|
LAPACK 3.3.0
|
|
LAPACK 3.3.0
|
00001 SUBROUTINE CHPTRF( UPLO, N, AP, IPIV, INFO ) 00002 * 00003 * -- LAPACK routine (version 3.2) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 CHARACTER UPLO 00010 INTEGER INFO, N 00011 * .. 00012 * .. Array Arguments .. 00013 INTEGER IPIV( * ) 00014 COMPLEX AP( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * CHPTRF 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 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', 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', 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 REAL ZERO, ONE 00112 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00113 REAL EIGHT, SEVTEN 00114 PARAMETER ( EIGHT = 8.0E+0, SEVTEN = 17.0E+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 REAL ABSAKK, ALPHA, COLMAX, D, D11, D22, R1, ROWMAX, 00121 $ TT 00122 COMPLEX D12, D21, T, WK, WKM1, WKP1, ZDUM 00123 * .. 00124 * .. External Functions .. 00125 LOGICAL LSAME 00126 INTEGER ICAMAX 00127 REAL SLAPY2 00128 EXTERNAL LSAME, ICAMAX, SLAPY2 00129 * .. 00130 * .. External Subroutines .. 00131 EXTERNAL CHPR, CSSCAL, CSWAP, XERBLA 00132 * .. 00133 * .. Intrinsic Functions .. 00134 INTRINSIC ABS, AIMAG, CMPLX, CONJG, MAX, REAL, SQRT 00135 * .. 00136 * .. Statement Functions .. 00137 REAL CABS1 00138 * .. 00139 * .. Statement Function definitions .. 00140 CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( 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( 'CHPTRF', -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' 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( REAL( 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 = ICAMAX( 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 ) = REAL( 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 = ICAMAX( 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( REAL( 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 CSWAP( 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 = CONJG( AP( KNC+J-1 ) ) 00265 AP( KNC+J-1 ) = CONJG( AP( KX ) ) 00266 AP( KX ) = T 00267 30 CONTINUE 00268 AP( KX+KK-1 ) = CONJG( AP( KX+KK-1 ) ) 00269 R1 = REAL( AP( KNC+KK-1 ) ) 00270 AP( KNC+KK-1 ) = REAL( AP( KPC+KP-1 ) ) 00271 AP( KPC+KP-1 ) = R1 00272 IF( KSTEP.EQ.2 ) THEN 00273 AP( KC+K-1 ) = REAL( 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 ) = REAL( AP( KC+K-1 ) ) 00280 IF( KSTEP.EQ.2 ) 00281 $ AP( KC-1 ) = REAL( 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)' = A - W(k)*1/D(k)*W(k)' 00297 * 00298 R1 = ONE / REAL( AP( KC+K-1 ) ) 00299 CALL CHPR( UPLO, K-1, -R1, AP( KC ), 1, AP ) 00300 * 00301 * Store U(k) in column k 00302 * 00303 CALL CSSCAL( 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) )' 00316 * = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )' 00317 * 00318 IF( K.GT.2 ) THEN 00319 * 00320 D = SLAPY2( REAL( AP( K-1+( K-1 )*K / 2 ) ), 00321 $ AIMAG( AP( K-1+( K-1 )*K / 2 ) ) ) 00322 D22 = REAL( AP( K-1+( K-2 )*( K-1 ) / 2 ) ) / D 00323 D11 = REAL( 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 $ CONJG( 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 )*CONJG( WK ) - 00336 $ AP( I+( K-2 )*( K-1 ) / 2 )*CONJG( 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 ) = CMPLX( REAL( AP( J+( J-1 )* $ J / 2 ) ), 0.0E+0 ) 00341 50 CONTINUE 00342 * 00343 END IF 00344 * 00345 END IF 00346 END IF 00347 * 00348 * Store details of the interchanges in IPIV 00349 * 00350 IF( KSTEP.EQ.1 ) THEN 00351 IPIV( K ) = KP 00352 ELSE 00353 IPIV( K ) = -KP 00354 IPIV( K-1 ) = -KP 00355 END IF 00356 * 00357 * Decrease K and return to the start of the main loop 00358 * 00359 K = K - KSTEP 00360 KC = KNC - K 00361 GO TO 10 00362 * 00363 ELSE 00364 * 00365 * Factorize A as L*D*L' using the lower triangle of A 00366 * 00367 * K is the main loop index, increasing from 1 to N in steps of 00368 * 1 or 2 00369 * 00370 K = 1 00371 KC = 1 00372 NPP = N*( N+1 ) / 2 00373 60 CONTINUE 00374 KNC = KC 00375 * 00376 * If K > N, exit from loop 00377 * 00378 IF( K.GT.N ) 00379 $ GO TO 110 00380 KSTEP = 1 00381 * 00382 * Determine rows and columns to be interchanged and whether 00383 * a 1-by-1 or 2-by-2 pivot block will be used 00384 * 00385 ABSAKK = ABS( REAL( AP( KC ) ) ) 00386 * 00387 * IMAX is the row-index of the largest off-diagonal element in 00388 * column K, and COLMAX is its absolute value 00389 * 00390 IF( K.LT.N ) THEN 00391 IMAX = K + ICAMAX( N-K, AP( KC+1 ), 1 ) 00392 COLMAX = CABS1( AP( KC+IMAX-K ) ) 00393 ELSE 00394 COLMAX = ZERO 00395 END IF 00396 * 00397 IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN 00398 * 00399 * Column K is zero: set INFO and continue 00400 * 00401 IF( INFO.EQ.0 ) 00402 $ INFO = K 00403 KP = K 00404 AP( KC ) = REAL( AP( KC ) ) 00405 ELSE 00406 IF( ABSAKK.GE.ALPHA*COLMAX ) THEN 00407 * 00408 * no interchange, use 1-by-1 pivot block 00409 * 00410 KP = K 00411 ELSE 00412 * 00413 * JMAX is the column-index of the largest off-diagonal 00414 * element in row IMAX, and ROWMAX is its absolute value 00415 * 00416 ROWMAX = ZERO 00417 KX = KC + IMAX - K 00418 DO 70 J = K, IMAX - 1 00419 IF( CABS1( AP( KX ) ).GT.ROWMAX ) THEN 00420 ROWMAX = CABS1( AP( KX ) ) 00421 JMAX = J 00422 END IF 00423 KX = KX + N - J 00424 70 CONTINUE 00425 KPC = NPP - ( N-IMAX+1 )*( N-IMAX+2 ) / 2 + 1 00426 IF( IMAX.LT.N ) THEN 00427 JMAX = IMAX + ICAMAX( N-IMAX, AP( KPC+1 ), 1 ) 00428 ROWMAX = MAX( ROWMAX, CABS1( AP( KPC+JMAX-IMAX ) ) ) 00429 END IF 00430 * 00431 IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN 00432 * 00433 * no interchange, use 1-by-1 pivot block 00434 * 00435 KP = K 00436 ELSE IF( ABS( REAL( AP( KPC ) ) ).GE.ALPHA*ROWMAX ) THEN 00437 * 00438 * interchange rows and columns K and IMAX, use 1-by-1 00439 * pivot block 00440 * 00441 KP = IMAX 00442 ELSE 00443 * 00444 * interchange rows and columns K+1 and IMAX, use 2-by-2 00445 * pivot block 00446 * 00447 KP = IMAX 00448 KSTEP = 2 00449 END IF 00450 END IF 00451 * 00452 KK = K + KSTEP - 1 00453 IF( KSTEP.EQ.2 ) 00454 $ KNC = KNC + N - K + 1 00455 IF( KP.NE.KK ) THEN 00456 * 00457 * Interchange rows and columns KK and KP in the trailing 00458 * submatrix A(k:n,k:n) 00459 * 00460 IF( KP.LT.N ) 00461 $ CALL CSWAP( N-KP, AP( KNC+KP-KK+1 ), 1, AP( KPC+1 ), 00462 $ 1 ) 00463 KX = KNC + KP - KK 00464 DO 80 J = KK + 1, KP - 1 00465 KX = KX + N - J + 1 00466 T = CONJG( AP( KNC+J-KK ) ) 00467 AP( KNC+J-KK ) = CONJG( AP( KX ) ) 00468 AP( KX ) = T 00469 80 CONTINUE 00470 AP( KNC+KP-KK ) = CONJG( AP( KNC+KP-KK ) ) 00471 R1 = REAL( AP( KNC ) ) 00472 AP( KNC ) = REAL( AP( KPC ) ) 00473 AP( KPC ) = R1 00474 IF( KSTEP.EQ.2 ) THEN 00475 AP( KC ) = REAL( AP( KC ) ) 00476 T = AP( KC+1 ) 00477 AP( KC+1 ) = AP( KC+KP-K ) 00478 AP( KC+KP-K ) = T 00479 END IF 00480 ELSE 00481 AP( KC ) = REAL( AP( KC ) ) 00482 IF( KSTEP.EQ.2 ) 00483 $ AP( KNC ) = REAL( AP( KNC ) ) 00484 END IF 00485 * 00486 * Update the trailing submatrix 00487 * 00488 IF( KSTEP.EQ.1 ) THEN 00489 * 00490 * 1-by-1 pivot block D(k): column k now holds 00491 * 00492 * W(k) = L(k)*D(k) 00493 * 00494 * where L(k) is the k-th column of L 00495 * 00496 IF( K.LT.N ) THEN 00497 * 00498 * Perform a rank-1 update of A(k+1:n,k+1:n) as 00499 * 00500 * A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)' 00501 * 00502 R1 = ONE / REAL( AP( KC ) ) 00503 CALL CHPR( UPLO, N-K, -R1, AP( KC+1 ), 1, 00504 $ AP( KC+N-K+1 ) ) 00505 * 00506 * Store L(k) in column K 00507 * 00508 CALL CSSCAL( N-K, R1, AP( KC+1 ), 1 ) 00509 END IF 00510 ELSE 00511 * 00512 * 2-by-2 pivot block D(k): columns K and K+1 now hold 00513 * 00514 * ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k) 00515 * 00516 * where L(k) and L(k+1) are the k-th and (k+1)-th columns 00517 * of L 00518 * 00519 IF( K.LT.N-1 ) THEN 00520 * 00521 * Perform a rank-2 update of A(k+2:n,k+2:n) as 00522 * 00523 * A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )' 00524 * = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )' 00525 * 00526 * where L(k) and L(k+1) are the k-th and (k+1)-th 00527 * columns of L 00528 * 00529 D = SLAPY2( REAL( AP( K+1+( K-1 )*( 2*N-K ) / 2 ) ), 00530 $ AIMAG( AP( K+1+( K-1 )*( 2*N-K ) / 2 ) ) ) 00531 D11 = REAL( AP( K+1+K*( 2*N-K-1 ) / 2 ) ) / D 00532 D22 = REAL( AP( K+( K-1 )*( 2*N-K ) / 2 ) ) / D 00533 TT = ONE / ( D11*D22-ONE ) 00534 D21 = AP( K+1+( K-1 )*( 2*N-K ) / 2 ) / D 00535 D = TT / D 00536 * 00537 DO 100 J = K + 2, N 00538 WK = D*( D11*AP( J+( K-1 )*( 2*N-K ) / 2 )-D21* 00539 $ AP( J+K*( 2*N-K-1 ) / 2 ) ) 00540 WKP1 = D*( D22*AP( J+K*( 2*N-K-1 ) / 2 )- 00541 $ CONJG( D21 )*AP( J+( K-1 )*( 2*N-K ) / 2 ) ) 00542 DO 90 I = J, N 00543 AP( I+( J-1 )*( 2*N-J ) / 2 ) = AP( I+( J-1 )* 00544 $ ( 2*N-J ) / 2 ) - AP( I+( K-1 )*( 2*N-K ) / 00545 $ 2 )*CONJG( WK ) - AP( I+K*( 2*N-K-1 ) / 2 )* 00546 $ CONJG( WKP1 ) 00547 90 CONTINUE 00548 AP( J+( K-1 )*( 2*N-K ) / 2 ) = WK 00549 AP( J+K*( 2*N-K-1 ) / 2 ) = WKP1 00550 AP( J+( J-1 )*( 2*N-J ) / 2 ) 00551 $ = CMPLX( REAL( AP( J+( J-1 )*( 2*N-J ) / 2 ) ), 00552 $ 0.0E+0 ) 00553 100 CONTINUE 00554 END IF 00555 END IF 00556 END IF 00557 * 00558 * Store details of the interchanges in IPIV 00559 * 00560 IF( KSTEP.EQ.1 ) THEN 00561 IPIV( K ) = KP 00562 ELSE 00563 IPIV( K ) = -KP 00564 IPIV( K+1 ) = -KP 00565 END IF 00566 * 00567 * Increase K and return to the start of the main loop 00568 * 00569 K = K + KSTEP 00570 KC = KNC + N - K + 2 00571 GO TO 60 00572 * 00573 END IF 00574 * 00575 110 CONTINUE 00576 RETURN 00577 * 00578 * End of CHPTRF 00579 * 00580 END 00581
1.7.3 
