Annotation of rpl/lapack/lapack/zgeequ.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
! 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: INTEGER INFO, LDA, M, N
! 11: DOUBLE PRECISION AMAX, COLCND, ROWCND
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION C( * ), R( * )
! 15: COMPLEX*16 A( LDA, * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZGEEQU computes row and column scalings intended to equilibrate an
! 22: * M-by-N matrix A and reduce its condition number. R returns the row
! 23: * scale factors and C the column scale factors, chosen to try to make
! 24: * the largest element in each row and column of the matrix B with
! 25: * elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
! 26: *
! 27: * R(i) and C(j) are restricted to be between SMLNUM = smallest safe
! 28: * number and BIGNUM = largest safe number. Use of these scaling
! 29: * factors is not guaranteed to reduce the condition number of A but
! 30: * works well in practice.
! 31: *
! 32: * Arguments
! 33: * =========
! 34: *
! 35: * M (input) INTEGER
! 36: * The number of rows of the matrix A. M >= 0.
! 37: *
! 38: * N (input) INTEGER
! 39: * The number of columns of the matrix A. N >= 0.
! 40: *
! 41: * A (input) COMPLEX*16 array, dimension (LDA,N)
! 42: * The M-by-N matrix whose equilibration factors are
! 43: * to be computed.
! 44: *
! 45: * LDA (input) INTEGER
! 46: * The leading dimension of the array A. LDA >= max(1,M).
! 47: *
! 48: * R (output) DOUBLE PRECISION array, dimension (M)
! 49: * If INFO = 0 or INFO > M, R contains the row scale factors
! 50: * for A.
! 51: *
! 52: * C (output) DOUBLE PRECISION array, dimension (N)
! 53: * If INFO = 0, C contains the column scale factors for A.
! 54: *
! 55: * ROWCND (output) DOUBLE PRECISION
! 56: * If INFO = 0 or INFO > M, ROWCND contains the ratio of the
! 57: * smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
! 58: * AMAX is neither too large nor too small, it is not worth
! 59: * scaling by R.
! 60: *
! 61: * COLCND (output) DOUBLE PRECISION
! 62: * If INFO = 0, COLCND contains the ratio of the smallest
! 63: * C(i) to the largest C(i). If COLCND >= 0.1, it is not
! 64: * worth scaling by C.
! 65: *
! 66: * AMAX (output) DOUBLE PRECISION
! 67: * Absolute value of largest matrix element. If AMAX is very
! 68: * close to overflow or very close to underflow, the matrix
! 69: * should be scaled.
! 70: *
! 71: * INFO (output) INTEGER
! 72: * = 0: successful exit
! 73: * < 0: if INFO = -i, the i-th argument had an illegal value
! 74: * > 0: if INFO = i, and i is
! 75: * <= M: the i-th row of A is exactly zero
! 76: * > M: the (i-M)-th column of A is exactly zero
! 77: *
! 78: * =====================================================================
! 79: *
! 80: * .. Parameters ..
! 81: DOUBLE PRECISION ONE, ZERO
! 82: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 83: * ..
! 84: * .. Local Scalars ..
! 85: INTEGER I, J
! 86: DOUBLE PRECISION BIGNUM, RCMAX, RCMIN, SMLNUM
! 87: COMPLEX*16 ZDUM
! 88: * ..
! 89: * .. External Functions ..
! 90: DOUBLE PRECISION DLAMCH
! 91: EXTERNAL DLAMCH
! 92: * ..
! 93: * .. External Subroutines ..
! 94: EXTERNAL XERBLA
! 95: * ..
! 96: * .. Intrinsic Functions ..
! 97: INTRINSIC ABS, DBLE, DIMAG, MAX, MIN
! 98: * ..
! 99: * .. Statement Functions ..
! 100: DOUBLE PRECISION CABS1
! 101: * ..
! 102: * .. Statement Function definitions ..
! 103: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 104: * ..
! 105: * .. Executable Statements ..
! 106: *
! 107: * Test the input parameters.
! 108: *
! 109: INFO = 0
! 110: IF( M.LT.0 ) THEN
! 111: INFO = -1
! 112: ELSE IF( N.LT.0 ) THEN
! 113: INFO = -2
! 114: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 115: INFO = -4
! 116: END IF
! 117: IF( INFO.NE.0 ) THEN
! 118: CALL XERBLA( 'ZGEEQU', -INFO )
! 119: RETURN
! 120: END IF
! 121: *
! 122: * Quick return if possible
! 123: *
! 124: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
! 125: ROWCND = ONE
! 126: COLCND = ONE
! 127: AMAX = ZERO
! 128: RETURN
! 129: END IF
! 130: *
! 131: * Get machine constants.
! 132: *
! 133: SMLNUM = DLAMCH( 'S' )
! 134: BIGNUM = ONE / SMLNUM
! 135: *
! 136: * Compute row scale factors.
! 137: *
! 138: DO 10 I = 1, M
! 139: R( I ) = ZERO
! 140: 10 CONTINUE
! 141: *
! 142: * Find the maximum element in each row.
! 143: *
! 144: DO 30 J = 1, N
! 145: DO 20 I = 1, M
! 146: R( I ) = MAX( R( I ), CABS1( A( I, J ) ) )
! 147: 20 CONTINUE
! 148: 30 CONTINUE
! 149: *
! 150: * Find the maximum and minimum scale factors.
! 151: *
! 152: RCMIN = BIGNUM
! 153: RCMAX = ZERO
! 154: DO 40 I = 1, M
! 155: RCMAX = MAX( RCMAX, R( I ) )
! 156: RCMIN = MIN( RCMIN, R( I ) )
! 157: 40 CONTINUE
! 158: AMAX = RCMAX
! 159: *
! 160: IF( RCMIN.EQ.ZERO ) THEN
! 161: *
! 162: * Find the first zero scale factor and return an error code.
! 163: *
! 164: DO 50 I = 1, M
! 165: IF( R( I ).EQ.ZERO ) THEN
! 166: INFO = I
! 167: RETURN
! 168: END IF
! 169: 50 CONTINUE
! 170: ELSE
! 171: *
! 172: * Invert the scale factors.
! 173: *
! 174: DO 60 I = 1, M
! 175: R( I ) = ONE / MIN( MAX( R( I ), SMLNUM ), BIGNUM )
! 176: 60 CONTINUE
! 177: *
! 178: * Compute ROWCND = min(R(I)) / max(R(I))
! 179: *
! 180: ROWCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
! 181: END IF
! 182: *
! 183: * Compute column scale factors
! 184: *
! 185: DO 70 J = 1, N
! 186: C( J ) = ZERO
! 187: 70 CONTINUE
! 188: *
! 189: * Find the maximum element in each column,
! 190: * assuming the row scaling computed above.
! 191: *
! 192: DO 90 J = 1, N
! 193: DO 80 I = 1, M
! 194: C( J ) = MAX( C( J ), CABS1( A( I, J ) )*R( I ) )
! 195: 80 CONTINUE
! 196: 90 CONTINUE
! 197: *
! 198: * Find the maximum and minimum scale factors.
! 199: *
! 200: RCMIN = BIGNUM
! 201: RCMAX = ZERO
! 202: DO 100 J = 1, N
! 203: RCMIN = MIN( RCMIN, C( J ) )
! 204: RCMAX = MAX( RCMAX, C( J ) )
! 205: 100 CONTINUE
! 206: *
! 207: IF( RCMIN.EQ.ZERO ) THEN
! 208: *
! 209: * Find the first zero scale factor and return an error code.
! 210: *
! 211: DO 110 J = 1, N
! 212: IF( C( J ).EQ.ZERO ) THEN
! 213: INFO = M + J
! 214: RETURN
! 215: END IF
! 216: 110 CONTINUE
! 217: ELSE
! 218: *
! 219: * Invert the scale factors.
! 220: *
! 221: DO 120 J = 1, N
! 222: C( J ) = ONE / MIN( MAX( C( J ), SMLNUM ), BIGNUM )
! 223: 120 CONTINUE
! 224: *
! 225: * Compute COLCND = min(C(J)) / max(C(J))
! 226: *
! 227: COLCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
! 228: END IF
! 229: *
! 230: RETURN
! 231: *
! 232: * End of ZGEEQU
! 233: *
! 234: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zgeequ.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack