1DLASD0(1) LAPACK auxiliary routine (version 3.1) DLASD0(1)
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6 DLASD0 - divide and conquer approach, DLASD0 computes the singular
7 value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B
8 with diagonal D and offdiagonal E, where M = N + SQRE
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11 SUBROUTINE DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
12 WORK, INFO )
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14 INTEGER INFO, LDU, LDVT, N, SMLSIZ, SQRE
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16 INTEGER IWORK( * )
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18 DOUBLE PRECISION D( * ), E( * ), U( LDU, * ), VT( LDVT, *
19 ), WORK( * )
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22 Using a divide and conquer approach, DLASD0 computes the singular value
23 decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with
24 diagonal D and offdiagonal E, where M = N + SQRE. The algorithm com‐
25 putes orthogonal matrices U and VT such that B = U * S * VT. The singu‐
26 lar values S are overwritten on D.
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28 A related subroutine, DLASDA, computes only the singular values, and
29 optionally, the singular vectors in compact form.
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33 N (input) INTEGER
34 On entry, the row dimension of the upper bidiagonal matrix.
35 This is also the dimension of the main diagonal array D.
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37 SQRE (input) INTEGER
38 Specifies the column dimension of the bidiagonal matrix. = 0:
39 The bidiagonal matrix has column dimension M = N;
40 = 1: The bidiagonal matrix has column dimension M = N+1;
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42 D (input/output) DOUBLE PRECISION array, dimension (N)
43 On entry D contains the main diagonal of the bidiagonal matrix.
44 On exit D, if INFO = 0, contains its singular values.
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46 E (input) DOUBLE PRECISION array, dimension (M-1)
47 Contains the subdiagonal entries of the bidiagonal matrix. On
48 exit, E has been destroyed.
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50 U (output) DOUBLE PRECISION array, dimension at least (LDQ, N)
51 On exit, U contains the left singular vectors.
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53 LDU (input) INTEGER
54 On entry, leading dimension of U.
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56 VT (output) DOUBLE PRECISION array, dimension at least (LDVT, M)
57 On exit, VT' contains the right singular vectors.
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59 LDVT (input) INTEGER
60 On entry, leading dimension of VT.
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62 SMLSIZ (input) INTEGER On entry, maximum size of the subproblems
63 at the bottom of the computation tree.
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65 IWORK (workspace) INTEGER work array.
66 Dimension must be at least (8 * N)
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68 WORK (workspace) DOUBLE PRECISION work array.
69 Dimension must be at least (3 * M**2 + 2 * M)
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71 INFO (output) INTEGER
72 = 0: successful exit.
73 < 0: if INFO = -i, the i-th argument had an illegal value.
74 > 0: if INFO = 1, an singular value did not converge
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77 Based on contributions by
78 Ming Gu and Huan Ren, Computer Science Division, University of
79 California at Berkeley, USA
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84 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006 DLASD0(1)