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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE ZHPTRF( UPLO, N, AP, IPIV, INFO ) 00002 * 00003 * -- LAPACK routine (version 3.3.1) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * -- April 2011 -- 00007 * 00008 * .. Scalar Arguments .. 00009 CHARACTER UPLO 00010 INTEGER INFO, N 00011 * .. 00012 * .. Array Arguments .. 00013 INTEGER IPIV( * ) 00014 COMPLEX*16 AP( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * ZHPTRF computes the factorization of a complex Hermitian packed 00021 * matrix A using the Bunch-Kaufman diagonal pivoting method: 00022 * 00023 * A = U*D*U**H or A = L*D*L**H 00024 * 00025 * where U (or L) is a product of permutation and unit upper (lower) 00026 * triangular matrices, and D is Hermitian and block diagonal with 00027 * 1-by-1 and 2-by-2 diagonal blocks. 00028 * 00029 * Arguments 00030 * ========= 00031 * 00032 * UPLO (input) CHARACTER*1 00033 * = 'U': Upper triangle of A is stored; 00034 * = 'L': Lower triangle of A is stored. 00035 * 00036 * N (input) INTEGER 00037 * The order of the matrix A. N >= 0. 00038 * 00039 * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) 00040 * On entry, the upper or lower triangle of the Hermitian matrix 00041 * A, packed columnwise in a linear array. The j-th column of A 00042 * is stored in the array AP as follows: 00043 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00044 * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 00045 * 00046 * On exit, the block diagonal matrix D and the multipliers used 00047 * to obtain the factor U or L, stored as a packed triangular 00048 * matrix overwriting A (see below for further details). 00049 * 00050 * IPIV (output) INTEGER array, dimension (N) 00051 * Details of the interchanges and the block structure of D. 00052 * If IPIV(k) > 0, then rows and columns k and IPIV(k) were 00053 * interchanged and D(k,k) is a 1-by-1 diagonal block. 00054 * If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and 00055 * columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) 00056 * is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = 00057 * IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were 00058 * interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. 00059 * 00060 * INFO (output) INTEGER 00061 * = 0: successful exit 00062 * < 0: if INFO = -i, the i-th argument had an illegal value 00063 * > 0: if INFO = i, D(i,i) is exactly zero. The factorization 00064 * has been completed, but the block diagonal matrix D is 00065 * exactly singular, and division by zero will occur if it 00066 * is used to solve a system of equations. 00067 * 00068 * Further Details 00069 * =============== 00070 * 00071 * 5-96 - Based on modifications by J. Lewis, Boeing Computer Services 00072 * Company 00073 * 00074 * If UPLO = 'U', then A = U*D*U**H, where 00075 * U = P(n)*U(n)* ... *P(k)U(k)* ..., 00076 * i.e., U is a product of terms P(k)*U(k), where k decreases from n to 00077 * 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 00078 * and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as 00079 * defined by IPIV(k), and U(k) is a unit upper triangular matrix, such 00080 * that if the diagonal block D(k) is of order s (s = 1 or 2), then 00081 * 00082 * ( I v 0 ) k-s 00083 * U(k) = ( 0 I 0 ) s 00084 * ( 0 0 I ) n-k 00085 * k-s s n-k 00086 * 00087 * If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). 00088 * If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), 00089 * and A(k,k), and v overwrites A(1:k-2,k-1:k). 00090 * 00091 * If UPLO = 'L', then A = L*D*L**H, where 00092 * L = P(1)*L(1)* ... *P(k)*L(k)* ..., 00093 * i.e., L is a product of terms P(k)*L(k), where k increases from 1 to 00094 * n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 00095 * and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as 00096 * defined by IPIV(k), and L(k) is a unit lower triangular matrix, such 00097 * that if the diagonal block D(k) is of order s (s = 1 or 2), then 00098 * 00099 * ( I 0 0 ) k-1 00100 * L(k) = ( 0 I 0 ) s 00101 * ( 0 v I ) n-k-s+1 00102 * k-1 s n-k-s+1 00103 * 00104 * If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). 00105 * If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), 00106 * and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). 00107 * 00108 * ===================================================================== 00109 * 00110 * .. Parameters .. 00111 DOUBLE PRECISION ZERO, ONE 00112 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00113 DOUBLE PRECISION EIGHT, SEVTEN 00114 PARAMETER ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 ) 00115 * .. 00116 * .. Local Scalars .. 00117 LOGICAL UPPER 00118 INTEGER I, IMAX, J, JMAX, K, KC, KK, KNC, KP, KPC, 00119 $ KSTEP, KX, NPP 00120 DOUBLE PRECISION ABSAKK, ALPHA, COLMAX, D, D11, D22, R1, ROWMAX, 00121 $ TT 00122 COMPLEX*16 D12, D21, T, WK, WKM1, WKP1, ZDUM 00123 * .. 00124 * .. External Functions .. 00125 LOGICAL LSAME 00126 INTEGER IZAMAX 00127 DOUBLE PRECISION DLAPY2 00128 EXTERNAL LSAME, IZAMAX, DLAPY2 00129 * .. 00130 * .. External Subroutines .. 00131 EXTERNAL XERBLA, ZDSCAL, ZHPR, ZSWAP 00132 * .. 00133 * .. Intrinsic Functions .. 00134 INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, MAX, SQRT 00135 * .. 00136 * .. Statement Functions .. 00137 DOUBLE PRECISION CABS1 00138 * .. 00139 * .. Statement Function definitions .. 00140 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00141 * .. 00142 * .. Executable Statements .. 00143 * 00144 * Test the input parameters. 00145 * 00146 INFO = 0 00147 UPPER = LSAME( UPLO, 'U' ) 00148 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00149 INFO = -1 00150 ELSE IF( N.LT.0 ) THEN 00151 INFO = -2 00152 END IF 00153 IF( INFO.NE.0 ) THEN 00154 CALL XERBLA( 'ZHPTRF', -INFO ) 00155 RETURN 00156 END IF 00157 * 00158 * Initialize ALPHA for use in choosing pivot block size. 00159 * 00160 ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT 00161 * 00162 IF( UPPER ) THEN 00163 * 00164 * Factorize A as U*D*U**H using the upper triangle of A 00165 * 00166 * K is the main loop index, decreasing from N to 1 in steps of 00167 * 1 or 2 00168 * 00169 K = N 00170 KC = ( N-1 )*N / 2 + 1 00171 10 CONTINUE 00172 KNC = KC 00173 * 00174 * If K < 1, exit from loop 00175 * 00176 IF( K.LT.1 ) 00177 $ GO TO 110 00178 KSTEP = 1 00179 * 00180 * Determine rows and columns to be interchanged and whether 00181 * a 1-by-1 or 2-by-2 pivot block will be used 00182 * 00183 ABSAKK = ABS( DBLE( AP( KC+K-1 ) ) ) 00184 * 00185 * IMAX is the row-index of the largest off-diagonal element in 00186 * column K, and COLMAX is its absolute value 00187 * 00188 IF( K.GT.1 ) THEN 00189 IMAX = IZAMAX( K-1, AP( KC ), 1 ) 00190 COLMAX = CABS1( AP( KC+IMAX-1 ) ) 00191 ELSE 00192 COLMAX = ZERO 00193 END IF 00194 * 00195 IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN 00196 * 00197 * Column K is zero: set INFO and continue 00198 * 00199 IF( INFO.EQ.0 ) 00200 $ INFO = K 00201 KP = K 00202 AP( KC+K-1 ) = DBLE( AP( KC+K-1 ) ) 00203 ELSE 00204 IF( ABSAKK.GE.ALPHA*COLMAX ) THEN 00205 * 00206 * no interchange, use 1-by-1 pivot block 00207 * 00208 KP = K 00209 ELSE 00210 * 00211 * JMAX is the column-index of the largest off-diagonal 00212 * element in row IMAX, and ROWMAX is its absolute value 00213 * 00214 ROWMAX = ZERO 00215 JMAX = IMAX 00216 KX = IMAX*( IMAX+1 ) / 2 + IMAX 00217 DO 20 J = IMAX + 1, K 00218 IF( CABS1( AP( KX ) ).GT.ROWMAX ) THEN 00219 ROWMAX = CABS1( AP( KX ) ) 00220 JMAX = J 00221 END IF 00222 KX = KX + J 00223 20 CONTINUE 00224 KPC = ( IMAX-1 )*IMAX / 2 + 1 00225 IF( IMAX.GT.1 ) THEN 00226 JMAX = IZAMAX( IMAX-1, AP( KPC ), 1 ) 00227 ROWMAX = MAX( ROWMAX, CABS1( AP( KPC+JMAX-1 ) ) ) 00228 END IF 00229 * 00230 IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN 00231 * 00232 * no interchange, use 1-by-1 pivot block 00233 * 00234 KP = K 00235 ELSE IF( ABS( DBLE( AP( KPC+IMAX-1 ) ) ).GE.ALPHA* 00236 $ ROWMAX ) THEN 00237 * 00238 * interchange rows and columns K and IMAX, use 1-by-1 00239 * pivot block 00240 * 00241 KP = IMAX 00242 ELSE 00243 * 00244 * interchange rows and columns K-1 and IMAX, use 2-by-2 00245 * pivot block 00246 * 00247 KP = IMAX 00248 KSTEP = 2 00249 END IF 00250 END IF 00251 * 00252 KK = K - KSTEP + 1 00253 IF( KSTEP.EQ.2 ) 00254 $ KNC = KNC - K + 1 00255 IF( KP.NE.KK ) THEN 00256 * 00257 * Interchange rows and columns KK and KP in the leading 00258 * submatrix A(1:k,1:k) 00259 * 00260 CALL ZSWAP( KP-1, AP( KNC ), 1, AP( KPC ), 1 ) 00261 KX = KPC + KP - 1 00262 DO 30 J = KP + 1, KK - 1 00263 KX = KX + J - 1 00264 T = DCONJG( AP( KNC+J-1 ) ) 00265 AP( KNC+J-1 ) = DCONJG( AP( KX ) ) 00266 AP( KX ) = T 00267 30 CONTINUE 00268 AP( KX+KK-1 ) = DCONJG( AP( KX+KK-1 ) ) 00269 R1 = DBLE( AP( KNC+KK-1 ) ) 00270 AP( KNC+KK-1 ) = DBLE( AP( KPC+KP-1 ) ) 00271 AP( KPC+KP-1 ) = R1 00272 IF( KSTEP.EQ.2 ) THEN 00273 AP( KC+K-1 ) = DBLE( AP( KC+K-1 ) ) 00274 T = AP( KC+K-2 ) 00275 AP( KC+K-2 ) = AP( KC+KP-1 ) 00276 AP( KC+KP-1 ) = T 00277 END IF 00278 ELSE 00279 AP( KC+K-1 ) = DBLE( AP( KC+K-1 ) ) 00280 IF( KSTEP.EQ.2 ) 00281 $ AP( KC-1 ) = DBLE( AP( KC-1 ) ) 00282 END IF 00283 * 00284 * Update the leading submatrix 00285 * 00286 IF( KSTEP.EQ.1 ) THEN 00287 * 00288 * 1-by-1 pivot block D(k): column k now holds 00289 * 00290 * W(k) = U(k)*D(k) 00291 * 00292 * where U(k) is the k-th column of U 00293 * 00294 * Perform a rank-1 update of A(1:k-1,1:k-1) as 00295 * 00296 * A := A - U(k)*D(k)*U(k)**H = A - W(k)*1/D(k)*W(k)**H 00297 * 00298 R1 = ONE / DBLE( AP( KC+K-1 ) ) 00299 CALL ZHPR( UPLO, K-1, -R1, AP( KC ), 1, AP ) 00300 * 00301 * Store U(k) in column k 00302 * 00303 CALL ZDSCAL( K-1, R1, AP( KC ), 1 ) 00304 ELSE 00305 * 00306 * 2-by-2 pivot block D(k): columns k and k-1 now hold 00307 * 00308 * ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) 00309 * 00310 * where U(k) and U(k-1) are the k-th and (k-1)-th columns 00311 * of U 00312 * 00313 * Perform a rank-2 update of A(1:k-2,1:k-2) as 00314 * 00315 * A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**H 00316 * = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**H 00317 * 00318 IF( K.GT.2 ) THEN 00319 * 00320 D = DLAPY2( DBLE( AP( K-1+( K-1 )*K / 2 ) ), 00321 $ DIMAG( AP( K-1+( K-1 )*K / 2 ) ) ) 00322 D22 = DBLE( AP( K-1+( K-2 )*( K-1 ) / 2 ) ) / D 00323 D11 = DBLE( AP( K+( K-1 )*K / 2 ) ) / D 00324 TT = ONE / ( D11*D22-ONE ) 00325 D12 = AP( K-1+( K-1 )*K / 2 ) / D 00326 D = TT / D 00327 * 00328 DO 50 J = K - 2, 1, -1 00329 WKM1 = D*( D11*AP( J+( K-2 )*( K-1 ) / 2 )- 00330 $ DCONJG( D12 )*AP( J+( K-1 )*K / 2 ) ) 00331 WK = D*( D22*AP( J+( K-1 )*K / 2 )-D12* 00332 $ AP( J+( K-2 )*( K-1 ) / 2 ) ) 00333 DO 40 I = J, 1, -1 00334 AP( I+( J-1 )*J / 2 ) = AP( I+( J-1 )*J / 2 ) - 00335 $ AP( I+( K-1 )*K / 2 )*DCONJG( WK ) - 00336 $ AP( I+( K-2 )*( K-1 ) / 2 )*DCONJG( WKM1 ) 00337 40 CONTINUE 00338 AP( J+( K-1 )*K / 2 ) = WK 00339 AP( J+( K-2 )*( K-1 ) / 2 ) = WKM1 00340 AP( J+( J-1 )*J / 2 ) = DCMPLX( DBLE( AP( J+( J- 00341 $ 1 )*J / 2 ) ), 0.0D+0 ) 00342 50 CONTINUE 00343 * 00344 END IF 00345 * 00346 END IF 00347 END IF 00348 * 00349 * Store details of the interchanges in IPIV 00350 * 00351 IF( KSTEP.EQ.1 ) THEN 00352 IPIV( K ) = KP 00353 ELSE 00354 IPIV( K ) = -KP 00355 IPIV( K-1 ) = -KP 00356 END IF 00357 * 00358 * Decrease K and return to the start of the main loop 00359 * 00360 K = K - KSTEP 00361 KC = KNC - K 00362 GO TO 10 00363 * 00364 ELSE 00365 * 00366 * Factorize A as L*D*L**H using the lower triangle of A 00367 * 00368 * K is the main loop index, increasing from 1 to N in steps of 00369 * 1 or 2 00370 * 00371 K = 1 00372 KC = 1 00373 NPP = N*( N+1 ) / 2 00374 60 CONTINUE 00375 KNC = KC 00376 * 00377 * If K > N, exit from loop 00378 * 00379 IF( K.GT.N ) 00380 $ GO TO 110 00381 KSTEP = 1 00382 * 00383 * Determine rows and columns to be interchanged and whether 00384 * a 1-by-1 or 2-by-2 pivot block will be used 00385 * 00386 ABSAKK = ABS( DBLE( AP( KC ) ) ) 00387 * 00388 * IMAX is the row-index of the largest off-diagonal element in 00389 * column K, and COLMAX is its absolute value 00390 * 00391 IF( K.LT.N ) THEN 00392 IMAX = K + IZAMAX( N-K, AP( KC+1 ), 1 ) 00393 COLMAX = CABS1( AP( KC+IMAX-K ) ) 00394 ELSE 00395 COLMAX = ZERO 00396 END IF 00397 * 00398 IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN 00399 * 00400 * Column K is zero: set INFO and continue 00401 * 00402 IF( INFO.EQ.0 ) 00403 $ INFO = K 00404 KP = K 00405 AP( KC ) = DBLE( AP( KC ) ) 00406 ELSE 00407 IF( ABSAKK.GE.ALPHA*COLMAX ) THEN 00408 * 00409 * no interchange, use 1-by-1 pivot block 00410 * 00411 KP = K 00412 ELSE 00413 * 00414 * JMAX is the column-index of the largest off-diagonal 00415 * element in row IMAX, and ROWMAX is its absolute value 00416 * 00417 ROWMAX = ZERO 00418 KX = KC + IMAX - K 00419 DO 70 J = K, IMAX - 1 00420 IF( CABS1( AP( KX ) ).GT.ROWMAX ) THEN 00421 ROWMAX = CABS1( AP( KX ) ) 00422 JMAX = J 00423 END IF 00424 KX = KX + N - J 00425 70 CONTINUE 00426 KPC = NPP - ( N-IMAX+1 )*( N-IMAX+2 ) / 2 + 1 00427 IF( IMAX.LT.N ) THEN 00428 JMAX = IMAX + IZAMAX( N-IMAX, AP( KPC+1 ), 1 ) 00429 ROWMAX = MAX( ROWMAX, CABS1( AP( KPC+JMAX-IMAX ) ) ) 00430 END IF 00431 * 00432 IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN 00433 * 00434 * no interchange, use 1-by-1 pivot block 00435 * 00436 KP = K 00437 ELSE IF( ABS( DBLE( AP( KPC ) ) ).GE.ALPHA*ROWMAX ) THEN 00438 * 00439 * interchange rows and columns K and IMAX, use 1-by-1 00440 * pivot block 00441 * 00442 KP = IMAX 00443 ELSE 00444 * 00445 * interchange rows and columns K+1 and IMAX, use 2-by-2 00446 * pivot block 00447 * 00448 KP = IMAX 00449 KSTEP = 2 00450 END IF 00451 END IF 00452 * 00453 KK = K + KSTEP - 1 00454 IF( KSTEP.EQ.2 ) 00455 $ KNC = KNC + N - K + 1 00456 IF( KP.NE.KK ) THEN 00457 * 00458 * Interchange rows and columns KK and KP in the trailing 00459 * submatrix A(k:n,k:n) 00460 * 00461 IF( KP.LT.N ) 00462 $ CALL ZSWAP( N-KP, AP( KNC+KP-KK+1 ), 1, AP( KPC+1 ), 00463 $ 1 ) 00464 KX = KNC + KP - KK 00465 DO 80 J = KK + 1, KP - 1 00466 KX = KX + N - J + 1 00467 T = DCONJG( AP( KNC+J-KK ) ) 00468 AP( KNC+J-KK ) = DCONJG( AP( KX ) ) 00469 AP( KX ) = T 00470 80 CONTINUE 00471 AP( KNC+KP-KK ) = DCONJG( AP( KNC+KP-KK ) ) 00472 R1 = DBLE( AP( KNC ) ) 00473 AP( KNC ) = DBLE( AP( KPC ) ) 00474 AP( KPC ) = R1 00475 IF( KSTEP.EQ.2 ) THEN 00476 AP( KC ) = DBLE( AP( KC ) ) 00477 T = AP( KC+1 ) 00478 AP( KC+1 ) = AP( KC+KP-K ) 00479 AP( KC+KP-K ) = T 00480 END IF 00481 ELSE 00482 AP( KC ) = DBLE( AP( KC ) ) 00483 IF( KSTEP.EQ.2 ) 00484 $ AP( KNC ) = DBLE( AP( KNC ) ) 00485 END IF 00486 * 00487 * Update the trailing submatrix 00488 * 00489 IF( KSTEP.EQ.1 ) THEN 00490 * 00491 * 1-by-1 pivot block D(k): column k now holds 00492 * 00493 * W(k) = L(k)*D(k) 00494 * 00495 * where L(k) is the k-th column of L 00496 * 00497 IF( K.LT.N ) THEN 00498 * 00499 * Perform a rank-1 update of A(k+1:n,k+1:n) as 00500 * 00501 * A := A - L(k)*D(k)*L(k)**H = A - W(k)*(1/D(k))*W(k)**H 00502 * 00503 R1 = ONE / DBLE( AP( KC ) ) 00504 CALL ZHPR( UPLO, N-K, -R1, AP( KC+1 ), 1, 00505 $ AP( KC+N-K+1 ) ) 00506 * 00507 * Store L(k) in column K 00508 * 00509 CALL ZDSCAL( N-K, R1, AP( KC+1 ), 1 ) 00510 END IF 00511 ELSE 00512 * 00513 * 2-by-2 pivot block D(k): columns K and K+1 now hold 00514 * 00515 * ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k) 00516 * 00517 * where L(k) and L(k+1) are the k-th and (k+1)-th columns 00518 * of L 00519 * 00520 IF( K.LT.N-1 ) THEN 00521 * 00522 * Perform a rank-2 update of A(k+2:n,k+2:n) as 00523 * 00524 * A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**H 00525 * = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**H 00526 * 00527 * where L(k) and L(k+1) are the k-th and (k+1)-th 00528 * columns of L 00529 * 00530 D = DLAPY2( DBLE( AP( K+1+( K-1 )*( 2*N-K ) / 2 ) ), 00531 $ DIMAG( AP( K+1+( K-1 )*( 2*N-K ) / 2 ) ) ) 00532 D11 = DBLE( AP( K+1+K*( 2*N-K-1 ) / 2 ) ) / D 00533 D22 = DBLE( AP( K+( K-1 )*( 2*N-K ) / 2 ) ) / D 00534 TT = ONE / ( D11*D22-ONE ) 00535 D21 = AP( K+1+( K-1 )*( 2*N-K ) / 2 ) / D 00536 D = TT / D 00537 * 00538 DO 100 J = K + 2, N 00539 WK = D*( D11*AP( J+( K-1 )*( 2*N-K ) / 2 )-D21* 00540 $ AP( J+K*( 2*N-K-1 ) / 2 ) ) 00541 WKP1 = D*( D22*AP( J+K*( 2*N-K-1 ) / 2 )- 00542 $ DCONJG( D21 )*AP( J+( K-1 )*( 2*N-K ) / 00543 $ 2 ) ) 00544 DO 90 I = J, N 00545 AP( I+( J-1 )*( 2*N-J ) / 2 ) = AP( I+( J-1 )* 00546 $ ( 2*N-J ) / 2 ) - AP( I+( K-1 )*( 2*N-K ) / 00547 $ 2 )*DCONJG( WK ) - AP( I+K*( 2*N-K-1 ) / 2 )* 00548 $ DCONJG( WKP1 ) 00549 90 CONTINUE 00550 AP( J+( K-1 )*( 2*N-K ) / 2 ) = WK 00551 AP( J+K*( 2*N-K-1 ) / 2 ) = WKP1 00552 AP( J+( J-1 )*( 2*N-J ) / 2 ) 00553 $ = DCMPLX( DBLE( AP( J+( J-1 )*( 2*N-J ) / 2 ) ), 00554 $ 0.0D+0 ) 00555 100 CONTINUE 00556 END IF 00557 END IF 00558 END IF 00559 * 00560 * Store details of the interchanges in IPIV 00561 * 00562 IF( KSTEP.EQ.1 ) THEN 00563 IPIV( K ) = KP 00564 ELSE 00565 IPIV( K ) = -KP 00566 IPIV( K+1 ) = -KP 00567 END IF 00568 * 00569 * Increase K and return to the start of the main loop 00570 * 00571 K = K + KSTEP 00572 KC = KNC + N - K + 2 00573 GO TO 60 00574 * 00575 END IF 00576 * 00577 110 CONTINUE 00578 RETURN 00579 * 00580 * End of ZHPTRF 00581 * 00582 END
1.7.3 
