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