1SORMQR(1) LAPACK routine (version 3.2) SORMQR(1)
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6 SORMQR - overwrites the general real M-by-N matrix C with SIDE = 'L'
7 SIDE = 'R' TRANS = 'N'
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10 SUBROUTINE SORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
11 LWORK, INFO )
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13 CHARACTER SIDE, TRANS
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15 INTEGER INFO, K, LDA, LDC, LWORK, M, N
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17 REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
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20 SORMQR overwrites the general real M-by-N matrix C with TRANS = 'T':
21 Q**T * C C * Q**T
22 where Q is a real orthogonal matrix defined as the product of k elemen‐
23 tary reflectors
24 Q = H(1) H(2) . . . H(k)
25 as returned by SGEQRF. Q is of order M if SIDE = 'L' and of order N if
26 SIDE = 'R'.
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29 SIDE (input) CHARACTER*1
30 = 'L': apply Q or Q**T from the Left;
31 = 'R': apply Q or Q**T from the Right.
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33 TRANS (input) CHARACTER*1
34 = 'N': No transpose, apply Q;
35 = 'T': Transpose, apply Q**T.
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37 M (input) INTEGER
38 The number of rows of the matrix C. M >= 0.
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40 N (input) INTEGER
41 The number of columns of the matrix C. N >= 0.
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43 K (input) INTEGER
44 The number of elementary reflectors whose product defines the
45 matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >=
46 0.
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48 A (input) REAL array, dimension (LDA,K)
49 The i-th column must contain the vector which defines the ele‐
50 mentary reflector H(i), for i = 1,2,...,k, as returned by SGE‐
51 QRF in the first k columns of its array argument A. A is modi‐
52 fied by the routine but restored on exit.
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54 LDA (input) INTEGER
55 The leading dimension of the array A. If SIDE = 'L', LDA >=
56 max(1,M); if SIDE = 'R', LDA >= max(1,N).
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58 TAU (input) REAL array, dimension (K)
59 TAU(i) must contain the scalar factor of the elementary reflec‐
60 tor H(i), as returned by SGEQRF.
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62 C (input/output) REAL array, dimension (LDC,N)
63 On entry, the M-by-N matrix C. On exit, C is overwritten by
64 Q*C or Q**T*C or C*Q**T or C*Q.
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66 LDC (input) INTEGER
67 The leading dimension of the array C. LDC >= max(1,M).
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69 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
70 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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72 LWORK (input) INTEGER
73 The dimension of the array WORK. If SIDE = 'L', LWORK >=
74 max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum per‐
75 formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
76 = 'R', where NB is the optimal blocksize. If LWORK = -1, then
77 a workspace query is assumed; the routine only calculates the
78 optimal size of the WORK array, returns this value as the first
79 entry of the WORK array, and no error message related to LWORK
80 is issued by XERBLA.
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82 INFO (output) INTEGER
83 = 0: successful exit
84 < 0: if INFO = -i, the i-th argument had an illegal value
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88 LAPACK routine (version 3.2) November 2008 SORMQR(1)