Annotation of rpl/lapack/lapack/dspgvd.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
! 2: $ LWORK, IWORK, LIWORK, INFO )
! 3: *
! 4: * -- LAPACK driver routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: CHARACTER JOBZ, UPLO
! 11: INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: INTEGER IWORK( * )
! 15: DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
! 16: $ Z( LDZ, * )
! 17: * ..
! 18: *
! 19: * Purpose
! 20: * =======
! 21: *
! 22: * DSPGVD computes all the eigenvalues, and optionally, the eigenvectors
! 23: * of a real generalized symmetric-definite eigenproblem, of the form
! 24: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
! 25: * B are assumed to be symmetric, stored in packed format, and B is also
! 26: * positive definite.
! 27: * If eigenvectors are desired, it uses a divide and conquer algorithm.
! 28: *
! 29: * The divide and conquer algorithm makes very mild assumptions about
! 30: * floating point arithmetic. It will work on machines with a guard
! 31: * digit in add/subtract, or on those binary machines without guard
! 32: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
! 33: * Cray-2. It could conceivably fail on hexadecimal or decimal machines
! 34: * without guard digits, but we know of none.
! 35: *
! 36: * Arguments
! 37: * =========
! 38: *
! 39: * ITYPE (input) INTEGER
! 40: * Specifies the problem type to be solved:
! 41: * = 1: A*x = (lambda)*B*x
! 42: * = 2: A*B*x = (lambda)*x
! 43: * = 3: B*A*x = (lambda)*x
! 44: *
! 45: * JOBZ (input) CHARACTER*1
! 46: * = 'N': Compute eigenvalues only;
! 47: * = 'V': Compute eigenvalues and eigenvectors.
! 48: *
! 49: * UPLO (input) CHARACTER*1
! 50: * = 'U': Upper triangles of A and B are stored;
! 51: * = 'L': Lower triangles of A and B are stored.
! 52: *
! 53: * N (input) INTEGER
! 54: * The order of the matrices A and B. N >= 0.
! 55: *
! 56: * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 57: * On entry, the upper or lower triangle of the symmetric matrix
! 58: * A, packed columnwise in a linear array. The j-th column of A
! 59: * is stored in the array AP as follows:
! 60: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 61: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
! 62: *
! 63: * On exit, the contents of AP are destroyed.
! 64: *
! 65: * BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 66: * On entry, the upper or lower triangle of the symmetric matrix
! 67: * B, packed columnwise in a linear array. The j-th column of B
! 68: * is stored in the array BP as follows:
! 69: * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
! 70: * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
! 71: *
! 72: * On exit, the triangular factor U or L from the Cholesky
! 73: * factorization B = U**T*U or B = L*L**T, in the same storage
! 74: * format as B.
! 75: *
! 76: * W (output) DOUBLE PRECISION array, dimension (N)
! 77: * If INFO = 0, the eigenvalues in ascending order.
! 78: *
! 79: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
! 80: * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
! 81: * eigenvectors. The eigenvectors are normalized as follows:
! 82: * if ITYPE = 1 or 2, Z**T*B*Z = I;
! 83: * if ITYPE = 3, Z**T*inv(B)*Z = I.
! 84: * If JOBZ = 'N', then Z is not referenced.
! 85: *
! 86: * LDZ (input) INTEGER
! 87: * The leading dimension of the array Z. LDZ >= 1, and if
! 88: * JOBZ = 'V', LDZ >= max(1,N).
! 89: *
! 90: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 91: * On exit, if INFO = 0, WORK(1) returns the required LWORK.
! 92: *
! 93: * LWORK (input) INTEGER
! 94: * The dimension of the array WORK.
! 95: * If N <= 1, LWORK >= 1.
! 96: * If JOBZ = 'N' and N > 1, LWORK >= 2*N.
! 97: * If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
! 98: *
! 99: * If LWORK = -1, then a workspace query is assumed; the routine
! 100: * only calculates the required sizes of the WORK and IWORK
! 101: * arrays, returns these values as the first entries of the WORK
! 102: * and IWORK arrays, and no error message related to LWORK or
! 103: * LIWORK is issued by XERBLA.
! 104: *
! 105: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
! 106: * On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
! 107: *
! 108: * LIWORK (input) INTEGER
! 109: * The dimension of the array IWORK.
! 110: * If JOBZ = 'N' or N <= 1, LIWORK >= 1.
! 111: * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
! 112: *
! 113: * If LIWORK = -1, then a workspace query is assumed; the
! 114: * routine only calculates the required sizes of the WORK and
! 115: * IWORK arrays, returns these values as the first entries of
! 116: * the WORK and IWORK arrays, and no error message related to
! 117: * LWORK or LIWORK is issued by XERBLA.
! 118: *
! 119: * INFO (output) INTEGER
! 120: * = 0: successful exit
! 121: * < 0: if INFO = -i, the i-th argument had an illegal value
! 122: * > 0: DPPTRF or DSPEVD returned an error code:
! 123: * <= N: if INFO = i, DSPEVD failed to converge;
! 124: * i off-diagonal elements of an intermediate
! 125: * tridiagonal form did not converge to zero;
! 126: * > N: if INFO = N + i, for 1 <= i <= N, then the leading
! 127: * minor of order i of B is not positive definite.
! 128: * The factorization of B could not be completed and
! 129: * no eigenvalues or eigenvectors were computed.
! 130: *
! 131: * Further Details
! 132: * ===============
! 133: *
! 134: * Based on contributions by
! 135: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
! 136: *
! 137: * =====================================================================
! 138: *
! 139: * .. Parameters ..
! 140: DOUBLE PRECISION TWO
! 141: PARAMETER ( TWO = 2.0D+0 )
! 142: * ..
! 143: * .. Local Scalars ..
! 144: LOGICAL LQUERY, UPPER, WANTZ
! 145: CHARACTER TRANS
! 146: INTEGER J, LIWMIN, LWMIN, NEIG
! 147: * ..
! 148: * .. External Functions ..
! 149: LOGICAL LSAME
! 150: EXTERNAL LSAME
! 151: * ..
! 152: * .. External Subroutines ..
! 153: EXTERNAL DPPTRF, DSPEVD, DSPGST, DTPMV, DTPSV, XERBLA
! 154: * ..
! 155: * .. Intrinsic Functions ..
! 156: INTRINSIC DBLE, MAX
! 157: * ..
! 158: * .. Executable Statements ..
! 159: *
! 160: * Test the input parameters.
! 161: *
! 162: WANTZ = LSAME( JOBZ, 'V' )
! 163: UPPER = LSAME( UPLO, 'U' )
! 164: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
! 165: *
! 166: INFO = 0
! 167: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
! 168: INFO = -1
! 169: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 170: INFO = -2
! 171: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
! 172: INFO = -3
! 173: ELSE IF( N.LT.0 ) THEN
! 174: INFO = -4
! 175: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 176: INFO = -9
! 177: END IF
! 178: *
! 179: IF( INFO.EQ.0 ) THEN
! 180: IF( N.LE.1 ) THEN
! 181: LIWMIN = 1
! 182: LWMIN = 1
! 183: ELSE
! 184: IF( WANTZ ) THEN
! 185: LIWMIN = 3 + 5*N
! 186: LWMIN = 1 + 6*N + 2*N**2
! 187: ELSE
! 188: LIWMIN = 1
! 189: LWMIN = 2*N
! 190: END IF
! 191: END IF
! 192: WORK( 1 ) = LWMIN
! 193: IWORK( 1 ) = LIWMIN
! 194: *
! 195: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 196: INFO = -11
! 197: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
! 198: INFO = -13
! 199: END IF
! 200: END IF
! 201: *
! 202: IF( INFO.NE.0 ) THEN
! 203: CALL XERBLA( 'DSPGVD', -INFO )
! 204: RETURN
! 205: ELSE IF( LQUERY ) THEN
! 206: RETURN
! 207: END IF
! 208: *
! 209: * Quick return if possible
! 210: *
! 211: IF( N.EQ.0 )
! 212: $ RETURN
! 213: *
! 214: * Form a Cholesky factorization of BP.
! 215: *
! 216: CALL DPPTRF( UPLO, N, BP, INFO )
! 217: IF( INFO.NE.0 ) THEN
! 218: INFO = N + INFO
! 219: RETURN
! 220: END IF
! 221: *
! 222: * Transform problem to standard eigenvalue problem and solve.
! 223: *
! 224: CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
! 225: CALL DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK,
! 226: $ LIWORK, INFO )
! 227: LWMIN = MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) )
! 228: LIWMIN = MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) )
! 229: *
! 230: IF( WANTZ ) THEN
! 231: *
! 232: * Backtransform eigenvectors to the original problem.
! 233: *
! 234: NEIG = N
! 235: IF( INFO.GT.0 )
! 236: $ NEIG = INFO - 1
! 237: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
! 238: *
! 239: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
! 240: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
! 241: *
! 242: IF( UPPER ) THEN
! 243: TRANS = 'N'
! 244: ELSE
! 245: TRANS = 'T'
! 246: END IF
! 247: *
! 248: DO 10 J = 1, NEIG
! 249: CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
! 250: $ 1 )
! 251: 10 CONTINUE
! 252: *
! 253: ELSE IF( ITYPE.EQ.3 ) THEN
! 254: *
! 255: * For B*A*x=(lambda)*x;
! 256: * backtransform eigenvectors: x = L*y or U'*y
! 257: *
! 258: IF( UPPER ) THEN
! 259: TRANS = 'T'
! 260: ELSE
! 261: TRANS = 'N'
! 262: END IF
! 263: *
! 264: DO 20 J = 1, NEIG
! 265: CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
! 266: $ 1 )
! 267: 20 CONTINUE
! 268: END IF
! 269: END IF
! 270: *
! 271: WORK( 1 ) = LWMIN
! 272: IWORK( 1 ) = LIWMIN
! 273: *
! 274: RETURN
! 275: *
! 276: * End of DSPGVD
! 277: *
! 278: END
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