Annotation of rpl/lapack/lapack/zhetf2.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHETF2( UPLO, N, A, LDA, IPIV, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: CHARACTER UPLO
! 10: INTEGER INFO, LDA, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: INTEGER IPIV( * )
! 14: COMPLEX*16 A( LDA, * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZHETF2 computes the factorization of a complex Hermitian matrix A
! 21: * using the Bunch-Kaufman diagonal pivoting method:
! 22: *
! 23: * A = U*D*U' or A = L*D*L'
! 24: *
! 25: * where U (or L) is a product of permutation and unit upper (lower)
! 26: * triangular matrices, U' is the conjugate transpose of U, and D is
! 27: * Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
! 28: *
! 29: * This is the unblocked version of the algorithm, calling Level 2 BLAS.
! 30: *
! 31: * Arguments
! 32: * =========
! 33: *
! 34: * UPLO (input) CHARACTER*1
! 35: * Specifies whether the upper or lower triangular part of the
! 36: * Hermitian matrix A is stored:
! 37: * = 'U': Upper triangular
! 38: * = 'L': Lower triangular
! 39: *
! 40: * N (input) INTEGER
! 41: * The order of the matrix A. N >= 0.
! 42: *
! 43: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 44: * On entry, the Hermitian matrix A. If UPLO = 'U', the leading
! 45: * n-by-n upper triangular part of A contains the upper
! 46: * triangular part of the matrix A, and the strictly lower
! 47: * triangular part of A is not referenced. If UPLO = 'L', the
! 48: * leading n-by-n lower triangular part of A contains the lower
! 49: * triangular part of the matrix A, and the strictly upper
! 50: * triangular part of A is not referenced.
! 51: *
! 52: * On exit, the block diagonal matrix D and the multipliers used
! 53: * to obtain the factor U or L (see below for further details).
! 54: *
! 55: * LDA (input) INTEGER
! 56: * The leading dimension of the array A. LDA >= max(1,N).
! 57: *
! 58: * IPIV (output) INTEGER array, dimension (N)
! 59: * Details of the interchanges and the block structure of D.
! 60: * If IPIV(k) > 0, then rows and columns k and IPIV(k) were
! 61: * interchanged and D(k,k) is a 1-by-1 diagonal block.
! 62: * If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
! 63: * columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
! 64: * is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) =
! 65: * IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
! 66: * interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
! 67: *
! 68: * INFO (output) INTEGER
! 69: * = 0: successful exit
! 70: * < 0: if INFO = -k, the k-th argument had an illegal value
! 71: * > 0: if INFO = k, D(k,k) is exactly zero. The factorization
! 72: * has been completed, but the block diagonal matrix D is
! 73: * exactly singular, and division by zero will occur if it
! 74: * is used to solve a system of equations.
! 75: *
! 76: * Further Details
! 77: * ===============
! 78: *
! 79: * 09-29-06 - patch from
! 80: * Bobby Cheng, MathWorks
! 81: *
! 82: * Replace l.210 and l.393
! 83: * IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
! 84: * by
! 85: * IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
! 86: *
! 87: * 01-01-96 - Based on modifications by
! 88: * J. Lewis, Boeing Computer Services Company
! 89: * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
! 90: *
! 91: * If UPLO = 'U', then A = U*D*U', where
! 92: * U = P(n)*U(n)* ... *P(k)U(k)* ...,
! 93: * i.e., U is a product of terms P(k)*U(k), where k decreases from n to
! 94: * 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
! 95: * and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
! 96: * defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
! 97: * that if the diagonal block D(k) is of order s (s = 1 or 2), then
! 98: *
! 99: * ( I v 0 ) k-s
! 100: * U(k) = ( 0 I 0 ) s
! 101: * ( 0 0 I ) n-k
! 102: * k-s s n-k
! 103: *
! 104: * If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
! 105: * If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
! 106: * and A(k,k), and v overwrites A(1:k-2,k-1:k).
! 107: *
! 108: * If UPLO = 'L', then A = L*D*L', where
! 109: * L = P(1)*L(1)* ... *P(k)*L(k)* ...,
! 110: * i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
! 111: * n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
! 112: * and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
! 113: * defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
! 114: * that if the diagonal block D(k) is of order s (s = 1 or 2), then
! 115: *
! 116: * ( I 0 0 ) k-1
! 117: * L(k) = ( 0 I 0 ) s
! 118: * ( 0 v I ) n-k-s+1
! 119: * k-1 s n-k-s+1
! 120: *
! 121: * If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
! 122: * If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
! 123: * and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
! 124: *
! 125: * =====================================================================
! 126: *
! 127: * .. Parameters ..
! 128: DOUBLE PRECISION ZERO, ONE
! 129: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 130: DOUBLE PRECISION EIGHT, SEVTEN
! 131: PARAMETER ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 )
! 132: * ..
! 133: * .. Local Scalars ..
! 134: LOGICAL UPPER
! 135: INTEGER I, IMAX, J, JMAX, K, KK, KP, KSTEP
! 136: DOUBLE PRECISION ABSAKK, ALPHA, COLMAX, D, D11, D22, R1, ROWMAX,
! 137: $ TT
! 138: COMPLEX*16 D12, D21, T, WK, WKM1, WKP1, ZDUM
! 139: * ..
! 140: * .. External Functions ..
! 141: LOGICAL LSAME, DISNAN
! 142: INTEGER IZAMAX
! 143: DOUBLE PRECISION DLAPY2
! 144: EXTERNAL LSAME, IZAMAX, DLAPY2, DISNAN
! 145: * ..
! 146: * .. External Subroutines ..
! 147: EXTERNAL XERBLA, ZDSCAL, ZHER, ZSWAP
! 148: * ..
! 149: * .. Intrinsic Functions ..
! 150: INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, MAX, SQRT
! 151: * ..
! 152: * .. Statement Functions ..
! 153: DOUBLE PRECISION CABS1
! 154: * ..
! 155: * .. Statement Function definitions ..
! 156: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 157: * ..
! 158: * .. Executable Statements ..
! 159: *
! 160: * Test the input parameters.
! 161: *
! 162: INFO = 0
! 163: UPPER = LSAME( UPLO, 'U' )
! 164: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 165: INFO = -1
! 166: ELSE IF( N.LT.0 ) THEN
! 167: INFO = -2
! 168: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 169: INFO = -4
! 170: END IF
! 171: IF( INFO.NE.0 ) THEN
! 172: CALL XERBLA( 'ZHETF2', -INFO )
! 173: RETURN
! 174: END IF
! 175: *
! 176: * Initialize ALPHA for use in choosing pivot block size.
! 177: *
! 178: ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
! 179: *
! 180: IF( UPPER ) THEN
! 181: *
! 182: * Factorize A as U*D*U' using the upper triangle of A
! 183: *
! 184: * K is the main loop index, decreasing from N to 1 in steps of
! 185: * 1 or 2
! 186: *
! 187: K = N
! 188: 10 CONTINUE
! 189: *
! 190: * If K < 1, exit from loop
! 191: *
! 192: IF( K.LT.1 )
! 193: $ GO TO 90
! 194: KSTEP = 1
! 195: *
! 196: * Determine rows and columns to be interchanged and whether
! 197: * a 1-by-1 or 2-by-2 pivot block will be used
! 198: *
! 199: ABSAKK = ABS( DBLE( A( K, K ) ) )
! 200: *
! 201: * IMAX is the row-index of the largest off-diagonal element in
! 202: * column K, and COLMAX is its absolute value
! 203: *
! 204: IF( K.GT.1 ) THEN
! 205: IMAX = IZAMAX( K-1, A( 1, K ), 1 )
! 206: COLMAX = CABS1( A( IMAX, K ) )
! 207: ELSE
! 208: COLMAX = ZERO
! 209: END IF
! 210: *
! 211: IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
! 212: *
! 213: * Column K is zero or contains a NaN: set INFO and continue
! 214: *
! 215: IF( INFO.EQ.0 )
! 216: $ INFO = K
! 217: KP = K
! 218: A( K, K ) = DBLE( A( K, K ) )
! 219: ELSE
! 220: IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
! 221: *
! 222: * no interchange, use 1-by-1 pivot block
! 223: *
! 224: KP = K
! 225: ELSE
! 226: *
! 227: * JMAX is the column-index of the largest off-diagonal
! 228: * element in row IMAX, and ROWMAX is its absolute value
! 229: *
! 230: JMAX = IMAX + IZAMAX( K-IMAX, A( IMAX, IMAX+1 ), LDA )
! 231: ROWMAX = CABS1( A( IMAX, JMAX ) )
! 232: IF( IMAX.GT.1 ) THEN
! 233: JMAX = IZAMAX( IMAX-1, A( 1, IMAX ), 1 )
! 234: ROWMAX = MAX( ROWMAX, CABS1( A( JMAX, IMAX ) ) )
! 235: END IF
! 236: *
! 237: IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
! 238: *
! 239: * no interchange, use 1-by-1 pivot block
! 240: *
! 241: KP = K
! 242: ELSE IF( ABS( DBLE( A( IMAX, IMAX ) ) ).GE.ALPHA*ROWMAX )
! 243: $ THEN
! 244: *
! 245: * interchange rows and columns K and IMAX, use 1-by-1
! 246: * pivot block
! 247: *
! 248: KP = IMAX
! 249: ELSE
! 250: *
! 251: * interchange rows and columns K-1 and IMAX, use 2-by-2
! 252: * pivot block
! 253: *
! 254: KP = IMAX
! 255: KSTEP = 2
! 256: END IF
! 257: END IF
! 258: *
! 259: KK = K - KSTEP + 1
! 260: IF( KP.NE.KK ) THEN
! 261: *
! 262: * Interchange rows and columns KK and KP in the leading
! 263: * submatrix A(1:k,1:k)
! 264: *
! 265: CALL ZSWAP( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 )
! 266: DO 20 J = KP + 1, KK - 1
! 267: T = DCONJG( A( J, KK ) )
! 268: A( J, KK ) = DCONJG( A( KP, J ) )
! 269: A( KP, J ) = T
! 270: 20 CONTINUE
! 271: A( KP, KK ) = DCONJG( A( KP, KK ) )
! 272: R1 = DBLE( A( KK, KK ) )
! 273: A( KK, KK ) = DBLE( A( KP, KP ) )
! 274: A( KP, KP ) = R1
! 275: IF( KSTEP.EQ.2 ) THEN
! 276: A( K, K ) = DBLE( A( K, K ) )
! 277: T = A( K-1, K )
! 278: A( K-1, K ) = A( KP, K )
! 279: A( KP, K ) = T
! 280: END IF
! 281: ELSE
! 282: A( K, K ) = DBLE( A( K, K ) )
! 283: IF( KSTEP.EQ.2 )
! 284: $ A( K-1, K-1 ) = DBLE( A( K-1, K-1 ) )
! 285: END IF
! 286: *
! 287: * Update the leading submatrix
! 288: *
! 289: IF( KSTEP.EQ.1 ) THEN
! 290: *
! 291: * 1-by-1 pivot block D(k): column k now holds
! 292: *
! 293: * W(k) = U(k)*D(k)
! 294: *
! 295: * where U(k) is the k-th column of U
! 296: *
! 297: * Perform a rank-1 update of A(1:k-1,1:k-1) as
! 298: *
! 299: * A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)'
! 300: *
! 301: R1 = ONE / DBLE( A( K, K ) )
! 302: CALL ZHER( UPLO, K-1, -R1, A( 1, K ), 1, A, LDA )
! 303: *
! 304: * Store U(k) in column k
! 305: *
! 306: CALL ZDSCAL( K-1, R1, A( 1, K ), 1 )
! 307: ELSE
! 308: *
! 309: * 2-by-2 pivot block D(k): columns k and k-1 now hold
! 310: *
! 311: * ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
! 312: *
! 313: * where U(k) and U(k-1) are the k-th and (k-1)-th columns
! 314: * of U
! 315: *
! 316: * Perform a rank-2 update of A(1:k-2,1:k-2) as
! 317: *
! 318: * A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )'
! 319: * = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )'
! 320: *
! 321: IF( K.GT.2 ) THEN
! 322: *
! 323: D = DLAPY2( DBLE( A( K-1, K ) ),
! 324: $ DIMAG( A( K-1, K ) ) )
! 325: D22 = DBLE( A( K-1, K-1 ) ) / D
! 326: D11 = DBLE( A( K, K ) ) / D
! 327: TT = ONE / ( D11*D22-ONE )
! 328: D12 = A( K-1, K ) / D
! 329: D = TT / D
! 330: *
! 331: DO 40 J = K - 2, 1, -1
! 332: WKM1 = D*( D11*A( J, K-1 )-DCONJG( D12 )*
! 333: $ A( J, K ) )
! 334: WK = D*( D22*A( J, K )-D12*A( J, K-1 ) )
! 335: DO 30 I = J, 1, -1
! 336: A( I, J ) = A( I, J ) - A( I, K )*DCONJG( WK ) -
! 337: $ A( I, K-1 )*DCONJG( WKM1 )
! 338: 30 CONTINUE
! 339: A( J, K ) = WK
! 340: A( J, K-1 ) = WKM1
! 341: A( J, J ) = DCMPLX( DBLE( A( J, J ) ), 0.0D+0 )
! 342: 40 CONTINUE
! 343: *
! 344: END IF
! 345: *
! 346: END IF
! 347: END IF
! 348: *
! 349: * Store details of the interchanges in IPIV
! 350: *
! 351: IF( KSTEP.EQ.1 ) THEN
! 352: IPIV( K ) = KP
! 353: ELSE
! 354: IPIV( K ) = -KP
! 355: IPIV( K-1 ) = -KP
! 356: END IF
! 357: *
! 358: * Decrease K and return to the start of the main loop
! 359: *
! 360: K = K - KSTEP
! 361: GO TO 10
! 362: *
! 363: ELSE
! 364: *
! 365: * Factorize A as L*D*L' using the lower triangle of A
! 366: *
! 367: * K is the main loop index, increasing from 1 to N in steps of
! 368: * 1 or 2
! 369: *
! 370: K = 1
! 371: 50 CONTINUE
! 372: *
! 373: * If K > N, exit from loop
! 374: *
! 375: IF( K.GT.N )
! 376: $ GO TO 90
! 377: KSTEP = 1
! 378: *
! 379: * Determine rows and columns to be interchanged and whether
! 380: * a 1-by-1 or 2-by-2 pivot block will be used
! 381: *
! 382: ABSAKK = ABS( DBLE( A( K, K ) ) )
! 383: *
! 384: * IMAX is the row-index of the largest off-diagonal element in
! 385: * column K, and COLMAX is its absolute value
! 386: *
! 387: IF( K.LT.N ) THEN
! 388: IMAX = K + IZAMAX( N-K, A( K+1, K ), 1 )
! 389: COLMAX = CABS1( A( IMAX, K ) )
! 390: ELSE
! 391: COLMAX = ZERO
! 392: END IF
! 393: *
! 394: IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
! 395: *
! 396: * Column K is zero or contains a NaN: set INFO and continue
! 397: *
! 398: IF( INFO.EQ.0 )
! 399: $ INFO = K
! 400: KP = K
! 401: A( K, K ) = DBLE( A( K, K ) )
! 402: ELSE
! 403: IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
! 404: *
! 405: * no interchange, use 1-by-1 pivot block
! 406: *
! 407: KP = K
! 408: ELSE
! 409: *
! 410: * JMAX is the column-index of the largest off-diagonal
! 411: * element in row IMAX, and ROWMAX is its absolute value
! 412: *
! 413: JMAX = K - 1 + IZAMAX( IMAX-K, A( IMAX, K ), LDA )
! 414: ROWMAX = CABS1( A( IMAX, JMAX ) )
! 415: IF( IMAX.LT.N ) THEN
! 416: JMAX = IMAX + IZAMAX( N-IMAX, A( IMAX+1, IMAX ), 1 )
! 417: ROWMAX = MAX( ROWMAX, CABS1( A( JMAX, IMAX ) ) )
! 418: END IF
! 419: *
! 420: IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
! 421: *
! 422: * no interchange, use 1-by-1 pivot block
! 423: *
! 424: KP = K
! 425: ELSE IF( ABS( DBLE( A( IMAX, IMAX ) ) ).GE.ALPHA*ROWMAX )
! 426: $ THEN
! 427: *
! 428: * interchange rows and columns K and IMAX, use 1-by-1
! 429: * pivot block
! 430: *
! 431: KP = IMAX
! 432: ELSE
! 433: *
! 434: * interchange rows and columns K+1 and IMAX, use 2-by-2
! 435: * pivot block
! 436: *
! 437: KP = IMAX
! 438: KSTEP = 2
! 439: END IF
! 440: END IF
! 441: *
! 442: KK = K + KSTEP - 1
! 443: IF( KP.NE.KK ) THEN
! 444: *
! 445: * Interchange rows and columns KK and KP in the trailing
! 446: * submatrix A(k:n,k:n)
! 447: *
! 448: IF( KP.LT.N )
! 449: $ CALL ZSWAP( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 )
! 450: DO 60 J = KK + 1, KP - 1
! 451: T = DCONJG( A( J, KK ) )
! 452: A( J, KK ) = DCONJG( A( KP, J ) )
! 453: A( KP, J ) = T
! 454: 60 CONTINUE
! 455: A( KP, KK ) = DCONJG( A( KP, KK ) )
! 456: R1 = DBLE( A( KK, KK ) )
! 457: A( KK, KK ) = DBLE( A( KP, KP ) )
! 458: A( KP, KP ) = R1
! 459: IF( KSTEP.EQ.2 ) THEN
! 460: A( K, K ) = DBLE( A( K, K ) )
! 461: T = A( K+1, K )
! 462: A( K+1, K ) = A( KP, K )
! 463: A( KP, K ) = T
! 464: END IF
! 465: ELSE
! 466: A( K, K ) = DBLE( A( K, K ) )
! 467: IF( KSTEP.EQ.2 )
! 468: $ A( K+1, K+1 ) = DBLE( A( K+1, K+1 ) )
! 469: END IF
! 470: *
! 471: * Update the trailing submatrix
! 472: *
! 473: IF( KSTEP.EQ.1 ) THEN
! 474: *
! 475: * 1-by-1 pivot block D(k): column k now holds
! 476: *
! 477: * W(k) = L(k)*D(k)
! 478: *
! 479: * where L(k) is the k-th column of L
! 480: *
! 481: IF( K.LT.N ) THEN
! 482: *
! 483: * Perform a rank-1 update of A(k+1:n,k+1:n) as
! 484: *
! 485: * A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)'
! 486: *
! 487: R1 = ONE / DBLE( A( K, K ) )
! 488: CALL ZHER( UPLO, N-K, -R1, A( K+1, K ), 1,
! 489: $ A( K+1, K+1 ), LDA )
! 490: *
! 491: * Store L(k) in column K
! 492: *
! 493: CALL ZDSCAL( N-K, R1, A( K+1, K ), 1 )
! 494: END IF
! 495: ELSE
! 496: *
! 497: * 2-by-2 pivot block D(k)
! 498: *
! 499: IF( K.LT.N-1 ) THEN
! 500: *
! 501: * Perform a rank-2 update of A(k+2:n,k+2:n) as
! 502: *
! 503: * A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )'
! 504: * = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )'
! 505: *
! 506: * where L(k) and L(k+1) are the k-th and (k+1)-th
! 507: * columns of L
! 508: *
! 509: D = DLAPY2( DBLE( A( K+1, K ) ),
! 510: $ DIMAG( A( K+1, K ) ) )
! 511: D11 = DBLE( A( K+1, K+1 ) ) / D
! 512: D22 = DBLE( A( K, K ) ) / D
! 513: TT = ONE / ( D11*D22-ONE )
! 514: D21 = A( K+1, K ) / D
! 515: D = TT / D
! 516: *
! 517: DO 80 J = K + 2, N
! 518: WK = D*( D11*A( J, K )-D21*A( J, K+1 ) )
! 519: WKP1 = D*( D22*A( J, K+1 )-DCONJG( D21 )*
! 520: $ A( J, K ) )
! 521: DO 70 I = J, N
! 522: A( I, J ) = A( I, J ) - A( I, K )*DCONJG( WK ) -
! 523: $ A( I, K+1 )*DCONJG( WKP1 )
! 524: 70 CONTINUE
! 525: A( J, K ) = WK
! 526: A( J, K+1 ) = WKP1
! 527: A( J, J ) = DCMPLX( DBLE( A( J, J ) ), 0.0D+0 )
! 528: 80 CONTINUE
! 529: END IF
! 530: END IF
! 531: END IF
! 532: *
! 533: * Store details of the interchanges in IPIV
! 534: *
! 535: IF( KSTEP.EQ.1 ) THEN
! 536: IPIV( K ) = KP
! 537: ELSE
! 538: IPIV( K ) = -KP
! 539: IPIV( K+1 ) = -KP
! 540: END IF
! 541: *
! 542: * Increase K and return to the start of the main loop
! 543: *
! 544: K = K + KSTEP
! 545: GO TO 50
! 546: *
! 547: END IF
! 548: *
! 549: 90 CONTINUE
! 550: RETURN
! 551: *
! 552: * End of ZHETF2
! 553: *
! 554: END
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