--- name: "cuncsd2by1.f" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/cuncsd2by1.f" --- # cuncsd2by1.f(3) ## NAME SRC/cuncsd2by1.f ## SYNOPSIS ### Functions/Subroutines subroutine **cuncsd2by1** (jobu1, jobu2, jobv1t, m, p, q, x11, ldx11, x21, ldx21, theta, u1, ldu1, u2, ldu2, v1t, ldv1t, work, lwork, rwork, lrwork, iwork, info)\ **CUNCSD2BY1** ## Function/Subroutine Documentation ### subroutine cuncsd2by1 (character jobu1, character jobu2, character jobv1t, integer m, integer p, integer q, complex, dimension(ldx11,\*) x11, integer ldx11, complex, dimension(ldx21,\*) x21, integer ldx21, real, dimension(\*) theta, complex, dimension(ldu1,\*) u1, integer ldu1, complex, dimension(ldu2,\*) u2, integer ldu2, complex, dimension(ldv1t,\*) v1t, integer ldv1t, complex, dimension(\*) work, integer lwork, real, dimension(\*) rwork, integer lrwork, integer, dimension(\*) iwork, integer info) **CUNCSD2BY1** **Purpose:** ``` !> !> CUNCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with !> orthonormal columns that has been partitioned into a 2-by-1 block !> structure: !> !> [ I1 0 0 ] !> [ 0 C 0 ] !> [ X11 ] [ U1 | ] [ 0 0 0 ] !> X = [-----] = [---------] [----------] V1**T . !> [ X21 ] [ | U2 ] [ 0 0 0 ] !> [ 0 S 0 ] !> [ 0 0 I2] !> !> X11 is P-by-Q. The unitary matrices U1, U2, and V1 are P-by-P, !> (M-P)-by-(M-P), and Q-by-Q, respectively. C and S are R-by-R !> nonnegative diagonal matrices satisfying C^2 + S^2 = I, in which !> R = MIN(P,M-P,Q,M-Q). I1 is a K1-by-K1 identity matrix and I2 is a !> K2-by-K2 identity matrix, where K1 = MAX(Q+P-M,0), K2 = MAX(Q-P,0). !> !> ``` **Parameters** *JOBU1* ``` !> JOBU1 is CHARACTER !> = 'Y': U1 is computed; !> otherwise: U1 is not computed. !> ``` *JOBU2* ``` !> JOBU2 is CHARACTER !> = 'Y': U2 is computed; !> otherwise: U2 is not computed. !> ``` *JOBV1T* ``` !> JOBV1T is CHARACTER !> = 'Y': V1T is computed; !> otherwise: V1T is not computed. !> ``` *M* ``` !> M is INTEGER !> The number of rows in X. !> ``` *P* ``` !> P is INTEGER !> The number of rows in X11. 0 <= P <= M. !> ``` *Q* ``` !> Q is INTEGER !> The number of columns in X11 and X21. 0 <= Q <= M. !> ``` *X11* ``` !> X11 is COMPLEX array, dimension (LDX11,Q) !> On entry, part of the unitary matrix whose CSD is desired. !> ``` *LDX11* ``` !> LDX11 is INTEGER !> The leading dimension of X11. LDX11 >= MAX(1,P). !> ``` *X21* ``` !> X21 is COMPLEX array, dimension (LDX21,Q) !> On entry, part of the unitary matrix whose CSD is desired. !> ``` *LDX21* ``` !> LDX21 is INTEGER !> The leading dimension of X21. LDX21 >= MAX(1,M-P). !> ``` *THETA* ``` !> THETA is REAL array, dimension (R), in which R = !> MIN(P,M-P,Q,M-Q). !> C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and !> S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ). !> ``` *U1* ``` !> U1 is COMPLEX array, dimension (P) !> If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1. !> ``` *LDU1* ``` !> LDU1 is INTEGER !> The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= !> MAX(1,P). !> ``` *U2* ``` !> U2 is COMPLEX array, dimension (M-P) !> If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary !> matrix U2. !> ``` *LDU2* ``` !> LDU2 is INTEGER !> The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= !> MAX(1,M-P). !> ``` *V1T* ``` !> V1T is COMPLEX array, dimension (Q) !> If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary !> matrix V1**T. !> ``` *LDV1T* ``` !> LDV1T is INTEGER !> The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= !> MAX(1,Q). !> ``` *WORK* ``` !> WORK is COMPLEX array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> ``` *LWORK* ``` !> LWORK is INTEGER !> The dimension of the array WORK. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK and RWORK !> arrays, returns this value as the first entry of the WORK !> and RWORK array, respectively, and no error message related !> to LWORK or LRWORK is issued by XERBLA. !> ``` *RWORK* ``` !> RWORK is REAL array, dimension (MAX(1,LRWORK)) !> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. !> If INFO > 0 on exit, RWORK(2:R) contains the values PHI(1), !> ..., PHI(R-1) that, together with THETA(1), ..., THETA(R), !> define the matrix in intermediate bidiagonal-block form !> remaining after nonconvergence. INFO specifies the number !> of nonzero PHI's. !> ``` *LRWORK* ``` !> LRWORK is INTEGER !> The dimension of the array RWORK. !> !> If LRWORK=-1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK and RWORK !> arrays, returns this value as the first entry of the WORK !> and RWORK array, respectively, and no error message related !> to LWORK or LRWORK is issued by XERBLA. !> ``` *IWORK* ``` !> IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q)) !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit. !> < 0: if INFO = -i, the i-th argument had an illegal value. !> > 0: CBBCSD did not converge. See the description of WORK !> above for details. !> ``` **References:** \[1\] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009. **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **253** of file **cuncsd2by1.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.