root / src / lapack / double / dtzrzf.f @ 2
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| 1 | 1 | equemene | SUBROUTINE DTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) |
|---|---|---|---|
| 2 | 1 | equemene | * |
| 3 | 1 | equemene | * -- LAPACK routine (version 3.2) -- |
| 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 | * November 2006 |
| 7 | 1 | equemene | * |
| 8 | 1 | equemene | * .. Scalar Arguments .. |
| 9 | 1 | equemene | INTEGER INFO, LDA, LWORK, 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 | * DTZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A |
| 19 | 1 | equemene | * to upper triangular form by means of orthogonal transformations. |
| 20 | 1 | equemene | * |
| 21 | 1 | equemene | * The upper trapezoidal matrix A is factored as |
| 22 | 1 | equemene | * |
| 23 | 1 | equemene | * A = ( R 0 ) * Z, |
| 24 | 1 | equemene | * |
| 25 | 1 | equemene | * where Z is an N-by-N orthogonal matrix and R is an M-by-M upper |
| 26 | 1 | equemene | * triangular matrix. |
| 27 | 1 | equemene | * |
| 28 | 1 | equemene | * Arguments |
| 29 | 1 | equemene | * ========= |
| 30 | 1 | equemene | * |
| 31 | 1 | equemene | * M (input) INTEGER |
| 32 | 1 | equemene | * The number of rows of the matrix A. M >= 0. |
| 33 | 1 | equemene | * |
| 34 | 1 | equemene | * N (input) INTEGER |
| 35 | 1 | equemene | * The number of columns of the matrix A. N >= M. |
| 36 | 1 | equemene | * |
| 37 | 1 | equemene | * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
| 38 | 1 | equemene | * On entry, the leading M-by-N upper trapezoidal part of the |
| 39 | 1 | equemene | * array A must contain the matrix to be factorized. |
| 40 | 1 | equemene | * On exit, the leading M-by-M upper triangular part of A |
| 41 | 1 | equemene | * contains the upper triangular matrix R, and elements M+1 to |
| 42 | 1 | equemene | * N of the first M rows of A, with the array TAU, represent the |
| 43 | 1 | equemene | * orthogonal matrix Z as a product of M elementary reflectors. |
| 44 | 1 | equemene | * |
| 45 | 1 | equemene | * LDA (input) INTEGER |
| 46 | 1 | equemene | * The leading dimension of the array A. LDA >= max(1,M). |
| 47 | 1 | equemene | * |
| 48 | 1 | equemene | * TAU (output) DOUBLE PRECISION array, dimension (M) |
| 49 | 1 | equemene | * The scalar factors of the elementary reflectors. |
| 50 | 1 | equemene | * |
| 51 | 1 | equemene | * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) |
| 52 | 1 | equemene | * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
| 53 | 1 | equemene | * |
| 54 | 1 | equemene | * LWORK (input) INTEGER |
| 55 | 1 | equemene | * The dimension of the array WORK. LWORK >= max(1,M). |
| 56 | 1 | equemene | * For optimum performance LWORK >= M*NB, where NB is |
| 57 | 1 | equemene | * the optimal blocksize. |
| 58 | 1 | equemene | * |
| 59 | 1 | equemene | * If LWORK = -1, then a workspace query is assumed; the routine |
| 60 | 1 | equemene | * only calculates the optimal size of the WORK array, returns |
| 61 | 1 | equemene | * this value as the first entry of the WORK array, and no error |
| 62 | 1 | equemene | * message related to LWORK is issued by XERBLA. |
| 63 | 1 | equemene | * |
| 64 | 1 | equemene | * INFO (output) INTEGER |
| 65 | 1 | equemene | * = 0: successful exit |
| 66 | 1 | equemene | * < 0: if INFO = -i, the i-th argument had an illegal value |
| 67 | 1 | equemene | * |
| 68 | 1 | equemene | * Further Details |
| 69 | 1 | equemene | * =============== |
| 70 | 1 | equemene | * |
| 71 | 1 | equemene | * Based on contributions by |
| 72 | 1 | equemene | * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
| 73 | 1 | equemene | * |
| 74 | 1 | equemene | * The factorization is obtained by Householder's method. The kth |
| 75 | 1 | equemene | * transformation matrix, Z( k ), which is used to introduce zeros into |
| 76 | 1 | equemene | * the ( m - k + 1 )th row of A, is given in the form |
| 77 | 1 | equemene | * |
| 78 | 1 | equemene | * Z( k ) = ( I 0 ), |
| 79 | 1 | equemene | * ( 0 T( k ) ) |
| 80 | 1 | equemene | * |
| 81 | 1 | equemene | * where |
| 82 | 1 | equemene | * |
| 83 | 1 | equemene | * T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ), |
| 84 | 1 | equemene | * ( 0 ) |
| 85 | 1 | equemene | * ( z( k ) ) |
| 86 | 1 | equemene | * |
| 87 | 1 | equemene | * tau is a scalar and z( k ) is an ( n - m ) element vector. |
| 88 | 1 | equemene | * tau and z( k ) are chosen to annihilate the elements of the kth row |
| 89 | 1 | equemene | * of X. |
| 90 | 1 | equemene | * |
| 91 | 1 | equemene | * The scalar tau is returned in the kth element of TAU and the vector |
| 92 | 1 | equemene | * u( k ) in the kth row of A, such that the elements of z( k ) are |
| 93 | 1 | equemene | * in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in |
| 94 | 1 | equemene | * the upper triangular part of A. |
| 95 | 1 | equemene | * |
| 96 | 1 | equemene | * Z is given by |
| 97 | 1 | equemene | * |
| 98 | 1 | equemene | * Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). |
| 99 | 1 | equemene | * |
| 100 | 1 | equemene | * ===================================================================== |
| 101 | 1 | equemene | * |
| 102 | 1 | equemene | * .. Parameters .. |
| 103 | 1 | equemene | DOUBLE PRECISION ZERO |
| 104 | 1 | equemene | PARAMETER ( ZERO = 0.0D+0 ) |
| 105 | 1 | equemene | * .. |
| 106 | 1 | equemene | * .. Local Scalars .. |
| 107 | 1 | equemene | LOGICAL LQUERY |
| 108 | 1 | equemene | INTEGER I, IB, IWS, KI, KK, LDWORK, LWKOPT, M1, MU, NB, |
| 109 | 1 | equemene | $ NBMIN, NX |
| 110 | 1 | equemene | * .. |
| 111 | 1 | equemene | * .. External Subroutines .. |
| 112 | 1 | equemene | EXTERNAL DLARZB, DLARZT, DLATRZ, XERBLA |
| 113 | 1 | equemene | * .. |
| 114 | 1 | equemene | * .. Intrinsic Functions .. |
| 115 | 1 | equemene | INTRINSIC MAX, MIN |
| 116 | 1 | equemene | * .. |
| 117 | 1 | equemene | * .. External Functions .. |
| 118 | 1 | equemene | INTEGER ILAENV |
| 119 | 1 | equemene | EXTERNAL ILAENV |
| 120 | 1 | equemene | * .. |
| 121 | 1 | equemene | * .. Executable Statements .. |
| 122 | 1 | equemene | * |
| 123 | 1 | equemene | * Test the input arguments |
| 124 | 1 | equemene | * |
| 125 | 1 | equemene | INFO = 0 |
| 126 | 1 | equemene | LQUERY = ( LWORK.EQ.-1 ) |
| 127 | 1 | equemene | IF( M.LT.0 ) THEN |
| 128 | 1 | equemene | INFO = -1 |
| 129 | 1 | equemene | ELSE IF( N.LT.M ) THEN |
| 130 | 1 | equemene | INFO = -2 |
| 131 | 1 | equemene | ELSE IF( LDA.LT.MAX( 1, M ) ) THEN |
| 132 | 1 | equemene | INFO = -4 |
| 133 | 1 | equemene | END IF |
| 134 | 1 | equemene | * |
| 135 | 1 | equemene | IF( INFO.EQ.0 ) THEN |
| 136 | 1 | equemene | IF( M.EQ.0 .OR. M.EQ.N ) THEN |
| 137 | 1 | equemene | LWKOPT = 1 |
| 138 | 1 | equemene | ELSE |
| 139 | 1 | equemene | * |
| 140 | 1 | equemene | * Determine the block size. |
| 141 | 1 | equemene | * |
| 142 | 1 | equemene | NB = ILAENV( 1, 'DGERQF', ' ', M, N, -1, -1 ) |
| 143 | 1 | equemene | LWKOPT = M*NB |
| 144 | 1 | equemene | END IF |
| 145 | 1 | equemene | WORK( 1 ) = LWKOPT |
| 146 | 1 | equemene | * |
| 147 | 1 | equemene | IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN |
| 148 | 1 | equemene | INFO = -7 |
| 149 | 1 | equemene | END IF |
| 150 | 1 | equemene | END IF |
| 151 | 1 | equemene | * |
| 152 | 1 | equemene | IF( INFO.NE.0 ) THEN |
| 153 | 1 | equemene | CALL XERBLA( 'DTZRZF', -INFO ) |
| 154 | 1 | equemene | RETURN |
| 155 | 1 | equemene | ELSE IF( LQUERY ) THEN |
| 156 | 1 | equemene | RETURN |
| 157 | 1 | equemene | END IF |
| 158 | 1 | equemene | * |
| 159 | 1 | equemene | * Quick return if possible |
| 160 | 1 | equemene | * |
| 161 | 1 | equemene | IF( M.EQ.0 ) THEN |
| 162 | 1 | equemene | RETURN |
| 163 | 1 | equemene | ELSE IF( M.EQ.N ) THEN |
| 164 | 1 | equemene | DO 10 I = 1, N |
| 165 | 1 | equemene | TAU( I ) = ZERO |
| 166 | 1 | equemene | 10 CONTINUE |
| 167 | 1 | equemene | RETURN |
| 168 | 1 | equemene | END IF |
| 169 | 1 | equemene | * |
| 170 | 1 | equemene | NBMIN = 2 |
| 171 | 1 | equemene | NX = 1 |
| 172 | 1 | equemene | IWS = M |
| 173 | 1 | equemene | IF( NB.GT.1 .AND. NB.LT.M ) THEN |
| 174 | 1 | equemene | * |
| 175 | 1 | equemene | * Determine when to cross over from blocked to unblocked code. |
| 176 | 1 | equemene | * |
| 177 | 1 | equemene | NX = MAX( 0, ILAENV( 3, 'DGERQF', ' ', M, N, -1, -1 ) ) |
| 178 | 1 | equemene | IF( NX.LT.M ) THEN |
| 179 | 1 | equemene | * |
| 180 | 1 | equemene | * Determine if workspace is large enough for blocked code. |
| 181 | 1 | equemene | * |
| 182 | 1 | equemene | LDWORK = M |
| 183 | 1 | equemene | IWS = LDWORK*NB |
| 184 | 1 | equemene | IF( LWORK.LT.IWS ) THEN |
| 185 | 1 | equemene | * |
| 186 | 1 | equemene | * Not enough workspace to use optimal NB: reduce NB and |
| 187 | 1 | equemene | * determine the minimum value of NB. |
| 188 | 1 | equemene | * |
| 189 | 1 | equemene | NB = LWORK / LDWORK |
| 190 | 1 | equemene | NBMIN = MAX( 2, ILAENV( 2, 'DGERQF', ' ', M, N, -1, |
| 191 | 1 | equemene | $ -1 ) ) |
| 192 | 1 | equemene | END IF |
| 193 | 1 | equemene | END IF |
| 194 | 1 | equemene | END IF |
| 195 | 1 | equemene | * |
| 196 | 1 | equemene | IF( NB.GE.NBMIN .AND. NB.LT.M .AND. NX.LT.M ) THEN |
| 197 | 1 | equemene | * |
| 198 | 1 | equemene | * Use blocked code initially. |
| 199 | 1 | equemene | * The last kk rows are handled by the block method. |
| 200 | 1 | equemene | * |
| 201 | 1 | equemene | M1 = MIN( M+1, N ) |
| 202 | 1 | equemene | KI = ( ( M-NX-1 ) / NB )*NB |
| 203 | 1 | equemene | KK = MIN( M, KI+NB ) |
| 204 | 1 | equemene | * |
| 205 | 1 | equemene | DO 20 I = M - KK + KI + 1, M - KK + 1, -NB |
| 206 | 1 | equemene | IB = MIN( M-I+1, NB ) |
| 207 | 1 | equemene | * |
| 208 | 1 | equemene | * Compute the TZ factorization of the current block |
| 209 | 1 | equemene | * A(i:i+ib-1,i:n) |
| 210 | 1 | equemene | * |
| 211 | 1 | equemene | CALL DLATRZ( IB, N-I+1, N-M, A( I, I ), LDA, TAU( I ), |
| 212 | 1 | equemene | $ WORK ) |
| 213 | 1 | equemene | IF( I.GT.1 ) THEN |
| 214 | 1 | equemene | * |
| 215 | 1 | equemene | * Form the triangular factor of the block reflector |
| 216 | 1 | equemene | * H = H(i+ib-1) . . . H(i+1) H(i) |
| 217 | 1 | equemene | * |
| 218 | 1 | equemene | CALL DLARZT( 'Backward', 'Rowwise', N-M, IB, A( I, M1 ), |
| 219 | 1 | equemene | $ LDA, TAU( I ), WORK, LDWORK ) |
| 220 | 1 | equemene | * |
| 221 | 1 | equemene | * Apply H to A(1:i-1,i:n) from the right |
| 222 | 1 | equemene | * |
| 223 | 1 | equemene | CALL DLARZB( 'Right', 'No transpose', 'Backward', |
| 224 | 1 | equemene | $ 'Rowwise', I-1, N-I+1, IB, N-M, A( I, M1 ), |
| 225 | 1 | equemene | $ LDA, WORK, LDWORK, A( 1, I ), LDA, |
| 226 | 1 | equemene | $ WORK( IB+1 ), LDWORK ) |
| 227 | 1 | equemene | END IF |
| 228 | 1 | equemene | 20 CONTINUE |
| 229 | 1 | equemene | MU = I + NB - 1 |
| 230 | 1 | equemene | ELSE |
| 231 | 1 | equemene | MU = M |
| 232 | 1 | equemene | END IF |
| 233 | 1 | equemene | * |
| 234 | 1 | equemene | * Use unblocked code to factor the last or only block |
| 235 | 1 | equemene | * |
| 236 | 1 | equemene | IF( MU.GT.0 ) |
| 237 | 1 | equemene | $ CALL DLATRZ( MU, N, N-M, A, LDA, TAU, WORK ) |
| 238 | 1 | equemene | * |
| 239 | 1 | equemene | WORK( 1 ) = LWKOPT |
| 240 | 1 | equemene | * |
| 241 | 1 | equemene | RETURN |
| 242 | 1 | equemene | * |
| 243 | 1 | equemene | * End of DTZRZF |
| 244 | 1 | equemene | * |
| 245 | 1 | equemene | END |