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