|
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 |
SUBROUTINE ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
* * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, ITYPE, N * .. * .. Array Arguments .. COMPLEX*16 AP( * ), BP( * ) * .. * * Purpose * ======= * * ZHPGST reduces a complex Hermitian-definite generalized * eigenproblem to standard form, using packed storage. * * If ITYPE = 1, the problem is A*x = lambda*B*x, * and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) * * If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or * B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L. * * B must have been previously factorized as U**H*U or L*L**H by ZPPTRF. * * Arguments * ========= * * ITYPE (input) INTEGER * = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); * = 2 or 3: compute U*A*U**H or L**H*A*L. * * UPLO (input) CHARACTER*1 * = 'U': Upper triangle of A is stored and B is factored as * U**H*U; * = 'L': Lower triangle of A is stored and B is factored as * L*L**H. * * N (input) INTEGER * The order of the matrices A and B. N >= 0. * * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) * On entry, the upper or lower triangle of the Hermitian matrix * A, packed columnwise in a linear array. The j-th column of A * is stored in the array AP as follows: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. * * On exit, if INFO = 0, the transformed matrix, stored in the * same format as A. * * BP (input) COMPLEX*16 array, dimension (N*(N+1)/2) * The triangular factor from the Cholesky factorization of B, * stored in the same format as A, as returned by ZPPTRF. * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, HALF PARAMETER ( ONE = 1.0D+0, HALF = 0.5D+0 ) COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J, J1, J1J1, JJ, K, K1, K1K1, KK DOUBLE PRECISION AJJ, AKK, BJJ, BKK COMPLEX*16 CT * .. * .. External Subroutines .. EXTERNAL XERBLA, ZAXPY, ZDSCAL, ZHPMV, ZHPR2, ZTPMV, $ ZTPSV * .. * .. Intrinsic Functions .. INTRINSIC DBLE * .. * .. External Functions .. LOGICAL LSAME COMPLEX*16 ZDOTC EXTERNAL LSAME, ZDOTC * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHPGST', -INFO ) RETURN END IF * IF( ITYPE.EQ.1 ) THEN IF( UPPER ) THEN * * Compute inv(U**H)*A*inv(U) * * J1 and JJ are the indices of A(1,j) and A(j,j) * JJ = 0 DO 10 J = 1, N J1 = JJ + 1 JJ = JJ + J * * Compute the j-th column of the upper triangle of A * AP( JJ ) = DBLE( AP( JJ ) ) BJJ = BP( JJ ) CALL ZTPSV( UPLO, 'Conjugate transpose', 'Non-unit', J, $ BP, AP( J1 ), 1 ) CALL ZHPMV( UPLO, J-1, -CONE, AP, BP( J1 ), 1, CONE, $ AP( J1 ), 1 ) CALL ZDSCAL( J-1, ONE / BJJ, AP( J1 ), 1 ) AP( JJ ) = ( AP( JJ )-ZDOTC( J-1, AP( J1 ), 1, BP( J1 ), $ 1 ) ) / BJJ 10 CONTINUE ELSE * * Compute inv(L)*A*inv(L**H) * * KK and K1K1 are the indices of A(k,k) and A(k+1,k+1) * KK = 1 DO 20 K = 1, N K1K1 = KK + N - K + 1 * * Update the lower triangle of A(k:n,k:n) * AKK = AP( KK ) BKK = BP( KK ) AKK = AKK / BKK**2 AP( KK ) = AKK IF( K.LT.N ) THEN CALL ZDSCAL( N-K, ONE / BKK, AP( KK+1 ), 1 ) CT = -HALF*AKK CALL ZAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 ) CALL ZHPR2( UPLO, N-K, -CONE, AP( KK+1 ), 1, $ BP( KK+1 ), 1, AP( K1K1 ) ) CALL ZAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 ) CALL ZTPSV( UPLO, 'No transpose', 'Non-unit', N-K, $ BP( K1K1 ), AP( KK+1 ), 1 ) END IF KK = K1K1 20 CONTINUE END IF ELSE IF( UPPER ) THEN * * Compute U*A*U**H * * K1 and KK are the indices of A(1,k) and A(k,k) * KK = 0 DO 30 K = 1, N K1 = KK + 1 KK = KK + K * * Update the upper triangle of A(1:k,1:k) * AKK = AP( KK ) BKK = BP( KK ) CALL ZTPMV( UPLO, 'No transpose', 'Non-unit', K-1, BP, $ AP( K1 ), 1 ) CT = HALF*AKK CALL ZAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 ) CALL ZHPR2( UPLO, K-1, CONE, AP( K1 ), 1, BP( K1 ), 1, $ AP ) CALL ZAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 ) CALL ZDSCAL( K-1, BKK, AP( K1 ), 1 ) AP( KK ) = AKK*BKK**2 30 CONTINUE ELSE * * Compute L**H *A*L * * JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1) * JJ = 1 DO 40 J = 1, N J1J1 = JJ + N - J + 1 * * Compute the j-th column of the lower triangle of A * AJJ = AP( JJ ) BJJ = BP( JJ ) AP( JJ ) = AJJ*BJJ + ZDOTC( N-J, AP( JJ+1 ), 1, $ BP( JJ+1 ), 1 ) CALL ZDSCAL( N-J, BJJ, AP( JJ+1 ), 1 ) CALL ZHPMV( UPLO, N-J, CONE, AP( J1J1 ), BP( JJ+1 ), 1, $ CONE, AP( JJ+1 ), 1 ) CALL ZTPMV( UPLO, 'Conjugate transpose', 'Non-unit', $ N-J+1, BP( JJ ), AP( JJ ), 1 ) JJ = J1J1 40 CONTINUE END IF END IF RETURN * * End of ZHPGST * END |