?orcsd/?uncsd

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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?orcsd/?uncsd

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 v₁^t is computed. Otherwise, v₁^t is not computed.

jobv2t

If equals Y, then v₂^t is computed. Otherwise, v₂^t is not computed.

trans

= 'T':: x, u₁, u₂, v₁^t, v₂^t are stored in row-major order.
otherwise: x, u₁, u₂, v₁^t, v₂^t 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 v₁^T or unitary matrix v₁^H.

v2t

Array, size at least max(1, ldv2t*(m - q)).

If jobv2t = 'Y', v2t contains the (m-q)-by-(m-q) orthogonal matrix v₂^T or unitary matrix v₂^H.

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.

Parent topic: Cosine-Sine Decomposition: LAPACK Driver Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?orcsd/?uncsd

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

See Also