Annotation of rpl/lapack/blas/ztbsv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
! 2: * .. Scalar Arguments ..
! 3: INTEGER INCX,K,LDA,N
! 4: CHARACTER DIAG,TRANS,UPLO
! 5: * ..
! 6: * .. Array Arguments ..
! 7: DOUBLE COMPLEX A(LDA,*),X(*)
! 8: * ..
! 9: *
! 10: * Purpose
! 11: * =======
! 12: *
! 13: * ZTBSV solves one of the systems of equations
! 14: *
! 15: * A*x = b, or A'*x = b, or conjg( A' )*x = b,
! 16: *
! 17: * where b and x are n element vectors and A is an n by n unit, or
! 18: * non-unit, upper or lower triangular band matrix, with ( k + 1 )
! 19: * diagonals.
! 20: *
! 21: * No test for singularity or near-singularity is included in this
! 22: * routine. Such tests must be performed before calling this routine.
! 23: *
! 24: * Arguments
! 25: * ==========
! 26: *
! 27: * UPLO - CHARACTER*1.
! 28: * On entry, UPLO specifies whether the matrix is an upper or
! 29: * lower triangular matrix as follows:
! 30: *
! 31: * UPLO = 'U' or 'u' A is an upper triangular matrix.
! 32: *
! 33: * UPLO = 'L' or 'l' A is a lower triangular matrix.
! 34: *
! 35: * Unchanged on exit.
! 36: *
! 37: * TRANS - CHARACTER*1.
! 38: * On entry, TRANS specifies the equations to be solved as
! 39: * follows:
! 40: *
! 41: * TRANS = 'N' or 'n' A*x = b.
! 42: *
! 43: * TRANS = 'T' or 't' A'*x = b.
! 44: *
! 45: * TRANS = 'C' or 'c' conjg( A' )*x = b.
! 46: *
! 47: * Unchanged on exit.
! 48: *
! 49: * DIAG - CHARACTER*1.
! 50: * On entry, DIAG specifies whether or not A is unit
! 51: * triangular as follows:
! 52: *
! 53: * DIAG = 'U' or 'u' A is assumed to be unit triangular.
! 54: *
! 55: * DIAG = 'N' or 'n' A is not assumed to be unit
! 56: * triangular.
! 57: *
! 58: * Unchanged on exit.
! 59: *
! 60: * N - INTEGER.
! 61: * On entry, N specifies the order of the matrix A.
! 62: * N must be at least zero.
! 63: * Unchanged on exit.
! 64: *
! 65: * K - INTEGER.
! 66: * On entry with UPLO = 'U' or 'u', K specifies the number of
! 67: * super-diagonals of the matrix A.
! 68: * On entry with UPLO = 'L' or 'l', K specifies the number of
! 69: * sub-diagonals of the matrix A.
! 70: * K must satisfy 0 .le. K.
! 71: * Unchanged on exit.
! 72: *
! 73: * A - COMPLEX*16 array of DIMENSION ( LDA, n ).
! 74: * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
! 75: * by n part of the array A must contain the upper triangular
! 76: * band part of the matrix of coefficients, supplied column by
! 77: * column, with the leading diagonal of the matrix in row
! 78: * ( k + 1 ) of the array, the first super-diagonal starting at
! 79: * position 2 in row k, and so on. The top left k by k triangle
! 80: * of the array A is not referenced.
! 81: * The following program segment will transfer an upper
! 82: * triangular band matrix from conventional full matrix storage
! 83: * to band storage:
! 84: *
! 85: * DO 20, J = 1, N
! 86: * M = K + 1 - J
! 87: * DO 10, I = MAX( 1, J - K ), J
! 88: * A( M + I, J ) = matrix( I, J )
! 89: * 10 CONTINUE
! 90: * 20 CONTINUE
! 91: *
! 92: * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
! 93: * by n part of the array A must contain the lower triangular
! 94: * band part of the matrix of coefficients, supplied column by
! 95: * column, with the leading diagonal of the matrix in row 1 of
! 96: * the array, the first sub-diagonal starting at position 1 in
! 97: * row 2, and so on. The bottom right k by k triangle of the
! 98: * array A is not referenced.
! 99: * The following program segment will transfer a lower
! 100: * triangular band matrix from conventional full matrix storage
! 101: * to band storage:
! 102: *
! 103: * DO 20, J = 1, N
! 104: * M = 1 - J
! 105: * DO 10, I = J, MIN( N, J + K )
! 106: * A( M + I, J ) = matrix( I, J )
! 107: * 10 CONTINUE
! 108: * 20 CONTINUE
! 109: *
! 110: * Note that when DIAG = 'U' or 'u' the elements of the array A
! 111: * corresponding to the diagonal elements of the matrix are not
! 112: * referenced, but are assumed to be unity.
! 113: * Unchanged on exit.
! 114: *
! 115: * LDA - INTEGER.
! 116: * On entry, LDA specifies the first dimension of A as declared
! 117: * in the calling (sub) program. LDA must be at least
! 118: * ( k + 1 ).
! 119: * Unchanged on exit.
! 120: *
! 121: * X - COMPLEX*16 array of dimension at least
! 122: * ( 1 + ( n - 1 )*abs( INCX ) ).
! 123: * Before entry, the incremented array X must contain the n
! 124: * element right-hand side vector b. On exit, X is overwritten
! 125: * with the solution vector x.
! 126: *
! 127: * INCX - INTEGER.
! 128: * On entry, INCX specifies the increment for the elements of
! 129: * X. INCX must not be zero.
! 130: * Unchanged on exit.
! 131: *
! 132: * Further Details
! 133: * ===============
! 134: *
! 135: * Level 2 Blas routine.
! 136: *
! 137: * -- Written on 22-October-1986.
! 138: * Jack Dongarra, Argonne National Lab.
! 139: * Jeremy Du Croz, Nag Central Office.
! 140: * Sven Hammarling, Nag Central Office.
! 141: * Richard Hanson, Sandia National Labs.
! 142: *
! 143: * =====================================================================
! 144: *
! 145: * .. Parameters ..
! 146: DOUBLE COMPLEX ZERO
! 147: PARAMETER (ZERO= (0.0D+0,0.0D+0))
! 148: * ..
! 149: * .. Local Scalars ..
! 150: DOUBLE COMPLEX TEMP
! 151: INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
! 152: LOGICAL NOCONJ,NOUNIT
! 153: * ..
! 154: * .. External Functions ..
! 155: LOGICAL LSAME
! 156: EXTERNAL LSAME
! 157: * ..
! 158: * .. External Subroutines ..
! 159: EXTERNAL XERBLA
! 160: * ..
! 161: * .. Intrinsic Functions ..
! 162: INTRINSIC DCONJG,MAX,MIN
! 163: * ..
! 164: *
! 165: * Test the input parameters.
! 166: *
! 167: INFO = 0
! 168: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
! 169: INFO = 1
! 170: ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
! 171: + .NOT.LSAME(TRANS,'C')) THEN
! 172: INFO = 2
! 173: ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
! 174: INFO = 3
! 175: ELSE IF (N.LT.0) THEN
! 176: INFO = 4
! 177: ELSE IF (K.LT.0) THEN
! 178: INFO = 5
! 179: ELSE IF (LDA.LT. (K+1)) THEN
! 180: INFO = 7
! 181: ELSE IF (INCX.EQ.0) THEN
! 182: INFO = 9
! 183: END IF
! 184: IF (INFO.NE.0) THEN
! 185: CALL XERBLA('ZTBSV ',INFO)
! 186: RETURN
! 187: END IF
! 188: *
! 189: * Quick return if possible.
! 190: *
! 191: IF (N.EQ.0) RETURN
! 192: *
! 193: NOCONJ = LSAME(TRANS,'T')
! 194: NOUNIT = LSAME(DIAG,'N')
! 195: *
! 196: * Set up the start point in X if the increment is not unity. This
! 197: * will be ( N - 1 )*INCX too small for descending loops.
! 198: *
! 199: IF (INCX.LE.0) THEN
! 200: KX = 1 - (N-1)*INCX
! 201: ELSE IF (INCX.NE.1) THEN
! 202: KX = 1
! 203: END IF
! 204: *
! 205: * Start the operations. In this version the elements of A are
! 206: * accessed by sequentially with one pass through A.
! 207: *
! 208: IF (LSAME(TRANS,'N')) THEN
! 209: *
! 210: * Form x := inv( A )*x.
! 211: *
! 212: IF (LSAME(UPLO,'U')) THEN
! 213: KPLUS1 = K + 1
! 214: IF (INCX.EQ.1) THEN
! 215: DO 20 J = N,1,-1
! 216: IF (X(J).NE.ZERO) THEN
! 217: L = KPLUS1 - J
! 218: IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J)
! 219: TEMP = X(J)
! 220: DO 10 I = J - 1,MAX(1,J-K),-1
! 221: X(I) = X(I) - TEMP*A(L+I,J)
! 222: 10 CONTINUE
! 223: END IF
! 224: 20 CONTINUE
! 225: ELSE
! 226: KX = KX + (N-1)*INCX
! 227: JX = KX
! 228: DO 40 J = N,1,-1
! 229: KX = KX - INCX
! 230: IF (X(JX).NE.ZERO) THEN
! 231: IX = KX
! 232: L = KPLUS1 - J
! 233: IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J)
! 234: TEMP = X(JX)
! 235: DO 30 I = J - 1,MAX(1,J-K),-1
! 236: X(IX) = X(IX) - TEMP*A(L+I,J)
! 237: IX = IX - INCX
! 238: 30 CONTINUE
! 239: END IF
! 240: JX = JX - INCX
! 241: 40 CONTINUE
! 242: END IF
! 243: ELSE
! 244: IF (INCX.EQ.1) THEN
! 245: DO 60 J = 1,N
! 246: IF (X(J).NE.ZERO) THEN
! 247: L = 1 - J
! 248: IF (NOUNIT) X(J) = X(J)/A(1,J)
! 249: TEMP = X(J)
! 250: DO 50 I = J + 1,MIN(N,J+K)
! 251: X(I) = X(I) - TEMP*A(L+I,J)
! 252: 50 CONTINUE
! 253: END IF
! 254: 60 CONTINUE
! 255: ELSE
! 256: JX = KX
! 257: DO 80 J = 1,N
! 258: KX = KX + INCX
! 259: IF (X(JX).NE.ZERO) THEN
! 260: IX = KX
! 261: L = 1 - J
! 262: IF (NOUNIT) X(JX) = X(JX)/A(1,J)
! 263: TEMP = X(JX)
! 264: DO 70 I = J + 1,MIN(N,J+K)
! 265: X(IX) = X(IX) - TEMP*A(L+I,J)
! 266: IX = IX + INCX
! 267: 70 CONTINUE
! 268: END IF
! 269: JX = JX + INCX
! 270: 80 CONTINUE
! 271: END IF
! 272: END IF
! 273: ELSE
! 274: *
! 275: * Form x := inv( A' )*x or x := inv( conjg( A') )*x.
! 276: *
! 277: IF (LSAME(UPLO,'U')) THEN
! 278: KPLUS1 = K + 1
! 279: IF (INCX.EQ.1) THEN
! 280: DO 110 J = 1,N
! 281: TEMP = X(J)
! 282: L = KPLUS1 - J
! 283: IF (NOCONJ) THEN
! 284: DO 90 I = MAX(1,J-K),J - 1
! 285: TEMP = TEMP - A(L+I,J)*X(I)
! 286: 90 CONTINUE
! 287: IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
! 288: ELSE
! 289: DO 100 I = MAX(1,J-K),J - 1
! 290: TEMP = TEMP - DCONJG(A(L+I,J))*X(I)
! 291: 100 CONTINUE
! 292: IF (NOUNIT) TEMP = TEMP/DCONJG(A(KPLUS1,J))
! 293: END IF
! 294: X(J) = TEMP
! 295: 110 CONTINUE
! 296: ELSE
! 297: JX = KX
! 298: DO 140 J = 1,N
! 299: TEMP = X(JX)
! 300: IX = KX
! 301: L = KPLUS1 - J
! 302: IF (NOCONJ) THEN
! 303: DO 120 I = MAX(1,J-K),J - 1
! 304: TEMP = TEMP - A(L+I,J)*X(IX)
! 305: IX = IX + INCX
! 306: 120 CONTINUE
! 307: IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
! 308: ELSE
! 309: DO 130 I = MAX(1,J-K),J - 1
! 310: TEMP = TEMP - DCONJG(A(L+I,J))*X(IX)
! 311: IX = IX + INCX
! 312: 130 CONTINUE
! 313: IF (NOUNIT) TEMP = TEMP/DCONJG(A(KPLUS1,J))
! 314: END IF
! 315: X(JX) = TEMP
! 316: JX = JX + INCX
! 317: IF (J.GT.K) KX = KX + INCX
! 318: 140 CONTINUE
! 319: END IF
! 320: ELSE
! 321: IF (INCX.EQ.1) THEN
! 322: DO 170 J = N,1,-1
! 323: TEMP = X(J)
! 324: L = 1 - J
! 325: IF (NOCONJ) THEN
! 326: DO 150 I = MIN(N,J+K),J + 1,-1
! 327: TEMP = TEMP - A(L+I,J)*X(I)
! 328: 150 CONTINUE
! 329: IF (NOUNIT) TEMP = TEMP/A(1,J)
! 330: ELSE
! 331: DO 160 I = MIN(N,J+K),J + 1,-1
! 332: TEMP = TEMP - DCONJG(A(L+I,J))*X(I)
! 333: 160 CONTINUE
! 334: IF (NOUNIT) TEMP = TEMP/DCONJG(A(1,J))
! 335: END IF
! 336: X(J) = TEMP
! 337: 170 CONTINUE
! 338: ELSE
! 339: KX = KX + (N-1)*INCX
! 340: JX = KX
! 341: DO 200 J = N,1,-1
! 342: TEMP = X(JX)
! 343: IX = KX
! 344: L = 1 - J
! 345: IF (NOCONJ) THEN
! 346: DO 180 I = MIN(N,J+K),J + 1,-1
! 347: TEMP = TEMP - A(L+I,J)*X(IX)
! 348: IX = IX - INCX
! 349: 180 CONTINUE
! 350: IF (NOUNIT) TEMP = TEMP/A(1,J)
! 351: ELSE
! 352: DO 190 I = MIN(N,J+K),J + 1,-1
! 353: TEMP = TEMP - DCONJG(A(L+I,J))*X(IX)
! 354: IX = IX - INCX
! 355: 190 CONTINUE
! 356: IF (NOUNIT) TEMP = TEMP/DCONJG(A(1,J))
! 357: END IF
! 358: X(JX) = TEMP
! 359: JX = JX - INCX
! 360: IF ((N-J).GE.K) KX = KX - INCX
! 361: 200 CONTINUE
! 362: END IF
! 363: END IF
! 364: END IF
! 365: *
! 366: RETURN
! 367: *
! 368: * End of ZTBSV .
! 369: *
! 370: END
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