Annotation of rpl/lapack/lapack/zgbequ.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
! 2: $ AMAX, 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, KL, KU, LDAB, M, N
! 11: DOUBLE PRECISION AMAX, COLCND, ROWCND
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION C( * ), R( * )
! 15: COMPLEX*16 AB( LDAB, * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZGBEQU computes row and column scalings intended to equilibrate an
! 22: * M-by-N band matrix A and reduce its condition number. R returns the
! 23: * row scale factors and C the column scale factors, chosen to try to
! 24: * make 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: * KL (input) INTEGER
! 42: * The number of subdiagonals within the band of A. KL >= 0.
! 43: *
! 44: * KU (input) INTEGER
! 45: * The number of superdiagonals within the band of A. KU >= 0.
! 46: *
! 47: * AB (input) COMPLEX*16 array, dimension (LDAB,N)
! 48: * The band matrix A, stored in rows 1 to KL+KU+1. The j-th
! 49: * column of A is stored in the j-th column of the array AB as
! 50: * follows:
! 51: * AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
! 52: *
! 53: * LDAB (input) INTEGER
! 54: * The leading dimension of the array AB. LDAB >= KL+KU+1.
! 55: *
! 56: * R (output) DOUBLE PRECISION array, dimension (M)
! 57: * If INFO = 0, or INFO > M, R contains the row scale factors
! 58: * for A.
! 59: *
! 60: * C (output) DOUBLE PRECISION array, dimension (N)
! 61: * If INFO = 0, C contains the column scale factors for A.
! 62: *
! 63: * ROWCND (output) DOUBLE PRECISION
! 64: * If INFO = 0 or INFO > M, ROWCND contains the ratio of the
! 65: * smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
! 66: * AMAX is neither too large nor too small, it is not worth
! 67: * scaling by R.
! 68: *
! 69: * COLCND (output) DOUBLE PRECISION
! 70: * If INFO = 0, COLCND contains the ratio of the smallest
! 71: * C(i) to the largest C(i). If COLCND >= 0.1, it is not
! 72: * worth scaling by C.
! 73: *
! 74: * AMAX (output) DOUBLE PRECISION
! 75: * Absolute value of largest matrix element. If AMAX is very
! 76: * close to overflow or very close to underflow, the matrix
! 77: * should be scaled.
! 78: *
! 79: * INFO (output) INTEGER
! 80: * = 0: successful exit
! 81: * < 0: if INFO = -i, the i-th argument had an illegal value
! 82: * > 0: if INFO = i, and i is
! 83: * <= M: the i-th row of A is exactly zero
! 84: * > M: the (i-M)-th column of A is exactly zero
! 85: *
! 86: * =====================================================================
! 87: *
! 88: * .. Parameters ..
! 89: DOUBLE PRECISION ONE, ZERO
! 90: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 91: * ..
! 92: * .. Local Scalars ..
! 93: INTEGER I, J, KD
! 94: DOUBLE PRECISION BIGNUM, RCMAX, RCMIN, SMLNUM
! 95: COMPLEX*16 ZDUM
! 96: * ..
! 97: * .. External Functions ..
! 98: DOUBLE PRECISION DLAMCH
! 99: EXTERNAL DLAMCH
! 100: * ..
! 101: * .. External Subroutines ..
! 102: EXTERNAL XERBLA
! 103: * ..
! 104: * .. Intrinsic Functions ..
! 105: INTRINSIC ABS, DBLE, DIMAG, MAX, MIN
! 106: * ..
! 107: * .. Statement Functions ..
! 108: DOUBLE PRECISION CABS1
! 109: * ..
! 110: * .. Statement Function definitions ..
! 111: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 112: * ..
! 113: * .. Executable Statements ..
! 114: *
! 115: * Test the input parameters
! 116: *
! 117: INFO = 0
! 118: IF( M.LT.0 ) THEN
! 119: INFO = -1
! 120: ELSE IF( N.LT.0 ) THEN
! 121: INFO = -2
! 122: ELSE IF( KL.LT.0 ) THEN
! 123: INFO = -3
! 124: ELSE IF( KU.LT.0 ) THEN
! 125: INFO = -4
! 126: ELSE IF( LDAB.LT.KL+KU+1 ) THEN
! 127: INFO = -6
! 128: END IF
! 129: IF( INFO.NE.0 ) THEN
! 130: CALL XERBLA( 'ZGBEQU', -INFO )
! 131: RETURN
! 132: END IF
! 133: *
! 134: * Quick return if possible
! 135: *
! 136: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
! 137: ROWCND = ONE
! 138: COLCND = ONE
! 139: AMAX = ZERO
! 140: RETURN
! 141: END IF
! 142: *
! 143: * Get machine constants.
! 144: *
! 145: SMLNUM = DLAMCH( 'S' )
! 146: BIGNUM = ONE / SMLNUM
! 147: *
! 148: * Compute row scale factors.
! 149: *
! 150: DO 10 I = 1, M
! 151: R( I ) = ZERO
! 152: 10 CONTINUE
! 153: *
! 154: * Find the maximum element in each row.
! 155: *
! 156: KD = KU + 1
! 157: DO 30 J = 1, N
! 158: DO 20 I = MAX( J-KU, 1 ), MIN( J+KL, M )
! 159: R( I ) = MAX( R( I ), CABS1( AB( KD+I-J, J ) ) )
! 160: 20 CONTINUE
! 161: 30 CONTINUE
! 162: *
! 163: * Find the maximum and minimum scale factors.
! 164: *
! 165: RCMIN = BIGNUM
! 166: RCMAX = ZERO
! 167: DO 40 I = 1, M
! 168: RCMAX = MAX( RCMAX, R( I ) )
! 169: RCMIN = MIN( RCMIN, R( I ) )
! 170: 40 CONTINUE
! 171: AMAX = RCMAX
! 172: *
! 173: IF( RCMIN.EQ.ZERO ) THEN
! 174: *
! 175: * Find the first zero scale factor and return an error code.
! 176: *
! 177: DO 50 I = 1, M
! 178: IF( R( I ).EQ.ZERO ) THEN
! 179: INFO = I
! 180: RETURN
! 181: END IF
! 182: 50 CONTINUE
! 183: ELSE
! 184: *
! 185: * Invert the scale factors.
! 186: *
! 187: DO 60 I = 1, M
! 188: R( I ) = ONE / MIN( MAX( R( I ), SMLNUM ), BIGNUM )
! 189: 60 CONTINUE
! 190: *
! 191: * Compute ROWCND = min(R(I)) / max(R(I))
! 192: *
! 193: ROWCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
! 194: END IF
! 195: *
! 196: * Compute column scale factors
! 197: *
! 198: DO 70 J = 1, N
! 199: C( J ) = ZERO
! 200: 70 CONTINUE
! 201: *
! 202: * Find the maximum element in each column,
! 203: * assuming the row scaling computed above.
! 204: *
! 205: KD = KU + 1
! 206: DO 90 J = 1, N
! 207: DO 80 I = MAX( J-KU, 1 ), MIN( J+KL, M )
! 208: C( J ) = MAX( C( J ), CABS1( AB( KD+I-J, J ) )*R( I ) )
! 209: 80 CONTINUE
! 210: 90 CONTINUE
! 211: *
! 212: * Find the maximum and minimum scale factors.
! 213: *
! 214: RCMIN = BIGNUM
! 215: RCMAX = ZERO
! 216: DO 100 J = 1, N
! 217: RCMIN = MIN( RCMIN, C( J ) )
! 218: RCMAX = MAX( RCMAX, C( J ) )
! 219: 100 CONTINUE
! 220: *
! 221: IF( RCMIN.EQ.ZERO ) THEN
! 222: *
! 223: * Find the first zero scale factor and return an error code.
! 224: *
! 225: DO 110 J = 1, N
! 226: IF( C( J ).EQ.ZERO ) THEN
! 227: INFO = M + J
! 228: RETURN
! 229: END IF
! 230: 110 CONTINUE
! 231: ELSE
! 232: *
! 233: * Invert the scale factors.
! 234: *
! 235: DO 120 J = 1, N
! 236: C( J ) = ONE / MIN( MAX( C( J ), SMLNUM ), BIGNUM )
! 237: 120 CONTINUE
! 238: *
! 239: * Compute COLCND = min(C(J)) / max(C(J))
! 240: *
! 241: COLCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
! 242: END IF
! 243: *
! 244: RETURN
! 245: *
! 246: * End of ZGBEQU
! 247: *
! 248: END
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