Annotation of rpl/lapack/lapack/dggbak.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
! 2: $ LDV, INFO )
! 3: *
! 4: * -- LAPACK 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 JOB, SIDE
! 11: INTEGER IHI, ILO, INFO, LDV, M, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION LSCALE( * ), RSCALE( * ), V( LDV, * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * DGGBAK forms the right or left eigenvectors of a real generalized
! 21: * eigenvalue problem A*x = lambda*B*x, by backward transformation on
! 22: * the computed eigenvectors of the balanced pair of matrices output by
! 23: * DGGBAL.
! 24: *
! 25: * Arguments
! 26: * =========
! 27: *
! 28: * JOB (input) CHARACTER*1
! 29: * Specifies the type of backward transformation required:
! 30: * = 'N': do nothing, return immediately;
! 31: * = 'P': do backward transformation for permutation only;
! 32: * = 'S': do backward transformation for scaling only;
! 33: * = 'B': do backward transformations for both permutation and
! 34: * scaling.
! 35: * JOB must be the same as the argument JOB supplied to DGGBAL.
! 36: *
! 37: * SIDE (input) CHARACTER*1
! 38: * = 'R': V contains right eigenvectors;
! 39: * = 'L': V contains left eigenvectors.
! 40: *
! 41: * N (input) INTEGER
! 42: * The number of rows of the matrix V. N >= 0.
! 43: *
! 44: * ILO (input) INTEGER
! 45: * IHI (input) INTEGER
! 46: * The integers ILO and IHI determined by DGGBAL.
! 47: * 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
! 48: *
! 49: * LSCALE (input) DOUBLE PRECISION array, dimension (N)
! 50: * Details of the permutations and/or scaling factors applied
! 51: * to the left side of A and B, as returned by DGGBAL.
! 52: *
! 53: * RSCALE (input) DOUBLE PRECISION array, dimension (N)
! 54: * Details of the permutations and/or scaling factors applied
! 55: * to the right side of A and B, as returned by DGGBAL.
! 56: *
! 57: * M (input) INTEGER
! 58: * The number of columns of the matrix V. M >= 0.
! 59: *
! 60: * V (input/output) DOUBLE PRECISION array, dimension (LDV,M)
! 61: * On entry, the matrix of right or left eigenvectors to be
! 62: * transformed, as returned by DTGEVC.
! 63: * On exit, V is overwritten by the transformed eigenvectors.
! 64: *
! 65: * LDV (input) INTEGER
! 66: * The leading dimension of the matrix V. LDV >= max(1,N).
! 67: *
! 68: * INFO (output) INTEGER
! 69: * = 0: successful exit.
! 70: * < 0: if INFO = -i, the i-th argument had an illegal value.
! 71: *
! 72: * Further Details
! 73: * ===============
! 74: *
! 75: * See R.C. Ward, Balancing the generalized eigenvalue problem,
! 76: * SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
! 77: *
! 78: * =====================================================================
! 79: *
! 80: * .. Local Scalars ..
! 81: LOGICAL LEFTV, RIGHTV
! 82: INTEGER I, K
! 83: * ..
! 84: * .. External Functions ..
! 85: LOGICAL LSAME
! 86: EXTERNAL LSAME
! 87: * ..
! 88: * .. External Subroutines ..
! 89: EXTERNAL DSCAL, DSWAP, XERBLA
! 90: * ..
! 91: * .. Intrinsic Functions ..
! 92: INTRINSIC MAX
! 93: * ..
! 94: * .. Executable Statements ..
! 95: *
! 96: * Test the input parameters
! 97: *
! 98: RIGHTV = LSAME( SIDE, 'R' )
! 99: LEFTV = LSAME( SIDE, 'L' )
! 100: *
! 101: INFO = 0
! 102: IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND.
! 103: $ .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN
! 104: INFO = -1
! 105: ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN
! 106: INFO = -2
! 107: ELSE IF( N.LT.0 ) THEN
! 108: INFO = -3
! 109: ELSE IF( ILO.LT.1 ) THEN
! 110: INFO = -4
! 111: ELSE IF( N.EQ.0 .AND. IHI.EQ.0 .AND. ILO.NE.1 ) THEN
! 112: INFO = -4
! 113: ELSE IF( N.GT.0 .AND. ( IHI.LT.ILO .OR. IHI.GT.MAX( 1, N ) ) )
! 114: $ THEN
! 115: INFO = -5
! 116: ELSE IF( N.EQ.0 .AND. ILO.EQ.1 .AND. IHI.NE.0 ) THEN
! 117: INFO = -5
! 118: ELSE IF( M.LT.0 ) THEN
! 119: INFO = -8
! 120: ELSE IF( LDV.LT.MAX( 1, N ) ) THEN
! 121: INFO = -10
! 122: END IF
! 123: IF( INFO.NE.0 ) THEN
! 124: CALL XERBLA( 'DGGBAK', -INFO )
! 125: RETURN
! 126: END IF
! 127: *
! 128: * Quick return if possible
! 129: *
! 130: IF( N.EQ.0 )
! 131: $ RETURN
! 132: IF( M.EQ.0 )
! 133: $ RETURN
! 134: IF( LSAME( JOB, 'N' ) )
! 135: $ RETURN
! 136: *
! 137: IF( ILO.EQ.IHI )
! 138: $ GO TO 30
! 139: *
! 140: * Backward balance
! 141: *
! 142: IF( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN
! 143: *
! 144: * Backward transformation on right eigenvectors
! 145: *
! 146: IF( RIGHTV ) THEN
! 147: DO 10 I = ILO, IHI
! 148: CALL DSCAL( M, RSCALE( I ), V( I, 1 ), LDV )
! 149: 10 CONTINUE
! 150: END IF
! 151: *
! 152: * Backward transformation on left eigenvectors
! 153: *
! 154: IF( LEFTV ) THEN
! 155: DO 20 I = ILO, IHI
! 156: CALL DSCAL( M, LSCALE( I ), V( I, 1 ), LDV )
! 157: 20 CONTINUE
! 158: END IF
! 159: END IF
! 160: *
! 161: * Backward permutation
! 162: *
! 163: 30 CONTINUE
! 164: IF( LSAME( JOB, 'P' ) .OR. LSAME( JOB, 'B' ) ) THEN
! 165: *
! 166: * Backward permutation on right eigenvectors
! 167: *
! 168: IF( RIGHTV ) THEN
! 169: IF( ILO.EQ.1 )
! 170: $ GO TO 50
! 171: *
! 172: DO 40 I = ILO - 1, 1, -1
! 173: K = RSCALE( I )
! 174: IF( K.EQ.I )
! 175: $ GO TO 40
! 176: CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
! 177: 40 CONTINUE
! 178: *
! 179: 50 CONTINUE
! 180: IF( IHI.EQ.N )
! 181: $ GO TO 70
! 182: DO 60 I = IHI + 1, N
! 183: K = RSCALE( I )
! 184: IF( K.EQ.I )
! 185: $ GO TO 60
! 186: CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
! 187: 60 CONTINUE
! 188: END IF
! 189: *
! 190: * Backward permutation on left eigenvectors
! 191: *
! 192: 70 CONTINUE
! 193: IF( LEFTV ) THEN
! 194: IF( ILO.EQ.1 )
! 195: $ GO TO 90
! 196: DO 80 I = ILO - 1, 1, -1
! 197: K = LSCALE( I )
! 198: IF( K.EQ.I )
! 199: $ GO TO 80
! 200: CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
! 201: 80 CONTINUE
! 202: *
! 203: 90 CONTINUE
! 204: IF( IHI.EQ.N )
! 205: $ GO TO 110
! 206: DO 100 I = IHI + 1, N
! 207: K = LSCALE( I )
! 208: IF( K.EQ.I )
! 209: $ GO TO 100
! 210: CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
! 211: 100 CONTINUE
! 212: END IF
! 213: END IF
! 214: *
! 215: 110 CONTINUE
! 216: *
! 217: RETURN
! 218: *
! 219: * End of DGGBAK
! 220: *
! 221: END
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