Annotation of rpl/lapack/lapack/zhetri.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHETRI( 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: * ZHETRI computes the inverse of a complex Hermitian indefinite matrix
! 21: * A using the factorization A = U*D*U**H or A = L*D*L**H computed by
! 22: * ZHETRF.
! 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: * 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 ZHETRF.
! 39: *
! 40: * On exit, if INFO = 0, the (Hermitian) 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 ZHETRF.
! 53: *
! 54: * WORK (workspace) COMPLEX*16 array, dimension (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: DOUBLE PRECISION ONE
! 66: COMPLEX*16 CONE, ZERO
! 67: PARAMETER ( ONE = 1.0D+0, CONE = ( 1.0D+0, 0.0D+0 ),
! 68: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
! 69: * ..
! 70: * .. Local Scalars ..
! 71: LOGICAL UPPER
! 72: INTEGER J, K, KP, KSTEP
! 73: DOUBLE PRECISION AK, AKP1, D, T
! 74: COMPLEX*16 AKKP1, TEMP
! 75: * ..
! 76: * .. External Functions ..
! 77: LOGICAL LSAME
! 78: COMPLEX*16 ZDOTC
! 79: EXTERNAL LSAME, ZDOTC
! 80: * ..
! 81: * .. External Subroutines ..
! 82: EXTERNAL XERBLA, ZCOPY, ZHEMV, ZSWAP
! 83: * ..
! 84: * .. Intrinsic Functions ..
! 85: INTRINSIC ABS, DBLE, DCONJG, MAX
! 86: * ..
! 87: * .. Executable Statements ..
! 88: *
! 89: * Test the input parameters.
! 90: *
! 91: INFO = 0
! 92: UPPER = LSAME( UPLO, 'U' )
! 93: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 94: INFO = -1
! 95: ELSE IF( N.LT.0 ) THEN
! 96: INFO = -2
! 97: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 98: INFO = -4
! 99: END IF
! 100: IF( INFO.NE.0 ) THEN
! 101: CALL XERBLA( 'ZHETRI', -INFO )
! 102: RETURN
! 103: END IF
! 104: *
! 105: * Quick return if possible
! 106: *
! 107: IF( N.EQ.0 )
! 108: $ RETURN
! 109: *
! 110: * Check that the diagonal matrix D is nonsingular.
! 111: *
! 112: IF( UPPER ) THEN
! 113: *
! 114: * Upper triangular storage: examine D from bottom to top
! 115: *
! 116: DO 10 INFO = N, 1, -1
! 117: IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
! 118: $ RETURN
! 119: 10 CONTINUE
! 120: ELSE
! 121: *
! 122: * Lower triangular storage: examine D from top to bottom.
! 123: *
! 124: DO 20 INFO = 1, N
! 125: IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
! 126: $ RETURN
! 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: 30 CONTINUE
! 140: *
! 141: * If K > N, exit from loop.
! 142: *
! 143: IF( K.GT.N )
! 144: $ GO TO 50
! 145: *
! 146: IF( IPIV( K ).GT.0 ) THEN
! 147: *
! 148: * 1 x 1 diagonal block
! 149: *
! 150: * Invert the diagonal block.
! 151: *
! 152: A( K, K ) = ONE / DBLE( A( K, K ) )
! 153: *
! 154: * Compute column K of the inverse.
! 155: *
! 156: IF( K.GT.1 ) THEN
! 157: CALL ZCOPY( K-1, A( 1, K ), 1, WORK, 1 )
! 158: CALL ZHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO,
! 159: $ A( 1, K ), 1 )
! 160: A( K, K ) = A( K, K ) - DBLE( ZDOTC( K-1, WORK, 1, A( 1,
! 161: $ K ), 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 = ABS( A( K, K+1 ) )
! 171: AK = DBLE( A( K, K ) ) / T
! 172: AKP1 = DBLE( A( K+1, K+1 ) ) / T
! 173: AKKP1 = A( K, K+1 ) / T
! 174: D = T*( AK*AKP1-ONE )
! 175: A( K, K ) = AKP1 / D
! 176: A( K+1, K+1 ) = AK / D
! 177: A( K, 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, A( 1, K ), 1, WORK, 1 )
! 183: CALL ZHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO,
! 184: $ A( 1, K ), 1 )
! 185: A( K, K ) = A( K, K ) - DBLE( ZDOTC( K-1, WORK, 1, A( 1,
! 186: $ K ), 1 ) )
! 187: A( K, K+1 ) = A( K, K+1 ) -
! 188: $ ZDOTC( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 )
! 189: CALL ZCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 )
! 190: CALL ZHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO,
! 191: $ A( 1, K+1 ), 1 )
! 192: A( K+1, K+1 ) = A( K+1, K+1 ) -
! 193: $ DBLE( ZDOTC( K-1, WORK, 1, A( 1, K+1 ),
! 194: $ 1 ) )
! 195: END IF
! 196: KSTEP = 2
! 197: END IF
! 198: *
! 199: KP = ABS( IPIV( K ) )
! 200: IF( KP.NE.K ) THEN
! 201: *
! 202: * Interchange rows and columns K and KP in the leading
! 203: * submatrix A(1:k+1,1:k+1)
! 204: *
! 205: CALL ZSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
! 206: DO 40 J = KP + 1, K - 1
! 207: TEMP = DCONJG( A( J, K ) )
! 208: A( J, K ) = DCONJG( A( KP, J ) )
! 209: A( KP, J ) = TEMP
! 210: 40 CONTINUE
! 211: A( KP, K ) = DCONJG( A( KP, K ) )
! 212: TEMP = A( K, K )
! 213: A( K, K ) = A( KP, KP )
! 214: A( KP, KP ) = TEMP
! 215: IF( KSTEP.EQ.2 ) THEN
! 216: TEMP = A( K, K+1 )
! 217: A( K, K+1 ) = A( KP, K+1 )
! 218: A( KP, K+1 ) = TEMP
! 219: END IF
! 220: END IF
! 221: *
! 222: K = K + KSTEP
! 223: GO TO 30
! 224: 50 CONTINUE
! 225: *
! 226: ELSE
! 227: *
! 228: * Compute inv(A) from the factorization A = L*D*L'.
! 229: *
! 230: * K is the main loop index, increasing from 1 to N in steps of
! 231: * 1 or 2, depending on the size of the diagonal blocks.
! 232: *
! 233: K = N
! 234: 60 CONTINUE
! 235: *
! 236: * If K < 1, exit from loop.
! 237: *
! 238: IF( K.LT.1 )
! 239: $ GO TO 80
! 240: *
! 241: IF( IPIV( K ).GT.0 ) THEN
! 242: *
! 243: * 1 x 1 diagonal block
! 244: *
! 245: * Invert the diagonal block.
! 246: *
! 247: A( K, K ) = ONE / DBLE( A( K, K ) )
! 248: *
! 249: * Compute column K of the inverse.
! 250: *
! 251: IF( K.LT.N ) THEN
! 252: CALL ZCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
! 253: CALL ZHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK,
! 254: $ 1, ZERO, A( K+1, K ), 1 )
! 255: A( K, K ) = A( K, K ) - DBLE( ZDOTC( N-K, WORK, 1,
! 256: $ A( K+1, K ), 1 ) )
! 257: END IF
! 258: KSTEP = 1
! 259: ELSE
! 260: *
! 261: * 2 x 2 diagonal block
! 262: *
! 263: * Invert the diagonal block.
! 264: *
! 265: T = ABS( A( K, K-1 ) )
! 266: AK = DBLE( A( K-1, K-1 ) ) / T
! 267: AKP1 = DBLE( A( K, K ) ) / T
! 268: AKKP1 = A( K, K-1 ) / T
! 269: D = T*( AK*AKP1-ONE )
! 270: A( K-1, K-1 ) = AKP1 / D
! 271: A( K, K ) = AK / D
! 272: A( K, K-1 ) = -AKKP1 / D
! 273: *
! 274: * Compute columns K-1 and K of the inverse.
! 275: *
! 276: IF( K.LT.N ) THEN
! 277: CALL ZCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
! 278: CALL ZHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK,
! 279: $ 1, ZERO, A( K+1, K ), 1 )
! 280: A( K, K ) = A( K, K ) - DBLE( ZDOTC( N-K, WORK, 1,
! 281: $ A( K+1, K ), 1 ) )
! 282: A( K, K-1 ) = A( K, K-1 ) -
! 283: $ ZDOTC( N-K, A( K+1, K ), 1, A( K+1, K-1 ),
! 284: $ 1 )
! 285: CALL ZCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 )
! 286: CALL ZHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK,
! 287: $ 1, ZERO, A( K+1, K-1 ), 1 )
! 288: A( K-1, K-1 ) = A( K-1, K-1 ) -
! 289: $ DBLE( ZDOTC( N-K, WORK, 1, A( K+1, K-1 ),
! 290: $ 1 ) )
! 291: END IF
! 292: KSTEP = 2
! 293: END IF
! 294: *
! 295: KP = ABS( IPIV( K ) )
! 296: IF( KP.NE.K ) THEN
! 297: *
! 298: * Interchange rows and columns K and KP in the trailing
! 299: * submatrix A(k-1:n,k-1:n)
! 300: *
! 301: IF( KP.LT.N )
! 302: $ CALL ZSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
! 303: DO 70 J = K + 1, KP - 1
! 304: TEMP = DCONJG( A( J, K ) )
! 305: A( J, K ) = DCONJG( A( KP, J ) )
! 306: A( KP, J ) = TEMP
! 307: 70 CONTINUE
! 308: A( KP, K ) = DCONJG( A( KP, K ) )
! 309: TEMP = A( K, K )
! 310: A( K, K ) = A( KP, KP )
! 311: A( KP, KP ) = TEMP
! 312: IF( KSTEP.EQ.2 ) THEN
! 313: TEMP = A( K, K-1 )
! 314: A( K, K-1 ) = A( KP, K-1 )
! 315: A( KP, K-1 ) = TEMP
! 316: END IF
! 317: END IF
! 318: *
! 319: K = K - KSTEP
! 320: GO TO 60
! 321: 80 CONTINUE
! 322: END IF
! 323: *
! 324: RETURN
! 325: *
! 326: * End of ZHETRI
! 327: *
! 328: END
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