Annotation of rpl/lapack/lapack/dgebak.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV,
! 2: $ 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 SCALE( * ), V( LDV, * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * DGEBAK forms the right or left eigenvectors of a real general matrix
! 21: * by backward transformation on the computed eigenvectors of the
! 22: * balanced matrix output by DGEBAL.
! 23: *
! 24: * Arguments
! 25: * =========
! 26: *
! 27: * JOB (input) CHARACTER*1
! 28: * Specifies the type of backward transformation required:
! 29: * = 'N', do nothing, return immediately;
! 30: * = 'P', do backward transformation for permutation only;
! 31: * = 'S', do backward transformation for scaling only;
! 32: * = 'B', do backward transformations for both permutation and
! 33: * scaling.
! 34: * JOB must be the same as the argument JOB supplied to DGEBAL.
! 35: *
! 36: * SIDE (input) CHARACTER*1
! 37: * = 'R': V contains right eigenvectors;
! 38: * = 'L': V contains left eigenvectors.
! 39: *
! 40: * N (input) INTEGER
! 41: * The number of rows of the matrix V. N >= 0.
! 42: *
! 43: * ILO (input) INTEGER
! 44: * IHI (input) INTEGER
! 45: * The integers ILO and IHI determined by DGEBAL.
! 46: * 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
! 47: *
! 48: * SCALE (input) DOUBLE PRECISION array, dimension (N)
! 49: * Details of the permutation and scaling factors, as returned
! 50: * by DGEBAL.
! 51: *
! 52: * M (input) INTEGER
! 53: * The number of columns of the matrix V. M >= 0.
! 54: *
! 55: * V (input/output) DOUBLE PRECISION array, dimension (LDV,M)
! 56: * On entry, the matrix of right or left eigenvectors to be
! 57: * transformed, as returned by DHSEIN or DTREVC.
! 58: * On exit, V is overwritten by the transformed eigenvectors.
! 59: *
! 60: * LDV (input) INTEGER
! 61: * The leading dimension of the array V. LDV >= max(1,N).
! 62: *
! 63: * INFO (output) INTEGER
! 64: * = 0: successful exit
! 65: * < 0: if INFO = -i, the i-th argument had an illegal value.
! 66: *
! 67: * =====================================================================
! 68: *
! 69: * .. Parameters ..
! 70: DOUBLE PRECISION ONE
! 71: PARAMETER ( ONE = 1.0D+0 )
! 72: * ..
! 73: * .. Local Scalars ..
! 74: LOGICAL LEFTV, RIGHTV
! 75: INTEGER I, II, K
! 76: DOUBLE PRECISION S
! 77: * ..
! 78: * .. External Functions ..
! 79: LOGICAL LSAME
! 80: EXTERNAL LSAME
! 81: * ..
! 82: * .. External Subroutines ..
! 83: EXTERNAL DSCAL, DSWAP, XERBLA
! 84: * ..
! 85: * .. Intrinsic Functions ..
! 86: INTRINSIC MAX, MIN
! 87: * ..
! 88: * .. Executable Statements ..
! 89: *
! 90: * Decode and Test the input parameters
! 91: *
! 92: RIGHTV = LSAME( SIDE, 'R' )
! 93: LEFTV = LSAME( SIDE, 'L' )
! 94: *
! 95: INFO = 0
! 96: IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND.
! 97: $ .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN
! 98: INFO = -1
! 99: ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN
! 100: INFO = -2
! 101: ELSE IF( N.LT.0 ) THEN
! 102: INFO = -3
! 103: ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
! 104: INFO = -4
! 105: ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
! 106: INFO = -5
! 107: ELSE IF( M.LT.0 ) THEN
! 108: INFO = -7
! 109: ELSE IF( LDV.LT.MAX( 1, N ) ) THEN
! 110: INFO = -9
! 111: END IF
! 112: IF( INFO.NE.0 ) THEN
! 113: CALL XERBLA( 'DGEBAK', -INFO )
! 114: RETURN
! 115: END IF
! 116: *
! 117: * Quick return if possible
! 118: *
! 119: IF( N.EQ.0 )
! 120: $ RETURN
! 121: IF( M.EQ.0 )
! 122: $ RETURN
! 123: IF( LSAME( JOB, 'N' ) )
! 124: $ RETURN
! 125: *
! 126: IF( ILO.EQ.IHI )
! 127: $ GO TO 30
! 128: *
! 129: * Backward balance
! 130: *
! 131: IF( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN
! 132: *
! 133: IF( RIGHTV ) THEN
! 134: DO 10 I = ILO, IHI
! 135: S = SCALE( I )
! 136: CALL DSCAL( M, S, V( I, 1 ), LDV )
! 137: 10 CONTINUE
! 138: END IF
! 139: *
! 140: IF( LEFTV ) THEN
! 141: DO 20 I = ILO, IHI
! 142: S = ONE / SCALE( I )
! 143: CALL DSCAL( M, S, V( I, 1 ), LDV )
! 144: 20 CONTINUE
! 145: END IF
! 146: *
! 147: END IF
! 148: *
! 149: * Backward permutation
! 150: *
! 151: * For I = ILO-1 step -1 until 1,
! 152: * IHI+1 step 1 until N do --
! 153: *
! 154: 30 CONTINUE
! 155: IF( LSAME( JOB, 'P' ) .OR. LSAME( JOB, 'B' ) ) THEN
! 156: IF( RIGHTV ) THEN
! 157: DO 40 II = 1, N
! 158: I = II
! 159: IF( I.GE.ILO .AND. I.LE.IHI )
! 160: $ GO TO 40
! 161: IF( I.LT.ILO )
! 162: $ I = ILO - II
! 163: K = SCALE( I )
! 164: IF( K.EQ.I )
! 165: $ GO TO 40
! 166: CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
! 167: 40 CONTINUE
! 168: END IF
! 169: *
! 170: IF( LEFTV ) THEN
! 171: DO 50 II = 1, N
! 172: I = II
! 173: IF( I.GE.ILO .AND. I.LE.IHI )
! 174: $ GO TO 50
! 175: IF( I.LT.ILO )
! 176: $ I = ILO - II
! 177: K = SCALE( I )
! 178: IF( K.EQ.I )
! 179: $ GO TO 50
! 180: CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
! 181: 50 CONTINUE
! 182: END IF
! 183: END IF
! 184: *
! 185: RETURN
! 186: *
! 187: * End of DGEBAK
! 188: *
! 189: END
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