Annotation of rpl/lapack/lapack/zlanhf.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLANHF( NORM, TRANSR, UPLO, N, A, WORK )
! 2: *
! 3: * -- LAPACK routine (version 3.2.1) --
! 4: *
! 5: * -- Contributed by Fred Gustavson of the IBM Watson Research Center --
! 6: * -- April 2009 --
! 7: *
! 8: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 9: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 10: *
! 11: * .. Scalar Arguments ..
! 12: CHARACTER NORM, TRANSR, UPLO
! 13: INTEGER N
! 14: * ..
! 15: * .. Array Arguments ..
! 16: DOUBLE PRECISION WORK( 0: * )
! 17: COMPLEX*16 A( 0: * )
! 18: * ..
! 19: *
! 20: * Purpose
! 21: * =======
! 22: *
! 23: * ZLANHF returns the value of the one norm, or the Frobenius norm, or
! 24: * the infinity norm, or the element of largest absolute value of a
! 25: * complex Hermitian matrix A in RFP format.
! 26: *
! 27: * Description
! 28: * ===========
! 29: *
! 30: * ZLANHF returns the value
! 31: *
! 32: * ZLANHF = ( max(abs(A(i,j))), NORM = 'M' or 'm'
! 33: * (
! 34: * ( norm1(A), NORM = '1', 'O' or 'o'
! 35: * (
! 36: * ( normI(A), NORM = 'I' or 'i'
! 37: * (
! 38: * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
! 39: *
! 40: * where norm1 denotes the one norm of a matrix (maximum column sum),
! 41: * normI denotes the infinity norm of a matrix (maximum row sum) and
! 42: * normF denotes the Frobenius norm of a matrix (square root of sum of
! 43: * squares). Note that max(abs(A(i,j))) is not a matrix norm.
! 44: *
! 45: * Arguments
! 46: * =========
! 47: *
! 48: * NORM (input) CHARACTER
! 49: * Specifies the value to be returned in ZLANHF as described
! 50: * above.
! 51: *
! 52: * TRANSR (input) CHARACTER
! 53: * Specifies whether the RFP format of A is normal or
! 54: * conjugate-transposed format.
! 55: * = 'N': RFP format is Normal
! 56: * = 'C': RFP format is Conjugate-transposed
! 57: *
! 58: * UPLO (input) CHARACTER
! 59: * On entry, UPLO specifies whether the RFP matrix A came from
! 60: * an upper or lower triangular matrix as follows:
! 61: *
! 62: * UPLO = 'U' or 'u' RFP A came from an upper triangular
! 63: * matrix
! 64: *
! 65: * UPLO = 'L' or 'l' RFP A came from a lower triangular
! 66: * matrix
! 67: *
! 68: * N (input) INTEGER
! 69: * The order of the matrix A. N >= 0. When N = 0, ZLANHF is
! 70: * set to zero.
! 71: *
! 72: * A (input) COMPLEX*16 array, dimension ( N*(N+1)/2 );
! 73: * On entry, the matrix A in RFP Format.
! 74: * RFP Format is described by TRANSR, UPLO and N as follows:
! 75: * If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even;
! 76: * K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If
! 77: * TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A
! 78: * as defined when TRANSR = 'N'. The contents of RFP A are
! 79: * defined by UPLO as follows: If UPLO = 'U' the RFP A
! 80: * contains the ( N*(N+1)/2 ) elements of upper packed A
! 81: * either in normal or conjugate-transpose Format. If
! 82: * UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements
! 83: * of lower packed A either in normal or conjugate-transpose
! 84: * Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When
! 85: * TRANSR is 'N' the LDA is N+1 when N is even and is N when
! 86: * is odd. See the Note below for more details.
! 87: * Unchanged on exit.
! 88: *
! 89: * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
! 90: * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
! 91: * WORK is not referenced.
! 92: *
! 93: * Further Details
! 94: * ===============
! 95: *
! 96: * We first consider Standard Packed Format when N is even.
! 97: * We give an example where N = 6.
! 98: *
! 99: * AP is Upper AP is Lower
! 100: *
! 101: * 00 01 02 03 04 05 00
! 102: * 11 12 13 14 15 10 11
! 103: * 22 23 24 25 20 21 22
! 104: * 33 34 35 30 31 32 33
! 105: * 44 45 40 41 42 43 44
! 106: * 55 50 51 52 53 54 55
! 107: *
! 108: *
! 109: * Let TRANSR = 'N'. RFP holds AP as follows:
! 110: * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
! 111: * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
! 112: * conjugate-transpose of the first three columns of AP upper.
! 113: * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
! 114: * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
! 115: * conjugate-transpose of the last three columns of AP lower.
! 116: * To denote conjugate we place -- above the element. This covers the
! 117: * case N even and TRANSR = 'N'.
! 118: *
! 119: * RFP A RFP A
! 120: *
! 121: * -- -- --
! 122: * 03 04 05 33 43 53
! 123: * -- --
! 124: * 13 14 15 00 44 54
! 125: * --
! 126: * 23 24 25 10 11 55
! 127: *
! 128: * 33 34 35 20 21 22
! 129: * --
! 130: * 00 44 45 30 31 32
! 131: * -- --
! 132: * 01 11 55 40 41 42
! 133: * -- -- --
! 134: * 02 12 22 50 51 52
! 135: *
! 136: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 137: * transpose of RFP A above. One therefore gets:
! 138: *
! 139: *
! 140: * RFP A RFP A
! 141: *
! 142: * -- -- -- -- -- -- -- -- -- --
! 143: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
! 144: * -- -- -- -- -- -- -- -- -- --
! 145: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
! 146: * -- -- -- -- -- -- -- -- -- --
! 147: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
! 148: *
! 149: *
! 150: * We next consider Standard Packed Format when N is odd.
! 151: * We give an example where N = 5.
! 152: *
! 153: * AP is Upper AP is Lower
! 154: *
! 155: * 00 01 02 03 04 00
! 156: * 11 12 13 14 10 11
! 157: * 22 23 24 20 21 22
! 158: * 33 34 30 31 32 33
! 159: * 44 40 41 42 43 44
! 160: *
! 161: *
! 162: * Let TRANSR = 'N'. RFP holds AP as follows:
! 163: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
! 164: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
! 165: * conjugate-transpose of the first two columns of AP upper.
! 166: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
! 167: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
! 168: * conjugate-transpose of the last two columns of AP lower.
! 169: * To denote conjugate we place -- above the element. This covers the
! 170: * case N odd and TRANSR = 'N'.
! 171: *
! 172: * RFP A RFP A
! 173: *
! 174: * -- --
! 175: * 02 03 04 00 33 43
! 176: * --
! 177: * 12 13 14 10 11 44
! 178: *
! 179: * 22 23 24 20 21 22
! 180: * --
! 181: * 00 33 34 30 31 32
! 182: * -- --
! 183: * 01 11 44 40 41 42
! 184: *
! 185: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 186: * transpose of RFP A above. One therefore gets:
! 187: *
! 188: *
! 189: * RFP A RFP A
! 190: *
! 191: * -- -- -- -- -- -- -- -- --
! 192: * 02 12 22 00 01 00 10 20 30 40 50
! 193: * -- -- -- -- -- -- -- -- --
! 194: * 03 13 23 33 11 33 11 21 31 41 51
! 195: * -- -- -- -- -- -- -- -- --
! 196: * 04 14 24 34 44 43 44 22 32 42 52
! 197: *
! 198: * =====================================================================
! 199: *
! 200: * .. Parameters ..
! 201: DOUBLE PRECISION ONE, ZERO
! 202: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 203: * ..
! 204: * .. Local Scalars ..
! 205: INTEGER I, J, IFM, ILU, NOE, N1, K, L, LDA
! 206: DOUBLE PRECISION SCALE, S, VALUE, AA
! 207: * ..
! 208: * .. External Functions ..
! 209: LOGICAL LSAME
! 210: INTEGER IDAMAX
! 211: EXTERNAL LSAME, IDAMAX
! 212: * ..
! 213: * .. External Subroutines ..
! 214: EXTERNAL ZLASSQ
! 215: * ..
! 216: * .. Intrinsic Functions ..
! 217: INTRINSIC ABS, DBLE, MAX, SQRT
! 218: * ..
! 219: * .. Executable Statements ..
! 220: *
! 221: IF( N.EQ.0 ) THEN
! 222: ZLANHF = ZERO
! 223: RETURN
! 224: END IF
! 225: *
! 226: * set noe = 1 if n is odd. if n is even set noe=0
! 227: *
! 228: NOE = 1
! 229: IF( MOD( N, 2 ).EQ.0 )
! 230: + NOE = 0
! 231: *
! 232: * set ifm = 0 when form='C' or 'c' and 1 otherwise
! 233: *
! 234: IFM = 1
! 235: IF( LSAME( TRANSR, 'C' ) )
! 236: + IFM = 0
! 237: *
! 238: * set ilu = 0 when uplo='U or 'u' and 1 otherwise
! 239: *
! 240: ILU = 1
! 241: IF( LSAME( UPLO, 'U' ) )
! 242: + ILU = 0
! 243: *
! 244: * set lda = (n+1)/2 when ifm = 0
! 245: * set lda = n when ifm = 1 and noe = 1
! 246: * set lda = n+1 when ifm = 1 and noe = 0
! 247: *
! 248: IF( IFM.EQ.1 ) THEN
! 249: IF( NOE.EQ.1 ) THEN
! 250: LDA = N
! 251: ELSE
! 252: * noe=0
! 253: LDA = N + 1
! 254: END IF
! 255: ELSE
! 256: * ifm=0
! 257: LDA = ( N+1 ) / 2
! 258: END IF
! 259: *
! 260: IF( LSAME( NORM, 'M' ) ) THEN
! 261: *
! 262: * Find max(abs(A(i,j))).
! 263: *
! 264: K = ( N+1 ) / 2
! 265: VALUE = ZERO
! 266: IF( NOE.EQ.1 ) THEN
! 267: * n is odd & n = k + k - 1
! 268: IF( IFM.EQ.1 ) THEN
! 269: * A is n by k
! 270: IF( ILU.EQ.1 ) THEN
! 271: * uplo ='L'
! 272: J = 0
! 273: * -> L(0,0)
! 274: VALUE = MAX( VALUE, ABS( DBLE( A( J+J*LDA ) ) ) )
! 275: DO I = 1, N - 1
! 276: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 277: END DO
! 278: DO J = 1, K - 1
! 279: DO I = 0, J - 2
! 280: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 281: END DO
! 282: I = J - 1
! 283: * L(k+j,k+j)
! 284: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 285: I = J
! 286: * -> L(j,j)
! 287: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 288: DO I = J + 1, N - 1
! 289: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 290: END DO
! 291: END DO
! 292: ELSE
! 293: * uplo = 'U'
! 294: DO J = 0, K - 2
! 295: DO I = 0, K + J - 2
! 296: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 297: END DO
! 298: I = K + J - 1
! 299: * -> U(i,i)
! 300: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 301: I = I + 1
! 302: * =k+j; i -> U(j,j)
! 303: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 304: DO I = K + J + 1, N - 1
! 305: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 306: END DO
! 307: END DO
! 308: DO I = 0, N - 2
! 309: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 310: * j=k-1
! 311: END DO
! 312: * i=n-1 -> U(n-1,n-1)
! 313: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 314: END IF
! 315: ELSE
! 316: * xpose case; A is k by n
! 317: IF( ILU.EQ.1 ) THEN
! 318: * uplo ='L'
! 319: DO J = 0, K - 2
! 320: DO I = 0, J - 1
! 321: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 322: END DO
! 323: I = J
! 324: * L(i,i)
! 325: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 326: I = J + 1
! 327: * L(j+k,j+k)
! 328: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 329: DO I = J + 2, K - 1
! 330: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 331: END DO
! 332: END DO
! 333: J = K - 1
! 334: DO I = 0, K - 2
! 335: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 336: END DO
! 337: I = K - 1
! 338: * -> L(i,i) is at A(i,j)
! 339: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 340: DO J = K, N - 1
! 341: DO I = 0, K - 1
! 342: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 343: END DO
! 344: END DO
! 345: ELSE
! 346: * uplo = 'U'
! 347: DO J = 0, K - 2
! 348: DO I = 0, K - 1
! 349: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 350: END DO
! 351: END DO
! 352: J = K - 1
! 353: * -> U(j,j) is at A(0,j)
! 354: VALUE = MAX( VALUE, ABS( DBLE( A( 0+J*LDA ) ) ) )
! 355: DO I = 1, K - 1
! 356: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 357: END DO
! 358: DO J = K, N - 1
! 359: DO I = 0, J - K - 1
! 360: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 361: END DO
! 362: I = J - K
! 363: * -> U(i,i) at A(i,j)
! 364: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 365: I = J - K + 1
! 366: * U(j,j)
! 367: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 368: DO I = J - K + 2, K - 1
! 369: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 370: END DO
! 371: END DO
! 372: END IF
! 373: END IF
! 374: ELSE
! 375: * n is even & k = n/2
! 376: IF( IFM.EQ.1 ) THEN
! 377: * A is n+1 by k
! 378: IF( ILU.EQ.1 ) THEN
! 379: * uplo ='L'
! 380: J = 0
! 381: * -> L(k,k) & j=1 -> L(0,0)
! 382: VALUE = MAX( VALUE, ABS( DBLE( A( J+J*LDA ) ) ) )
! 383: VALUE = MAX( VALUE, ABS( DBLE( A( J+1+J*LDA ) ) ) )
! 384: DO I = 2, N
! 385: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 386: END DO
! 387: DO J = 1, K - 1
! 388: DO I = 0, J - 1
! 389: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 390: END DO
! 391: I = J
! 392: * L(k+j,k+j)
! 393: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 394: I = J + 1
! 395: * -> L(j,j)
! 396: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 397: DO I = J + 2, N
! 398: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 399: END DO
! 400: END DO
! 401: ELSE
! 402: * uplo = 'U'
! 403: DO J = 0, K - 2
! 404: DO I = 0, K + J - 1
! 405: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 406: END DO
! 407: I = K + J
! 408: * -> U(i,i)
! 409: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 410: I = I + 1
! 411: * =k+j+1; i -> U(j,j)
! 412: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 413: DO I = K + J + 2, N
! 414: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 415: END DO
! 416: END DO
! 417: DO I = 0, N - 2
! 418: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 419: * j=k-1
! 420: END DO
! 421: * i=n-1 -> U(n-1,n-1)
! 422: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 423: I = N
! 424: * -> U(k-1,k-1)
! 425: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 426: END IF
! 427: ELSE
! 428: * xpose case; A is k by n+1
! 429: IF( ILU.EQ.1 ) THEN
! 430: * uplo ='L'
! 431: J = 0
! 432: * -> L(k,k) at A(0,0)
! 433: VALUE = MAX( VALUE, ABS( DBLE( A( J+J*LDA ) ) ) )
! 434: DO I = 1, K - 1
! 435: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 436: END DO
! 437: DO J = 1, K - 1
! 438: DO I = 0, J - 2
! 439: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 440: END DO
! 441: I = J - 1
! 442: * L(i,i)
! 443: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 444: I = J
! 445: * L(j+k,j+k)
! 446: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 447: DO I = J + 1, K - 1
! 448: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 449: END DO
! 450: END DO
! 451: J = K
! 452: DO I = 0, K - 2
! 453: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 454: END DO
! 455: I = K - 1
! 456: * -> L(i,i) is at A(i,j)
! 457: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 458: DO J = K + 1, N
! 459: DO I = 0, K - 1
! 460: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 461: END DO
! 462: END DO
! 463: ELSE
! 464: * uplo = 'U'
! 465: DO J = 0, K - 1
! 466: DO I = 0, K - 1
! 467: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 468: END DO
! 469: END DO
! 470: J = K
! 471: * -> U(j,j) is at A(0,j)
! 472: VALUE = MAX( VALUE, ABS( DBLE( A( 0+J*LDA ) ) ) )
! 473: DO I = 1, K - 1
! 474: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 475: END DO
! 476: DO J = K + 1, N - 1
! 477: DO I = 0, J - K - 2
! 478: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 479: END DO
! 480: I = J - K - 1
! 481: * -> U(i,i) at A(i,j)
! 482: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 483: I = J - K
! 484: * U(j,j)
! 485: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 486: DO I = J - K + 1, K - 1
! 487: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 488: END DO
! 489: END DO
! 490: J = N
! 491: DO I = 0, K - 2
! 492: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
! 493: END DO
! 494: I = K - 1
! 495: * U(k,k) at A(i,j)
! 496: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
! 497: END IF
! 498: END IF
! 499: END IF
! 500: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
! 501: + ( NORM.EQ.'1' ) ) THEN
! 502: *
! 503: * Find normI(A) ( = norm1(A), since A is Hermitian).
! 504: *
! 505: IF( IFM.EQ.1 ) THEN
! 506: * A is 'N'
! 507: K = N / 2
! 508: IF( NOE.EQ.1 ) THEN
! 509: * n is odd & A is n by (n+1)/2
! 510: IF( ILU.EQ.0 ) THEN
! 511: * uplo = 'U'
! 512: DO I = 0, K - 1
! 513: WORK( I ) = ZERO
! 514: END DO
! 515: DO J = 0, K
! 516: S = ZERO
! 517: DO I = 0, K + J - 1
! 518: AA = ABS( A( I+J*LDA ) )
! 519: * -> A(i,j+k)
! 520: S = S + AA
! 521: WORK( I ) = WORK( I ) + AA
! 522: END DO
! 523: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 524: * -> A(j+k,j+k)
! 525: WORK( J+K ) = S + AA
! 526: IF( I.EQ.K+K )
! 527: + GO TO 10
! 528: I = I + 1
! 529: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 530: * -> A(j,j)
! 531: WORK( J ) = WORK( J ) + AA
! 532: S = ZERO
! 533: DO L = J + 1, K - 1
! 534: I = I + 1
! 535: AA = ABS( A( I+J*LDA ) )
! 536: * -> A(l,j)
! 537: S = S + AA
! 538: WORK( L ) = WORK( L ) + AA
! 539: END DO
! 540: WORK( J ) = WORK( J ) + S
! 541: END DO
! 542: 10 CONTINUE
! 543: I = IDAMAX( N, WORK, 1 )
! 544: VALUE = WORK( I-1 )
! 545: ELSE
! 546: * ilu = 1 & uplo = 'L'
! 547: K = K + 1
! 548: * k=(n+1)/2 for n odd and ilu=1
! 549: DO I = K, N - 1
! 550: WORK( I ) = ZERO
! 551: END DO
! 552: DO J = K - 1, 0, -1
! 553: S = ZERO
! 554: DO I = 0, J - 2
! 555: AA = ABS( A( I+J*LDA ) )
! 556: * -> A(j+k,i+k)
! 557: S = S + AA
! 558: WORK( I+K ) = WORK( I+K ) + AA
! 559: END DO
! 560: IF( J.GT.0 ) THEN
! 561: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 562: * -> A(j+k,j+k)
! 563: S = S + AA
! 564: WORK( I+K ) = WORK( I+K ) + S
! 565: * i=j
! 566: I = I + 1
! 567: END IF
! 568: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 569: * -> A(j,j)
! 570: WORK( J ) = AA
! 571: S = ZERO
! 572: DO L = J + 1, N - 1
! 573: I = I + 1
! 574: AA = ABS( A( I+J*LDA ) )
! 575: * -> A(l,j)
! 576: S = S + AA
! 577: WORK( L ) = WORK( L ) + AA
! 578: END DO
! 579: WORK( J ) = WORK( J ) + S
! 580: END DO
! 581: I = IDAMAX( N, WORK, 1 )
! 582: VALUE = WORK( I-1 )
! 583: END IF
! 584: ELSE
! 585: * n is even & A is n+1 by k = n/2
! 586: IF( ILU.EQ.0 ) THEN
! 587: * uplo = 'U'
! 588: DO I = 0, K - 1
! 589: WORK( I ) = ZERO
! 590: END DO
! 591: DO J = 0, K - 1
! 592: S = ZERO
! 593: DO I = 0, K + J - 1
! 594: AA = ABS( A( I+J*LDA ) )
! 595: * -> A(i,j+k)
! 596: S = S + AA
! 597: WORK( I ) = WORK( I ) + AA
! 598: END DO
! 599: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 600: * -> A(j+k,j+k)
! 601: WORK( J+K ) = S + AA
! 602: I = I + 1
! 603: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 604: * -> A(j,j)
! 605: WORK( J ) = WORK( J ) + AA
! 606: S = ZERO
! 607: DO L = J + 1, K - 1
! 608: I = I + 1
! 609: AA = ABS( A( I+J*LDA ) )
! 610: * -> A(l,j)
! 611: S = S + AA
! 612: WORK( L ) = WORK( L ) + AA
! 613: END DO
! 614: WORK( J ) = WORK( J ) + S
! 615: END DO
! 616: I = IDAMAX( N, WORK, 1 )
! 617: VALUE = WORK( I-1 )
! 618: ELSE
! 619: * ilu = 1 & uplo = 'L'
! 620: DO I = K, N - 1
! 621: WORK( I ) = ZERO
! 622: END DO
! 623: DO J = K - 1, 0, -1
! 624: S = ZERO
! 625: DO I = 0, J - 1
! 626: AA = ABS( A( I+J*LDA ) )
! 627: * -> A(j+k,i+k)
! 628: S = S + AA
! 629: WORK( I+K ) = WORK( I+K ) + AA
! 630: END DO
! 631: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 632: * -> A(j+k,j+k)
! 633: S = S + AA
! 634: WORK( I+K ) = WORK( I+K ) + S
! 635: * i=j
! 636: I = I + 1
! 637: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 638: * -> A(j,j)
! 639: WORK( J ) = AA
! 640: S = ZERO
! 641: DO L = J + 1, N - 1
! 642: I = I + 1
! 643: AA = ABS( A( I+J*LDA ) )
! 644: * -> A(l,j)
! 645: S = S + AA
! 646: WORK( L ) = WORK( L ) + AA
! 647: END DO
! 648: WORK( J ) = WORK( J ) + S
! 649: END DO
! 650: I = IDAMAX( N, WORK, 1 )
! 651: VALUE = WORK( I-1 )
! 652: END IF
! 653: END IF
! 654: ELSE
! 655: * ifm=0
! 656: K = N / 2
! 657: IF( NOE.EQ.1 ) THEN
! 658: * n is odd & A is (n+1)/2 by n
! 659: IF( ILU.EQ.0 ) THEN
! 660: * uplo = 'U'
! 661: N1 = K
! 662: * n/2
! 663: K = K + 1
! 664: * k is the row size and lda
! 665: DO I = N1, N - 1
! 666: WORK( I ) = ZERO
! 667: END DO
! 668: DO J = 0, N1 - 1
! 669: S = ZERO
! 670: DO I = 0, K - 1
! 671: AA = ABS( A( I+J*LDA ) )
! 672: * A(j,n1+i)
! 673: WORK( I+N1 ) = WORK( I+N1 ) + AA
! 674: S = S + AA
! 675: END DO
! 676: WORK( J ) = S
! 677: END DO
! 678: * j=n1=k-1 is special
! 679: S = ABS( DBLE( A( 0+J*LDA ) ) )
! 680: * A(k-1,k-1)
! 681: DO I = 1, K - 1
! 682: AA = ABS( A( I+J*LDA ) )
! 683: * A(k-1,i+n1)
! 684: WORK( I+N1 ) = WORK( I+N1 ) + AA
! 685: S = S + AA
! 686: END DO
! 687: WORK( J ) = WORK( J ) + S
! 688: DO J = K, N - 1
! 689: S = ZERO
! 690: DO I = 0, J - K - 1
! 691: AA = ABS( A( I+J*LDA ) )
! 692: * A(i,j-k)
! 693: WORK( I ) = WORK( I ) + AA
! 694: S = S + AA
! 695: END DO
! 696: * i=j-k
! 697: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 698: * A(j-k,j-k)
! 699: S = S + AA
! 700: WORK( J-K ) = WORK( J-K ) + S
! 701: I = I + 1
! 702: S = ABS( DBLE( A( I+J*LDA ) ) )
! 703: * A(j,j)
! 704: DO L = J + 1, N - 1
! 705: I = I + 1
! 706: AA = ABS( A( I+J*LDA ) )
! 707: * A(j,l)
! 708: WORK( L ) = WORK( L ) + AA
! 709: S = S + AA
! 710: END DO
! 711: WORK( J ) = WORK( J ) + S
! 712: END DO
! 713: I = IDAMAX( N, WORK, 1 )
! 714: VALUE = WORK( I-1 )
! 715: ELSE
! 716: * ilu=1 & uplo = 'L'
! 717: K = K + 1
! 718: * k=(n+1)/2 for n odd and ilu=1
! 719: DO I = K, N - 1
! 720: WORK( I ) = ZERO
! 721: END DO
! 722: DO J = 0, K - 2
! 723: * process
! 724: S = ZERO
! 725: DO I = 0, J - 1
! 726: AA = ABS( A( I+J*LDA ) )
! 727: * A(j,i)
! 728: WORK( I ) = WORK( I ) + AA
! 729: S = S + AA
! 730: END DO
! 731: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 732: * i=j so process of A(j,j)
! 733: S = S + AA
! 734: WORK( J ) = S
! 735: * is initialised here
! 736: I = I + 1
! 737: * i=j process A(j+k,j+k)
! 738: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 739: S = AA
! 740: DO L = K + J + 1, N - 1
! 741: I = I + 1
! 742: AA = ABS( A( I+J*LDA ) )
! 743: * A(l,k+j)
! 744: S = S + AA
! 745: WORK( L ) = WORK( L ) + AA
! 746: END DO
! 747: WORK( K+J ) = WORK( K+J ) + S
! 748: END DO
! 749: * j=k-1 is special :process col A(k-1,0:k-1)
! 750: S = ZERO
! 751: DO I = 0, K - 2
! 752: AA = ABS( A( I+J*LDA ) )
! 753: * A(k,i)
! 754: WORK( I ) = WORK( I ) + AA
! 755: S = S + AA
! 756: END DO
! 757: * i=k-1
! 758: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 759: * A(k-1,k-1)
! 760: S = S + AA
! 761: WORK( I ) = S
! 762: * done with col j=k+1
! 763: DO J = K, N - 1
! 764: * process col j of A = A(j,0:k-1)
! 765: S = ZERO
! 766: DO I = 0, K - 1
! 767: AA = ABS( A( I+J*LDA ) )
! 768: * A(j,i)
! 769: WORK( I ) = WORK( I ) + AA
! 770: S = S + AA
! 771: END DO
! 772: WORK( J ) = WORK( J ) + S
! 773: END DO
! 774: I = IDAMAX( N, WORK, 1 )
! 775: VALUE = WORK( I-1 )
! 776: END IF
! 777: ELSE
! 778: * n is even & A is k=n/2 by n+1
! 779: IF( ILU.EQ.0 ) THEN
! 780: * uplo = 'U'
! 781: DO I = K, N - 1
! 782: WORK( I ) = ZERO
! 783: END DO
! 784: DO J = 0, K - 1
! 785: S = ZERO
! 786: DO I = 0, K - 1
! 787: AA = ABS( A( I+J*LDA ) )
! 788: * A(j,i+k)
! 789: WORK( I+K ) = WORK( I+K ) + AA
! 790: S = S + AA
! 791: END DO
! 792: WORK( J ) = S
! 793: END DO
! 794: * j=k
! 795: AA = ABS( DBLE( A( 0+J*LDA ) ) )
! 796: * A(k,k)
! 797: S = AA
! 798: DO I = 1, K - 1
! 799: AA = ABS( A( I+J*LDA ) )
! 800: * A(k,k+i)
! 801: WORK( I+K ) = WORK( I+K ) + AA
! 802: S = S + AA
! 803: END DO
! 804: WORK( J ) = WORK( J ) + S
! 805: DO J = K + 1, N - 1
! 806: S = ZERO
! 807: DO I = 0, J - 2 - K
! 808: AA = ABS( A( I+J*LDA ) )
! 809: * A(i,j-k-1)
! 810: WORK( I ) = WORK( I ) + AA
! 811: S = S + AA
! 812: END DO
! 813: * i=j-1-k
! 814: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 815: * A(j-k-1,j-k-1)
! 816: S = S + AA
! 817: WORK( J-K-1 ) = WORK( J-K-1 ) + S
! 818: I = I + 1
! 819: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 820: * A(j,j)
! 821: S = AA
! 822: DO L = J + 1, N - 1
! 823: I = I + 1
! 824: AA = ABS( A( I+J*LDA ) )
! 825: * A(j,l)
! 826: WORK( L ) = WORK( L ) + AA
! 827: S = S + AA
! 828: END DO
! 829: WORK( J ) = WORK( J ) + S
! 830: END DO
! 831: * j=n
! 832: S = ZERO
! 833: DO I = 0, K - 2
! 834: AA = ABS( A( I+J*LDA ) )
! 835: * A(i,k-1)
! 836: WORK( I ) = WORK( I ) + AA
! 837: S = S + AA
! 838: END DO
! 839: * i=k-1
! 840: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 841: * A(k-1,k-1)
! 842: S = S + AA
! 843: WORK( I ) = WORK( I ) + S
! 844: I = IDAMAX( N, WORK, 1 )
! 845: VALUE = WORK( I-1 )
! 846: ELSE
! 847: * ilu=1 & uplo = 'L'
! 848: DO I = K, N - 1
! 849: WORK( I ) = ZERO
! 850: END DO
! 851: * j=0 is special :process col A(k:n-1,k)
! 852: S = ABS( DBLE( A( 0 ) ) )
! 853: * A(k,k)
! 854: DO I = 1, K - 1
! 855: AA = ABS( A( I ) )
! 856: * A(k+i,k)
! 857: WORK( I+K ) = WORK( I+K ) + AA
! 858: S = S + AA
! 859: END DO
! 860: WORK( K ) = WORK( K ) + S
! 861: DO J = 1, K - 1
! 862: * process
! 863: S = ZERO
! 864: DO I = 0, J - 2
! 865: AA = ABS( A( I+J*LDA ) )
! 866: * A(j-1,i)
! 867: WORK( I ) = WORK( I ) + AA
! 868: S = S + AA
! 869: END DO
! 870: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 871: * i=j-1 so process of A(j-1,j-1)
! 872: S = S + AA
! 873: WORK( J-1 ) = S
! 874: * is initialised here
! 875: I = I + 1
! 876: * i=j process A(j+k,j+k)
! 877: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 878: S = AA
! 879: DO L = K + J + 1, N - 1
! 880: I = I + 1
! 881: AA = ABS( A( I+J*LDA ) )
! 882: * A(l,k+j)
! 883: S = S + AA
! 884: WORK( L ) = WORK( L ) + AA
! 885: END DO
! 886: WORK( K+J ) = WORK( K+J ) + S
! 887: END DO
! 888: * j=k is special :process col A(k,0:k-1)
! 889: S = ZERO
! 890: DO I = 0, K - 2
! 891: AA = ABS( A( I+J*LDA ) )
! 892: * A(k,i)
! 893: WORK( I ) = WORK( I ) + AA
! 894: S = S + AA
! 895: END DO
! 896: *
! 897: * i=k-1
! 898: AA = ABS( DBLE( A( I+J*LDA ) ) )
! 899: * A(k-1,k-1)
! 900: S = S + AA
! 901: WORK( I ) = S
! 902: * done with col j=k+1
! 903: DO J = K + 1, N
! 904: *
! 905: * process col j-1 of A = A(j-1,0:k-1)
! 906: S = ZERO
! 907: DO I = 0, K - 1
! 908: AA = ABS( A( I+J*LDA ) )
! 909: * A(j-1,i)
! 910: WORK( I ) = WORK( I ) + AA
! 911: S = S + AA
! 912: END DO
! 913: WORK( J-1 ) = WORK( J-1 ) + S
! 914: END DO
! 915: I = IDAMAX( N, WORK, 1 )
! 916: VALUE = WORK( I-1 )
! 917: END IF
! 918: END IF
! 919: END IF
! 920: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
! 921: *
! 922: * Find normF(A).
! 923: *
! 924: K = ( N+1 ) / 2
! 925: SCALE = ZERO
! 926: S = ONE
! 927: IF( NOE.EQ.1 ) THEN
! 928: * n is odd
! 929: IF( IFM.EQ.1 ) THEN
! 930: * A is normal & A is n by k
! 931: IF( ILU.EQ.0 ) THEN
! 932: * A is upper
! 933: DO J = 0, K - 3
! 934: CALL ZLASSQ( K-J-2, A( K+J+1+J*LDA ), 1, SCALE, S )
! 935: * L at A(k,0)
! 936: END DO
! 937: DO J = 0, K - 1
! 938: CALL ZLASSQ( K+J-1, A( 0+J*LDA ), 1, SCALE, S )
! 939: * trap U at A(0,0)
! 940: END DO
! 941: S = S + S
! 942: * double s for the off diagonal elements
! 943: L = K - 1
! 944: * -> U(k,k) at A(k-1,0)
! 945: DO I = 0, K - 2
! 946: AA = DBLE( A( L ) )
! 947: * U(k+i,k+i)
! 948: IF( AA.NE.ZERO ) THEN
! 949: IF( SCALE.LT.AA ) THEN
! 950: S = ONE + S*( SCALE / AA )**2
! 951: SCALE = AA
! 952: ELSE
! 953: S = S + ( AA / SCALE )**2
! 954: END IF
! 955: END IF
! 956: AA = DBLE( A( L+1 ) )
! 957: * U(i,i)
! 958: IF( AA.NE.ZERO ) THEN
! 959: IF( SCALE.LT.AA ) THEN
! 960: S = ONE + S*( SCALE / AA )**2
! 961: SCALE = AA
! 962: ELSE
! 963: S = S + ( AA / SCALE )**2
! 964: END IF
! 965: END IF
! 966: L = L + LDA + 1
! 967: END DO
! 968: AA = DBLE( A( L ) )
! 969: * U(n-1,n-1)
! 970: IF( AA.NE.ZERO ) THEN
! 971: IF( SCALE.LT.AA ) THEN
! 972: S = ONE + S*( SCALE / AA )**2
! 973: SCALE = AA
! 974: ELSE
! 975: S = S + ( AA / SCALE )**2
! 976: END IF
! 977: END IF
! 978: ELSE
! 979: * ilu=1 & A is lower
! 980: DO J = 0, K - 1
! 981: CALL ZLASSQ( N-J-1, A( J+1+J*LDA ), 1, SCALE, S )
! 982: * trap L at A(0,0)
! 983: END DO
! 984: DO J = 1, K - 2
! 985: CALL ZLASSQ( J, A( 0+( 1+J )*LDA ), 1, SCALE, S )
! 986: * U at A(0,1)
! 987: END DO
! 988: S = S + S
! 989: * double s for the off diagonal elements
! 990: AA = DBLE( A( 0 ) )
! 991: * L(0,0) at A(0,0)
! 992: IF( AA.NE.ZERO ) THEN
! 993: IF( SCALE.LT.AA ) THEN
! 994: S = ONE + S*( SCALE / AA )**2
! 995: SCALE = AA
! 996: ELSE
! 997: S = S + ( AA / SCALE )**2
! 998: END IF
! 999: END IF
! 1000: L = LDA
! 1001: * -> L(k,k) at A(0,1)
! 1002: DO I = 1, K - 1
! 1003: AA = DBLE( A( L ) )
! 1004: * L(k-1+i,k-1+i)
! 1005: IF( AA.NE.ZERO ) THEN
! 1006: IF( SCALE.LT.AA ) THEN
! 1007: S = ONE + S*( SCALE / AA )**2
! 1008: SCALE = AA
! 1009: ELSE
! 1010: S = S + ( AA / SCALE )**2
! 1011: END IF
! 1012: END IF
! 1013: AA = DBLE( A( L+1 ) )
! 1014: * L(i,i)
! 1015: IF( AA.NE.ZERO ) THEN
! 1016: IF( SCALE.LT.AA ) THEN
! 1017: S = ONE + S*( SCALE / AA )**2
! 1018: SCALE = AA
! 1019: ELSE
! 1020: S = S + ( AA / SCALE )**2
! 1021: END IF
! 1022: END IF
! 1023: L = L + LDA + 1
! 1024: END DO
! 1025: END IF
! 1026: ELSE
! 1027: * A is xpose & A is k by n
! 1028: IF( ILU.EQ.0 ) THEN
! 1029: * A' is upper
! 1030: DO J = 1, K - 2
! 1031: CALL ZLASSQ( J, A( 0+( K+J )*LDA ), 1, SCALE, S )
! 1032: * U at A(0,k)
! 1033: END DO
! 1034: DO J = 0, K - 2
! 1035: CALL ZLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
! 1036: * k by k-1 rect. at A(0,0)
! 1037: END DO
! 1038: DO J = 0, K - 2
! 1039: CALL ZLASSQ( K-J-1, A( J+1+( J+K-1 )*LDA ), 1,
! 1040: + SCALE, S )
! 1041: * L at A(0,k-1)
! 1042: END DO
! 1043: S = S + S
! 1044: * double s for the off diagonal elements
! 1045: L = 0 + K*LDA - LDA
! 1046: * -> U(k-1,k-1) at A(0,k-1)
! 1047: AA = DBLE( A( L ) )
! 1048: * U(k-1,k-1)
! 1049: IF( AA.NE.ZERO ) THEN
! 1050: IF( SCALE.LT.AA ) THEN
! 1051: S = ONE + S*( SCALE / AA )**2
! 1052: SCALE = AA
! 1053: ELSE
! 1054: S = S + ( AA / SCALE )**2
! 1055: END IF
! 1056: END IF
! 1057: L = L + LDA
! 1058: * -> U(0,0) at A(0,k)
! 1059: DO J = K, N - 1
! 1060: AA = DBLE( A( L ) )
! 1061: * -> U(j-k,j-k)
! 1062: IF( AA.NE.ZERO ) THEN
! 1063: IF( SCALE.LT.AA ) THEN
! 1064: S = ONE + S*( SCALE / AA )**2
! 1065: SCALE = AA
! 1066: ELSE
! 1067: S = S + ( AA / SCALE )**2
! 1068: END IF
! 1069: END IF
! 1070: AA = DBLE( A( L+1 ) )
! 1071: * -> U(j,j)
! 1072: IF( AA.NE.ZERO ) THEN
! 1073: IF( SCALE.LT.AA ) THEN
! 1074: S = ONE + S*( SCALE / AA )**2
! 1075: SCALE = AA
! 1076: ELSE
! 1077: S = S + ( AA / SCALE )**2
! 1078: END IF
! 1079: END IF
! 1080: L = L + LDA + 1
! 1081: END DO
! 1082: ELSE
! 1083: * A' is lower
! 1084: DO J = 1, K - 1
! 1085: CALL ZLASSQ( J, A( 0+J*LDA ), 1, SCALE, S )
! 1086: * U at A(0,0)
! 1087: END DO
! 1088: DO J = K, N - 1
! 1089: CALL ZLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
! 1090: * k by k-1 rect. at A(0,k)
! 1091: END DO
! 1092: DO J = 0, K - 3
! 1093: CALL ZLASSQ( K-J-2, A( J+2+J*LDA ), 1, SCALE, S )
! 1094: * L at A(1,0)
! 1095: END DO
! 1096: S = S + S
! 1097: * double s for the off diagonal elements
! 1098: L = 0
! 1099: * -> L(0,0) at A(0,0)
! 1100: DO I = 0, K - 2
! 1101: AA = DBLE( A( L ) )
! 1102: * L(i,i)
! 1103: IF( AA.NE.ZERO ) THEN
! 1104: IF( SCALE.LT.AA ) THEN
! 1105: S = ONE + S*( SCALE / AA )**2
! 1106: SCALE = AA
! 1107: ELSE
! 1108: S = S + ( AA / SCALE )**2
! 1109: END IF
! 1110: END IF
! 1111: AA = DBLE( A( L+1 ) )
! 1112: * L(k+i,k+i)
! 1113: IF( AA.NE.ZERO ) THEN
! 1114: IF( SCALE.LT.AA ) THEN
! 1115: S = ONE + S*( SCALE / AA )**2
! 1116: SCALE = AA
! 1117: ELSE
! 1118: S = S + ( AA / SCALE )**2
! 1119: END IF
! 1120: END IF
! 1121: L = L + LDA + 1
! 1122: END DO
! 1123: * L-> k-1 + (k-1)*lda or L(k-1,k-1) at A(k-1,k-1)
! 1124: AA = DBLE( A( L ) )
! 1125: * L(k-1,k-1) at A(k-1,k-1)
! 1126: IF( AA.NE.ZERO ) THEN
! 1127: IF( SCALE.LT.AA ) THEN
! 1128: S = ONE + S*( SCALE / AA )**2
! 1129: SCALE = AA
! 1130: ELSE
! 1131: S = S + ( AA / SCALE )**2
! 1132: END IF
! 1133: END IF
! 1134: END IF
! 1135: END IF
! 1136: ELSE
! 1137: * n is even
! 1138: IF( IFM.EQ.1 ) THEN
! 1139: * A is normal
! 1140: IF( ILU.EQ.0 ) THEN
! 1141: * A is upper
! 1142: DO J = 0, K - 2
! 1143: CALL ZLASSQ( K-J-1, A( K+J+2+J*LDA ), 1, SCALE, S )
! 1144: * L at A(k+1,0)
! 1145: END DO
! 1146: DO J = 0, K - 1
! 1147: CALL ZLASSQ( K+J, A( 0+J*LDA ), 1, SCALE, S )
! 1148: * trap U at A(0,0)
! 1149: END DO
! 1150: S = S + S
! 1151: * double s for the off diagonal elements
! 1152: L = K
! 1153: * -> U(k,k) at A(k,0)
! 1154: DO I = 0, K - 1
! 1155: AA = DBLE( A( L ) )
! 1156: * U(k+i,k+i)
! 1157: IF( AA.NE.ZERO ) THEN
! 1158: IF( SCALE.LT.AA ) THEN
! 1159: S = ONE + S*( SCALE / AA )**2
! 1160: SCALE = AA
! 1161: ELSE
! 1162: S = S + ( AA / SCALE )**2
! 1163: END IF
! 1164: END IF
! 1165: AA = DBLE( A( L+1 ) )
! 1166: * U(i,i)
! 1167: IF( AA.NE.ZERO ) THEN
! 1168: IF( SCALE.LT.AA ) THEN
! 1169: S = ONE + S*( SCALE / AA )**2
! 1170: SCALE = AA
! 1171: ELSE
! 1172: S = S + ( AA / SCALE )**2
! 1173: END IF
! 1174: END IF
! 1175: L = L + LDA + 1
! 1176: END DO
! 1177: ELSE
! 1178: * ilu=1 & A is lower
! 1179: DO J = 0, K - 1
! 1180: CALL ZLASSQ( N-J-1, A( J+2+J*LDA ), 1, SCALE, S )
! 1181: * trap L at A(1,0)
! 1182: END DO
! 1183: DO J = 1, K - 1
! 1184: CALL ZLASSQ( J, A( 0+J*LDA ), 1, SCALE, S )
! 1185: * U at A(0,0)
! 1186: END DO
! 1187: S = S + S
! 1188: * double s for the off diagonal elements
! 1189: L = 0
! 1190: * -> L(k,k) at A(0,0)
! 1191: DO I = 0, K - 1
! 1192: AA = DBLE( A( L ) )
! 1193: * L(k-1+i,k-1+i)
! 1194: IF( AA.NE.ZERO ) THEN
! 1195: IF( SCALE.LT.AA ) THEN
! 1196: S = ONE + S*( SCALE / AA )**2
! 1197: SCALE = AA
! 1198: ELSE
! 1199: S = S + ( AA / SCALE )**2
! 1200: END IF
! 1201: END IF
! 1202: AA = DBLE( A( L+1 ) )
! 1203: * L(i,i)
! 1204: IF( AA.NE.ZERO ) THEN
! 1205: IF( SCALE.LT.AA ) THEN
! 1206: S = ONE + S*( SCALE / AA )**2
! 1207: SCALE = AA
! 1208: ELSE
! 1209: S = S + ( AA / SCALE )**2
! 1210: END IF
! 1211: END IF
! 1212: L = L + LDA + 1
! 1213: END DO
! 1214: END IF
! 1215: ELSE
! 1216: * A is xpose
! 1217: IF( ILU.EQ.0 ) THEN
! 1218: * A' is upper
! 1219: DO J = 1, K - 1
! 1220: CALL ZLASSQ( J, A( 0+( K+1+J )*LDA ), 1, SCALE, S )
! 1221: * U at A(0,k+1)
! 1222: END DO
! 1223: DO J = 0, K - 1
! 1224: CALL ZLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
! 1225: * k by k rect. at A(0,0)
! 1226: END DO
! 1227: DO J = 0, K - 2
! 1228: CALL ZLASSQ( K-J-1, A( J+1+( J+K )*LDA ), 1, SCALE,
! 1229: + S )
! 1230: * L at A(0,k)
! 1231: END DO
! 1232: S = S + S
! 1233: * double s for the off diagonal elements
! 1234: L = 0 + K*LDA
! 1235: * -> U(k,k) at A(0,k)
! 1236: AA = DBLE( A( L ) )
! 1237: * U(k,k)
! 1238: IF( AA.NE.ZERO ) THEN
! 1239: IF( SCALE.LT.AA ) THEN
! 1240: S = ONE + S*( SCALE / AA )**2
! 1241: SCALE = AA
! 1242: ELSE
! 1243: S = S + ( AA / SCALE )**2
! 1244: END IF
! 1245: END IF
! 1246: L = L + LDA
! 1247: * -> U(0,0) at A(0,k+1)
! 1248: DO J = K + 1, N - 1
! 1249: AA = DBLE( A( L ) )
! 1250: * -> U(j-k-1,j-k-1)
! 1251: IF( AA.NE.ZERO ) THEN
! 1252: IF( SCALE.LT.AA ) THEN
! 1253: S = ONE + S*( SCALE / AA )**2
! 1254: SCALE = AA
! 1255: ELSE
! 1256: S = S + ( AA / SCALE )**2
! 1257: END IF
! 1258: END IF
! 1259: AA = DBLE( A( L+1 ) )
! 1260: * -> U(j,j)
! 1261: IF( AA.NE.ZERO ) THEN
! 1262: IF( SCALE.LT.AA ) THEN
! 1263: S = ONE + S*( SCALE / AA )**2
! 1264: SCALE = AA
! 1265: ELSE
! 1266: S = S + ( AA / SCALE )**2
! 1267: END IF
! 1268: END IF
! 1269: L = L + LDA + 1
! 1270: END DO
! 1271: * L=k-1+n*lda
! 1272: * -> U(k-1,k-1) at A(k-1,n)
! 1273: AA = DBLE( A( L ) )
! 1274: * U(k,k)
! 1275: IF( AA.NE.ZERO ) THEN
! 1276: IF( SCALE.LT.AA ) THEN
! 1277: S = ONE + S*( SCALE / AA )**2
! 1278: SCALE = AA
! 1279: ELSE
! 1280: S = S + ( AA / SCALE )**2
! 1281: END IF
! 1282: END IF
! 1283: ELSE
! 1284: * A' is lower
! 1285: DO J = 1, K - 1
! 1286: CALL ZLASSQ( J, A( 0+( J+1 )*LDA ), 1, SCALE, S )
! 1287: * U at A(0,1)
! 1288: END DO
! 1289: DO J = K + 1, N
! 1290: CALL ZLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
! 1291: * k by k rect. at A(0,k+1)
! 1292: END DO
! 1293: DO J = 0, K - 2
! 1294: CALL ZLASSQ( K-J-1, A( J+1+J*LDA ), 1, SCALE, S )
! 1295: * L at A(0,0)
! 1296: END DO
! 1297: S = S + S
! 1298: * double s for the off diagonal elements
! 1299: L = 0
! 1300: * -> L(k,k) at A(0,0)
! 1301: AA = DBLE( A( L ) )
! 1302: * L(k,k) at A(0,0)
! 1303: IF( AA.NE.ZERO ) THEN
! 1304: IF( SCALE.LT.AA ) THEN
! 1305: S = ONE + S*( SCALE / AA )**2
! 1306: SCALE = AA
! 1307: ELSE
! 1308: S = S + ( AA / SCALE )**2
! 1309: END IF
! 1310: END IF
! 1311: L = LDA
! 1312: * -> L(0,0) at A(0,1)
! 1313: DO I = 0, K - 2
! 1314: AA = DBLE( A( L ) )
! 1315: * L(i,i)
! 1316: IF( AA.NE.ZERO ) THEN
! 1317: IF( SCALE.LT.AA ) THEN
! 1318: S = ONE + S*( SCALE / AA )**2
! 1319: SCALE = AA
! 1320: ELSE
! 1321: S = S + ( AA / SCALE )**2
! 1322: END IF
! 1323: END IF
! 1324: AA = DBLE( A( L+1 ) )
! 1325: * L(k+i+1,k+i+1)
! 1326: IF( AA.NE.ZERO ) THEN
! 1327: IF( SCALE.LT.AA ) THEN
! 1328: S = ONE + S*( SCALE / AA )**2
! 1329: SCALE = AA
! 1330: ELSE
! 1331: S = S + ( AA / SCALE )**2
! 1332: END IF
! 1333: END IF
! 1334: L = L + LDA + 1
! 1335: END DO
! 1336: * L-> k - 1 + k*lda or L(k-1,k-1) at A(k-1,k)
! 1337: AA = DBLE( A( L ) )
! 1338: * L(k-1,k-1) at A(k-1,k)
! 1339: IF( AA.NE.ZERO ) THEN
! 1340: IF( SCALE.LT.AA ) THEN
! 1341: S = ONE + S*( SCALE / AA )**2
! 1342: SCALE = AA
! 1343: ELSE
! 1344: S = S + ( AA / SCALE )**2
! 1345: END IF
! 1346: END IF
! 1347: END IF
! 1348: END IF
! 1349: END IF
! 1350: VALUE = SCALE*SQRT( S )
! 1351: END IF
! 1352: *
! 1353: ZLANHF = VALUE
! 1354: RETURN
! 1355: *
! 1356: * End of ZLANHF
! 1357: *
! 1358: END
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