Annotation of rpl/lapack/lapack/zsytri.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZSYTRI( UPLO, N, A, LDA, 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, LDA, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: INTEGER IPIV( * )
! 14: COMPLEX*16 A( LDA, * ), WORK( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZSYTRI computes the inverse of a complex symmetric indefinite matrix
! 21: * A using the factorization A = U*D*U**T or A = L*D*L**T computed by
! 22: * ZSYTRF.
! 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: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 37: * On entry, the block diagonal matrix D and the multipliers
! 38: * used to obtain the factor U or L as computed by ZSYTRF.
! 39: *
! 40: * On exit, if INFO = 0, the (symmetric) inverse of the original
! 41: * matrix. If UPLO = 'U', the upper triangular part of the
! 42: * inverse is formed and the part of A below the diagonal is not
! 43: * referenced; if UPLO = 'L' the lower triangular part of the
! 44: * inverse is formed and the part of A above the diagonal is
! 45: * not referenced.
! 46: *
! 47: * LDA (input) INTEGER
! 48: * The leading dimension of the array A. LDA >= max(1,N).
! 49: *
! 50: * IPIV (input) INTEGER array, dimension (N)
! 51: * Details of the interchanges and the block structure of D
! 52: * as determined by ZSYTRF.
! 53: *
! 54: * WORK (workspace) COMPLEX*16 array, dimension (2*N)
! 55: *
! 56: * INFO (output) INTEGER
! 57: * = 0: successful exit
! 58: * < 0: if INFO = -i, the i-th argument had an illegal value
! 59: * > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
! 60: * inverse could not be computed.
! 61: *
! 62: * =====================================================================
! 63: *
! 64: * .. Parameters ..
! 65: COMPLEX*16 ONE, ZERO
! 66: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
! 67: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
! 68: * ..
! 69: * .. Local Scalars ..
! 70: LOGICAL UPPER
! 71: INTEGER K, KP, KSTEP
! 72: COMPLEX*16 AK, AKKP1, AKP1, D, T, TEMP
! 73: * ..
! 74: * .. External Functions ..
! 75: LOGICAL LSAME
! 76: COMPLEX*16 ZDOTU
! 77: EXTERNAL LSAME, ZDOTU
! 78: * ..
! 79: * .. External Subroutines ..
! 80: EXTERNAL XERBLA, ZCOPY, ZSWAP, ZSYMV
! 81: * ..
! 82: * .. Intrinsic Functions ..
! 83: INTRINSIC ABS, MAX
! 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: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 96: INFO = -4
! 97: END IF
! 98: IF( INFO.NE.0 ) THEN
! 99: CALL XERBLA( 'ZSYTRI', -INFO )
! 100: RETURN
! 101: END IF
! 102: *
! 103: * Quick return if possible
! 104: *
! 105: IF( N.EQ.0 )
! 106: $ RETURN
! 107: *
! 108: * Check that the diagonal matrix D is nonsingular.
! 109: *
! 110: IF( UPPER ) THEN
! 111: *
! 112: * Upper triangular storage: examine D from bottom to top
! 113: *
! 114: DO 10 INFO = N, 1, -1
! 115: IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
! 116: $ RETURN
! 117: 10 CONTINUE
! 118: ELSE
! 119: *
! 120: * Lower triangular storage: examine D from top to bottom.
! 121: *
! 122: DO 20 INFO = 1, N
! 123: IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
! 124: $ RETURN
! 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: 30 CONTINUE
! 138: *
! 139: * If K > N, exit from loop.
! 140: *
! 141: IF( K.GT.N )
! 142: $ GO TO 40
! 143: *
! 144: IF( IPIV( K ).GT.0 ) THEN
! 145: *
! 146: * 1 x 1 diagonal block
! 147: *
! 148: * Invert the diagonal block.
! 149: *
! 150: A( K, K ) = ONE / A( K, K )
! 151: *
! 152: * Compute column K of the inverse.
! 153: *
! 154: IF( K.GT.1 ) THEN
! 155: CALL ZCOPY( K-1, A( 1, K ), 1, WORK, 1 )
! 156: CALL ZSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
! 157: $ A( 1, K ), 1 )
! 158: A( K, K ) = A( K, K ) - ZDOTU( K-1, WORK, 1, A( 1, K ),
! 159: $ 1 )
! 160: END IF
! 161: KSTEP = 1
! 162: ELSE
! 163: *
! 164: * 2 x 2 diagonal block
! 165: *
! 166: * Invert the diagonal block.
! 167: *
! 168: T = A( K, K+1 )
! 169: AK = A( K, K ) / T
! 170: AKP1 = A( K+1, K+1 ) / T
! 171: AKKP1 = A( K, K+1 ) / T
! 172: D = T*( AK*AKP1-ONE )
! 173: A( K, K ) = AKP1 / D
! 174: A( K+1, K+1 ) = AK / D
! 175: A( K, K+1 ) = -AKKP1 / D
! 176: *
! 177: * Compute columns K and K+1 of the inverse.
! 178: *
! 179: IF( K.GT.1 ) THEN
! 180: CALL ZCOPY( K-1, A( 1, K ), 1, WORK, 1 )
! 181: CALL ZSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
! 182: $ A( 1, K ), 1 )
! 183: A( K, K ) = A( K, K ) - ZDOTU( K-1, WORK, 1, A( 1, K ),
! 184: $ 1 )
! 185: A( K, K+1 ) = A( K, K+1 ) -
! 186: $ ZDOTU( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 )
! 187: CALL ZCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 )
! 188: CALL ZSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
! 189: $ A( 1, K+1 ), 1 )
! 190: A( K+1, K+1 ) = A( K+1, K+1 ) -
! 191: $ ZDOTU( K-1, WORK, 1, A( 1, K+1 ), 1 )
! 192: END IF
! 193: KSTEP = 2
! 194: END IF
! 195: *
! 196: KP = ABS( IPIV( K ) )
! 197: IF( KP.NE.K ) THEN
! 198: *
! 199: * Interchange rows and columns K and KP in the leading
! 200: * submatrix A(1:k+1,1:k+1)
! 201: *
! 202: CALL ZSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
! 203: CALL ZSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
! 204: TEMP = A( K, K )
! 205: A( K, K ) = A( KP, KP )
! 206: A( KP, KP ) = TEMP
! 207: IF( KSTEP.EQ.2 ) THEN
! 208: TEMP = A( K, K+1 )
! 209: A( K, K+1 ) = A( KP, K+1 )
! 210: A( KP, K+1 ) = TEMP
! 211: END IF
! 212: END IF
! 213: *
! 214: K = K + KSTEP
! 215: GO TO 30
! 216: 40 CONTINUE
! 217: *
! 218: ELSE
! 219: *
! 220: * Compute inv(A) from the factorization A = L*D*L'.
! 221: *
! 222: * K is the main loop index, increasing from 1 to N in steps of
! 223: * 1 or 2, depending on the size of the diagonal blocks.
! 224: *
! 225: K = N
! 226: 50 CONTINUE
! 227: *
! 228: * If K < 1, exit from loop.
! 229: *
! 230: IF( K.LT.1 )
! 231: $ GO TO 60
! 232: *
! 233: IF( IPIV( K ).GT.0 ) THEN
! 234: *
! 235: * 1 x 1 diagonal block
! 236: *
! 237: * Invert the diagonal block.
! 238: *
! 239: A( K, K ) = ONE / A( K, K )
! 240: *
! 241: * Compute column K of the inverse.
! 242: *
! 243: IF( K.LT.N ) THEN
! 244: CALL ZCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
! 245: CALL ZSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
! 246: $ ZERO, A( K+1, K ), 1 )
! 247: A( K, K ) = A( K, K ) - ZDOTU( N-K, WORK, 1, A( K+1, K ),
! 248: $ 1 )
! 249: END IF
! 250: KSTEP = 1
! 251: ELSE
! 252: *
! 253: * 2 x 2 diagonal block
! 254: *
! 255: * Invert the diagonal block.
! 256: *
! 257: T = A( K, K-1 )
! 258: AK = A( K-1, K-1 ) / T
! 259: AKP1 = A( K, K ) / T
! 260: AKKP1 = A( K, K-1 ) / T
! 261: D = T*( AK*AKP1-ONE )
! 262: A( K-1, K-1 ) = AKP1 / D
! 263: A( K, K ) = AK / D
! 264: A( K, K-1 ) = -AKKP1 / D
! 265: *
! 266: * Compute columns K-1 and K of the inverse.
! 267: *
! 268: IF( K.LT.N ) THEN
! 269: CALL ZCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
! 270: CALL ZSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
! 271: $ ZERO, A( K+1, K ), 1 )
! 272: A( K, K ) = A( K, K ) - ZDOTU( N-K, WORK, 1, A( K+1, K ),
! 273: $ 1 )
! 274: A( K, K-1 ) = A( K, K-1 ) -
! 275: $ ZDOTU( N-K, A( K+1, K ), 1, A( K+1, K-1 ),
! 276: $ 1 )
! 277: CALL ZCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 )
! 278: CALL ZSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
! 279: $ ZERO, A( K+1, K-1 ), 1 )
! 280: A( K-1, K-1 ) = A( K-1, K-1 ) -
! 281: $ ZDOTU( N-K, WORK, 1, A( K+1, K-1 ), 1 )
! 282: END IF
! 283: KSTEP = 2
! 284: END IF
! 285: *
! 286: KP = ABS( IPIV( K ) )
! 287: IF( KP.NE.K ) THEN
! 288: *
! 289: * Interchange rows and columns K and KP in the trailing
! 290: * submatrix A(k-1:n,k-1:n)
! 291: *
! 292: IF( KP.LT.N )
! 293: $ CALL ZSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
! 294: CALL ZSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
! 295: TEMP = A( K, K )
! 296: A( K, K ) = A( KP, KP )
! 297: A( KP, KP ) = TEMP
! 298: IF( KSTEP.EQ.2 ) THEN
! 299: TEMP = A( K, K-1 )
! 300: A( K, K-1 ) = A( KP, K-1 )
! 301: A( KP, K-1 ) = TEMP
! 302: END IF
! 303: END IF
! 304: *
! 305: K = K - KSTEP
! 306: GO TO 50
! 307: 60 CONTINUE
! 308: END IF
! 309: *
! 310: RETURN
! 311: *
! 312: * End of ZSYTRI
! 313: *
! 314: END
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