1t, char jobv2t, char trans, char signs, lapack_int m, lapack_int p, lapack_int q, double* x11, lapack_int ldx11, double* x12, lapack_int ldx12, double* x21, lapack_int ldx21, double* x22, lapack_int ldx22, double* theta, double* u1, lapack_int ldu1, double* u2, lapack_int ldu2, double* v1t, lapack_int ldv1t, double* v2t, lapack_int ldv2t );
lapack_int LAPACKE_cuncsd( int matrix_layout, char jobu1, char jobu2, char jobv1t, char jobv2t, char trans, char signs, lapack_int m, lapack_int p, lapack_int q, lapack_complex_float* x11, lapack_int ldx11, lapack_complex_float* x12, lapack_int ldx12, lapack_complex_float* x21, lapack_int ldx21, lapack_complex_float* x22, lapack_int ldx22, float* theta, lapack_complex_float* u1, lapack_int ldu1, lapack_complex_float* u2, lapack_int ldu2, lapack_complex_float* v1t, lapack_int ldv1t, lapack_complex_float* v2t, lapack_int ldv2t );
lapack_int LAPACKE_zuncsd( int matrix_layout, char jobu1, char jobu2, char jobv1t, char jobv2t, char trans, char signs, lapack_int m, lapack_int p, lapack_int q, lapack_complex_double* x11, lapack_int ldx11, lapack_complex_double* x12, lapack_int ldx12, lapack_complex_double* x21, lapack_int ldx21, lapack_complex_double* x22, lapack_int ldx22, double* theta, lapack_complex_double* u1, lapack_int ldu1, lapack_complex_double* u2, lapack_int ldu2, lapack_complex_double* v1t, lapack_int ldv1t, lapack_complex_double* v2t, lapack_int ldv2t );
Include Files
- mkl.h
Description
The routines ?orcsd/?uncsd compute the CS decomposition of an m-by-m partitioned orthogonal matrix X:
or unitary matrix:
x11 is p-by-q. The orthogonal/unitary matrices u1, u2, v1, and v2 are p-by-p, (m-p)-by-(m-p), q-by-q, (m-q)-by-(m-q), respectively. C and S are r-by-r nonnegative diagonal matrices satisfying C2 + S2 = I, in which r = min(p,m-p,q,m-q).
Input Parameters
- matrix_layout
Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
- jobu1
If equals Y, then u1 is computed. Otherwise, u1 is not computed.
- jobu2
If equals Y, then u2 is computed. Otherwise, u2 is not computed.
- jobv1t
If equals Y, then v1t is computed. Otherwise, v1t is not computed.
- jobv2t
If equals Y, then v2t is computed. Otherwise, v2t is not computed.
- trans
- = 'T':
- x, u1, u2, v1t, v2t are stored in row-major order.
- otherwise
- x, u1, u2, v1t, v2t are stored in column-major order.
- signs
- = 'O':
- The lower-left block is made nonpositive (the "other" convention).
- otherwise
- The upper-right block is made nonpositive (the "default" convention).
- 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≤m.
- x11, x12, x21, x22
Arrays of size x11 (ldx11,q), x12 (ldx12,m - q), x21 (ldx21,q), and x22 (ldx22,m - q).
Contain the parts of the orthogonal/unitary matrix whose CSD is desired.
- ldx11, ldx12, ldx21, ldx22
The leading dimensions of the parts of array X. ldx11≥ max(1, p), ldx12≥ max(1, p), ldx21≥ max(1, m - p), ldx22≥ max(1, m - p).
- ldu1
The leading dimension of the array u1. If jobu1 = 'Y', ldu1≥ max(1,p).
- ldu2
The leading dimension of the array u2. If jobu2 = 'Y', ldu2≥ max(1,m-p).
- ldv1t
The leading dimension of the array v1t. If jobv1t = 'Y', ldv1t≥ max(1,q).
- ldv2t
The leading dimension of the array v2t. If jobv2t = 'Y', ldv2t≥ max(1,m-q).
Output Parameters
- theta
Array, size r, in which r = min(p,m-p,q,m-q).
C = diag( cos(theta[0]), ..., cos(theta[r - 1]) ), and
S = diag( sin(theta[0]), ..., sin(theta[r - 1]) ).
- u1
Array, size at least max(1, ldu1*p).
If jobu1 = 'Y', u1 contains the p-by-p orthogonal/unitary matrix u1.
- u2
Array, size at least max(1, ldu2*(m - p)).
If jobu2 = 'Y', u2 contains the (m-p)-by-(m-p) orthogonal/unitary matrix u2.
- v1t
Array, size at least max(1, ldv1t*q) .
If jobv1t = 'Y', v1t contains the q-by-q orthogonal matrix v1T or unitary matrix v1H.
- v2t
Array, size at least max(1, ldv2t*(m - q)).
If jobv2t = 'Y', v2t contains the (m-q)-by-(m-q) orthogonal matrix v2T or unitary matrix v2H.
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.
> 0: ?orcsd/?uncsd did not converge.