Annotation of rpl/lapack/lapack/zhpgv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
! 2: $ RWORK, 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, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION RWORK( * ), W( * )
! 15: COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZHPGV computes all the eigenvalues and, optionally, the eigenvectors
! 22: * of a complex generalized Hermitian-definite eigenproblem, of the form
! 23: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
! 24: * Here A and B are assumed to be Hermitian, stored in packed format,
! 25: * and B is also positive definite.
! 26: *
! 27: * Arguments
! 28: * =========
! 29: *
! 30: * ITYPE (input) INTEGER
! 31: * Specifies the problem type to be solved:
! 32: * = 1: A*x = (lambda)*B*x
! 33: * = 2: A*B*x = (lambda)*x
! 34: * = 3: B*A*x = (lambda)*x
! 35: *
! 36: * JOBZ (input) CHARACTER*1
! 37: * = 'N': Compute eigenvalues only;
! 38: * = 'V': Compute eigenvalues and eigenvectors.
! 39: *
! 40: * UPLO (input) CHARACTER*1
! 41: * = 'U': Upper triangles of A and B are stored;
! 42: * = 'L': Lower triangles of A and B are stored.
! 43: *
! 44: * N (input) INTEGER
! 45: * The order of the matrices A and B. N >= 0.
! 46: *
! 47: * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
! 48: * On entry, the upper or lower triangle of the Hermitian matrix
! 49: * A, packed columnwise in a linear array. The j-th column of A
! 50: * is stored in the array AP as follows:
! 51: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 52: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
! 53: *
! 54: * On exit, the contents of AP are destroyed.
! 55: *
! 56: * BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
! 57: * On entry, the upper or lower triangle of the Hermitian matrix
! 58: * B, packed columnwise in a linear array. The j-th column of B
! 59: * is stored in the array BP as follows:
! 60: * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
! 61: * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
! 62: *
! 63: * On exit, the triangular factor U or L from the Cholesky
! 64: * factorization B = U**H*U or B = L*L**H, in the same storage
! 65: * format as B.
! 66: *
! 67: * W (output) DOUBLE PRECISION array, dimension (N)
! 68: * If INFO = 0, the eigenvalues in ascending order.
! 69: *
! 70: * Z (output) COMPLEX*16 array, dimension (LDZ, N)
! 71: * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
! 72: * eigenvectors. The eigenvectors are normalized as follows:
! 73: * if ITYPE = 1 or 2, Z**H*B*Z = I;
! 74: * if ITYPE = 3, Z**H*inv(B)*Z = I.
! 75: * If JOBZ = 'N', then Z is not referenced.
! 76: *
! 77: * LDZ (input) INTEGER
! 78: * The leading dimension of the array Z. LDZ >= 1, and if
! 79: * JOBZ = 'V', LDZ >= max(1,N).
! 80: *
! 81: * WORK (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1))
! 82: *
! 83: * RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))
! 84: *
! 85: * INFO (output) INTEGER
! 86: * = 0: successful exit
! 87: * < 0: if INFO = -i, the i-th argument had an illegal value
! 88: * > 0: ZPPTRF or ZHPEV returned an error code:
! 89: * <= N: if INFO = i, ZHPEV failed to converge;
! 90: * i off-diagonal elements of an intermediate
! 91: * tridiagonal form did not convergeto zero;
! 92: * > N: if INFO = N + i, for 1 <= i <= n, then the leading
! 93: * minor of order i of B is not positive definite.
! 94: * The factorization of B could not be completed and
! 95: * no eigenvalues or eigenvectors were computed.
! 96: *
! 97: * =====================================================================
! 98: *
! 99: * .. Local Scalars ..
! 100: LOGICAL UPPER, WANTZ
! 101: CHARACTER TRANS
! 102: INTEGER J, NEIG
! 103: * ..
! 104: * .. External Functions ..
! 105: LOGICAL LSAME
! 106: EXTERNAL LSAME
! 107: * ..
! 108: * .. External Subroutines ..
! 109: EXTERNAL XERBLA, ZHPEV, ZHPGST, ZPPTRF, ZTPMV, ZTPSV
! 110: * ..
! 111: * .. Executable Statements ..
! 112: *
! 113: * Test the input parameters.
! 114: *
! 115: WANTZ = LSAME( JOBZ, 'V' )
! 116: UPPER = LSAME( UPLO, 'U' )
! 117: *
! 118: INFO = 0
! 119: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
! 120: INFO = -1
! 121: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 122: INFO = -2
! 123: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
! 124: INFO = -3
! 125: ELSE IF( N.LT.0 ) THEN
! 126: INFO = -4
! 127: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 128: INFO = -9
! 129: END IF
! 130: IF( INFO.NE.0 ) THEN
! 131: CALL XERBLA( 'ZHPGV ', -INFO )
! 132: RETURN
! 133: END IF
! 134: *
! 135: * Quick return if possible
! 136: *
! 137: IF( N.EQ.0 )
! 138: $ RETURN
! 139: *
! 140: * Form a Cholesky factorization of B.
! 141: *
! 142: CALL ZPPTRF( UPLO, N, BP, INFO )
! 143: IF( INFO.NE.0 ) THEN
! 144: INFO = N + INFO
! 145: RETURN
! 146: END IF
! 147: *
! 148: * Transform problem to standard eigenvalue problem and solve.
! 149: *
! 150: CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
! 151: CALL ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO )
! 152: *
! 153: IF( WANTZ ) THEN
! 154: *
! 155: * Backtransform eigenvectors to the original problem.
! 156: *
! 157: NEIG = N
! 158: IF( INFO.GT.0 )
! 159: $ NEIG = INFO - 1
! 160: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
! 161: *
! 162: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
! 163: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
! 164: *
! 165: IF( UPPER ) THEN
! 166: TRANS = 'N'
! 167: ELSE
! 168: TRANS = 'C'
! 169: END IF
! 170: *
! 171: DO 10 J = 1, NEIG
! 172: CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
! 173: $ 1 )
! 174: 10 CONTINUE
! 175: *
! 176: ELSE IF( ITYPE.EQ.3 ) THEN
! 177: *
! 178: * For B*A*x=(lambda)*x;
! 179: * backtransform eigenvectors: x = L*y or U'*y
! 180: *
! 181: IF( UPPER ) THEN
! 182: TRANS = 'C'
! 183: ELSE
! 184: TRANS = 'N'
! 185: END IF
! 186: *
! 187: DO 20 J = 1, NEIG
! 188: CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
! 189: $ 1 )
! 190: 20 CONTINUE
! 191: END IF
! 192: END IF
! 193: RETURN
! 194: *
! 195: * End of ZHPGV
! 196: *
! 197: END
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