root / src / lapack / double / dgeqr2.f @ 1
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| 1 | 1 | equemene | SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO ) |
|---|---|---|---|
| 2 | 1 | equemene | * |
| 3 | 1 | equemene | * -- LAPACK routine (version 3.2.2) -- |
| 4 | 1 | equemene | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| 5 | 1 | equemene | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| 6 | 1 | equemene | * June 2010 |
| 7 | 1 | equemene | * |
| 8 | 1 | equemene | * .. Scalar Arguments .. |
| 9 | 1 | equemene | INTEGER INFO, LDA, M, N |
| 10 | 1 | equemene | * .. |
| 11 | 1 | equemene | * .. Array Arguments .. |
| 12 | 1 | equemene | DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) |
| 13 | 1 | equemene | * .. |
| 14 | 1 | equemene | * |
| 15 | 1 | equemene | * Purpose |
| 16 | 1 | equemene | * ======= |
| 17 | 1 | equemene | * |
| 18 | 1 | equemene | * DGEQR2 computes a QR factorization of a real m by n matrix A: |
| 19 | 1 | equemene | * A = Q * R. |
| 20 | 1 | equemene | * |
| 21 | 1 | equemene | * Arguments |
| 22 | 1 | equemene | * ========= |
| 23 | 1 | equemene | * |
| 24 | 1 | equemene | * M (input) INTEGER |
| 25 | 1 | equemene | * The number of rows of the matrix A. M >= 0. |
| 26 | 1 | equemene | * |
| 27 | 1 | equemene | * N (input) INTEGER |
| 28 | 1 | equemene | * The number of columns of the matrix A. N >= 0. |
| 29 | 1 | equemene | * |
| 30 | 1 | equemene | * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
| 31 | 1 | equemene | * On entry, the m by n matrix A. |
| 32 | 1 | equemene | * On exit, the elements on and above the diagonal of the array |
| 33 | 1 | equemene | * contain the min(m,n) by n upper trapezoidal matrix R (R is |
| 34 | 1 | equemene | * upper triangular if m >= n); the elements below the diagonal, |
| 35 | 1 | equemene | * with the array TAU, represent the orthogonal matrix Q as a |
| 36 | 1 | equemene | * product of elementary reflectors (see Further Details). |
| 37 | 1 | equemene | * |
| 38 | 1 | equemene | * LDA (input) INTEGER |
| 39 | 1 | equemene | * The leading dimension of the array A. LDA >= max(1,M). |
| 40 | 1 | equemene | * |
| 41 | 1 | equemene | * TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) |
| 42 | 1 | equemene | * The scalar factors of the elementary reflectors (see Further |
| 43 | 1 | equemene | * Details). |
| 44 | 1 | equemene | * |
| 45 | 1 | equemene | * WORK (workspace) DOUBLE PRECISION array, dimension (N) |
| 46 | 1 | equemene | * |
| 47 | 1 | equemene | * INFO (output) INTEGER |
| 48 | 1 | equemene | * = 0: successful exit |
| 49 | 1 | equemene | * < 0: if INFO = -i, the i-th argument had an illegal value |
| 50 | 1 | equemene | * |
| 51 | 1 | equemene | * Further Details |
| 52 | 1 | equemene | * =============== |
| 53 | 1 | equemene | * |
| 54 | 1 | equemene | * The matrix Q is represented as a product of elementary reflectors |
| 55 | 1 | equemene | * |
| 56 | 1 | equemene | * Q = H(1) H(2) . . . H(k), where k = min(m,n). |
| 57 | 1 | equemene | * |
| 58 | 1 | equemene | * Each H(i) has the form |
| 59 | 1 | equemene | * |
| 60 | 1 | equemene | * H(i) = I - tau * v * v' |
| 61 | 1 | equemene | * |
| 62 | 1 | equemene | * where tau is a real scalar, and v is a real vector with |
| 63 | 1 | equemene | * v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), |
| 64 | 1 | equemene | * and tau in TAU(i). |
| 65 | 1 | equemene | * |
| 66 | 1 | equemene | * ===================================================================== |
| 67 | 1 | equemene | * |
| 68 | 1 | equemene | * .. Parameters .. |
| 69 | 1 | equemene | DOUBLE PRECISION ONE |
| 70 | 1 | equemene | PARAMETER ( ONE = 1.0D+0 ) |
| 71 | 1 | equemene | * .. |
| 72 | 1 | equemene | * .. Local Scalars .. |
| 73 | 1 | equemene | INTEGER I, K |
| 74 | 1 | equemene | DOUBLE PRECISION AII |
| 75 | 1 | equemene | * .. |
| 76 | 1 | equemene | * .. External Subroutines .. |
| 77 | 1 | equemene | EXTERNAL DLARF, DLARFG, XERBLA |
| 78 | 1 | equemene | * .. |
| 79 | 1 | equemene | * .. Intrinsic Functions .. |
| 80 | 1 | equemene | INTRINSIC MAX, MIN |
| 81 | 1 | equemene | * .. |
| 82 | 1 | equemene | * .. Executable Statements .. |
| 83 | 1 | equemene | * |
| 84 | 1 | equemene | * Test the input arguments |
| 85 | 1 | equemene | * |
| 86 | 1 | equemene | INFO = 0 |
| 87 | 1 | equemene | IF( M.LT.0 ) THEN |
| 88 | 1 | equemene | INFO = -1 |
| 89 | 1 | equemene | ELSE IF( N.LT.0 ) THEN |
| 90 | 1 | equemene | INFO = -2 |
| 91 | 1 | equemene | ELSE IF( LDA.LT.MAX( 1, M ) ) THEN |
| 92 | 1 | equemene | INFO = -4 |
| 93 | 1 | equemene | END IF |
| 94 | 1 | equemene | IF( INFO.NE.0 ) THEN |
| 95 | 1 | equemene | CALL XERBLA( 'DGEQR2', -INFO ) |
| 96 | 1 | equemene | RETURN |
| 97 | 1 | equemene | END IF |
| 98 | 1 | equemene | * |
| 99 | 1 | equemene | K = MIN( M, N ) |
| 100 | 1 | equemene | * |
| 101 | 1 | equemene | DO 10 I = 1, K |
| 102 | 1 | equemene | * |
| 103 | 1 | equemene | * Generate elementary reflector H(i) to annihilate A(i+1:m,i) |
| 104 | 1 | equemene | * |
| 105 | 1 | equemene | CALL DLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1, |
| 106 | 1 | equemene | $ TAU( I ) ) |
| 107 | 1 | equemene | IF( I.LT.N ) THEN |
| 108 | 1 | equemene | * |
| 109 | 1 | equemene | * Apply H(i) to A(i:m,i+1:n) from the left |
| 110 | 1 | equemene | * |
| 111 | 1 | equemene | AII = A( I, I ) |
| 112 | 1 | equemene | A( I, I ) = ONE |
| 113 | 1 | equemene | CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ), |
| 114 | 1 | equemene | $ A( I, I+1 ), LDA, WORK ) |
| 115 | 1 | equemene | A( I, I ) = AII |
| 116 | 1 | equemene | END IF |
| 117 | 1 | equemene | 10 CONTINUE |
| 118 | 1 | equemene | RETURN |
| 119 | 1 | equemene | * |
| 120 | 1 | equemene | * End of DGEQR2 |
| 121 | 1 | equemene | * |
| 122 | 1 | equemene | END |