1CGELSS(1) LAPACK driver routine (version 3.2) CGELSS(1)
2
6 CGELSS - computes the minimum norm solution to a complex linear least
7 squares problem
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10 SUBROUTINE CGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK,
11 LWORK, RWORK, INFO )
12 INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
14 REAL RCOND
16 REAL RWORK( * ), S( * )
18 COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
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22 CGELSS computes the minimum norm solution to a complex linear least
23 squares problem: Minimize 2-norm(| b - A*x |).
24 using the singular value decomposition (SVD) of A. A is an M-by-N
25 matrix which may be rank-deficient.
26 Several right hand side vectors b and solution vectors x can be handled
27 in a single call; they are stored as the columns of the M-by-NRHS right
28 hand side matrix B and the N-by-NRHS solution matrix X.
29 The effective rank of A is determined by treating as zero those singu‐
30 lar values which are less than RCOND times the largest singular value.
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33 M (input) INTEGER
34 The number of rows of the matrix A. M >= 0.
35 N (input) INTEGER
37 The number of columns of the matrix A. N >= 0.
38 NRHS (input) INTEGER
40 The number of right hand sides, i.e., the number of columns of
41 the matrices B and X. NRHS >= 0.
42 A (input/output) COMPLEX array, dimension (LDA,N)
44 On entry, the M-by-N matrix A. On exit, the first min(m,n)
45 rows of A are overwritten with its right singular vectors,
46 stored rowwise.
47 LDA (input) INTEGER
49 The leading dimension of the array A. LDA >= max(1,M).
50 B (input/output) COMPLEX array, dimension (LDB,NRHS)
52 On entry, the M-by-NRHS right hand side matrix B. On exit, B
53 is overwritten by the N-by-NRHS solution matrix X. If m >= n
54 and RANK = n, the residual sum-of-squares for the solution in
55 the i-th column is given by the sum of squares of the modulus
56 of elements n+1:m in that column.
57 LDB (input) INTEGER
59 The leading dimension of the array B. LDB >= max(1,M,N).
60 S (output) REAL array, dimension (min(M,N))
62 The singular values of A in decreasing order. The condition
63 number of A in the 2-norm = S(1)/S(min(m,n)).
64 RCOND (input) REAL
66 RCOND is used to determine the effective rank of A. Singular
67 values S(i) <= RCOND*S(1) are treated as zero. If RCOND < 0,
68 machine precision is used instead.
69 RANK (output) INTEGER
71 The effective rank of A, i.e., the number of singular values
72 which are greater than RCOND*S(1).
73 WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
75 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
76 LWORK (input) INTEGER
78 The dimension of the array WORK. LWORK >= 1, and also: LWORK >=
79 2*min(M,N) + max(M,N,NRHS) For good performance, LWORK should
80 generally be larger. If LWORK = -1, then a workspace query is
81 assumed; the routine only calculates the optimal size of the
82 WORK array, returns this value as the first entry of the WORK
83 array, and no error message related to LWORK is issued by
84 XERBLA.
85 RWORK (workspace) REAL array, dimension (5*min(M,N))
87 INFO (output) INTEGER
89 = 0: successful exit
90 < 0: if INFO = -i, the i-th argument had an illegal value.
91 > 0: the algorithm for computing the SVD failed to converge;
92 if INFO = i, i off-diagonal elements of an intermediate bidiag‐
93 onal form did not converge to zero.
94 LAPACK driver routine (version 3.N2o)vember 2008 CGELSS(1)