Annotation of rpl/lapack/lapack/zlantb.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLANTB( NORM, UPLO, DIAG, N, K, AB,
! 2: $ LDAB, WORK )
! 3: *
! 4: * -- LAPACK auxiliary routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: CHARACTER DIAG, NORM, UPLO
! 11: INTEGER K, LDAB, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION WORK( * )
! 15: COMPLEX*16 AB( LDAB, * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZLANTB returns the value of the one norm, or the Frobenius norm, or
! 22: * the infinity norm, or the element of largest absolute value of an
! 23: * n by n triangular band matrix A, with ( k + 1 ) diagonals.
! 24: *
! 25: * Description
! 26: * ===========
! 27: *
! 28: * ZLANTB returns the value
! 29: *
! 30: * ZLANTB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
! 31: * (
! 32: * ( norm1(A), NORM = '1', 'O' or 'o'
! 33: * (
! 34: * ( normI(A), NORM = 'I' or 'i'
! 35: * (
! 36: * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
! 37: *
! 38: * where norm1 denotes the one norm of a matrix (maximum column sum),
! 39: * normI denotes the infinity norm of a matrix (maximum row sum) and
! 40: * normF denotes the Frobenius norm of a matrix (square root of sum of
! 41: * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
! 42: *
! 43: * Arguments
! 44: * =========
! 45: *
! 46: * NORM (input) CHARACTER*1
! 47: * Specifies the value to be returned in ZLANTB as described
! 48: * above.
! 49: *
! 50: * UPLO (input) CHARACTER*1
! 51: * Specifies whether the matrix A is upper or lower triangular.
! 52: * = 'U': Upper triangular
! 53: * = 'L': Lower triangular
! 54: *
! 55: * DIAG (input) CHARACTER*1
! 56: * Specifies whether or not the matrix A is unit triangular.
! 57: * = 'N': Non-unit triangular
! 58: * = 'U': Unit triangular
! 59: *
! 60: * N (input) INTEGER
! 61: * The order of the matrix A. N >= 0. When N = 0, ZLANTB is
! 62: * set to zero.
! 63: *
! 64: * K (input) INTEGER
! 65: * The number of super-diagonals of the matrix A if UPLO = 'U',
! 66: * or the number of sub-diagonals of the matrix A if UPLO = 'L'.
! 67: * K >= 0.
! 68: *
! 69: * AB (input) COMPLEX*16 array, dimension (LDAB,N)
! 70: * The upper or lower triangular band matrix A, stored in the
! 71: * first k+1 rows of AB. The j-th column of A is stored
! 72: * in the j-th column of the array AB as follows:
! 73: * if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
! 74: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
! 75: * Note that when DIAG = 'U', the elements of the array AB
! 76: * corresponding to the diagonal elements of the matrix A are
! 77: * not referenced, but are assumed to be one.
! 78: *
! 79: * LDAB (input) INTEGER
! 80: * The leading dimension of the array AB. LDAB >= K+1.
! 81: *
! 82: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 83: * where LWORK >= N when NORM = 'I'; otherwise, WORK is not
! 84: * referenced.
! 85: *
! 86: * =====================================================================
! 87: *
! 88: * .. Parameters ..
! 89: DOUBLE PRECISION ONE, ZERO
! 90: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 91: * ..
! 92: * .. Local Scalars ..
! 93: LOGICAL UDIAG
! 94: INTEGER I, J, L
! 95: DOUBLE PRECISION SCALE, SUM, VALUE
! 96: * ..
! 97: * .. External Functions ..
! 98: LOGICAL LSAME
! 99: EXTERNAL LSAME
! 100: * ..
! 101: * .. External Subroutines ..
! 102: EXTERNAL ZLASSQ
! 103: * ..
! 104: * .. Intrinsic Functions ..
! 105: INTRINSIC ABS, MAX, MIN, SQRT
! 106: * ..
! 107: * .. Executable Statements ..
! 108: *
! 109: IF( N.EQ.0 ) THEN
! 110: VALUE = ZERO
! 111: ELSE IF( LSAME( NORM, 'M' ) ) THEN
! 112: *
! 113: * Find max(abs(A(i,j))).
! 114: *
! 115: IF( LSAME( DIAG, 'U' ) ) THEN
! 116: VALUE = ONE
! 117: IF( LSAME( UPLO, 'U' ) ) THEN
! 118: DO 20 J = 1, N
! 119: DO 10 I = MAX( K+2-J, 1 ), K
! 120: VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
! 121: 10 CONTINUE
! 122: 20 CONTINUE
! 123: ELSE
! 124: DO 40 J = 1, N
! 125: DO 30 I = 2, MIN( N+1-J, K+1 )
! 126: VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
! 127: 30 CONTINUE
! 128: 40 CONTINUE
! 129: END IF
! 130: ELSE
! 131: VALUE = ZERO
! 132: IF( LSAME( UPLO, 'U' ) ) THEN
! 133: DO 60 J = 1, N
! 134: DO 50 I = MAX( K+2-J, 1 ), K + 1
! 135: VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
! 136: 50 CONTINUE
! 137: 60 CONTINUE
! 138: ELSE
! 139: DO 80 J = 1, N
! 140: DO 70 I = 1, MIN( N+1-J, K+1 )
! 141: VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
! 142: 70 CONTINUE
! 143: 80 CONTINUE
! 144: END IF
! 145: END IF
! 146: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
! 147: *
! 148: * Find norm1(A).
! 149: *
! 150: VALUE = ZERO
! 151: UDIAG = LSAME( DIAG, 'U' )
! 152: IF( LSAME( UPLO, 'U' ) ) THEN
! 153: DO 110 J = 1, N
! 154: IF( UDIAG ) THEN
! 155: SUM = ONE
! 156: DO 90 I = MAX( K+2-J, 1 ), K
! 157: SUM = SUM + ABS( AB( I, J ) )
! 158: 90 CONTINUE
! 159: ELSE
! 160: SUM = ZERO
! 161: DO 100 I = MAX( K+2-J, 1 ), K + 1
! 162: SUM = SUM + ABS( AB( I, J ) )
! 163: 100 CONTINUE
! 164: END IF
! 165: VALUE = MAX( VALUE, SUM )
! 166: 110 CONTINUE
! 167: ELSE
! 168: DO 140 J = 1, N
! 169: IF( UDIAG ) THEN
! 170: SUM = ONE
! 171: DO 120 I = 2, MIN( N+1-J, K+1 )
! 172: SUM = SUM + ABS( AB( I, J ) )
! 173: 120 CONTINUE
! 174: ELSE
! 175: SUM = ZERO
! 176: DO 130 I = 1, MIN( N+1-J, K+1 )
! 177: SUM = SUM + ABS( AB( I, J ) )
! 178: 130 CONTINUE
! 179: END IF
! 180: VALUE = MAX( VALUE, SUM )
! 181: 140 CONTINUE
! 182: END IF
! 183: ELSE IF( LSAME( NORM, 'I' ) ) THEN
! 184: *
! 185: * Find normI(A).
! 186: *
! 187: VALUE = ZERO
! 188: IF( LSAME( UPLO, 'U' ) ) THEN
! 189: IF( LSAME( DIAG, 'U' ) ) THEN
! 190: DO 150 I = 1, N
! 191: WORK( I ) = ONE
! 192: 150 CONTINUE
! 193: DO 170 J = 1, N
! 194: L = K + 1 - J
! 195: DO 160 I = MAX( 1, J-K ), J - 1
! 196: WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
! 197: 160 CONTINUE
! 198: 170 CONTINUE
! 199: ELSE
! 200: DO 180 I = 1, N
! 201: WORK( I ) = ZERO
! 202: 180 CONTINUE
! 203: DO 200 J = 1, N
! 204: L = K + 1 - J
! 205: DO 190 I = MAX( 1, J-K ), J
! 206: WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
! 207: 190 CONTINUE
! 208: 200 CONTINUE
! 209: END IF
! 210: ELSE
! 211: IF( LSAME( DIAG, 'U' ) ) THEN
! 212: DO 210 I = 1, N
! 213: WORK( I ) = ONE
! 214: 210 CONTINUE
! 215: DO 230 J = 1, N
! 216: L = 1 - J
! 217: DO 220 I = J + 1, MIN( N, J+K )
! 218: WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
! 219: 220 CONTINUE
! 220: 230 CONTINUE
! 221: ELSE
! 222: DO 240 I = 1, N
! 223: WORK( I ) = ZERO
! 224: 240 CONTINUE
! 225: DO 260 J = 1, N
! 226: L = 1 - J
! 227: DO 250 I = J, MIN( N, J+K )
! 228: WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
! 229: 250 CONTINUE
! 230: 260 CONTINUE
! 231: END IF
! 232: END IF
! 233: DO 270 I = 1, N
! 234: VALUE = MAX( VALUE, WORK( I ) )
! 235: 270 CONTINUE
! 236: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
! 237: *
! 238: * Find normF(A).
! 239: *
! 240: IF( LSAME( UPLO, 'U' ) ) THEN
! 241: IF( LSAME( DIAG, 'U' ) ) THEN
! 242: SCALE = ONE
! 243: SUM = N
! 244: IF( K.GT.0 ) THEN
! 245: DO 280 J = 2, N
! 246: CALL ZLASSQ( MIN( J-1, K ),
! 247: $ AB( MAX( K+2-J, 1 ), J ), 1, SCALE,
! 248: $ SUM )
! 249: 280 CONTINUE
! 250: END IF
! 251: ELSE
! 252: SCALE = ZERO
! 253: SUM = ONE
! 254: DO 290 J = 1, N
! 255: CALL ZLASSQ( MIN( J, K+1 ), AB( MAX( K+2-J, 1 ), J ),
! 256: $ 1, SCALE, SUM )
! 257: 290 CONTINUE
! 258: END IF
! 259: ELSE
! 260: IF( LSAME( DIAG, 'U' ) ) THEN
! 261: SCALE = ONE
! 262: SUM = N
! 263: IF( K.GT.0 ) THEN
! 264: DO 300 J = 1, N - 1
! 265: CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
! 266: $ SUM )
! 267: 300 CONTINUE
! 268: END IF
! 269: ELSE
! 270: SCALE = ZERO
! 271: SUM = ONE
! 272: DO 310 J = 1, N
! 273: CALL ZLASSQ( MIN( N-J+1, K+1 ), AB( 1, J ), 1, SCALE,
! 274: $ SUM )
! 275: 310 CONTINUE
! 276: END IF
! 277: END IF
! 278: VALUE = SCALE*SQRT( SUM )
! 279: END IF
! 280: *
! 281: ZLANTB = VALUE
! 282: RETURN
! 283: *
! 284: * End of ZLANTB
! 285: *
! 286: END
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