.TH DLASD0 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME DLASD0 - divide and conquer approach, DLASD0 computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE .SH SYNOPSIS .TP 19 SUBROUTINE DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK, WORK, INFO ) .TP 19 .ti +4 INTEGER INFO, LDU, LDVT, N, SMLSIZ, SQRE .TP 19 .ti +4 INTEGER IWORK( * ) .TP 19 .ti +4 DOUBLE PRECISION D( * ), E( * ), U( LDU, * ), VT( LDVT, * ), WORK( * ) .SH PURPOSE Using a divide and conquer approach, DLASD0 computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE. The algorithm computes orthogonal matrices U and VT such that B = U * S * VT. The singular values S are overwritten on D. A related subroutine, DLASDA, computes only the singular values, and optionally, the singular vectors in compact form. .br .SH ARGUMENTS .TP 7 N (input) INTEGER On entry, the row dimension of the upper bidiagonal matrix. This is also the dimension of the main diagonal array D. .TP 7 SQRE (input) INTEGER Specifies the column dimension of the bidiagonal matrix. = 0: The bidiagonal matrix has column dimension M = N; .br = 1: The bidiagonal matrix has column dimension M = N+1; .TP 7 D (input/output) DOUBLE PRECISION array, dimension (N) On entry D contains the main diagonal of the bidiagonal matrix. On exit D, if INFO = 0, contains its singular values. .TP 7 E (input) DOUBLE PRECISION array, dimension (M-1) Contains the subdiagonal entries of the bidiagonal matrix. On exit, E has been destroyed. .TP 7 U (output) DOUBLE PRECISION array, dimension at least (LDQ, N) On exit, U contains the left singular vectors. .TP 7 LDU (input) INTEGER On entry, leading dimension of U. .TP 7 VT (output) DOUBLE PRECISION array, dimension at least (LDVT, M) On exit, VT\(aq contains the right singular vectors. .TP 7 LDVT (input) INTEGER On entry, leading dimension of VT. SMLSIZ (input) INTEGER On entry, maximum size of the subproblems at the bottom of the computation tree. .TP 7 IWORK (workspace) INTEGER work array. Dimension must be at least (8 * N) .TP 7 WORK (workspace) DOUBLE PRECISION work array. Dimension must be at least (3 * M**2 + 2 * M) .TP 7 INFO (output) INTEGER = 0: successful exit. .br < 0: if INFO = -i, the i-th argument had an illegal value. .br > 0: if INFO = 1, an singular value did not converge .SH FURTHER DETAILS Based on contributions by .br Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA .br