Annotation of rpl/lapack/lapack/zhptri.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHPTRI( UPLO, N, AP, IPIV, WORK, 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, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: INTEGER IPIV( * )
! 14: COMPLEX*16 AP( * ), WORK( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZHPTRI computes the inverse of a complex Hermitian indefinite matrix
! 21: * A in packed storage using the factorization A = U*D*U**H or
! 22: * A = L*D*L**H computed by ZHPTRF.
! 23: *
! 24: * Arguments
! 25: * =========
! 26: *
! 27: * UPLO (input) CHARACTER*1
! 28: * Specifies whether the details of the factorization are stored
! 29: * as an upper or lower triangular matrix.
! 30: * = 'U': Upper triangular, form is A = U*D*U**H;
! 31: * = 'L': Lower triangular, form is A = L*D*L**H.
! 32: *
! 33: * N (input) INTEGER
! 34: * The order of the matrix A. N >= 0.
! 35: *
! 36: * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
! 37: * On entry, the block diagonal matrix D and the multipliers
! 38: * used to obtain the factor U or L as computed by ZHPTRF,
! 39: * stored as a packed triangular matrix.
! 40: *
! 41: * On exit, if INFO = 0, the (Hermitian) inverse of the original
! 42: * matrix, stored as a packed triangular matrix. The j-th column
! 43: * of inv(A) is stored in the array AP as follows:
! 44: * if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
! 45: * if UPLO = 'L',
! 46: * AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
! 47: *
! 48: * IPIV (input) INTEGER array, dimension (N)
! 49: * Details of the interchanges and the block structure of D
! 50: * as determined by ZHPTRF.
! 51: *
! 52: * WORK (workspace) COMPLEX*16 array, dimension (N)
! 53: *
! 54: * INFO (output) INTEGER
! 55: * = 0: successful exit
! 56: * < 0: if INFO = -i, the i-th argument had an illegal value
! 57: * > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
! 58: * inverse could not be computed.
! 59: *
! 60: * =====================================================================
! 61: *
! 62: * .. Parameters ..
! 63: DOUBLE PRECISION ONE
! 64: COMPLEX*16 CONE, ZERO
! 65: PARAMETER ( ONE = 1.0D+0, CONE = ( 1.0D+0, 0.0D+0 ),
! 66: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
! 67: * ..
! 68: * .. Local Scalars ..
! 69: LOGICAL UPPER
! 70: INTEGER J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP
! 71: DOUBLE PRECISION AK, AKP1, D, T
! 72: COMPLEX*16 AKKP1, TEMP
! 73: * ..
! 74: * .. External Functions ..
! 75: LOGICAL LSAME
! 76: COMPLEX*16 ZDOTC
! 77: EXTERNAL LSAME, ZDOTC
! 78: * ..
! 79: * .. External Subroutines ..
! 80: EXTERNAL XERBLA, ZCOPY, ZHPMV, ZSWAP
! 81: * ..
! 82: * .. Intrinsic Functions ..
! 83: INTRINSIC ABS, DBLE, DCONJG
! 84: * ..
! 85: * .. Executable Statements ..
! 86: *
! 87: * Test the input parameters.
! 88: *
! 89: INFO = 0
! 90: UPPER = LSAME( UPLO, 'U' )
! 91: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 92: INFO = -1
! 93: ELSE IF( N.LT.0 ) THEN
! 94: INFO = -2
! 95: END IF
! 96: IF( INFO.NE.0 ) THEN
! 97: CALL XERBLA( 'ZHPTRI', -INFO )
! 98: RETURN
! 99: END IF
! 100: *
! 101: * Quick return if possible
! 102: *
! 103: IF( N.EQ.0 )
! 104: $ RETURN
! 105: *
! 106: * Check that the diagonal matrix D is nonsingular.
! 107: *
! 108: IF( UPPER ) THEN
! 109: *
! 110: * Upper triangular storage: examine D from bottom to top
! 111: *
! 112: KP = N*( N+1 ) / 2
! 113: DO 10 INFO = N, 1, -1
! 114: IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
! 115: $ RETURN
! 116: KP = KP - INFO
! 117: 10 CONTINUE
! 118: ELSE
! 119: *
! 120: * Lower triangular storage: examine D from top to bottom.
! 121: *
! 122: KP = 1
! 123: DO 20 INFO = 1, N
! 124: IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
! 125: $ RETURN
! 126: KP = KP + N - INFO + 1
! 127: 20 CONTINUE
! 128: END IF
! 129: INFO = 0
! 130: *
! 131: IF( UPPER ) THEN
! 132: *
! 133: * Compute inv(A) from the factorization A = U*D*U'.
! 134: *
! 135: * K is the main loop index, increasing from 1 to N in steps of
! 136: * 1 or 2, depending on the size of the diagonal blocks.
! 137: *
! 138: K = 1
! 139: KC = 1
! 140: 30 CONTINUE
! 141: *
! 142: * If K > N, exit from loop.
! 143: *
! 144: IF( K.GT.N )
! 145: $ GO TO 50
! 146: *
! 147: KCNEXT = KC + K
! 148: IF( IPIV( K ).GT.0 ) THEN
! 149: *
! 150: * 1 x 1 diagonal block
! 151: *
! 152: * Invert the diagonal block.
! 153: *
! 154: AP( KC+K-1 ) = ONE / DBLE( AP( KC+K-1 ) )
! 155: *
! 156: * Compute column K of the inverse.
! 157: *
! 158: IF( K.GT.1 ) THEN
! 159: CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 )
! 160: CALL ZHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO,
! 161: $ AP( KC ), 1 )
! 162: AP( KC+K-1 ) = AP( KC+K-1 ) -
! 163: $ DBLE( ZDOTC( K-1, WORK, 1, AP( KC ), 1 ) )
! 164: END IF
! 165: KSTEP = 1
! 166: ELSE
! 167: *
! 168: * 2 x 2 diagonal block
! 169: *
! 170: * Invert the diagonal block.
! 171: *
! 172: T = ABS( AP( KCNEXT+K-1 ) )
! 173: AK = DBLE( AP( KC+K-1 ) ) / T
! 174: AKP1 = DBLE( AP( KCNEXT+K ) ) / T
! 175: AKKP1 = AP( KCNEXT+K-1 ) / T
! 176: D = T*( AK*AKP1-ONE )
! 177: AP( KC+K-1 ) = AKP1 / D
! 178: AP( KCNEXT+K ) = AK / D
! 179: AP( KCNEXT+K-1 ) = -AKKP1 / D
! 180: *
! 181: * Compute columns K and K+1 of the inverse.
! 182: *
! 183: IF( K.GT.1 ) THEN
! 184: CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 )
! 185: CALL ZHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO,
! 186: $ AP( KC ), 1 )
! 187: AP( KC+K-1 ) = AP( KC+K-1 ) -
! 188: $ DBLE( ZDOTC( K-1, WORK, 1, AP( KC ), 1 ) )
! 189: AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) -
! 190: $ ZDOTC( K-1, AP( KC ), 1, AP( KCNEXT ),
! 191: $ 1 )
! 192: CALL ZCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 )
! 193: CALL ZHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO,
! 194: $ AP( KCNEXT ), 1 )
! 195: AP( KCNEXT+K ) = AP( KCNEXT+K ) -
! 196: $ DBLE( ZDOTC( K-1, WORK, 1, AP( KCNEXT ),
! 197: $ 1 ) )
! 198: END IF
! 199: KSTEP = 2
! 200: KCNEXT = KCNEXT + K + 1
! 201: END IF
! 202: *
! 203: KP = ABS( IPIV( K ) )
! 204: IF( KP.NE.K ) THEN
! 205: *
! 206: * Interchange rows and columns K and KP in the leading
! 207: * submatrix A(1:k+1,1:k+1)
! 208: *
! 209: KPC = ( KP-1 )*KP / 2 + 1
! 210: CALL ZSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 )
! 211: KX = KPC + KP - 1
! 212: DO 40 J = KP + 1, K - 1
! 213: KX = KX + J - 1
! 214: TEMP = DCONJG( AP( KC+J-1 ) )
! 215: AP( KC+J-1 ) = DCONJG( AP( KX ) )
! 216: AP( KX ) = TEMP
! 217: 40 CONTINUE
! 218: AP( KC+KP-1 ) = DCONJG( AP( KC+KP-1 ) )
! 219: TEMP = AP( KC+K-1 )
! 220: AP( KC+K-1 ) = AP( KPC+KP-1 )
! 221: AP( KPC+KP-1 ) = TEMP
! 222: IF( KSTEP.EQ.2 ) THEN
! 223: TEMP = AP( KC+K+K-1 )
! 224: AP( KC+K+K-1 ) = AP( KC+K+KP-1 )
! 225: AP( KC+K+KP-1 ) = TEMP
! 226: END IF
! 227: END IF
! 228: *
! 229: K = K + KSTEP
! 230: KC = KCNEXT
! 231: GO TO 30
! 232: 50 CONTINUE
! 233: *
! 234: ELSE
! 235: *
! 236: * Compute inv(A) from the factorization A = L*D*L'.
! 237: *
! 238: * K is the main loop index, increasing from 1 to N in steps of
! 239: * 1 or 2, depending on the size of the diagonal blocks.
! 240: *
! 241: NPP = N*( N+1 ) / 2
! 242: K = N
! 243: KC = NPP
! 244: 60 CONTINUE
! 245: *
! 246: * If K < 1, exit from loop.
! 247: *
! 248: IF( K.LT.1 )
! 249: $ GO TO 80
! 250: *
! 251: KCNEXT = KC - ( N-K+2 )
! 252: IF( IPIV( K ).GT.0 ) THEN
! 253: *
! 254: * 1 x 1 diagonal block
! 255: *
! 256: * Invert the diagonal block.
! 257: *
! 258: AP( KC ) = ONE / DBLE( AP( KC ) )
! 259: *
! 260: * Compute column K of the inverse.
! 261: *
! 262: IF( K.LT.N ) THEN
! 263: CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
! 264: CALL ZHPMV( UPLO, N-K, -CONE, AP( KC+N-K+1 ), WORK, 1,
! 265: $ ZERO, AP( KC+1 ), 1 )
! 266: AP( KC ) = AP( KC ) - DBLE( ZDOTC( N-K, WORK, 1,
! 267: $ AP( KC+1 ), 1 ) )
! 268: END IF
! 269: KSTEP = 1
! 270: ELSE
! 271: *
! 272: * 2 x 2 diagonal block
! 273: *
! 274: * Invert the diagonal block.
! 275: *
! 276: T = ABS( AP( KCNEXT+1 ) )
! 277: AK = DBLE( AP( KCNEXT ) ) / T
! 278: AKP1 = DBLE( AP( KC ) ) / T
! 279: AKKP1 = AP( KCNEXT+1 ) / T
! 280: D = T*( AK*AKP1-ONE )
! 281: AP( KCNEXT ) = AKP1 / D
! 282: AP( KC ) = AK / D
! 283: AP( KCNEXT+1 ) = -AKKP1 / D
! 284: *
! 285: * Compute columns K-1 and K of the inverse.
! 286: *
! 287: IF( K.LT.N ) THEN
! 288: CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
! 289: CALL ZHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK,
! 290: $ 1, ZERO, AP( KC+1 ), 1 )
! 291: AP( KC ) = AP( KC ) - DBLE( ZDOTC( N-K, WORK, 1,
! 292: $ AP( KC+1 ), 1 ) )
! 293: AP( KCNEXT+1 ) = AP( KCNEXT+1 ) -
! 294: $ ZDOTC( N-K, AP( KC+1 ), 1,
! 295: $ AP( KCNEXT+2 ), 1 )
! 296: CALL ZCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 )
! 297: CALL ZHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK,
! 298: $ 1, ZERO, AP( KCNEXT+2 ), 1 )
! 299: AP( KCNEXT ) = AP( KCNEXT ) -
! 300: $ DBLE( ZDOTC( N-K, WORK, 1, AP( KCNEXT+2 ),
! 301: $ 1 ) )
! 302: END IF
! 303: KSTEP = 2
! 304: KCNEXT = KCNEXT - ( N-K+3 )
! 305: END IF
! 306: *
! 307: KP = ABS( IPIV( K ) )
! 308: IF( KP.NE.K ) THEN
! 309: *
! 310: * Interchange rows and columns K and KP in the trailing
! 311: * submatrix A(k-1:n,k-1:n)
! 312: *
! 313: KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1
! 314: IF( KP.LT.N )
! 315: $ CALL ZSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 )
! 316: KX = KC + KP - K
! 317: DO 70 J = K + 1, KP - 1
! 318: KX = KX + N - J + 1
! 319: TEMP = DCONJG( AP( KC+J-K ) )
! 320: AP( KC+J-K ) = DCONJG( AP( KX ) )
! 321: AP( KX ) = TEMP
! 322: 70 CONTINUE
! 323: AP( KC+KP-K ) = DCONJG( AP( KC+KP-K ) )
! 324: TEMP = AP( KC )
! 325: AP( KC ) = AP( KPC )
! 326: AP( KPC ) = TEMP
! 327: IF( KSTEP.EQ.2 ) THEN
! 328: TEMP = AP( KC-N+K-1 )
! 329: AP( KC-N+K-1 ) = AP( KC-N+KP-1 )
! 330: AP( KC-N+KP-1 ) = TEMP
! 331: END IF
! 332: END IF
! 333: *
! 334: K = K - KSTEP
! 335: KC = KCNEXT
! 336: GO TO 60
! 337: 80 CONTINUE
! 338: END IF
! 339: *
! 340: RETURN
! 341: *
! 342: * End of ZHPTRI
! 343: *
! 344: END
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