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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, 00002 $ LWORK, IWORK, LIWORK, INFO ) 00003 * 00004 * -- LAPACK driver routine (version 3.3.1) -- 00005 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00006 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00007 * -- April 2011 -- 00008 * 00009 * .. Scalar Arguments .. 00010 CHARACTER JOBZ, UPLO 00011 INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N 00012 * .. 00013 * .. Array Arguments .. 00014 INTEGER IWORK( * ) 00015 DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ), 00016 $ Z( LDZ, * ) 00017 * .. 00018 * 00019 * Purpose 00020 * ======= 00021 * 00022 * DSPGVD computes all the eigenvalues, and optionally, the eigenvectors 00023 * of a real generalized symmetric-definite eigenproblem, of the form 00024 * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and 00025 * B are assumed to be symmetric, stored in packed format, and B is also 00026 * positive definite. 00027 * If eigenvectors are desired, it uses a divide and conquer algorithm. 00028 * 00029 * The divide and conquer algorithm makes very mild assumptions about 00030 * floating point arithmetic. It will work on machines with a guard 00031 * digit in add/subtract, or on those binary machines without guard 00032 * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or 00033 * Cray-2. It could conceivably fail on hexadecimal or decimal machines 00034 * without guard digits, but we know of none. 00035 * 00036 * Arguments 00037 * ========= 00038 * 00039 * ITYPE (input) INTEGER 00040 * Specifies the problem type to be solved: 00041 * = 1: A*x = (lambda)*B*x 00042 * = 2: A*B*x = (lambda)*x 00043 * = 3: B*A*x = (lambda)*x 00044 * 00045 * JOBZ (input) CHARACTER*1 00046 * = 'N': Compute eigenvalues only; 00047 * = 'V': Compute eigenvalues and eigenvectors. 00048 * 00049 * UPLO (input) CHARACTER*1 00050 * = 'U': Upper triangles of A and B are stored; 00051 * = 'L': Lower triangles of A and B are stored. 00052 * 00053 * N (input) INTEGER 00054 * The order of the matrices A and B. N >= 0. 00055 * 00056 * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) 00057 * On entry, the upper or lower triangle of the symmetric matrix 00058 * A, packed columnwise in a linear array. The j-th column of A 00059 * is stored in the array AP as follows: 00060 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00061 * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. 00062 * 00063 * On exit, the contents of AP are destroyed. 00064 * 00065 * BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) 00066 * On entry, the upper or lower triangle of the symmetric matrix 00067 * B, packed columnwise in a linear array. The j-th column of B 00068 * is stored in the array BP as follows: 00069 * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; 00070 * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. 00071 * 00072 * On exit, the triangular factor U or L from the Cholesky 00073 * factorization B = U**T*U or B = L*L**T, in the same storage 00074 * format as B. 00075 * 00076 * W (output) DOUBLE PRECISION array, dimension (N) 00077 * If INFO = 0, the eigenvalues in ascending order. 00078 * 00079 * Z (output) DOUBLE PRECISION array, dimension (LDZ, N) 00080 * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of 00081 * eigenvectors. The eigenvectors are normalized as follows: 00082 * if ITYPE = 1 or 2, Z**T*B*Z = I; 00083 * if ITYPE = 3, Z**T*inv(B)*Z = I. 00084 * If JOBZ = 'N', then Z is not referenced. 00085 * 00086 * LDZ (input) INTEGER 00087 * The leading dimension of the array Z. LDZ >= 1, and if 00088 * JOBZ = 'V', LDZ >= max(1,N). 00089 * 00090 * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00091 * On exit, if INFO = 0, WORK(1) returns the required LWORK. 00092 * 00093 * LWORK (input) INTEGER 00094 * The dimension of the array WORK. 00095 * If N <= 1, LWORK >= 1. 00096 * If JOBZ = 'N' and N > 1, LWORK >= 2*N. 00097 * If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. 00098 * 00099 * If LWORK = -1, then a workspace query is assumed; the routine 00100 * only calculates the required sizes of the WORK and IWORK 00101 * arrays, returns these values as the first entries of the WORK 00102 * and IWORK arrays, and no error message related to LWORK or 00103 * LIWORK is issued by XERBLA. 00104 * 00105 * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) 00106 * On exit, if INFO = 0, IWORK(1) returns the required LIWORK. 00107 * 00108 * LIWORK (input) INTEGER 00109 * The dimension of the array IWORK. 00110 * If JOBZ = 'N' or N <= 1, LIWORK >= 1. 00111 * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. 00112 * 00113 * If LIWORK = -1, then a workspace query is assumed; the 00114 * routine only calculates the required sizes of the WORK and 00115 * IWORK arrays, returns these values as the first entries of 00116 * the WORK and IWORK arrays, and no error message related to 00117 * LWORK or LIWORK is issued by XERBLA. 00118 * 00119 * INFO (output) INTEGER 00120 * = 0: successful exit 00121 * < 0: if INFO = -i, the i-th argument had an illegal value 00122 * > 0: DPPTRF or DSPEVD returned an error code: 00123 * <= N: if INFO = i, DSPEVD failed to converge; 00124 * i off-diagonal elements of an intermediate 00125 * tridiagonal form did not converge to zero; 00126 * > N: if INFO = N + i, for 1 <= i <= N, then the leading 00127 * minor of order i of B is not positive definite. 00128 * The factorization of B could not be completed and 00129 * no eigenvalues or eigenvectors were computed. 00130 * 00131 * Further Details 00132 * =============== 00133 * 00134 * Based on contributions by 00135 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 00136 * 00137 * ===================================================================== 00138 * 00139 * .. Parameters .. 00140 DOUBLE PRECISION TWO 00141 PARAMETER ( TWO = 2.0D+0 ) 00142 * .. 00143 * .. Local Scalars .. 00144 LOGICAL LQUERY, UPPER, WANTZ 00145 CHARACTER TRANS 00146 INTEGER J, LIWMIN, LWMIN, NEIG 00147 * .. 00148 * .. External Functions .. 00149 LOGICAL LSAME 00150 EXTERNAL LSAME 00151 * .. 00152 * .. External Subroutines .. 00153 EXTERNAL DPPTRF, DSPEVD, DSPGST, DTPMV, DTPSV, XERBLA 00154 * .. 00155 * .. Intrinsic Functions .. 00156 INTRINSIC DBLE, MAX 00157 * .. 00158 * .. Executable Statements .. 00159 * 00160 * Test the input parameters. 00161 * 00162 WANTZ = LSAME( JOBZ, 'V' ) 00163 UPPER = LSAME( UPLO, 'U' ) 00164 LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) 00165 * 00166 INFO = 0 00167 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 00168 INFO = -1 00169 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 00170 INFO = -2 00171 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 00172 INFO = -3 00173 ELSE IF( N.LT.0 ) THEN 00174 INFO = -4 00175 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 00176 INFO = -9 00177 END IF 00178 * 00179 IF( INFO.EQ.0 ) THEN 00180 IF( N.LE.1 ) THEN 00181 LIWMIN = 1 00182 LWMIN = 1 00183 ELSE 00184 IF( WANTZ ) THEN 00185 LIWMIN = 3 + 5*N 00186 LWMIN = 1 + 6*N + 2*N**2 00187 ELSE 00188 LIWMIN = 1 00189 LWMIN = 2*N 00190 END IF 00191 END IF 00192 WORK( 1 ) = LWMIN 00193 IWORK( 1 ) = LIWMIN 00194 IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 00195 INFO = -11 00196 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN 00197 INFO = -13 00198 END IF 00199 END IF 00200 * 00201 IF( INFO.NE.0 ) THEN 00202 CALL XERBLA( 'DSPGVD', -INFO ) 00203 RETURN 00204 ELSE IF( LQUERY ) THEN 00205 RETURN 00206 END IF 00207 * 00208 * Quick return if possible 00209 * 00210 IF( N.EQ.0 ) 00211 $ RETURN 00212 * 00213 * Form a Cholesky factorization of BP. 00214 * 00215 CALL DPPTRF( UPLO, N, BP, INFO ) 00216 IF( INFO.NE.0 ) THEN 00217 INFO = N + INFO 00218 RETURN 00219 END IF 00220 * 00221 * Transform problem to standard eigenvalue problem and solve. 00222 * 00223 CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO ) 00224 CALL DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK, 00225 $ LIWORK, INFO ) 00226 LWMIN = MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) ) 00227 LIWMIN = MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) ) 00228 * 00229 IF( WANTZ ) THEN 00230 * 00231 * Backtransform eigenvectors to the original problem. 00232 * 00233 NEIG = N 00234 IF( INFO.GT.0 ) 00235 $ NEIG = INFO - 1 00236 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN 00237 * 00238 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; 00239 * backtransform eigenvectors: x = inv(L)**T *y or inv(U)*y 00240 * 00241 IF( UPPER ) THEN 00242 TRANS = 'N' 00243 ELSE 00244 TRANS = 'T' 00245 END IF 00246 * 00247 DO 10 J = 1, NEIG 00248 CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 00249 $ 1 ) 00250 10 CONTINUE 00251 * 00252 ELSE IF( ITYPE.EQ.3 ) THEN 00253 * 00254 * For B*A*x=(lambda)*x; 00255 * backtransform eigenvectors: x = L*y or U**T *y 00256 * 00257 IF( UPPER ) THEN 00258 TRANS = 'T' 00259 ELSE 00260 TRANS = 'N' 00261 END IF 00262 * 00263 DO 20 J = 1, NEIG 00264 CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 00265 $ 1 ) 00266 20 CONTINUE 00267 END IF 00268 END IF 00269 * 00270 WORK( 1 ) = LWMIN 00271 IWORK( 1 ) = LIWMIN 00272 * 00273 RETURN 00274 * 00275 * End of DSPGVD 00276 * 00277 END
1.7.3 
