--- rpl/lapack/lapack/zuncsd2by1.f 2014/01/27 09:28:45 1.2 +++ rpl/lapack/lapack/zuncsd2by1.f 2015/11/26 11:44:27 1.3 @@ -55,12 +55,11 @@ *> [ 0 S 0 ] *> [ 0 0 I ] *> -*> X11 is P-by-Q. The unitary matrices U1, U2, V1, and V2 are P-by-P, -*> (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-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). -*> -*>\endverbatim +*> 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). +*> \endverbatim * * Arguments: * ========== @@ -68,172 +67,165 @@ *> \param[in] JOBU1 *> \verbatim *> JOBU1 is CHARACTER -*> = 'Y': U1 is computed; -*> otherwise: U1 is not computed. +*> = 'Y': U1 is computed; +*> otherwise: U1 is not computed. *> \endverbatim *> *> \param[in] JOBU2 *> \verbatim *> JOBU2 is CHARACTER -*> = 'Y': U2 is computed; -*> otherwise: U2 is not computed. +*> = 'Y': U2 is computed; +*> otherwise: U2 is not computed. *> \endverbatim *> *> \param[in] JOBV1T *> \verbatim *> JOBV1T is CHARACTER -*> = 'Y': V1T is computed; -*> otherwise: V1T is not computed. +*> = 'Y': V1T is computed; +*> otherwise: V1T is not computed. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER -*> The number of rows and columns in X. +*> The number of rows in X. *> \endverbatim *> *> \param[in] P *> \verbatim *> P is INTEGER -*> The number of rows in X11 and X12. 0 <= P <= M. +*> The number of rows in X11. 0 <= P <= M. *> \endverbatim *> *> \param[in] Q *> \verbatim *> Q is INTEGER -*> The number of columns in X11 and X21. 0 <= Q <= M. +*> The number of columns in X11 and X21. 0 <= Q <= M. *> \endverbatim *> *> \param[in,out] X11 *> \verbatim *> X11 is COMPLEX*16 array, dimension (LDX11,Q) -*> On entry, part of the unitary matrix whose CSD is -*> desired. +*> On entry, part of the unitary matrix whose CSD is desired. *> \endverbatim *> *> \param[in] LDX11 *> \verbatim *> LDX11 is INTEGER -*> The leading dimension of X11. LDX11 >= MAX(1,P). +*> The leading dimension of X11. LDX11 >= MAX(1,P). *> \endverbatim *> *> \param[in,out] X21 *> \verbatim *> X21 is COMPLEX*16 array, dimension (LDX21,Q) -*> On entry, part of the unitary matrix whose CSD is -*> desired. +*> On entry, part of the unitary matrix whose CSD is desired. *> \endverbatim *> *> \param[in] LDX21 *> \verbatim *> LDX21 is INTEGER -*> The leading dimension of X21. LDX21 >= MAX(1,M-P). +*> The leading dimension of X21. LDX21 >= MAX(1,M-P). *> \endverbatim *> *> \param[out] THETA *> \verbatim -*> THETA is COMPLEX*16 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)) ). +*> THETA is DOUBLE PRECISION 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)) ). *> \endverbatim *> *> \param[out] U1 *> \verbatim *> U1 is COMPLEX*16 array, dimension (P) -*> If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1. +*> If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1. *> \endverbatim *> *> \param[in] LDU1 *> \verbatim *> LDU1 is INTEGER -*> The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= -*> MAX(1,P). +*> The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= +*> MAX(1,P). *> \endverbatim *> *> \param[out] U2 *> \verbatim *> U2 is COMPLEX*16 array, dimension (M-P) -*> If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary -*> matrix U2. +*> If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary +*> matrix U2. *> \endverbatim *> *> \param[in] LDU2 *> \verbatim *> LDU2 is INTEGER -*> The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= -*> MAX(1,M-P). +*> The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= +*> MAX(1,M-P). *> \endverbatim *> *> \param[out] V1T *> \verbatim *> V1T is COMPLEX*16 array, dimension (Q) -*> If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary -*> matrix V1**T. +*> If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary +*> matrix V1**T. *> \endverbatim *> *> \param[in] LDV1T *> \verbatim *> LDV1T is INTEGER -*> The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= -*> MAX(1,Q). +*> The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= +*> MAX(1,Q). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> If INFO > 0 on exit, WORK(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. +*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. -*> \endverbatim -*> \verbatim -*> 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. +*> 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 array, returns +*> this value as the first entry of the work array, and no error +*> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION 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. +*> 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. *> \endverbatim *> *> \param[in] LRWORK *> \verbatim *> LRWORK is INTEGER -*> The dimension of the array RWORK. +*> The dimension of the array RWORK. *> -*> If LRWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the RWORK array, returns -*> this value as the first entry of the work array, and no error -*> message related to LRWORK is issued by XERBLA. +*> If LRWORK = -1, then a workspace query is assumed; the routine +*> only calculates the optimal size of the RWORK array, returns +*> this value as the first entry of the work array, and no error +*> message related to LRWORK is issued by XERBLA. +*> \endverbatim +* *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q)) *> \endverbatim -*> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: ZBBCSD did not converge. See the description of WORK +*> = 0: successful exit. +*> < 0: if INFO = -i, the i-th argument had an illegal value. +*> > 0: ZBBCSD did not converge. See the description of WORK *> above for details. *> \endverbatim * @@ -261,7 +253,7 @@ $ LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, $ INFO ) * -* -- LAPACK computational routine (version 3.5.0) -- +* -- LAPACK computational routine (version 3.6.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * July 2012