Annotation of rpl/lapack/lapack/dsptri.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSPTRI( 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: DOUBLE PRECISION AP( * ), WORK( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * DSPTRI computes the inverse of a real 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 DSPTRF.
! 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) DOUBLE PRECISION 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 DSPTRF,
! 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 DSPTRF.
! 51: *
! 52: * WORK (workspace) DOUBLE PRECISION 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, ZERO
! 64: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 65: * ..
! 66: * .. Local Scalars ..
! 67: LOGICAL UPPER
! 68: INTEGER J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP
! 69: DOUBLE PRECISION AK, AKKP1, AKP1, D, T, TEMP
! 70: * ..
! 71: * .. External Functions ..
! 72: LOGICAL LSAME
! 73: DOUBLE PRECISION DDOT
! 74: EXTERNAL LSAME, DDOT
! 75: * ..
! 76: * .. External Subroutines ..
! 77: EXTERNAL DCOPY, DSPMV, DSWAP, XERBLA
! 78: * ..
! 79: * .. Intrinsic Functions ..
! 80: INTRINSIC ABS
! 81: * ..
! 82: * .. Executable Statements ..
! 83: *
! 84: * Test the input parameters.
! 85: *
! 86: INFO = 0
! 87: UPPER = LSAME( UPLO, 'U' )
! 88: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 89: INFO = -1
! 90: ELSE IF( N.LT.0 ) THEN
! 91: INFO = -2
! 92: END IF
! 93: IF( INFO.NE.0 ) THEN
! 94: CALL XERBLA( 'DSPTRI', -INFO )
! 95: RETURN
! 96: END IF
! 97: *
! 98: * Quick return if possible
! 99: *
! 100: IF( N.EQ.0 )
! 101: $ RETURN
! 102: *
! 103: * Check that the diagonal matrix D is nonsingular.
! 104: *
! 105: IF( UPPER ) THEN
! 106: *
! 107: * Upper triangular storage: examine D from bottom to top
! 108: *
! 109: KP = N*( N+1 ) / 2
! 110: DO 10 INFO = N, 1, -1
! 111: IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
! 112: $ RETURN
! 113: KP = KP - INFO
! 114: 10 CONTINUE
! 115: ELSE
! 116: *
! 117: * Lower triangular storage: examine D from top to bottom.
! 118: *
! 119: KP = 1
! 120: DO 20 INFO = 1, N
! 121: IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
! 122: $ RETURN
! 123: KP = KP + N - INFO + 1
! 124: 20 CONTINUE
! 125: END IF
! 126: INFO = 0
! 127: *
! 128: IF( UPPER ) THEN
! 129: *
! 130: * Compute inv(A) from the factorization A = U*D*U'.
! 131: *
! 132: * K is the main loop index, increasing from 1 to N in steps of
! 133: * 1 or 2, depending on the size of the diagonal blocks.
! 134: *
! 135: K = 1
! 136: KC = 1
! 137: 30 CONTINUE
! 138: *
! 139: * If K > N, exit from loop.
! 140: *
! 141: IF( K.GT.N )
! 142: $ GO TO 50
! 143: *
! 144: KCNEXT = KC + K
! 145: IF( IPIV( K ).GT.0 ) THEN
! 146: *
! 147: * 1 x 1 diagonal block
! 148: *
! 149: * Invert the diagonal block.
! 150: *
! 151: AP( KC+K-1 ) = ONE / AP( KC+K-1 )
! 152: *
! 153: * Compute column K of the inverse.
! 154: *
! 155: IF( K.GT.1 ) THEN
! 156: CALL DCOPY( K-1, AP( KC ), 1, WORK, 1 )
! 157: CALL DSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ),
! 158: $ 1 )
! 159: AP( KC+K-1 ) = AP( KC+K-1 ) -
! 160: $ DDOT( K-1, WORK, 1, AP( KC ), 1 )
! 161: END IF
! 162: KSTEP = 1
! 163: ELSE
! 164: *
! 165: * 2 x 2 diagonal block
! 166: *
! 167: * Invert the diagonal block.
! 168: *
! 169: T = ABS( AP( KCNEXT+K-1 ) )
! 170: AK = AP( KC+K-1 ) / T
! 171: AKP1 = AP( KCNEXT+K ) / T
! 172: AKKP1 = AP( KCNEXT+K-1 ) / T
! 173: D = T*( AK*AKP1-ONE )
! 174: AP( KC+K-1 ) = AKP1 / D
! 175: AP( KCNEXT+K ) = AK / D
! 176: AP( KCNEXT+K-1 ) = -AKKP1 / D
! 177: *
! 178: * Compute columns K and K+1 of the inverse.
! 179: *
! 180: IF( K.GT.1 ) THEN
! 181: CALL DCOPY( K-1, AP( KC ), 1, WORK, 1 )
! 182: CALL DSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ),
! 183: $ 1 )
! 184: AP( KC+K-1 ) = AP( KC+K-1 ) -
! 185: $ DDOT( K-1, WORK, 1, AP( KC ), 1 )
! 186: AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) -
! 187: $ DDOT( K-1, AP( KC ), 1, AP( KCNEXT ),
! 188: $ 1 )
! 189: CALL DCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 )
! 190: CALL DSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO,
! 191: $ AP( KCNEXT ), 1 )
! 192: AP( KCNEXT+K ) = AP( KCNEXT+K ) -
! 193: $ DDOT( K-1, WORK, 1, AP( KCNEXT ), 1 )
! 194: END IF
! 195: KSTEP = 2
! 196: KCNEXT = KCNEXT + K + 1
! 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: KPC = ( KP-1 )*KP / 2 + 1
! 206: CALL DSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 )
! 207: KX = KPC + KP - 1
! 208: DO 40 J = KP + 1, K - 1
! 209: KX = KX + J - 1
! 210: TEMP = AP( KC+J-1 )
! 211: AP( KC+J-1 ) = AP( KX )
! 212: AP( KX ) = TEMP
! 213: 40 CONTINUE
! 214: TEMP = AP( KC+K-1 )
! 215: AP( KC+K-1 ) = AP( KPC+KP-1 )
! 216: AP( KPC+KP-1 ) = TEMP
! 217: IF( KSTEP.EQ.2 ) THEN
! 218: TEMP = AP( KC+K+K-1 )
! 219: AP( KC+K+K-1 ) = AP( KC+K+KP-1 )
! 220: AP( KC+K+KP-1 ) = TEMP
! 221: END IF
! 222: END IF
! 223: *
! 224: K = K + KSTEP
! 225: KC = KCNEXT
! 226: GO TO 30
! 227: 50 CONTINUE
! 228: *
! 229: ELSE
! 230: *
! 231: * Compute inv(A) from the factorization A = L*D*L'.
! 232: *
! 233: * K is the main loop index, increasing from 1 to N in steps of
! 234: * 1 or 2, depending on the size of the diagonal blocks.
! 235: *
! 236: NPP = N*( N+1 ) / 2
! 237: K = N
! 238: KC = NPP
! 239: 60 CONTINUE
! 240: *
! 241: * If K < 1, exit from loop.
! 242: *
! 243: IF( K.LT.1 )
! 244: $ GO TO 80
! 245: *
! 246: KCNEXT = KC - ( N-K+2 )
! 247: IF( IPIV( K ).GT.0 ) THEN
! 248: *
! 249: * 1 x 1 diagonal block
! 250: *
! 251: * Invert the diagonal block.
! 252: *
! 253: AP( KC ) = ONE / AP( KC )
! 254: *
! 255: * Compute column K of the inverse.
! 256: *
! 257: IF( K.LT.N ) THEN
! 258: CALL DCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
! 259: CALL DSPMV( UPLO, N-K, -ONE, AP( KC+N-K+1 ), WORK, 1,
! 260: $ ZERO, AP( KC+1 ), 1 )
! 261: AP( KC ) = AP( KC ) - DDOT( N-K, WORK, 1, AP( KC+1 ), 1 )
! 262: END IF
! 263: KSTEP = 1
! 264: ELSE
! 265: *
! 266: * 2 x 2 diagonal block
! 267: *
! 268: * Invert the diagonal block.
! 269: *
! 270: T = ABS( AP( KCNEXT+1 ) )
! 271: AK = AP( KCNEXT ) / T
! 272: AKP1 = AP( KC ) / T
! 273: AKKP1 = AP( KCNEXT+1 ) / T
! 274: D = T*( AK*AKP1-ONE )
! 275: AP( KCNEXT ) = AKP1 / D
! 276: AP( KC ) = AK / D
! 277: AP( KCNEXT+1 ) = -AKKP1 / D
! 278: *
! 279: * Compute columns K-1 and K of the inverse.
! 280: *
! 281: IF( K.LT.N ) THEN
! 282: CALL DCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
! 283: CALL DSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1,
! 284: $ ZERO, AP( KC+1 ), 1 )
! 285: AP( KC ) = AP( KC ) - DDOT( N-K, WORK, 1, AP( KC+1 ), 1 )
! 286: AP( KCNEXT+1 ) = AP( KCNEXT+1 ) -
! 287: $ DDOT( N-K, AP( KC+1 ), 1,
! 288: $ AP( KCNEXT+2 ), 1 )
! 289: CALL DCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 )
! 290: CALL DSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1,
! 291: $ ZERO, AP( KCNEXT+2 ), 1 )
! 292: AP( KCNEXT ) = AP( KCNEXT ) -
! 293: $ DDOT( N-K, WORK, 1, AP( KCNEXT+2 ), 1 )
! 294: END IF
! 295: KSTEP = 2
! 296: KCNEXT = KCNEXT - ( N-K+3 )
! 297: END IF
! 298: *
! 299: KP = ABS( IPIV( K ) )
! 300: IF( KP.NE.K ) THEN
! 301: *
! 302: * Interchange rows and columns K and KP in the trailing
! 303: * submatrix A(k-1:n,k-1:n)
! 304: *
! 305: KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1
! 306: IF( KP.LT.N )
! 307: $ CALL DSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 )
! 308: KX = KC + KP - K
! 309: DO 70 J = K + 1, KP - 1
! 310: KX = KX + N - J + 1
! 311: TEMP = AP( KC+J-K )
! 312: AP( KC+J-K ) = AP( KX )
! 313: AP( KX ) = TEMP
! 314: 70 CONTINUE
! 315: TEMP = AP( KC )
! 316: AP( KC ) = AP( KPC )
! 317: AP( KPC ) = TEMP
! 318: IF( KSTEP.EQ.2 ) THEN
! 319: TEMP = AP( KC-N+K-1 )
! 320: AP( KC-N+K-1 ) = AP( KC-N+KP-1 )
! 321: AP( KC-N+KP-1 ) = TEMP
! 322: END IF
! 323: END IF
! 324: *
! 325: K = K - KSTEP
! 326: KC = KCNEXT
! 327: GO TO 60
! 328: 80 CONTINUE
! 329: END IF
! 330: *
! 331: RETURN
! 332: *
! 333: * End of DSPTRI
! 334: *
! 335: END
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