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