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