Annotation of rpl/lapack/blas/ztrmv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
! 2: * .. Scalar Arguments ..
! 3: INTEGER INCX,LDA,N
! 4: CHARACTER DIAG,TRANS,UPLO
! 5: * ..
! 6: * .. Array Arguments ..
! 7: DOUBLE COMPLEX A(LDA,*),X(*)
! 8: * ..
! 9: *
! 10: * Purpose
! 11: * =======
! 12: *
! 13: * ZTRMV 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 matrix.
! 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: * A - COMPLEX*16 array of DIMENSION ( LDA, n ).
! 62: * Before entry with UPLO = 'U' or 'u', the leading n by n
! 63: * upper triangular part of the array A must contain the upper
! 64: * triangular matrix and the strictly lower triangular part of
! 65: * A is not referenced.
! 66: * Before entry with UPLO = 'L' or 'l', the leading n by n
! 67: * lower triangular part of the array A must contain the lower
! 68: * triangular matrix and the strictly upper triangular part of
! 69: * A is not referenced.
! 70: * Note that when DIAG = 'U' or 'u', the diagonal elements of
! 71: * A are not referenced either, but are assumed to be unity.
! 72: * Unchanged on exit.
! 73: *
! 74: * LDA - INTEGER.
! 75: * On entry, LDA specifies the first dimension of A as declared
! 76: * in the calling (sub) program. LDA must be at least
! 77: * max( 1, n ).
! 78: * Unchanged on exit.
! 79: *
! 80: * X - COMPLEX*16 array of dimension at least
! 81: * ( 1 + ( n - 1 )*abs( INCX ) ).
! 82: * Before entry, the incremented array X must contain the n
! 83: * element vector x. On exit, X is overwritten with the
! 84: * tranformed vector x.
! 85: *
! 86: * INCX - INTEGER.
! 87: * On entry, INCX specifies the increment for the elements of
! 88: * X. INCX must not be zero.
! 89: * Unchanged on exit.
! 90: *
! 91: * Further Details
! 92: * ===============
! 93: *
! 94: * Level 2 Blas routine.
! 95: *
! 96: * -- Written on 22-October-1986.
! 97: * Jack Dongarra, Argonne National Lab.
! 98: * Jeremy Du Croz, Nag Central Office.
! 99: * Sven Hammarling, Nag Central Office.
! 100: * Richard Hanson, Sandia National Labs.
! 101: *
! 102: * =====================================================================
! 103: *
! 104: * .. Parameters ..
! 105: DOUBLE COMPLEX ZERO
! 106: PARAMETER (ZERO= (0.0D+0,0.0D+0))
! 107: * ..
! 108: * .. Local Scalars ..
! 109: DOUBLE COMPLEX TEMP
! 110: INTEGER I,INFO,IX,J,JX,KX
! 111: LOGICAL NOCONJ,NOUNIT
! 112: * ..
! 113: * .. External Functions ..
! 114: LOGICAL LSAME
! 115: EXTERNAL LSAME
! 116: * ..
! 117: * .. External Subroutines ..
! 118: EXTERNAL XERBLA
! 119: * ..
! 120: * .. Intrinsic Functions ..
! 121: INTRINSIC DCONJG,MAX
! 122: * ..
! 123: *
! 124: * Test the input parameters.
! 125: *
! 126: INFO = 0
! 127: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
! 128: INFO = 1
! 129: ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
! 130: + .NOT.LSAME(TRANS,'C')) THEN
! 131: INFO = 2
! 132: ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
! 133: INFO = 3
! 134: ELSE IF (N.LT.0) THEN
! 135: INFO = 4
! 136: ELSE IF (LDA.LT.MAX(1,N)) THEN
! 137: INFO = 6
! 138: ELSE IF (INCX.EQ.0) THEN
! 139: INFO = 8
! 140: END IF
! 141: IF (INFO.NE.0) THEN
! 142: CALL XERBLA('ZTRMV ',INFO)
! 143: RETURN
! 144: END IF
! 145: *
! 146: * Quick return if possible.
! 147: *
! 148: IF (N.EQ.0) RETURN
! 149: *
! 150: NOCONJ = LSAME(TRANS,'T')
! 151: NOUNIT = LSAME(DIAG,'N')
! 152: *
! 153: * Set up the start point in X if the increment is not unity. This
! 154: * will be ( N - 1 )*INCX too small for descending loops.
! 155: *
! 156: IF (INCX.LE.0) THEN
! 157: KX = 1 - (N-1)*INCX
! 158: ELSE IF (INCX.NE.1) THEN
! 159: KX = 1
! 160: END IF
! 161: *
! 162: * Start the operations. In this version the elements of A are
! 163: * accessed sequentially with one pass through A.
! 164: *
! 165: IF (LSAME(TRANS,'N')) THEN
! 166: *
! 167: * Form x := A*x.
! 168: *
! 169: IF (LSAME(UPLO,'U')) THEN
! 170: IF (INCX.EQ.1) THEN
! 171: DO 20 J = 1,N
! 172: IF (X(J).NE.ZERO) THEN
! 173: TEMP = X(J)
! 174: DO 10 I = 1,J - 1
! 175: X(I) = X(I) + TEMP*A(I,J)
! 176: 10 CONTINUE
! 177: IF (NOUNIT) X(J) = X(J)*A(J,J)
! 178: END IF
! 179: 20 CONTINUE
! 180: ELSE
! 181: JX = KX
! 182: DO 40 J = 1,N
! 183: IF (X(JX).NE.ZERO) THEN
! 184: TEMP = X(JX)
! 185: IX = KX
! 186: DO 30 I = 1,J - 1
! 187: X(IX) = X(IX) + TEMP*A(I,J)
! 188: IX = IX + INCX
! 189: 30 CONTINUE
! 190: IF (NOUNIT) X(JX) = X(JX)*A(J,J)
! 191: END IF
! 192: JX = JX + INCX
! 193: 40 CONTINUE
! 194: END IF
! 195: ELSE
! 196: IF (INCX.EQ.1) THEN
! 197: DO 60 J = N,1,-1
! 198: IF (X(J).NE.ZERO) THEN
! 199: TEMP = X(J)
! 200: DO 50 I = N,J + 1,-1
! 201: X(I) = X(I) + TEMP*A(I,J)
! 202: 50 CONTINUE
! 203: IF (NOUNIT) X(J) = X(J)*A(J,J)
! 204: END IF
! 205: 60 CONTINUE
! 206: ELSE
! 207: KX = KX + (N-1)*INCX
! 208: JX = KX
! 209: DO 80 J = N,1,-1
! 210: IF (X(JX).NE.ZERO) THEN
! 211: TEMP = X(JX)
! 212: IX = KX
! 213: DO 70 I = N,J + 1,-1
! 214: X(IX) = X(IX) + TEMP*A(I,J)
! 215: IX = IX - INCX
! 216: 70 CONTINUE
! 217: IF (NOUNIT) X(JX) = X(JX)*A(J,J)
! 218: END IF
! 219: JX = JX - INCX
! 220: 80 CONTINUE
! 221: END IF
! 222: END IF
! 223: ELSE
! 224: *
! 225: * Form x := A'*x or x := conjg( A' )*x.
! 226: *
! 227: IF (LSAME(UPLO,'U')) THEN
! 228: IF (INCX.EQ.1) THEN
! 229: DO 110 J = N,1,-1
! 230: TEMP = X(J)
! 231: IF (NOCONJ) THEN
! 232: IF (NOUNIT) TEMP = TEMP*A(J,J)
! 233: DO 90 I = J - 1,1,-1
! 234: TEMP = TEMP + A(I,J)*X(I)
! 235: 90 CONTINUE
! 236: ELSE
! 237: IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
! 238: DO 100 I = J - 1,1,-1
! 239: TEMP = TEMP + DCONJG(A(I,J))*X(I)
! 240: 100 CONTINUE
! 241: END IF
! 242: X(J) = TEMP
! 243: 110 CONTINUE
! 244: ELSE
! 245: JX = KX + (N-1)*INCX
! 246: DO 140 J = N,1,-1
! 247: TEMP = X(JX)
! 248: IX = JX
! 249: IF (NOCONJ) THEN
! 250: IF (NOUNIT) TEMP = TEMP*A(J,J)
! 251: DO 120 I = J - 1,1,-1
! 252: IX = IX - INCX
! 253: TEMP = TEMP + A(I,J)*X(IX)
! 254: 120 CONTINUE
! 255: ELSE
! 256: IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
! 257: DO 130 I = J - 1,1,-1
! 258: IX = IX - INCX
! 259: TEMP = TEMP + DCONJG(A(I,J))*X(IX)
! 260: 130 CONTINUE
! 261: END IF
! 262: X(JX) = TEMP
! 263: JX = JX - INCX
! 264: 140 CONTINUE
! 265: END IF
! 266: ELSE
! 267: IF (INCX.EQ.1) THEN
! 268: DO 170 J = 1,N
! 269: TEMP = X(J)
! 270: IF (NOCONJ) THEN
! 271: IF (NOUNIT) TEMP = TEMP*A(J,J)
! 272: DO 150 I = J + 1,N
! 273: TEMP = TEMP + A(I,J)*X(I)
! 274: 150 CONTINUE
! 275: ELSE
! 276: IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
! 277: DO 160 I = J + 1,N
! 278: TEMP = TEMP + DCONJG(A(I,J))*X(I)
! 279: 160 CONTINUE
! 280: END IF
! 281: X(J) = TEMP
! 282: 170 CONTINUE
! 283: ELSE
! 284: JX = KX
! 285: DO 200 J = 1,N
! 286: TEMP = X(JX)
! 287: IX = JX
! 288: IF (NOCONJ) THEN
! 289: IF (NOUNIT) TEMP = TEMP*A(J,J)
! 290: DO 180 I = J + 1,N
! 291: IX = IX + INCX
! 292: TEMP = TEMP + A(I,J)*X(IX)
! 293: 180 CONTINUE
! 294: ELSE
! 295: IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
! 296: DO 190 I = J + 1,N
! 297: IX = IX + INCX
! 298: TEMP = TEMP + DCONJG(A(I,J))*X(IX)
! 299: 190 CONTINUE
! 300: END IF
! 301: X(JX) = TEMP
! 302: JX = JX + INCX
! 303: 200 CONTINUE
! 304: END IF
! 305: END IF
! 306: END IF
! 307: *
! 308: RETURN
! 309: *
! 310: * End of ZTRMV .
! 311: *
! 312: END
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