Annotation of rpl/lapack/lapack/zpftrs.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2.1) --
! 4: *
! 5: * -- Contributed by Fred Gustavson of the IBM Watson Research Center --
! 6: * -- April 2009 --
! 7: *
! 8: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 9: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 10: *
! 11: * .. Scalar Arguments ..
! 12: CHARACTER TRANSR, UPLO
! 13: INTEGER INFO, LDB, N, NRHS
! 14: * ..
! 15: * .. Array Arguments ..
! 16: COMPLEX*16 A( 0: * ), B( LDB, * )
! 17: * ..
! 18: *
! 19: * Purpose
! 20: * =======
! 21: *
! 22: * ZPFTRS solves a system of linear equations A*X = B with a Hermitian
! 23: * positive definite matrix A using the Cholesky factorization
! 24: * A = U**H*U or A = L*L**H computed by ZPFTRF.
! 25: *
! 26: * Arguments
! 27: * =========
! 28: *
! 29: * TRANSR (input) CHARACTER
! 30: * = 'N': The Normal TRANSR of RFP A is stored;
! 31: * = 'C': The Conjugate-transpose TRANSR of RFP A is stored.
! 32: *
! 33: * UPLO (input) CHARACTER
! 34: * = 'U': Upper triangle of RFP A is stored;
! 35: * = 'L': Lower triangle of RFP A is stored.
! 36: *
! 37: * N (input) INTEGER
! 38: * The order of the matrix A. N >= 0.
! 39: *
! 40: * NRHS (input) INTEGER
! 41: * The number of right hand sides, i.e., the number of columns
! 42: * of the matrix B. NRHS >= 0.
! 43: *
! 44: * A (input) COMPLEX*16 array, dimension ( N*(N+1)/2 );
! 45: * The triangular factor U or L from the Cholesky factorization
! 46: * of RFP A = U**H*U or RFP A = L*L**H, as computed by ZPFTRF.
! 47: * See note below for more details about RFP A.
! 48: *
! 49: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
! 50: * On entry, the right hand side matrix B.
! 51: * On exit, the solution matrix X.
! 52: *
! 53: * LDB (input) INTEGER
! 54: * The leading dimension of the array B. LDB >= max(1,N).
! 55: *
! 56: * INFO (output) INTEGER
! 57: * = 0: successful exit
! 58: * < 0: if INFO = -i, the i-th argument had an illegal value
! 59: *
! 60: * Further Details
! 61: * ===============
! 62: *
! 63: * We first consider Standard Packed Format when N is even.
! 64: * We give an example where N = 6.
! 65: *
! 66: * AP is Upper AP is Lower
! 67: *
! 68: * 00 01 02 03 04 05 00
! 69: * 11 12 13 14 15 10 11
! 70: * 22 23 24 25 20 21 22
! 71: * 33 34 35 30 31 32 33
! 72: * 44 45 40 41 42 43 44
! 73: * 55 50 51 52 53 54 55
! 74: *
! 75: *
! 76: * Let TRANSR = 'N'. RFP holds AP as follows:
! 77: * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
! 78: * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
! 79: * conjugate-transpose of the first three columns of AP upper.
! 80: * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
! 81: * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
! 82: * conjugate-transpose of the last three columns of AP lower.
! 83: * To denote conjugate we place -- above the element. This covers the
! 84: * case N even and TRANSR = 'N'.
! 85: *
! 86: * RFP A RFP A
! 87: *
! 88: * -- -- --
! 89: * 03 04 05 33 43 53
! 90: * -- --
! 91: * 13 14 15 00 44 54
! 92: * --
! 93: * 23 24 25 10 11 55
! 94: *
! 95: * 33 34 35 20 21 22
! 96: * --
! 97: * 00 44 45 30 31 32
! 98: * -- --
! 99: * 01 11 55 40 41 42
! 100: * -- -- --
! 101: * 02 12 22 50 51 52
! 102: *
! 103: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 104: * transpose of RFP A above. One therefore gets:
! 105: *
! 106: *
! 107: * RFP A RFP A
! 108: *
! 109: * -- -- -- -- -- -- -- -- -- --
! 110: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
! 111: * -- -- -- -- -- -- -- -- -- --
! 112: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
! 113: * -- -- -- -- -- -- -- -- -- --
! 114: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
! 115: *
! 116: *
! 117: * We next consider Standard Packed Format when N is odd.
! 118: * We give an example where N = 5.
! 119: *
! 120: * AP is Upper AP is Lower
! 121: *
! 122: * 00 01 02 03 04 00
! 123: * 11 12 13 14 10 11
! 124: * 22 23 24 20 21 22
! 125: * 33 34 30 31 32 33
! 126: * 44 40 41 42 43 44
! 127: *
! 128: *
! 129: * Let TRANSR = 'N'. RFP holds AP as follows:
! 130: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
! 131: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
! 132: * conjugate-transpose of the first two columns of AP upper.
! 133: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
! 134: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
! 135: * conjugate-transpose of the last two columns of AP lower.
! 136: * To denote conjugate we place -- above the element. This covers the
! 137: * case N odd and TRANSR = 'N'.
! 138: *
! 139: * RFP A RFP A
! 140: *
! 141: * -- --
! 142: * 02 03 04 00 33 43
! 143: * --
! 144: * 12 13 14 10 11 44
! 145: *
! 146: * 22 23 24 20 21 22
! 147: * --
! 148: * 00 33 34 30 31 32
! 149: * -- --
! 150: * 01 11 44 40 41 42
! 151: *
! 152: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
! 153: * transpose of RFP A above. One therefore gets:
! 154: *
! 155: *
! 156: * RFP A RFP A
! 157: *
! 158: * -- -- -- -- -- -- -- -- --
! 159: * 02 12 22 00 01 00 10 20 30 40 50
! 160: * -- -- -- -- -- -- -- -- --
! 161: * 03 13 23 33 11 33 11 21 31 41 51
! 162: * -- -- -- -- -- -- -- -- --
! 163: * 04 14 24 34 44 43 44 22 32 42 52
! 164: *
! 165: * =====================================================================
! 166: *
! 167: * .. Parameters ..
! 168: COMPLEX*16 CONE
! 169: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
! 170: * ..
! 171: * .. Local Scalars ..
! 172: LOGICAL LOWER, NORMALTRANSR
! 173: * ..
! 174: * .. External Functions ..
! 175: LOGICAL LSAME
! 176: EXTERNAL LSAME
! 177: * ..
! 178: * .. External Subroutines ..
! 179: EXTERNAL XERBLA, ZTFSM
! 180: * ..
! 181: * .. Intrinsic Functions ..
! 182: INTRINSIC MAX
! 183: * ..
! 184: * .. Executable Statements ..
! 185: *
! 186: * Test the input parameters.
! 187: *
! 188: INFO = 0
! 189: NORMALTRANSR = LSAME( TRANSR, 'N' )
! 190: LOWER = LSAME( UPLO, 'L' )
! 191: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
! 192: INFO = -1
! 193: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
! 194: INFO = -2
! 195: ELSE IF( N.LT.0 ) THEN
! 196: INFO = -3
! 197: ELSE IF( NRHS.LT.0 ) THEN
! 198: INFO = -4
! 199: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 200: INFO = -7
! 201: END IF
! 202: IF( INFO.NE.0 ) THEN
! 203: CALL XERBLA( 'ZPFTRS', -INFO )
! 204: RETURN
! 205: END IF
! 206: *
! 207: * Quick return if possible
! 208: *
! 209: IF( N.EQ.0 .OR. NRHS.EQ.0 )
! 210: + RETURN
! 211: *
! 212: * start execution: there are two triangular solves
! 213: *
! 214: IF( LOWER ) THEN
! 215: CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B,
! 216: + LDB )
! 217: CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B,
! 218: + LDB )
! 219: ELSE
! 220: CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B,
! 221: + LDB )
! 222: CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B,
! 223: + LDB )
! 224: END IF
! 225: *
! 226: RETURN
! 227: *
! 228: * End of ZPFTRS
! 229: *
! 230: END
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